Instruction,Input,response
"Solve the problem systematically, showing each step clearly.","a and b can together finish a work in 30 days . they worked together for 20 days and then b left . after another 20 days , a finished the remaining work . in how many days a alone can finish the job ? a) 40 , b) 50 , c) 54 , d) 60 , e) none of these","""(a + b)' s 20 days work = (1 / 30 * 20) = 2 / 3 . remaining work = (1 - 2 / 3) = 1 / 3 . now , 1 / 3 work is done by a in 20 days . whole work will be done by a in (20 * 3) = 60 days . correct option : d"""
"Work through the equation methodically, ensuring clarity at each step.","if 20 men can build a water fountain 56 metres long in 6 days , what length of a similar water fountain can be built by 35 men in 3 days ? a) 40 m , b) 44 m , c) 47 m , d) 49 m , e) 50 m","explanation : let the required length be x metres more men , more length built (direct proportion) less days , less length built (direct proportion) men 20 : 35 days 6 : 3 : : 56 : x therefore (20 x 6 x x) = (35 x 3 x 56) x = (35 x 3 x 56) / 120 = 49 hence , the required length is 49 m . answer : d"
Provide a detailed solution to the given mathematical problem.,"a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 15 days before the project is completed , in how many days total will the project be completed ? a) 18 , b) 21 , c) 24 , d) 27 , e) 30","a' s rate is 1 / 20 of the project per day . b' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 15 days , b can do 1 / 2 of the project . thus a and b must complete 1 / 2 of the project , which takes 6 days . the total number of days is 6 + 15 = 21 . the answer is b ."
"Solve the problem systematically, showing each step clearly.","a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 60 sq . feet , how many feet of fencing will be required ? a) 34 , b) 40 , c) 68 , d) 88 , e) 26","""we have : l = 20 ft and lb = 60 sq . ft . so , b = 3 ft . length of fencing = (l + 2 b) = (20 + 6) ft = 26 ft . answer : e"""
Provide a detailed solution to the given mathematical problem.,"define a = the sum of digits of the number 7 ^ 100 and b = the sum of the digits of a . what is the sum of the digits of b ? a) 7 , b) 16 , c) 10 , d) 11 , e) can not be determined","following approach will take you only couple of sec . \ (7 ^ { 100 } = (7 ^ { 50 }) ^ 2 \) the sum of digits (digital root) of a perfect square can only be 1 , 4 , 7 or 9 . for example \ (7 ^ 2 = 49 \) = > dr = 4 + 9 = 13 = > 1 + 3 = 4 and etc . checking available options . answer a ."
Provide a detailed solution to the given mathematical problem.,"10 machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ? a) 2 , b) 3 , c) 4 , d) 5 , e) 8","""another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 10 = 15 so we need 15 - 10 = 5 more machines . answer : d"""
"Solve the problem systematically, showing each step clearly.","2 a 33 + b 9 ____ 99 if a and b represent positive single digits in the correctly worked computation above , what is the value of a + 3 b ? a) 2 , b) 7 , c) 9 , d) 11 , e) 12","adding the digits in unit' s place , a + 3 + 9 = 19 (since a and b are positive single digits) = > a = 7 now adding the digits in ten' s place , 2 + 3 + b + 1 = 9 (1 has been carried over from nit' s place addition) = > b = 3 a + 3 b = 2 + 2 * 3 = 11 answer d"
"Solve the problem systematically, showing each step clearly.","a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 12 hours of the journey . a) 342 km , b) 352 km , c) 642 km , d) 742 km , e) 492 km","""the total distance covered by the car in the first 12 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 = sum of 12 terms in ap whose first term is 30 and last term is 52 = 12 / 2 [ 30 + 52 ] = 492 km . answer : e"""
Provide a detailed solution to the given mathematical problem.,"the effective annual rate of interest corresponding to a nominal rate of 12 % per annum payable half - yearly is ? a) 16.06 % , b) 16.07 % , c) 12.36 % , d) 6.09 % , e) 6.19 %","""amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * (1 + 6 / 100) 2 ] = rs . 112.36 effective rate = (112.36 - 100) = 12.36 % answer : c"""
Explain the solution process for the given equation.,"in a school 10 % of the boys are same in number as 1 / 4 th of the girls . what is the ratio of boys to the girls in the school ? a) 5 : 2 , b) 2 : 3 , c) 1 : 4 , d) 3 : 7 , e) 2 : 5","""10 % of b = 1 / 4 g 10 b / 100 = g / 4 b = 5 g / 2 b / g = 5 / 2 b : g = 5 : 2 answer is a"""
Break down and solve the equation step by step.,"two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 216 marks in the second test and failed by 75 marks in that test . find the pass mark in the first test ? a) 768 , b) 243 , c) 246 , d) 288 , e) 224",let the maximum mark in each test be m . the candidate failed by 75 marks in the second test . pass mark in the second test = 249 + 75 = 324 45 / 100 m = 324 pass mark in the first test = 40 / 100 m = 40 / 45 * 324 = 288 . answer : d
"Solve the problem systematically, showing each step clearly.","10 play kabadi , 40 play kho kho only , 5 play both gmaes . then how many in total ? a) 30 , b) 35 , c) 38 , d) 40 , e) 50","""10 play kabadi = > n (a) = 10 , 5 play both gmaes . = > n (anb) = 5 40 play kho kho only , = > n (b) = n (b only) + n (anb) = 40 + 5 = 45 total = > n (aub) = n (a) + n (b) - n (anb) = 10 + 45 - 5 = 50 answer : e"""
Provide a detailed solution to the given mathematical problem.,"two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number is ? a) 36 , b) 76 , c) 98 , d) 27 , e) 24","""(3 x - 9) : (5 x - 9) = 9 : 17 x = 12 = > 3 x = 36 answer : a"""
"Solve the problem systematically, showing each step clearly.","if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is a) 50 km , b) 56 km , c) 70 km , d) 80 km , e) 90 km",let the actual distance travelled be x km . then x / 10 = (x + 20) / 14 - - > 14 x = 10 x + 200 - - > 4 x = 200 - - > x = 50 km . answer : a .
Explain the solution process for the given equation.,"a retailer buys 40 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ? a) 5 , b) 10 , c) 15 , d) 20 , e) none of them","""let the market price of each pen be rs 1 then , c . p of 40 pens = rs 36 s . p of 40 pens = 99 % of rs 40 = rs 39.60 profit % = ((3.60 * 100) / 36) % = 10 % answer is b ."""
Provide a detailed solution to the given mathematical problem.,"a bullet train 130 m long is running with a speed of 50 kmph . in what time will it pass a man who is running at 10 kmph in the direction opposite to that in which the bullet train is going ? a) 23 sec , b) 13 sec , c) 12 sec , d) 11 sec , e) 16 sec","""b 13 sec speed of the bullet train relative to man = (50 + 10) kmph = 60 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 130 m at (30 / 3) m / sec = (130 * 3 / 30) sec = 13 sec"""
"Solve the problem systematically, showing each step clearly.","what is the sum of all even numbers from 1 to 501 ? a) 122821 , b) 281228 , c) 281199 , d) 62750 , e) 128111","""explanation : 500 / 2 = 250 250 * 251 = 62750 answer : d"""
Explain the solution process for the given equation.,"a straight line in the xy - plane has y - intercept of 12 and a slope of 4 / 7 . given the x - coordinate of the point is 49 , find it' s y - coordinate . a) 27 , b) 16 , c) 29.7 , d) 28 , e) 18","""eq of line = y = mx + c m = 4 / 7 c = 12 x = 49 substitute the givens : y = (4 / 7 * 49) + 12 , y = 16 + 12 = 28 correct option is d"""
Explain the solution process for the given equation.,"if the ratio of a to b is 7 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ? a) 4 / 15 , b) 1 / 3 , c) 2 / 5 , d) 4 / 5 , e) 7 / 15","""a : b = 7 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 7 : 15 answer e"""
Explain the solution process for the given equation.,"a sum fetched a total simple interest of rs . 4016.25 at the rate of 5 % p . a . in 5 years . what is the sum ? a) 12021 , b) 14520 , c) 16065 , d) 18925 , e) 12887","""principal = (100 * 4016.25) / (5 * 5) = rs . 16065 . answer : c"""
Explain the solution process for the given equation.,"find the greatest number that will divide 256 , 193 and 210 leaving 6 , 18 and 100 as remainders respectively a) 19 , b) 25 , c) 23 , d) 20 , e) 26","""explanation : answer will be hcf of (256 - 6 , 193 - 18 , 210 - 10) hcf of (250 , 175 , 200) = 25 option b"""
Provide a detailed solution to the given mathematical problem.,"there were totally 100 men . 83 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ? a) 11 , b) 12 , c) 13 , d) 14 , e) 15",100 - (100 - 83) - (100 - 75) - (100 - 85) - (100 - 70) = 100 - 17 - 25 - 15 - 30 = 100 - 87 = 13 answer : c
"Solve the problem systematically, showing each step clearly.","if a rectangular billboard has an area of 91 square feet and a perimeter of 40 feet , what is the length of each of the shorter sides ? a) 4 , b) 7 , c) 8 , d) 13 , e) 26","""this question can be solved algebraically or by testing the answers . we' re told that a rectangle has an area of 91 and a perimeter of 40 . we' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 91 , the shorter side will almost certainly be less than 10 (since 10 x 10 = 100 , but we' re not dealing with a square) . let' s test answer b : 7 if . . . the shorter side = 7 . . . the area = 91 . . . . 91 / 7 = 13 = the longer side perimeter = 7 + 7 + 13 + 13 = 40 b"""
Break down and solve the equation step by step.,"6) a marketing firm determined that , of 160 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ? a) a) 15 , b) b) 20 , c) c) 30 , d) d) 40 , e) e) 5","""80 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 120 = > 4 x = 20 = > x = 5 answer - e"""
Break down and solve the equation step by step.,"what is the value of (p + q) / (p - q) if p / q is 7 ? a) 4 / 3 , b) 2 / 3 , c) 2 / 6 , d) 7 / 8 , e) 8 / 7","""(p + q) / (p - q) = [ (p / q) + 1 ] / [ (p / q) - 1 ] = (7 + 1) / (7 - 1) = 8 / 6 = 4 / 3 answer : a"""
"Solve the problem systematically, showing each step clearly.","how many different positive integers exist between 10 ^ 6 and 10 ^ 7 , the sum of whose digits is equal to 2 ? a) 5 , b) 6 , c) 7 , d) 8 , e) 18","""total cases = > 1000000 = > 6 cases for 1 being present at any of the 6 zero and last case 2000000 hence & cases answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","a thief is spotted by a policeman from a distance of 225 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ? a) 350 m , b) 200 m , c) 400 m , d) 900 m , e) none of them","""relative speed of the policeman = (10 - 8) km / hr = 2 km / hr . time taken by police man to cover (225 m / 1000) x 1 / 2 hr = 9 / 80 hr . in 9 / 80 hrs , the thief covers a distance of 8 x 9 / 80 km = 9 / 10 km = 900 m answer is d ."""
"Solve the problem systematically, showing each step clearly.","a shopkeeper sells 450 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ? a) 12 , b) 27 , c) 29 , d) 45 , e) 21",sp per metre = 18000 / 450 = rs . 40 loss per metre = rs . 5 cp per metre = 40 + 5 = rs . 45 . answer : d
"Solve the problem systematically, showing each step clearly.","if one and a half women , drink one and a half tea in one and a half minutes . how many tea can 9 women drink in 3 minutes ? a) 11 , b) 8 , c) 37 , d) 15 , e) 18",e 18 explanation : more minutes implies more tea . more women implies more tea . the time become twice (3 minutes / 1.5 minutes) . women become six times (9 / 1.5) . number of tea = 2 * 6 * original (1.5)
"Solve the problem systematically, showing each step clearly.","a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 15 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ? a) 14 , b) 16 , c) 21 , d) 22 , e) 40","""i treat such problems as work ones . work = rate * time mileage (m) = rate (mpg) * gallons (g) x gallons is a full tank { 462 = rx { 336 = (r - 15) x solve for r , r = 55 55 - 15 = 40 mpg e"""
Explain the solution process for the given equation.,"what is x if x + 2 y = 10 and y = 4 ? a) a) 10 , b) b) 8 , c) c) 6 , d) d) 4 , e) e) 2","""x = 10 - 2 y x = 10 - 8 . x = 2 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","after decreasing 24 % in the price of an article costs rs . 320 . find the actual cost of an article ? a) 400 , b) 520 , c) 651 , d) 525 , e) 421","""cp * (76 / 100) = 320 cp = 4.21 * 100 = > cp = 421 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","a business finds that their ratio of spending to income is 5 to 9 . their total profit is $ 48000 . what is their total income ? a) $ 90000 , b) $ 108000 , c) $ 119000 , d) $ 126000 , e) $ 140000","let x equal the amount of spending , and y equal the amount of income . we know that x = 5 / 9 y we also know that x = y - 48000 therefore we can simplify to : y - 48000 = 5 / 9 y we isolate y , and get : 4 / 9 y = 48000 and to solve for y , we get : y = 48000 answer : b"
"Solve the problem systematically, showing each step clearly.","when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 62 . what is the value of x ? a) - 4 , b) - 2 , c) 11 , d) 13 , e) 22","""the equation that can be formed is : 3 x - 26 = 62 - x or , 4 x = 88 or , x = 22 . answer : e"""
Break down and solve the equation step by step.,"two trains start from p and q respectively and travel towards each other at a speed of 50 km / hr and 40 km / hr respectively . by the time they meet , the first train has travelled 1 ookm more than the second . the distance between p and q is a) 500 km , b) 600 km , c) 700 km , d) 900 km , e) 400 km","""explanation : at the time of meeting , let the distance travelled by the second train be x km then , distance covered by the first train is (x + 100) km = > x / 40 = (x + 100) / 50 = > 50 x = 40 x + 4000 = > x = 400 km so , distance between p and q = (x + x + 100) km = 900 km answer : option d"""
"Work through the equation methodically, ensuring clarity at each step.","the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half yearly is a) 6.06 % , b) 6.07 % , c) 6.08 % , d) 6.09 % , e) none","""solution amount of rs . 100 for 1 year when compounded half yearly = rs . [ 100 x (1 + 3 / 100) 2 ] = rs . 106.09 % . effective rate = (106.09 - 100) % = rs . 6.09 % . answer d"""
"Solve the problem systematically, showing each step clearly.","if rs . 480 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ? a) s . 575 , b) s . 595 , c) s . 590 , d) s . 570 , e) s . 585","""80 = (480 * 4 * r) / 100 r = 3.125 % i = (480 * 6 * 3.125) / 100 = 90 480 + 90 = 570 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a sum of money lent out at s . i . amounts to a total of $ 590 after 2 years and to $ 815 after a further period of 5 years . what was the initial sum of money that was invested ? a) $ 490 , b) $ 500 , c) $ 510 , d) $ 520 , e) $ 530","""s . i for 5 years = $ 815 - $ 590 = $ 225 the s . i . is $ 45 / year s . i . for 2 years = $ 90 principal = $ 590 - $ 90 = $ 500 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","what least number should be added to 1052 , so that the sum is completely divisible by 23 a) a) 4 , b) b) 1 , c) c) 6 , d) d) 3 , e) e) 5","""explanation : (1052 / 23) gives remainder 17 17 + 6 = 23 , so we need to add 6 answer : option c"""
Provide a detailed solution to the given mathematical problem.,"kavi had a stock of 600 bags in his bookshop . he sold 25 on monday , 70 on tuesday , 100 on wednesday , 110 on thursday and 145 on friday . what percentage of the bags were not sold ? a) 10 % , b) 25 % , c) 64 % , d) 42 % , e) 17 %",let n be the total number of bags sold . hence n = 25 + 70 + 100 + 110 + 145 = 450 let m be the bags not sold m = 600 - n = 600 - 450 = 150 percentage bags not sold / total number of bags = 150 / 600 = 0.25 = 25 % correct answer b
Explain the solution process for the given equation.,"4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 16 mat - weavers in 16 days ? a) 25 , b) 19 , c) 39 , d) 61 , e) 64","""let the required number of bottles be x . more weavers , more mats (direct proportion) more days , more mats (direct proportion) wavers 4 : 16 : : 4 : x days 4 : 16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4) / (4 x 4) x = 64 . answer is e ."""
Break down and solve the equation step by step.,"on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is a) 20 , b) 30 , c) 40 , d) 50 , e) 60","""(c . p . of 17 balls) - (s . p . of 17 balls) = (c . p . of 5 balls) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : e"""
Provide a detailed solution to the given mathematical problem.,"cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ? a) 2 : 5 , b) 3 : 5 , c) 4 : 7 , d) 2 : 6 , e) 1 : 4","""2 % is 3 % - points below 5 % and 10 % is 5 % - points above 5 % . the ratio of a : b should be 3 : 5 . the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","square abcd is the base of the cube while square efgh is the cube' s top face such that point e is above point a , point f is above point b etc . what is the distance between the midpoint of edge ab and the midpoint of edge eh if the area of square abcd is 2 ? ['a) 1 / sqrt 2','b) 1','c) sqrt 2','d) sqrt 3','e) 2 sqrt 3']",distance from mid point of ab to ad = sqrt [ (1 / sqrt 2) ^ 2 + (1 / sqrt 2) ^ 2 ] = 1 the distance between the midpoint of edge ab and the midpoint of edge eh = sqrt [ 1 ^ 2 + (sqrt 2) ^ 2 ] = sqrt 3 . answer : d
Explain the solution process for the given equation.,"what is the value of n if the sum of the consecutive odd integers from 1 to n equals 169 ? a) 47 , b) 25 , c) 37 , d) 33 , e) 29",# of terms = (n - 1 / 2) + 1 { (last term - first term) / 2 + 1 | sum = (1 + n) / 2 * # of terms = (n + 1) ^ 2 / 4 = 169 n + 1 = 13 * 2 n + 1 = 26 n = 25 . answer : b
Break down and solve the equation step by step.,"a small college reduced its faculty by approximately 23 percent to 195 professors . what was the original number of faculty members ? a) 253 , b) 208 , c) 224 , d) 254 , e) 302","""if x is the original number of faculty members , then after 23 % reduction in faculty members number is . 77 x but we are given . 77 x = 195 x = 253 so the original number of faculty members is 253 correct answer - a"""
"Solve the problem systematically, showing each step clearly.","if 3 cats can kill 3 rats in 3 minutes , how long will it take 100 cats to kill 100 rats ? a) 1 minutes , b) 2 minutes , c) 3 minutes , d) 4 minutes , e) 5 minutes","""it will take 3 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 3 minutes , so 100 cats can kill 100 rats in 3 minutes answer c"""
"Work through the equation methodically, ensuring clarity at each step.","pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 8 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ? a) 13 , b) 24 , c) 18 , d) 19 , e) 12","""let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 8 = > 1 / x = 1 / 6 - 1 / 8 = (4 - 3) / 24 = 1 / 24 = > x = 24 . answer : b"""
"Solve the problem systematically, showing each step clearly.","{ - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation (x 3) (x + 14) (2 x + 5) = 0 ? a) 1 / 12 , b) 1 / 6 , c) 1 / 4 , d) 1 / 3 , e) 1 / 2",x = - 4 prob = 1 / 12 answer - a
Explain the solution process for the given equation.,"two pipes a and b can fill a tank in 4 and 5 hours respectively . if they are turned up alternately for one hour each , the time taken to fill the tank is ? a) 4 hrs 29 min , b) 4 hrs 24 min , c) 8 hrs 24 min , d) 4 hrs 44 min , e) 5 hrs 24 min",1 / 4 + 1 / 5 = 9 / 20 20 / 9 = 2 2 / 9 9 / 20 * 2 = 9 / 10 - - - - 4 hours wr = 1 - 9 / 10 = 1 / 10 1 h - - - - 1 / 4 ? - - - - - 1 / 10 2 / 5 * 60 = 24 = 4 hrs 24 min answer : b
"Solve the problem systematically, showing each step clearly.","a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 30 - sided polygon have ? a) 875 , b) 405 , c) 1425 , d) 2025 , e) 2500","""there' s a direct formula for this . number of diagonals in a regular polygon = [ n * (n - 3) ] / 2 , n = number of sides of the regular polygon . here , n = 30 . plugging it in , we get 405 diagonals ! answer (b) ."""
"Solve the problem systematically, showing each step clearly.","a corporation that had $ 10 billion in profits for the year paid out $ 500 million in employee benefits . approximately what percent of the profits were the employee benefits ? (note : 1 billion = 10 ^ 9) a) 50 % , b) 20 % , c) 5 % , d) 2 % , e) 0.2 %","""required answer = [ employee benefit / profit ] * 100 = [ (500 million) / (10 billion) ] * 100 = [ (500 * 10 ^ 6) / (10 * 10 ^ 9) ] * 100 = (50 / 1000) * 100 = 5 % so answer is (c)"""
"Work through the equation methodically, ensuring clarity at each step.","to produce an annual income of rs . 1200 from a 12 % stock at 90 , the amount of stock needed is : a) rs . 10,000 , b) rs . 10,800 , c) rs . 14,400 , d) rs . 16,000 , e) none of these","solution for an income of rs . 12 , stock needed = rs . 100 . for an income of rs . 1200 , stock needed = rs . 100 / 12 x 1200 = 10000 answer a"
"Solve the problem systematically, showing each step clearly.","a cubical block of metal weighs 4 pounds . how much will another cube of the same metal weigh if its sides are twice as long ? a) 48 , b) 32 , c) 24 , d) 18 , e) 12","""for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 4 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 4 pounds = 32 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 4 * 8 = 32 so answer is b"""
Explain the solution process for the given equation.,"a boat running downstream covers a distance of 12 km in 2 hours while for covering the same distance upstream , it takes 3 hours . what is the speed of the boat in still water ? a) 8 kmph , b) 5 kmph , c) 4 kmph , d) 6 kmph , e) 7 kmph","""speed downstream = 12 / 2 = 6 kmph speed upstream = 12 / 3 = 4 kmph speed of the boat in still water = 6 + 4 / 2 = 5 kmph answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a student scored an average of 75 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ? a) 86 , b) 16 , c) 76 , d) 95 , e) 26","""given m + p + c = 75 * 3 = 225 - - - (1) m + p = 90 * 2 = 180 - - - (2) p + c = 70 * 2 = 140 - - - (3) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = (2) + (3) - (1) = 180 + 140 - 225 = 95 answer : d"""
Explain the solution process for the given equation.,"in a certain pond , 30 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ? a) 750 , b) 625 , c) 1,250 , d) 2,500 , e) 10,000","""this is a rather straight forward ratio problem . 1 . 30 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 30 / x thus , x = 750 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . a"""
"Solve the problem systematically, showing each step clearly.","if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 1 strokes ? a) 1 / 2 , b) 7 / 8 , c) 1 / 4 , d) 1 / 8 , e) 1 / 16","""left after 1 st stroke = 1 / 2 so removed = 1 - 1 / 2 = 1 / 2"""
"Work through the equation methodically, ensuring clarity at each step.","if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke' s parents invested $ 13,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ? a) 62,000 , b) 85,500 , c) 95,500 , d) 100,500 , e) 100,000","answer equals d in 48 years . i thought by 50 th year it would reach 100,500 . options should have been separated more widely for clarity ."
Provide a detailed solution to the given mathematical problem.,"there are two inlets and one outlet to a cistern . one of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern . both of the inlets are turned on at 8 : 30 am with the cistern completely empty , and at 10 : 30 am , the outlet is turned on and it takes 1 more hour to fill the cistern completely . how much time does the outlet working alone takes to empty the cistern when the cistern is full ? a) 2 hours , b) 2.5 hours , c) 3 hours , d) 3.5 hours , e) 8 hours","""the combined inflow rate of the two inlets is 1 / 4 + 1 / 8 = 3 / 8 cistern / hour . thus , working together , it takes 8 / 3 hours (time is reciprocal of rate) to fill the cistern . from 8 : 30 am to 10 : 30 am , so in 2 hours , the inlet pipes will fill (time) * (rate) = 2 * 3 / 8 = 3 / 4 th of the cistern . then the outlet is turned on and the remaining 1 / 4 th of the cistern is filled in 1 hour . letting x to be the rate of the outlet , we would have : 3 / 8 - x = 1 / 4 - - > x = 1 / 8 cistern / hour , which means that it takes 8 hours the outlet working alone to empty the cistern . answer : e ."""
"Work through the equation methodically, ensuring clarity at each step.","40 men shake hands with each other . maximum no of handshakes without cyclic handshakes . a) 780 , b) 200 , c) 210 , d) 220 , e) 230","""or , if there are n persons then no . of shakehands = nc 2 = 40 c 2 = 780 answer : a"""
Explain the solution process for the given equation.,"if the volume of two cubes are in the ratio 125 : 1 , the ratio of their edges is : a) 3 : 1 , b) 5 : 1 , c) 3 : 5 , d) 3 : 7 , e) none of these","""explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 125 / 1 = > (a / b) 3 = (5 / 1) 3 a / b = 5 / 1 = > a : b = 5 : 1 option b"""
"Work through the equation methodically, ensuring clarity at each step.","in x game of billiards , x can give y 20 points in 60 and he can give z 50 points in 60 . how many points can y give z in x game of 100 ? a) 30 , b) 20 , c) 25 , d) 40 , e) 75","""x scores 60 while y score 40 and z scores 10 . the number of points that z scores when y scores 100 = (100 * 50) / 40 = 25 . in x game of 100 points , y gives (100 - 25) = 75 points to c . e"""
Break down and solve the equation step by step.,"the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ? a) a) 10 , b) b) 12 , c) c) 15 , d) d) 14 , e) e) 9","""let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e"""
Provide a detailed solution to the given mathematical problem.,"there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 16,000 after 3 years at the same rate ? a) 2372 , b) 2572 , c) 4542 , d) 2343 , e) 5296","""let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 16000 . t = 3 years and r = 10 % p . a . c . i . = rs . 16000 x 1 + 10 3 - 1 100 = rs . 16000 x 331 1000 = 5296 . e"""
"Work through the equation methodically, ensuring clarity at each step.","a prize of $ 600 is to be distributed among 15 winners , each of whom must be awarded at least $ 15 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ? a) $ 200 , b) $ 220 , c) $ 285 , d) $ 300 , e) $ 360","""total value of the prize = $ 600 number of people = 15 2 / 5 of 600 (= $ 240) should be distributed among 3 / 5 of 15 (= 9 people) with each getting $ 15 each . remaining money = 600 - 240 = $ 360 . now in order to' maximize' 1 prize , we need to minimise the others and we have been given that each should get $ 15 . thus , minimising the remaining 5 people (= 15 - 9 - 1 .' - 1' to exclude 1 that needs to be maximised) = 5 * 15 = 75 . thus the maximum award can be = 360 - 75 = $ 285 , hence c is the correct answer ."""
Provide a detailed solution to the given mathematical problem.,"a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 10 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 30 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage . a) 20 % , b) 43 % , c) 99.33 % , d) 75.109 % , e) 47 %","anyways , one can infer that he' steals' 10 % from suppliers and then charges 30 % extra to customers so basically 1.1 * 1.3 = 1.43 given that 1 is start point , we get 43 % more hence answer is b"
"Work through the equation methodically, ensuring clarity at each step.","walking 6 / 7 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ? a) 28 m , b) 20 m , c) 22 m , d) 23 m , e) 24 m",speed ratio = 1 : 6 / 7 = 7 : 6 time ratio = 6 : 4 1 - - - - - - - - 6 4 - - - - - - - - - ? = > 24 m answer : e
"Work through the equation methodically, ensuring clarity at each step.","machine p and machine q are each used to manufacture 330 sprockets . it takes machine p 10 hours longer to produce 330 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ? a) 5 , b) 15 , c) 3 , d) 95 , e) 125","""p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 330 / x = 330 / 1.1 x + 10 1.1 (330) = 330 + 11 x 11 x = 33 x = 3 the answer is c ."""
"Solve the problem systematically, showing each step clearly.","0.0003 x 0.3 = ? a) 0.0009 , b) 9.0 e - 05 , c) 0.09 , d) 0.009 , e) 9.0","""3 x 3 = 9 . sum of decimal places = 5 0.0003 x 0.3 = 0.00009 answer : option b"""
"Solve the problem systematically, showing each step clearly.","when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction e of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ? a) 11 / 14 , b) 13 / 18 , c) 4 / 7 , d) 3 / 7 , e) 3 / 14","if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus e = 11 / 14 of the remaining votes must be against . answer : a ."
"Work through the equation methodically, ensuring clarity at each step.","raman mixed 54 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ? a) 129 , b) 287 , c) 196 , d) 188 , e) 112","""explanation : cp per kg of mixture = [ 54 (150) + 36 (125) ] / (54 + 36) = rs . 140 sp = cp [ (100 + profit %) / 100 ] = 140 * [ (100 + 40) / 100 ] = rs . 196 . answer : c"""
"Solve the problem systematically, showing each step clearly.","a man whose bowling average is 12.4 , takes 3 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ? a) 23 , b) 24 , c) 25 , d) 26 , e) 27","""12.4 * x + 26 = (3 + x) 12 solve equation x = 25 answer : c"""
Provide a detailed solution to the given mathematical problem.,"if 80 % of a number is equal to four - third of another number , what is the ratio of first number to the second number ? a) 5 : 3 , b) 1 : 4 , c) 3 : 7 , d) 6 : 11 , e) 2 : 3","""let 80 % of a = 4 / 3 b then 80 a / 100 = 4 b / 3 4 a / 5 = 4 b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is a"""
Break down and solve the equation step by step.,"a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ? a) 5 / 6 , b) 5 / 12 , c) 7 / 12 , d) 11 / 12 , e) 11 / 15","""the searchlight completes one revolution every 30 seconds . the probability that the man' s area will be lit up is 5 / 30 = 1 / 6 . the probability that he will stay in the dark is 1 - 1 / 6 = 5 / 6 the answer is a ."""
Break down and solve the equation step by step.,"a certain no . when divided by 110 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? a) 2 , b) 4 , c) 7 , d) 8 , e) 9","""explanation : 110 + 25 = 135 / 15 = 9 (remainder) e"""
"Solve the problem systematically, showing each step clearly.","when a = x + (3 / x) and b = x - (3 / x) , (2 ^ a ^ 2) / (2 ^ b ^ 2) = ? a) 2 , b) 4 , c) 8 , d) 16 , e) 4096","""- - > (2 ^ a ^ 2) / (2 ^ b ^ 2) = { (2) ^ (a ^ 2 - b ^ 2) } = 2 ^ (a - b) (a + b) . since a - b = 6 / x and a + b = 2 x , 2 ^ (a - b) (a + b) = 2 ^ (6 / x) (2 x) = 2 ^ 12 = 4096 therefore , the answer is e"""
"Work through the equation methodically, ensuring clarity at each step.","a cube of edge 15 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ? a) 6 cm , b) 8.25 cm , c) 11.25 cm , d) 15.12 cm , e) 20.62 cm","""increase in volume = volume of the cube = 15 * 15 * 15 cm ^ 3 rise in water level = volume / area = 15 * 15 * 15 / 20 * 15 = 11.25 cm answer is c"""
Break down and solve the equation step by step.,"what is the smallest positive integer x such that (x + 1) ^ 2 is divisible by 28 , 98 , 242 , and 308 ? a) 153 , b) 308 , c) 121 , d) 96 , e) 511","""28 = 2 * 2 * 7 98 = 2 * 7 * 7 242 = 2 * 11 * 11 308 = 2 * 2 * 7 * 11 so (x + 1) ^ 2 = 2 * 2 * 7 * 7 * 11 * 11 , which means (x + 1) = 2 * 7 * 11 = 154 , which means x = 153 , which is option a"""
Provide a detailed solution to the given mathematical problem.,"what is the area of a triangle with the following vertices l (2 , 3) , m (5 , 1) , and n (3 , 5) ? ['a) 3','b) 4','c) 5','d) 6','e) 7']",there is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem . though if you make a diagram minimum simple calculations will be needed : answer : b .
"Solve the problem systematically, showing each step clearly.","pipe a can fill a tank in 32 minutes . pipe b can fill the same tank 5 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ? a) 4 minutes , b) 2 / 7 minutes , c) 32 / 7 minutes , d) 224 / 7 minutes , e) 28 minutes","""pipe a can fill a tank in 32 minutes - - > the rate of a = 1 / 32 tank / minute ; pipe b can fill the same tank 5 times fasterthan pipe a - - > the rate of b = 1 / 32 + 5 / 32 = 6 / 32 tank / minute . their combined rate = 1 / 32 + 6 / 32 = 7 / 32 tank / minute ; therefore , a and b can fill the tank in 32 / 7 minutes . answer : c"""
Explain the solution process for the given equation.,"find number which is 70 % less than 60 . a) 18 , b) 22 , c) 28 , d) 26 , e) 98","""explanation : 70 % less is 30 % of the given number therefore , 30 % of 60 is 18 . answer : a"""
Provide a detailed solution to the given mathematical problem.,"x can give y 100 meters start and z 200 meters start in x kilometer race . how much start can y give z in x kilometer race ? a) 112.2 m , b) 216.3 m , c) 111.12 m , d) 213.27 m , e) 222.40 m","c 111.12 m x runs 1000 m while y runs 900 m and z runs 800 m . the number of meters that z runs when y runs 1000 m , = (1000 * 800) / 900 = 8000 / 9 = 888.88 m . y can give z = 1000 - 888.88 = 111.12 m ."
Break down and solve the equation step by step.,"if 0.75 of a number is equal to 0.025 of another number , the ratio of the numbers is : a) 2 : 3 , b) 3 : 4 , c) 1 : 30 , d) 20 : 3 , e) 30 : 7","""0.75 a = 0.025 b - > a / b = 0.025 / 0.75 = 25 / 750 = 1 / 30 : . a : b = 1 : 30 answer : c"""
Explain the solution process for the given equation.,"how many different values of positive integer x , for which | x + 5 | < x , are there ? a) 0 , b) 2 , c) 3 , d) 8 , e) 16","""answer e i opted to put the random value option . i used 0 , 5 , - 5 and the the extreme of 40 and - 40 . . i was able to solve it in 1 : 09 e"""
Explain the solution process for the given equation.,"a tank is filled by 3 pipes a , b , c in 10 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ? a) 20 hr , b) 52 hr , c) 70 hr , d) 66 hr , e) 48 hr","""suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 10 7 / x = 1 / 10 x = 70 hours answer is c"""
"Work through the equation methodically, ensuring clarity at each step.","due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 25 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? a) a) 6.24 , b) b) 13.1 , c) c) 10 , d) d) 15 , e) e) 24","""old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 25 = 10 * 12 / 5 = 24 time difference = 13.1 ans : b"""
"Work through the equation methodically, ensuring clarity at each step.","two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 12 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ? a) 19 : 2 , b) 18 : 3 , c) 11 : 1 , d) 11 : 5 , e) 11 : 4","""quantity of alcohol in vessel p = 62.5 / 100 * 2 = 15 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 2 + 7 / 2 = 11 litres as 16 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 11 : 5 answer : d"""
Break down and solve the equation step by step.,"if p (a) = 4 / 5 and p (b) = 2 / 5 , find p (a n b) if a and b are independent events . a) 8 / 25 , b) 1 / 25 , c) 2 / 25 , d) 3 / 14 , e) 25 / 8","""p (a n b) = p (a) . p (b) p (a n b) = 4 / 5 . 2 / 5 p (a n b) = 8 / 25 . a"""
Explain the solution process for the given equation.,"find the greatest number of 5 digits which is exactly divisible by 12 , 15 and 18 ? a) a) 13050 , b) b) 12960 , c) c) 10025 , d) d) 11080 , e) e) 12080","the largest five digit numbers are 13050 , 12960,12080 13050 is not divisible by 12 12960 is divisible by 18 , 12 and 15 answer : b"
"Work through the equation methodically, ensuring clarity at each step.","solve the equation for x : 6 x - 87 + 3 x = 4 + 9 - x a) 12 , b) 5 , c) 10 , d) 9 , e) 3","""c 10 9 x + x = 13 + 87 10 x = 100 = > x = 10"""
"Solve the problem systematically, showing each step clearly.","the average (arithmetic mean) of 16 students first quiz scores in a difficult english class is 60.5 . when one student dropped the class , the average of the remaining scores increased to 64.0 . what is the quiz score of the student who dropped the class ? a) a) 8 , b) b) 25 , c) c) 40 , d) d) 55 , e) e) 70","""total score of 16 students is 16 * 60.50 = 968 total score of 15 students is 15 * 64 = 960 so , the score of the person who left is 8 (968 - 960) answer will be (a"""
Break down and solve the equation step by step.,"how many integers between 0 and 1000 do not contain the integer 1 a) 727 , b) 728 , c) 758 , d) 748 , e) 792","from 1 to 99 = 19 integers having 1 from 101 to 199 = all are having 1 similarly 201 - 299 , 301 - 399 , 401 - 499 , . . . . . so on , will have 19 integers having 1 answer = 1000 - (19 * 9 + 99 + 2) / / 2 is added for 100 and 1000 = 728 answer : b"
"Solve the problem systematically, showing each step clearly.","if 8 people take an hour to complete a piece of work , then how long should 16 people will take to complete the same piece of work ? a) 15 min , b) 30 min , c) 26 min , d) 28 min , e) 18 min","if 8 people take an hour to complete a piece of work , then 16 people will take 8 * 60 / 16 = 30 mins to complete the same piece of work . answer : b"
"Solve the problem systematically, showing each step clearly.","if grapes are 90 % water and raisins are 17 % water , then how many kilograms did a quantity of raisins , which currently weighs 14 kilograms , weigh when all the raisins were grapes ? (assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation .) a) 108.6 , b) 110.4 , c) 112.6 , d) 114.8 , e) 116.2","""let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 83 % of the raisins , 0.1 x = 0.83 (14 kg) . then x = 8.3 * 14 = 116.2 kg . the answer is e ."""
"Solve the problem systematically, showing each step clearly.","what is the smallest integer that is multiple of 3 , 5,9 a) a) 70 , b) b) 45 , c) c) 200 , d) d) 280 , e) e) 140","""it is the lcm of 3 , 5 and 9 which is 45 . the answer is b ."""
"Solve the problem systematically, showing each step clearly.","mixture contains alcohol and water in the ratio 4 : 3 . if 8 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture . a) 10 , b) 99 , c) 27 , d) 4 , e) 29","""let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 32 x = 4 (3 x + 5) 20 x = 20 x = 1 quantity of alcohol = (4 x 1) litres = 4 litres . answer : d"""
Provide a detailed solution to the given mathematical problem.,"what is the units digit of (493) (915) (381) (756) (22) a) 0 , b) 1 , c) 4 , d) 5 , e) 6","""just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 1 . imo b ."""
"Work through the equation methodically, ensuring clarity at each step.","the dimensions of a rectangular solid are 4 inches , 5 inches , and 9 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ? a) 2 : 5 , b) 5 : 9 , c) 5 : 16 , d) 25 : 7 , e) 32 : 25",answer : b .
Provide a detailed solution to the given mathematical problem.,"a number a is squared and then multiplied by negative 6 . the result of this operation is equal to 3 times the sum of fourth times a and two . what is one possible value of a ? a) 2 , b) 3 , c) 4 , d) 1 , e) 5",- 6 * a ^ 2 = 3 (4 a + 2) a = - 1 or - 1 a = - 1 = b answer : d
Provide a detailed solution to the given mathematical problem.,"find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 13 cm a) 178 cm 2 , b) 179 cm 2 , c) 285 cm 2 , d) 247 cm 2 , e) 197 cm 2","""area of a trapezium = 1 / 2 (sum of parallel sides) * (perpendicular distance between them) = 1 / 2 (20 + 18) * (13) = 247 cm 2 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3 kilometers per hour , what was her average speed (in kilometers per hour) while climbing to the top ? a) 1.75 , b) 2.25 , c) 2.5 , d) 2.75 , e) 3.25","let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 3 km / hour x / 3 = 3 x = 9 km the average speed while climbing = distance / time = 9 / 4 = 2.25 km / h the answer is b ."
"Solve the problem systematically, showing each step clearly.","water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 135 grams of water ? a) 120 , b) 116 , c) 112 , d) 108 , e) 104","""(16 / 18) * 144 = 120 grams the answer is a ."""
Explain the solution process for the given equation.,"if 12 % of x is equal to 6 % of y , then 18 % of x will be equal to how much % of y ? a) 7 % , b) 9 % , c) 11 % , d) 12 % , e) none of these","we have , 12 % of x = 6 % of y = > 2 % of x = 1 % of y = > (2 x 9) % of x = (1 x 9) % of y thus , 18 % of x = 9 % of y . answer : b"
Provide a detailed solution to the given mathematical problem.,"if the numbers 1 to 100 are written on 100 pieces of paper , (one on each) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ? a) 1 / 50 , b) 1 / 25 , c) 1 / 100 , d) 1 , e) 2","""there are 25 primes , 74 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 100 . answer : c"""
Provide a detailed solution to the given mathematical problem.,"john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 8,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ? a) 10000 , b) 12000 , c) 16160.8 , d) 14000 , e) 15000","""a = p (1 + r / n) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x (1 + 0.02 / 2) ^ 2 - x = 8,000 (1 + 0.04 / 4) ^ 4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal) = > x [ (1.01) ^ 2 - 1 ] = 8,000 [ (1.01) ^ 4 - 1 ] = > x [ (1.01) ^ 2 - 1 ] = 8,000 [ (1.01) ^ 2 + 1 ] [ (1.01) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 8,000 (1.0201 + 1) = 16160.8 hence answer is c ."""
Break down and solve the equation step by step.,"a can do a job in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is ? a) 2 / 15 , b) 8 / 15 , c) 3 / 11 , d) 5 / 12 , e) 6 / 13","""a' s 1 day work = 1 / 15 b' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 5 days work = 7 / 60 * 5 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is d"""
Provide a detailed solution to the given mathematical problem.,"on the first day of her vacation , louisa traveled 240 miles . on the second day , traveling at the same average speed , she traveled 420 miles . if the 240 - mile trip took 3 hours less than the 420 - mile trip , what was the average speed , in miles per hour ? a) 65 , b) 50 , c) 55 , d) 60 , e) 58","""(time) * (rate) = (distance) - - > (rate) = (distance) / (time) - - > given : (rate) = 240 / t = 420 / (t + 3) - - > 4 / t = 7 / (t + 3) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > (rate) = 240 / 4 = 60 answer : d"""
Explain the solution process for the given equation.,"hillary and eddy are climbing to the summit of mt . everest from a base camp 5,100 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1100 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ? a) 14.0 , b) 9.0 , c) 10.0 , d) 11.0 , e) 12.0","""solution : h stopped 800 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance between them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . e"""
Explain the solution process for the given equation.,"a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 18 km / hr . what is the length of the platform ? a) 80 , b) 240 , c) 288 , d) 277 , e) 221","""speed = 18 * 5 / 18 = 5 m / sec . length of the train = 5 * 20 = 100 m . let the length of the platform be x m . then , (x + 100) / 36 = 5 = > x = 80 m . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","if 2 x = 4 y = z , what is x - y , in terms of z ? a) z / 4 , b) z / 2 , c) z , d) 2 z , e) 4 z","""2 x = 4 y = z i . e . x = z / 2 and y = z / 4 x - y = z / 2 - z / 4 = z / 4 answer : option a"""
Provide a detailed solution to the given mathematical problem.,"sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 8 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ? a) 11 / 30 , b) 29 / 60 , c) 17 / 24 , d) 19 / 30 , e) 11 / 15",let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 8 x = 7 / 8 x so if gold card balance is transferred then the rest unspent will be 7 / 8 x - x / 6 = 17 / 24 x so the ans is c
Explain the solution process for the given equation.,"1396 x 1396 a) 1948816 , b) 1981709 , c) 18362619 , d) 2031719 , e) none of these","""1396 x 1396 = (1396) 2 = (1400 - 2) 2 = (1400) 2 + (4) 2 - (4 x 1400 x 4) = 1948816 . answer : option a"""
"Work through the equation methodically, ensuring clarity at each step.","at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 11 charts have been brought to the meeting , how many people are present ? a) 6 , b) 7 , c) 8 , d) 9 , e) 10","""say there are' a' associate professors . so we have 2 a pencils and a charts . say there are' b' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 21 so a + b = 7 total number of people = 7 answer : b"""
Provide a detailed solution to the given mathematical problem.,"five 6 faced dice are thrown together . the probability that all the three show the same number on them is ? a) 1 / 32 , b) 1 / 1296 , c) 1 / 33 , d) 1 / 38 , e) 1 / 34",the three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways . hence the probability is 6 / 7776 = 1 / 1296 answer : b
"Work through the equation methodically, ensuring clarity at each step.","each factor of 210 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 40 ? a) 1 / 16 , b) 5 / 42 , c) 1 / 8 , d) 3 / 16 , e) 1 / 4","""210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is (1 + 1) (1 + 1) (1 + 1) (1 + 1) = 16 (see below) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 16 . answer : a"""
Explain the solution process for the given equation.,"a worker earns $ 24 on the first day and spends $ 18 on the second day . the worker earns $ 24 on the third day and spends $ 18 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 72 ? a) 9 , b) 12 , c) 17 , d) 21 , e) 24","""every two days , the net total is $ 6 . after 16 days , the worker will have $ 48 . on day 17 , the worker will receive $ 24 for a net total of $ 72 . the answer is c ."""
Break down and solve the equation step by step.,"in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each 100 m in length both trains running with a speed of 80 kmph ? a) 4.5 sec , b) 4.8 sec , c) 4.2 sec , d) 5.0 sec , e) 5.2 sec",d = 100 m + 100 m = 200 m * 1 / 1000 = 0.2 kms rs = 80 + 80 = 160 kmph t = (0.2 / 160) * 3600 = 4.5 sec answer : a
Explain the solution process for the given equation.,"a cube has four of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ? a) 1 : 4 , b) 1 : 3 , c) 1 : 2 , d) 2 : 5 , e) 2 : 11","""let x be the area of each face of the cube . the area painted red is 4 (x / 2) = 2 x the area painted white is 4 (x / 2) + 2 x = 4 x the ratio of red to white is 2 x : 4 x which is 1 : 2 . the answer is c ."""
Explain the solution process for the given equation.,"the sum of two numbers is 528 and their h . c . f is 33 . the number of pairs of numbers satisfying the above conditions is : a) 4 , b) 5 , c) 6 , d) 6 , e) 1","""let the required numbers be 33 a and 33 b . then , 33 a + 33 b = 528 = > a + b = 16 . now , co - primes with sum 16 are (1 , 15) , (3 , 13) , (5 , 11) and (7 , 9) . required numbers are (33 * 1 , 33 * 15) , (33 * 3 , 33 * 13) , (33 * 5 , 33 * 11) , (33 * 7 , 33 * 9) . the number of such pairs is 4 . answer : a"""
Explain the solution process for the given equation.,"solve below question 4 x + 1 = 37 a) - 8 , b) - 9 , c) - 5 , d) 9 , e) 1",1 . subtract 1 from both sides : 4 x + 1 - 1 = 37 - 1 2 . simplify both sides : 4 x = 36 3 . divide both sides by 4 : 4 . simplify both sides : x = 9 d
Provide a detailed solution to the given mathematical problem.,"among 400 students , 51 % study sociology , 46 % study mathematics and 40 % study biology . if 34 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ? a) 30 , b) 90 , c) 148 , d) 172 , e) 188","i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 136 using your analysis : we see that the total number of students who study either maths or sociology = 184 + 204 - 136 = 252 so , in the image we know that the number of students in the zone with the black boundary = 252 let' s assume the number of students who studyonlybiology to beb (this is the number that we have to maximize) and , let' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 252 + b + w = 400 or , b + w = 400 - 252 = 148 that is , b = 148 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 148 c"
Provide a detailed solution to the given mathematical problem.,"wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 3 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? a) 1 / 20 , b) 3 / 40 , c) 13 / 40 , d) 3 / 20 , e) 13 / 22","""p (1 and not 2) = 3 / 8 * (1 - 3 / 5) = 14 / 40 = 3 / 20 . answer : d ."""
Break down and solve the equation step by step.,"if the cost price of 50 articles is equal to the selling price of 25 articles , then the gain or loss percent is ? a) 16 , b) 127 , c) 12 , d) 18 , e) 100","""percentage of profit = 25 / 25 * 100 = 100 % answer : e"""
Explain the solution process for the given equation.,"the difference between the ages of two persons is 20 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ? a) 30 , b) 35 , c) 25 , d) 28 , e) 32","let their ages be x years and (x + 20) years then , (x + 20) - 15 = 2 (x - 15) x + 5 = 2 x - 30 x = 35 answer is b"
Explain the solution process for the given equation.,"how many different pairs of numbers (s , t) such that s = 3 t can be obtained if s and t are selected from the set of number { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } a) 1 , b) 2 , c) 3 , d) 4 , e) 5","given s = 3 t t can take 0,1 , 2,3 , 4 and so s = 0,3 , 6,9 , 12 4 such pairs can be formed . answer e"
Break down and solve the equation step by step.,"what is the greatest value of x such that 4 ^ x is a factor of 21 ! ? a) 5 , b) 6 , c) 3 , d) 2 , e) 4","pretty simple , really . if m = 6 , then 4 m = 24 , which is 12 x 2 , both of which are included in 21 ! since 6 is the largest number here , its the answer . answer is b"
Explain the solution process for the given equation.,"there were two candidates in an election . winner candidate received 62 % of votes and won the election by 312 votes . find the number of votes casted to the winning candidate ? a) 806 , b) 744 , c) 912 , d) 1200 , e) 1400","""w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 312 62 % - - - - - - - - ? = > 806 answer : a"""
Break down and solve the equation step by step.,"a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 50 kmph . when and at what distance from mumbai do the two trains meet ? a) 276 , b) 271 , c) 200 , d) 278 , e) 268","""when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / (50 - 40) = 4 hours so , the two trains meet at 2 p . m . the two trains meet 4 * 50 = 200 km away from mumbai . answer : c"""
Provide a detailed solution to the given mathematical problem.,"225 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees a) 10 , b) 12 , c) 14 , d) 16 , e) 17","""26 trees have 25 gaps between them , required distance (225 / 25) = 10 a"""
Explain the solution process for the given equation.,"nitin ranks 15 th in a class of 47 students . what is rank from the last ? a) 33 , b) 38 , c) 32 , d) 28 , e) 19","""explanation : number students behind the nitin in rank = (47 - 15) = 32 nitin is 33 rd from the last answer : a) 33"""
"Work through the equation methodically, ensuring clarity at each step.","shop offered 25 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop' s original selling price ? a) 500 , b) 550 , c) 746 , d) 700 , e) 750",sp * (75 / 100) = 560 sp = 7.46 * 100 = > cp = 746 answer : c
Explain the solution process for the given equation.,"8 x 5.4 - 0.6 x 10 / 1.2 = ? a) 30 , b) 45 , c) 50 , d) 31 , e) 21","""given expression = (43.2 - 6) / 1.2 = 37.2 / 1.2 = 31 answer is d ."""
Provide a detailed solution to the given mathematical problem.,"what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 7 a) 2 / 15 , b) 3 / 5 , c) 1 / 6 , d) 1 / 7 , e) none of these","explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 7 = . 71 so biggest is 4 / 5 and smallest is 2 / 3 their difference is 4 / 5 - 2 / 3 = 2 / 15 option a"
Provide a detailed solution to the given mathematical problem.,"if x > 0 , x / 50 + x / 5 is what percent of x ? a) 6 % , b) 25 % , c) 37 1 / 2 % , d) 60 % , e) 75 %","""just plug and chug . since the question asks for percents , pick 100 . (but any number will do .) 100 / 50 + 100 / 5 = 2 + 20 = 25 25 is 25 % of 100 = b"""
Provide a detailed solution to the given mathematical problem.,"the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling alongthe boundary ofthe park at the speed of 12 km / hr completes one round in 8 min , then the area of the park (in sq . m) is ? a) 13400 m , b) 147600 m , c) 153600 m , d) 187500 m , e) 196700 m","""perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 (3 x + 2 x) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = (480 x 320) m 2 = 153600 m c"""
"Solve the problem systematically, showing each step clearly.","paul has to secure 50 % marks to clear his exam of class 7 th . he got 50 marks and failed by 10 marks . what is the maximum marks ? a) 100 , b) 110 , c) 120 , d) 210 , e) 200",c 120 to pass the exam ravish needs 50 + 10 = 60 marks . = > (60 / 50) * 100 = 120
"Solve the problem systematically, showing each step clearly.","calculate the area of a triangle , if the sides are 13 cm , 12 cm and 5 cm , what is its area ? ['a) 36 cm 2','b) 35 cm 2','c) 30 cm 2','d) 32 cm 2','e) 31 cm 2']","the triangle with sides 13 cm , 12 cm and 5 cm is right angled , where the hypotenuse is 13 cm . area of the triangle = 1 / 2 * 12 * 5 = 30 cm 2 answer : c"
"Solve the problem systematically, showing each step clearly.","two whales are moving in the same direction at 18 mps and 15 mps . the faster whale crosses the slow whale in 15 seconds . what is the length of the slower whale in meters ? a) 45 m , b) 56 m , c) 39 m , d) 33 m , e) 62 m",relative speed = (18 - 15) = 3 mps . distance covered in 15 sec = 15 * 3 = 45 m . the length of the faster train = 45 m . answer : a
"Solve the problem systematically, showing each step clearly.","if a certain number is divided by 2 , the quotient , dividend , and divisor , added together , will amount to 62 . what is the number ? a) 18 , b) 28 , c) 40 , d) 38 , e) 59","""let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c"""
Provide a detailed solution to the given mathematical problem.,"a train running at the speed of 180 km / hr crosses a pole in 9 seconds . find the length of the train . a) 150 meter , b) 286 meter , c) 186 meter , d) 288 meter , e) 450 meter","""speed = 180 * (5 / 18) m / sec = 50 m / sec length of train (distance) = speed * time (50) * 9 = 450 meter answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","potato chips are on sale , buy 2 get 1 free . there are only 9 bags of chips left (4 plain and 5 bbq) . a shopper randomly grabs 3 bags . what is the probability the shopper will grab exactly 3 bags of bbq chips ? a) 2 / 3 , b) 1 / 3 , c) 1 / 5 , d) 5 / 42 , e) 7 / 42","combination probability formula : ncr = n ! / [ r ! (n - r) ! ] total possible , select 3 bags from 9 bags = 9 c 3 = 9 ! / [ 3 ! (9 - 3) ! ] = 84 . to have 3 bbq there must be 0 plain , select 0 plain from 4 = 4 c 0 = 1 . and , select 3 bbq from 5 = 5 c 3 = 10 . 3 bbq and 0 plain = (1) (10) = 10 probability = (number outcomes favorable) / (total number outcomes) = 10 / 84 = 5 / 42 answer : d"
Break down and solve the equation step by step.,"how many even integers n , such that 20 < = n < = 220 are of the form 3 k + 4 , where k is any natural number ? a) 28 , b) 31 , c) 34 , d) 37 , e) 40","""the first number is 22 = 16 + 6 (1) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 220 = 16 + 6 (34) there are 34 numbers in the list . the answer is c ."""
Break down and solve the equation step by step.,"a person' s present age is two - fifth of the age of his mother . after 6 years , he will be one - half of the age of his mother . how old is the mother at present ? a) a) 25 , b) b) 40 , c) c) 32 , d) d) 45 , e) e) 30","""let the mother' s present age be x years then the person' s present age = 2 x / 5 (2 x / 5) + 6 = 1 / 2 (x + 6) 2 (2 x + 30) = 5 (x + 6) x = 30 answer is e"""
Break down and solve the equation step by step.,"the proportion of water to alcohol in solution a is 5 : 4 and the proportion of water to alcohol in solution b is 6 : 5 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ? a) 40.9 % , b) 41.9 % , c) 42.9 % , d) 43.9 % , e) 44.9 %","""let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : (4 / 9) (v / 2) + (5 / 11) (v / 2) = 2 v / 9 + 5 v / 22 = 89 v / 198 . the concentration of alcohol is 89 / 198 = 44.9 % the answer is e ."""
Explain the solution process for the given equation.,"find the average of all the numbers between 6 and 29 which are divisible by 5 ? a) 17 , b) 20 , c) 25 , d) 30 , e) 15",average = (10 + 15 + 20 + 25) 4 = 70 / 4 = 17 answer is a
"Solve the problem systematically, showing each step clearly.","the cost price of a radio is rs . 1860 and it was sold for rs . 1340 , find the loss % ? a) 18 % , b) 12 % , c) 22 % , d) 27 % , e) 21","""1860 - - - - 520 100 - - - - ? = > 27 % answer : d"""
Explain the solution process for the given equation.,"if the cost price of 81 chocolates is equal to the selling price of 45 chocolates , the gain percent is : a) 80 % , b) 85 % , c) 82 % , d) 70 % , e) 75 %","""explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 45 chocolates = rs . 45 ; s . p . of 45 chocolates = rs . 81 . .' . gain % = 36 * 100 / 45 = 80 % answer : a"""
Break down and solve the equation step by step.,"what is the difference between the place values of two 1' s in the numeral 135.21 a) 99.999 , b) 100.2 , c) 134 , d) 99.99 , e) 99.9",required difference = 100 - 0.01 = 99.99 answer is d
"Solve the problem systematically, showing each step clearly.","a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 9 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ? a) 3 , b) 4 , c) 18 / 5 , d) 9 , e) 12","""yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 9 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a (rate of machine r) = 1 / 36 r _ s (rate of machine s) = 1 / 9 lets say x machines are used to attain the desired rate , thus x / 36 + x / 9 = 1 / 2 (desired r = 1 / 2 i . e . to complete the job in 2 hours) (x + 4 x) / 36 = 1 / 2 5 x / 36 = 1 / 2 x = 18 / 5 . qa = 18 / 5 (answer c)"""
Break down and solve the equation step by step.,"i remember during the school days , the teacher asked the class ` ` can you tell me the sum of the first 50 odd numbers ? ` ` . i ran quickly to the teacher and told her ` ` the answer is 2500'' . the teacher replied ` ` lucky guess'' . she then asked me ` ` can you tell me the sum of first 75 odd numbers ? ` ` . i wait for approx 10 seconds and replied with the correct answer . how can i answer so quickly and whats the correct answer ? a) 5624 , b) 5625 , c) 5626 , d) 5627 , e) none",solution : 5625 n ^ 1 75 * 75 = 5625 (sum of first 75 odd numbers) . 50 * 50 = 2500 (sum of first 50 odd numbers) . answer b
Explain the solution process for the given equation.,"the sum of the first 92 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? a) 5,050 , b) 7,500 , c) 10,500 , d) 11,700 , e) 19,600","""101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 92 * 100 + (1 + 3 + 5 + 7 + . . . . . .) sum of 1 st 100 natural numbers = (100 * 101) / 2 = 5050 sum of 1 st 92 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 92 * 100 + (1 + 3 + 5 + 7 + . . . . . .) = 9200 + 2500 = 11700 d is the answer ."""
Provide a detailed solution to the given mathematical problem.,"a train 250 m long is running at a speed of 58 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ? a) 5 sec , b) 9 sec , c) 12 sec , d) 18 sec , e) 15 sec","""answer : d . speed of the train relative to man = (58 - 8) kmph = (50 * 5 / 18) m / sec = (125 / 9) m / sec time taken by the train to cross the man = time taken by it to cover 250 m at 125 / 9 m / sec = 250 * 9 / 125 sec = 18 sec"""
"Solve the problem systematically, showing each step clearly.","in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 107800 . how many times did he participate in the competition ? a) 4 , b) 5 , c) 6 , d) 7 , e) 8","""107800 = 2 * 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 8 times . the answer is e ."""
Break down and solve the equation step by step.,"what is the compound interest paid on a sum of rs . 4500 for the period of 2 years at 10 % per annum . a) 945 , b) 620 , c) 610 , d) 600 , e) none of these","""solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 4500 = 4500 * (21 / 100) = 945 answer a"""
"Solve the problem systematically, showing each step clearly.","in a class of 30 students , 5 students did not borrow any books from the library , 12 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average (arithmetic mean) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ? a) 5 , b) 8 , c) 15 , d) 18 , e) 20","the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 32 - 12 = 20 books . answer : e ."
Break down and solve the equation step by step.,"calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 20 % and its breadth is decreased by 5 % ? ['a) 14 percent increase','b) 5 percent increase','c) 24 percent increase','d) 13 percent increase','e) 11 percent increase']",let l and b be 100 each 100 * 100 = 10000 l increase by 20 % = 120 b decrease by 5 % = 95 120 * 95 = 11400 14 percent increase answer : a
"Work through the equation methodically, ensuring clarity at each step.","if x , y , and z are positive integers , and 4 x = 5 y = 8 z , then the least possible value of x + y + z is a) 15 , b) 23 , c) 37 , d) 42 , e) 60","""take lcm of 4,5 and 8 = 40 now 4 x = 40 = > x = 10 5 y = 40 = > y = 8 8 z = 40 = > z = 5 10 + 8 + 5 = 23 . option b ."""
Provide a detailed solution to the given mathematical problem.,"lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 20 more photos than claire . how many photos has claire taken ? a) 6 , b) 8 , c) 10 , d) 12 , e) 14","""l = r l = 3 c r = c + 20 3 c = c + 20 c = 10 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"in a group of buffaloes and ducks , the number of legs are 24 more than twice the number of heads . what is the number of buffaloes in the group ? a) 12 , b) 13 , c) 14 , d) 15 , e) 16",let no . of buffaloes be x & no . of ducks be y buffaloes have 4 legs while ducks have 2 4 x + 2 y = 2 * (x + y) + 24 = > 4 x + 2 y - 2 x - 2 y = 24 = > x = 12 number of buffaloes in the group = 12 answer : a
"Solve the problem systematically, showing each step clearly.","a firm is comprised of partners and associates in a ratio of 2 : 63 . if 35 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ? a) 12 , b) 14 , c) 16 , d) 18 , e) 20","""the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 7 of the increase in 35 associates . the ratio changed from 14 : 441 to 14 : 476 . thus the number of partners is 14 . the answer is b ."""
Explain the solution process for the given equation.,"a dishonest dealer professes to sell goods at the cost price but uses a weight of 780 grams per kg , what is his percent ? a) 28 % , b) 25 % , c) 55 % , d) 28 % , e) 28.2 %","""780 - - - 220 100 - - - ? = > 28.2 % answer : e"""
Break down and solve the equation step by step.,"a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ? a) 180 , b) 270 , c) 360 , d) 500 , e) 550","""12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 870 = 270 answer b"""
Provide a detailed solution to the given mathematical problem.,"a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9 . in all papers together , the candidate obtained 60 % of the total marks . then the number of papers in which he got more than 50 % marks is a) 2 , b) 3 , c) 4 , d) 5 , e) 1","here we can assume that one subject is of 100 marks so total there are 5 subjects = > 100 * 5 = 500 . now according to the question he secured 60 % of those which is 60 % of 500 = 300 marks in total . the ratio between the marks is given as 5 : 6 : 7 : 8 : 9 , so now we can distribute 300 marks according to the ratio . total ratio = 35 for 6 : (300 / 35) * 6 = 51.4 similarly , we will get for others as 60 , 68.57 , 77.14 hence , there are 5 subject where he secured more that 50 % . the answer is 5 . d"
"Solve the problem systematically, showing each step clearly.","two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 10 seconds . the length of the faster train is a) 225 m , b) 100 m , c) 120 m , d) 180 m , e) none","""solution relative speed = (36 + 45) km / hr = (81 x 5 / 18) m / sec = (45 / 2) m / sec length of the train = (45 / 2 x 10) m = 225 m . answer a"""
"Work through the equation methodically, ensuring clarity at each step.","a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 80 inches . find b . ['a) 8','b) 16','c) 24','d) 32','e) 48']","from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 (= 2 ^ 2 * 3) andbis 4 (= 2 ^ 2) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 (2 ^ 2 * 3) andbis 80 (2 ^ 4 * 5) , sob = 2 ^ 4 or 2 ^ 4 * 5 (16 or 80) . combining 2 premises shows the answer is b (16) ."
Explain the solution process for the given equation.,"find the number of factors of 180 that are in the form (4 * k + 2) , where k is a non - negative integer ? a) 1 , b) 2 , c) 3 , d) 4 , e) 6","make sure to follow posting guidelines (link in my signatures) . title of the thread must mention the first few words of the question itself . as for the question , the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number) . number of factors of 180 (= 2 ^ 2 * 3 ^ 2 * 5) = 18 . so listing the factors gives us : 1 , 180 2 , 90 3 , 60 4 , 45 5 , 36 6 , 30 9 , 20 10 , 18 12 , 15 as the question asks us about the factors of the form 4 k + 2 - - - > eliminate all odd factors . you are now left with 24 , 610 , 1218 , 2030 , 3660 , 90180 for the form 4 k + 2 , the first few values are 2 , 6 , 10 , 14 , 18 , 22 , 26 , 30 . . . already giving you 5 factors (= 2 , 610 , 1830) . you can stop here and mark 6 (6 th one = 90) as the correct answer as 5 is not given . for checking any particular factor whether they conform to the form 4 k + 2 - - - > do the following 4 k + 2 = 36 - - - > 4 k = 34 - - > this will not give you an integer value for k - - - > reject . proceed with others until you find all the values asked . e is thus the correct answer ."
Break down and solve the equation step by step.,"company x provides bottled water to its employees in 1 liter bottles , $ 2 each . at least how many 1 l bottles must company x buy monthly , so that new contract with $ 50 fixed monthly rate and $ 1 for 10 l bottle each paid off ? (assume that no other costs apply) a) 28 , b) 29 , c) 30 , d) 31 , e) 27","let the no . of 1 liter bottles be x , so the no . of 10 l bottles will be x / 10 (to equate the vol .) since the total cost will be equal , 2 x = 50 + x / 10 so x = 26.31 or 27 . answer is (e) ."
"Solve the problem systematically, showing each step clearly.","the average age of a group of persons going for picnic is years . fifteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is a) 5 , b) 10 , c) 15 , d) 40 , e) 50",solution let the initial number of persons be x . then 16 x + 15 x 15 = 15.5 (x + 20) = 0.5 x = 7.5 x = 15 . answer c
"Work through the equation methodically, ensuring clarity at each step.","when 100 is divided by positive integer x , the remainder is 3 . what is the remainder when 197 is divided by x ? a) 2 , b) 3 , c) 4 , d) 6 , e) 8",if 100 / x leaves a reminder 3 then (100 - 3) i . e . 97 is divisible by x so (100 + 97) / x leaves a reminder rem (100 / x) + rem (97 / x) = > 3 + 0 = 3 answer : b
Explain the solution process for the given equation.,"in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates (0 , 7.5) , (8 , 0) , (0 , - 7.5) , (- 8 , 0) ? a) 56 , b) 88 , c) 112 , d) 116 , e) 120","""ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 7.5 + 7.5 = 15 area = 1 / 2 * 16 * 15 = 120 e is the answer"""
Break down and solve the equation step by step.,"a chemical supply company has 60 liters of a 30 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ? a) 12 , b) 15 , c) 20 , d) 24 , e) 30","60 liters of a 30 % hno 3 solution means hno 3 = 18 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 18 + x = 50 % of (60 + x) or x = 24 . hence , d"
"Solve the problem systematically, showing each step clearly.","60 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ? a) 80 litres , b) 90 litres , c) 120 litres , d) 170 litres , e) none of these","explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 60 = 80 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 80 = 120 litres . answer c"
Break down and solve the equation step by step.,"find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 18 per cubic meter ? ['a) 2998','b) 2799','c) 1782','d) 1485','e) 2780']",22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 18 = 1782 answer : c
Provide a detailed solution to the given mathematical problem.,"the grade point average of one third of the classroom is 60 ; the grade point average of the rest is 66 . what is the grade point average of the whole class ? a) 55 , b) 56 , c) 64 , d) 65 , e) 66","""let n = total students in class total points for 1 / 3 class = 60 n / 3 = 20 n total points for 2 / 3 class = 66 * 2 n / 3 = 44 n total points for whole class = 20 n + 44 n = 64 n 64 n total class points / n total students = 64 grade point average for total class answer : c"""
"Solve the problem systematically, showing each step clearly.","(x) + 3612 + 16125 - 6149 = 90189 . calculate the value of x a) 76601 , b) 76600 , c) 76655 , d) 76313 , e) 76723","""x + 3612 + 16125 - 6149 = 90189 = x + 3612 + 16125 = 90189 + 6149 = x + 19737 = 96338 = x = 96338 - 19737 = 76601 answer is a"""
"Work through the equation methodically, ensuring clarity at each step.","suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 112 runs thereby increasing his average by 6 runs . what is his average after the 17 th innings ? a) 18 , b) 25 , c) 16 , d) 72 , e) 27","""to improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings . thus , the average after the 17 th innings = 112 - 96 = 16 . answer : c"""
Provide a detailed solution to the given mathematical problem.,"a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 10 pounds of the body weight , by what percent was the prescribed dosage lesser than the typical dosage ? a) 8 % , b) - 37.5 % , c) 11 % , d) 12.5 % , e) 14.8 %",typical dosage per 10 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * (120 / 10) = 2 * 12 = 24 c . c dosage prescribed by doctor for 120 pound patient = 18 c . c % prescribed dosage greater than the typical dosage = (18 - 24 / 16) * 100 % = (- 6 / 16) * 100 % = - 37.5 % answer b
"Work through the equation methodically, ensuring clarity at each step.","a reduction of 30 % in the price of oil enables a house wife to obtain 3 kgs more for rs . 700 , what is the reduced price for kg ? a) 70 , b) 50 , c) 60 , d) 80 , e) 65","""700 * (30 / 100) = 210 - - - - 3 ? - - - - 1 = > rs . 70 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","in the xy - plane , the point (1 , 3) is the center of a circle . the point (- 2 , 3) lies inside the circle and the point (1 , - 2) lies outside the circle . if the radius r of the circle is an integer , then r = a) 6 , b) 5 , c) 4 , d) 3 , e) 2","""an easy way to solve this question will be just to mark the points on the coordinate plane . you' ll see that the distance between the center (1 , 3) and the point inside the circle (- 2 , 3) is 3 units (both points are on y = 3 line so the distance will simply be 1 - (- 2) = 3) so the radius must be more than 3 units . the distance between the center (1,3) and the point outside the circle (1 , - 2) is 5 units (both points are on x = 1 line so the distance will simply be 3 - (- 2) = 5) so the radius must be less than 5 units , which implies 3 < r < 5 , thus as r is an integer then r = 4 . answer : c ."""
Provide a detailed solution to the given mathematical problem.,"if it takes a tub 2 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ? a) 48 seconds , b) 1 minute , 12 seconds , c) 1 minute , 50 seconds , d) 2 minutes , 14 seconds , e) 4 minutes , 12 seconds","""if 5 / 7 of tub' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 2 minutes to drain 5 / 7 th of tub it takes 2 * (7 / 5) minutes to drain the entire tub and 2 * (7 / 5) * (2 / 7) min to drain 2 / 7 th of the tub which is 4 / 5 minutes or 48 minutes so answer is a"""
Explain the solution process for the given equation.,"the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 90 instead of 10 then find the correct average marks ? a) a) 78 , b) b) 82 , c) c) 92 , d) d) 91 , e) e) 85","""correct avg marks = 100 + (10 - 90) / 10 avg = 100 - 8 = 92 answer is c"""
"Work through the equation methodically, ensuring clarity at each step.","if (a + b) = 4 , (b + c) = 9 and (c + d) = 3 , what is the value of (a + d) ? a) 16 . , b) 8 . , c) 7 , d) 2 . , e) - 2","""given a + b = 4 = > a = 4 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 4 - b + 3 - c = > 7 - (b + c) = > 7 - 9 = - 2 . option e . . ."""
Explain the solution process for the given equation.,"a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 12 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ? a) 14 , b) 16 , c) 21 , d) 22 , e) 32","""i treat such problems as work ones . work = rate * time mileage (m) = rate (mpg) * gallons (g) x gallons is a full tank { 462 = rx { 336 = (r - 12) x solve for r , r = 44 44 - 12 = 32 mpg e"""
"Work through the equation methodically, ensuring clarity at each step.","on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 630 , the rate of interest being the same in both the cases . the rate of interest is ? a) 8 % , b) 10 % , c) 12 % , d) 14 % , e) 16 %","""difference in c . i . and s . i for 2 years = $ 630 - $ 600 = $ 30 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 30 rate = (100 * 30) / (300) = 10 % the answer is b ."""
Explain the solution process for the given equation.,"90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 20 % of the total school population of x students , what is x ? a) 125 , b) 150 , c) 212 , d) 250 , e) 500",90 = x / 100 * 20 / 100 * x = > x ^ 2 = 9 * 10000 / 2 = > x = 212 c
Provide a detailed solution to the given mathematical problem.,"how many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 4 percent sugar solution ? a) 12.5 , b) 15.5 , c) 17.5 , d) 21.5 , e) 24.5","""let x be the amount that needs to be evaporated . 0.03 (50) = 0.04 (50 - x) 0.04 x = 2 - 1.5 x = 0.5 / 0.04 = 12.5 liters the answer is a ."""
"Work through the equation methodically, ensuring clarity at each step.","a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter e of liquid a was contained by the can initially ? a) 10 , b) 20 , c) 21 , d) 25 , e) 27","""as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = (712) * total and b = (5 / 12) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove (7 / 12) * 9 of a - - - > a remaining = 21 - (7 / 12) * 9 = 63 / 4 similarly , for b , you remove (5 / 12) * 9 - - - > b remaining = 15 - (5 / 12) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b (final ratio) = (45 / 4) / (81 / 4) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = (7 x - (7 / 12) * 9) / (5 x - (5 / 12) * 9 + 9) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = (7 x - (7 / 12) * 9) / (5 x - (5 / 12) * 9 + 9) - - - > giving you x = 3 . thus a (original) e = 7 * 3 = 21 . c"""
Provide a detailed solution to the given mathematical problem.,"the average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? a) 120 kg , b) 130 kg , c) 137 kg , d) 190 kg , e) none","""solution total weight increased = (10 x 7.2) kg = 72 kg . weight of new person = (65 + 72) kg = 137 kg . answer c"""
Explain the solution process for the given equation.,"a train speeds past a pole in 15 sec and a platform 130 m long in 25 sec , its length is ? a) 195 , b) 150 , c) 160 , d) 170 , e) 180","""let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 (x + 130) / 25 = x / 15 = > x = 195 m . answer : option a"""
Provide a detailed solution to the given mathematical problem.,"what least number must be subtracted from 427398 so that remaining no . is divisible by 11 a) 3 , b) 4 , c) 6 , d) 7 , e) 8","""explanation : on dividing 427398 by 11 we get the remainder 4 , so 4 should be subtracted answer : option b"""
"Work through the equation methodically, ensuring clarity at each step.","if each side of a square is increased by 25 % , find the percentage change in its area . a) 46.25 % , b) 56.25 % , c) 56 % , d) 50.25 % , e) 36.25 %","""let each side of the square be a . then , area = a 2 . new side = (125 a / 100) = (5 a / 4) . new area = (5 a / 4) 2 = (25 a 2) / 16 . increase in area = ((25 a 2) / 16) - a 2 = (9 a 2) / 16 . increase % = [ ((9 a 2) / 16) * (1 / a 2) * 100 ] % = 56.25 % . answer b 56.25 %"""
"Work through the equation methodically, ensuring clarity at each step.","carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 6 inches tall . how tall are the sculpture andbase together ? a) 3.1 feet , b) 3.2 feet , c) 3.3 feet , d) 3.4 feet , e) 3.5 feet","""we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 6 = 40 40 / 12 = 3.3 feet answer : c"""
Break down and solve the equation step by step.,"if you multiply all the numbers on your mobile phone , what is the answer ? a) 2 , b) 6 , c) 1 , d) 0 , e) 7",d 0 their is a zero in your phone .
Provide a detailed solution to the given mathematical problem.,"rectangular tile each of size 20 cm by 30 cm must be laid horizontally on a rectangular floor of size 100 cm by 150 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is : a) 40 , b) 15 , c) 25 , d) 32 , e) 45","""area of tile = 20 * 30 = 600 area of floor = 100 * 150 = 15000 no of tiles = 15000 / 600 = 25 so , the no of tile = 25 answer : c"""
Provide a detailed solution to the given mathematical problem.,"how many paying stones , each measuring 3 * 2 m are required to pave a rectangular court yard 15 m long and 6 m board ? a) 99 , b) 18 , c) 26 , d) 15 , e) 12","""15 * 6 = 3 * 2 * x = > x = 15 answer : d"""
Provide a detailed solution to the given mathematical problem.,"if a : b = 4 : 7 and b : c = 5 : 9 , then a : c = ? a) 28 : 37 , b) 18 : 37 , c) 16 : 53 , d) 20 : 63 , e) 15 : 48",a / b = 4 / 7 and b / c = 5 / 9 a / b * b / c = 4 / 7 * 5 / 9 = 20 / 63 so a / c = 20 / 63 20 : 63 answer d
"Work through the equation methodically, ensuring clarity at each step.","[ 1 / (1 . 2.3) ] + [ 1 / (2 . 3.4) ] + [ 1 / (3 . 4.5) ] + [ 1 / (4 . 5.6) ] is equal to a) 7 / 30 , b) 11 / 30 , c) 13 / 30 , d) 17 / 30 , e) none",answer given exp . = [ (4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3) ] / [ (2 x 3 x 4 x 5 x 6) ] = 168 / (24 x 30) = 7 / 30 correct option : a
"Work through the equation methodically, ensuring clarity at each step.","a shopkeeper sold an article offering a discount of 5 % and earned a profit of 19.7 % . what would have been the percentage of profit earned if no discount was offered ? a) 60 % , b) 26 % , c) 30 % , d) 56 % , e) 73 %","""let c . p . be rs . 100 . then , s . p . = rs . 19.70 let marked price be rs . x . then , 95 / 100 x = 119.70 x = 11970 / 95 = rs . 126 now , s . p . = rs . 126 , c . p . = rs . 100 profit % = 26 % . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a man buys an article for $ 110 . and sells it for $ 125 . find the gain percent ? a) 10 % , b) 13.6 % , c) 25 % , d) 20 % , e) 30 %","""c . p . = $ 110 s . p . = $ 125 gain = $ 15 gain % = 15 / 110 * 100 = 13.6 % answer is b"""
Provide a detailed solution to the given mathematical problem.,"what is value of x if 32 - y = 16 x - y ? a) 1 , b) 3 , c) 4 , d) 2 , e) 6","""32 - y = 16 x - y 32 = 16 x - y + y 16 x = 32 x = 2 answer is option d"""
"Solve the problem systematically, showing each step clearly.","15.06 * 0.00000001 = ? a) 15060000 , b) 0.001506 , c) 0.01506 , d) 1.506 e - 07 , e) none of these","""explanation : clearly after decimal 10 digits should be there . option d"""
"Work through the equation methodically, ensuring clarity at each step.","city x has a population 7 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ? a) 1 : 8 , b) 1 : 4 , c) 2 : 1 , d) 14 : 1 , e) 18 : 1","x = 7 y , y = 2 * z x : y , y : z 7 : 1 , 2 : 1 14 : 2 , 2 : 1 so , x : z = 14 : 1 (d)"
"Work through the equation methodically, ensuring clarity at each step.","seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ? a) 10 % , b) 33.33 % , c) 40 % , d) 50 % , e) 66.67 %","""x - wt of mix x added y - wt of mix y added 0.4 x + 0.25 y = 0.3 (x + y) 0.1 x = 0.05 y x / y = 5 / 10 = 1 / 2 y / x = 2 (y + x) / x = 3 = > x / (y + x) * 100 = 100 / 3 = 33.33 % answer : b"""
"Solve the problem systematically, showing each step clearly.","a certain machine produces 550 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 5 days ? a) 7,000 , b) 24,000 , c) 66,000 , d) 100,000 , e) 168,000","""since 5 days consist of 24 * 5 hours the total is 120 hours . since every hour the machine produces 550 units of product p the total product during 120 hours is 120 * 550 = 66,000 . correct option : c"""
Explain the solution process for the given equation.,"if 2 ^ 4 , 3 ^ 3 , and 10 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ? a) 198 , b) 288 , c) 363 , d) 360 , e) 484",i will go with d (pending elements to match is 2 ^ 2 * 3 ^ 2 * 10 ^ 1 = 360
Break down and solve the equation step by step.,"xy = 2 then what is (2 ^ (x + y) ^ 2) / (2 ^ (x - y) ^ 2) a) 2 , b) 4 , c) 8 , d) 16 , e) 256",(x + y) ^ 2 - (x - y) ^ 2 (x + y + x - y) (x + y - x + y) (2 x) (2 y) 4 xy 8 2 ^ 8 = 256 answer e
Break down and solve the equation step by step.,"how many 3 - digit even numbers are possible such that if one of the digits is 4 , the next / succeeding digit to it should be 7 ? a) 305 , b) 5 , c) 365 , d) 405 , e) 495","470 , 472 , 474 , 476 , and 478 , so total 5 . hence option b ."
Provide a detailed solution to the given mathematical problem.,"a cycle is bought for rs . 900 and sold for rs . 1120 , find the gain percent ? a) 11 , b) 24 , c) 99 , d) 77 , e) 18","""900 - - - - 220 100 - - - - ? = > 24 % answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","in what time will a train 100 m long cross an electric pole , it its speed be 72 km / hr ? a) 2.5 , b) 5 , c) 2.4 , d) 2.8 , e) 2.1","""speed = 72 * 5 / 18 = 20 m / sec time taken = 100 / 20 = 5 sec . answer : b"""
Explain the solution process for the given equation.,"3 business people wish to invest in a new company . each person is willing to pay one third of the total investment . after careful calculations , they realize that each of them would pay $ 2200 less if they could find two more equal investors . how much is the total investment in the new business ? a) $ 11,000 , b) $ 50,000 , c) $ 16,500 , d) $ 6,600 , e) $ 3,600","total investment between 5 : (x / 5) total investment including 2200 less between 3 people (x - (2200 * 3)) / 3 set both eq . equal to each other . 16,500 answer c)"
Break down and solve the equation step by step.,"if you keep rolling a pair of dice together till a sum of 5 or 7 is obtained , then what is the probability that a sum of 5 comes before a sum of 7 ? a) 5 / 5 , b) 4 / 5 , c) 3 / 5 , d) 2 / 5 , e) 1 / 5","this can be solved in a generic and complex way but let us not go into all that . there can be four ways through which the pair of dice results in a sum of 5 . there can be six ways through which the pair of dice can result in a sum of 7 . now , we want the probability of the pair of dice resulting in a sum of 5 before a sum of 7 . thus probability = 4 / (4 + 6) = 4 / 10 or 2 / 5 . correct answer is d) 2 / 5"
Break down and solve the equation step by step.,"a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 10 : 30 am in the same direction at the rate of 84 km / h . at what time will the second train catch the first train ? a) 4 : 30 , b) 5 : 00 , c) 5 : 30 , d) 6 : 00 , e) 6 : 30","""in one hour and thirty minutes the first train travels 105 km . the second train catches the first train at a rate of 84 km / h - 70 km / h = 14 km / h . the second train will catch the first train in 105 / 14 = 7.5 hours , so at 6 : 00 pm . the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","a man buys a cycle for rs . 2300 and sells it at a loss of 30 % . what is the selling price of the cycle ? a) s . 1690 , b) s . 1610 , c) s . 1890 , d) s . 1602 , e) s . 1092","""s . p . = 70 % of rs . 2300 = rs . 70 x 2300 / 100 = rs . 1610 answer : option b"""
"Solve the problem systematically, showing each step clearly.","for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 315 what is the least possible value of k ? a) 5 , b) 7 , c) 9 , d) 11 , e) 13",315 = 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 7 . the answer is b .
"Solve the problem systematically, showing each step clearly.","if integer k is equal to the sum of all even multiples of 25 between 200 and 600 , what is the greatest prime factor of k ? a) 5 , b) 7 , c) 11 , d) 13 , e) 17","""if we break down what the stem is asking what is the sum of all mult of 50 between 200 and 600 . using arithmetic progression to find n : 600 = 200 + (n - 1) 50 400 + 50 = 50 n 450 = 50 n = > n = 9 the sum would be : 9 * mean mean = [ 600 + 200 ] / 2 = 400 9 * 400 = 3600 d"""
"Work through the equation methodically, ensuring clarity at each step.","36 welders work at a constant rate they complete an order in 3 days . if after the first day , 12 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ? a) 3 , b) 2 , c) 8 , d) 4 , e) 6","""1 . we need to find out the time taken by 24 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 36 * 3 = 108 days 4 . but on day 1 thirty - six workers had already worked finishing 1 / 3 of the job . so 24 workers have to finish only 2 / 3 of the job . 5 . total time taken by 24 workers can be got from formula used at (2) . i . e . , 24 * total time taken = 108 . total time taken by 6 workers to finish the complete job is 108 / 24 = 4.5 days . 6 . time taken by 24 workers to finish 2 / 3 of the job is 2 / 3 * 4.5 = 3 days . the answer is choice a"""
Break down and solve the equation step by step.,"on the first of the year , james invested x dollars at proudstar bank in an account that yields 3 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ? a) 22.04 % , b) 16.12 % , c) 12.5 % , d) 18.25 % , e) 10 %","per quarter , interest = 3 % so for a year , interest = 12 % due to quarter cumulation , effective yield (ytm) would be slight higher than 12 % answer = 12.5 % = answer : c"
Provide a detailed solution to the given mathematical problem.,"how many positive integers will divide evenly into 190 ? a) 4 , b) 6 , c) 8 , d) 12 , e) 16",the question is asking how many factors 190 has . 190 = 2 * 5 * 19 the number of factors is 2 ^ 3 = 8 the answer is c .
Break down and solve the equation step by step.,"two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 10 hours respectively . the ratio of their speeds is a) 4 : 9 , b) 4 : 3 , c) 4 : 12 , d) 4 : 8 , e) 5 : 2","let us name the trains as a and b . then , (a' s speed) : (b' s speed) = b : a = 10 : 4 = 5 : 2 . answer : e"
Break down and solve the equation step by step.,"find number which is 60 % less than 120 . a) 18 , b) 22 , c) 28 , d) 48 , e) 98","""explanation : 60 % less is 40 % of the given number therefore , 40 % of 120 is 48 . answer : d"""
Provide a detailed solution to the given mathematical problem.,"if 7 spiders make 7 webs in 7 days , then 1 spider will make 1 web in how many days ? a) 7 , b) 6 , c) 5 , d) 4 , e) 3","let the required number days be x . less spiders , more days (indirect proportion) less webs , less days (direct proportion) spiders 1 : 7 webs 7 : 1 1 x 7 x x = 7 x 1 x 7 = > x = 7 answer is 7"
Break down and solve the equation step by step.,"two cars start from the opposite places of a main road , 150 km apart . first car runs for 30 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ? a) 65 , b) 38 , c) 60 , d) 28 , e) 21",answer : c) 60 km
"Solve the problem systematically, showing each step clearly.","difference between the length and breadth of a rectangle is 23 m . ifits perimeter is 206 m , then its area is ? ? ['a) 1220 m ^ 2','b) 1520 m ^ 2','c) 2520 m ^ 2','d) 2600 m ^ 2','e) 3420 m ^ 2']","we have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103 . solving the two equations , we get : l = 63 and b = 40 . area = (l x b) = (63 x 40) m 2 = 2520 m ^ 2 c"
"Work through the equation methodically, ensuring clarity at each step.","if 30 honey bees make 30 grams of honey in 30 days , then 1 honey bee will make 1 gram of honey in how many days ? a) 1 , b) 3.5 , c) 30 , d) 49 , e) 30","""explanation : let the required number days be x . less honey bees , more days (indirect proportion) less honey , less days (direct proportion) honey bees 1 : 30 : : 30 : x honey 30 : 1 = > 1 x 30 x x = 30 x 1 x 30 = > x = 30 . answer : c"""
Explain the solution process for the given equation.,"find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 2030 ? a) rs . 2000 , b) rs . 1750 , c) rs . 2010 , d) rs . 2005 , e) none of these","""explanation : 2030 = p [ 1 + (5 * 16 / 5) / 100 ] p = 1750 answer : option b"""
"Work through the equation methodically, ensuring clarity at each step.","24 * 22 = ? / 8 a) 4224 , b) 2224 , c) 5374 , d) 2434 , e) 4254","""a 4224 ? / 8 = 24 * 22 ? = 24 * 22 * 8 ? = 4224"""
"Solve the problem systematically, showing each step clearly.","john was 43 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty' s age is now 7 / 8 of john' s . how old is betty ? a) 24 , b) 26 , c) 42 , d) 30 , e) 32","""assume betty' s age on marriage = x years . john' s age on marriage = 43 john' s age after 5 years = 48 years . betty' s age after 5 years = x + 5 given : x + 5 = 7 / 8 (48) = 42 therefore betty' s current age = 42 option c"""
Explain the solution process for the given equation.,"in a class of 50 students , 3 / 5 went away do painting , 1 / 5 went to play in the field . how many students are left in the classroom ? a) 20 , b) 30 , c) 5 , d) 8 , e) 10","3 / 5 + 1 / 5 are the students who have left the classroom 3 / 5 + 1 / 5 = (3 + 1) / 5 , since denominator is same for both fractions = 4 / 5 remaining students in the classroom = 1 - 4 / 5 = 5 / 5 - 4 / 5 = (5 - 4) / 5 = 1 / 5 1 / 5 of 50 = 10 ans : e"
"Work through the equation methodically, ensuring clarity at each step.","the average of 8 numbers is 25 , that of the first 2 is 20 and of the next 3 is 26 . the sixth number is less than the seventh by 4 , and less than the eighth by 6 . the last number is a) 30 , b) 32 , c) 40 , d) 36 , e) 38","explanation : sum of all the numbers = 25 * 8 = 200 sum of first two numbers = 40 sum of next three numbers (i . e . , 3 rd , 4 th and 5 th) = 78 so , sum of first five numbers = 118 and sum of 6 th , 7 th and 8 th number = 82 assuming sixth number to be x , we get 7 th number = x + 4 and 8 th number = x + 6 . so , x + (x + 4) + (x + 6) = 82 = > x = 24 . hence , last number (8 th number) = 30 . answer : a"
Explain the solution process for the given equation.,"if the numbers 1 to 96 are written on 96 pieces of paper , (one on each) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ? a) 1 / 50 , b) 1 / 25 , c) 1 / 96 , d) 1 , e) 2","there are 25 primes , 70 composite numbers from 1 to 96 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 96 . answer : c"
"Solve the problem systematically, showing each step clearly.","jim drove 642 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ? a) 113 miles , b) 432 miles , c) 558 miles , d) 887 miles , e) 767 miles","""the number of miles to drive to finish his journey is given by 1200 - 642 = 558 miles correct answer c"""
Explain the solution process for the given equation.,"the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 145 , what is the difference between the ages of patrick and monica ? a) 27 , b) 48 , c) 45 , d) 72 , e) 18","""ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 145 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"""
"Work through the equation methodically, ensuring clarity at each step.","evaluate : 1234562 - 12 * 3 * 2 = ? a) 32435453 , b) 1234554 , c) 76768786 , d) 97979797 , e) 75868656","""according to order of operations , 12 ? 3 ? 2 (division and multiplication) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1234562 - 12 * 3 * 2 = 1234562 - 8 = 1234554 correct answer b"""
Explain the solution process for the given equation.,"two stations p and q are 200 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ? a) 10 am , b) 12 noon , c) 10.30 am , d) 12.30 am , e) 11 am","""assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in (x - 1) hours = 25 (x - 1) total distance = 200 = > 20 x + 25 (x - 1) = 200 = > 45 x = 225 = > x = 5 means , they meet after 5 hours after 7 am , ie , they meet at 12 noon answer is b ."""
"Solve the problem systematically, showing each step clearly.","a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is five times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ? a) 1 : 1 , b) 2 : 3 , c) 3 : 2 , d) 9 : 4 , e) 45 : 8","""water : soap = 3 : 2 soap : salt = 15 : 2 = > for 15 soap , salt = 2 = > for 2 soap , salt = (2 / 15) * 2 = 4 / 15 so , water : soap : salt = 3 : 2 : 4 / 15 = 45 : 30 : 4 after open container , water : soap : salt = 22.5 : 30 : 4 so , water : salt = 22.5 : 4 = 45 : 8 e"""
Explain the solution process for the given equation.,"four machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 10 days ? a) 5 , b) 3 , c) 4 , d) 6 , e) 1","""rate of one machine = 1 job / (20 * 4) days let x = number of machines needed to complete the job in 10 days 1 / (4 * 20) * 10 * x = 1 job x = 8 8 - 4 = 4 answer : c"""
Explain the solution process for the given equation.,"what could be the range of a set consisting of odd multiples of (6 + 1) ? a) 70 , b) 24 , c) 35 , d) 62 , e) 21","""range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 7 * (2 n + 1) where n is any positive integer . range = 7 * (2 m + 1) - 7 * (2 n + 1) = 7 * 2 * (m - n) = 14 * (m - n) . m , n - any positive integers the answer must be divisible by 14 , which is only 70 . the correct answer is a ."""
Provide a detailed solution to the given mathematical problem.,"a manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18 % . the wholesaler sells the same to retailer at a profit of 20 % . the retailer in turn sells them to a customer for rs . 30.09 , there by earning a profit of 25 % . the cost price for the manufacturer is ? a) 33 , b) 29 , c) 17 , d) 10 , e) 16","""explanation : let the cost price for the manufacturer be rs . x . then , 125 % of 120 % of 118 % of x = 30.09 . 125 / 100 * 120 / 100 * 118 / 100 * x = 3009 / 100 177 / 100 x = 3009 / 100 = > x = 17 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number is : a) 36 , b) 77 , c) 88 , d) 55 , e) 221","""(3 x - 9) : (5 x - 9) = 9 : 17 x = 12 = > 3 x = 36 answer : a"""
Provide a detailed solution to the given mathematical problem.,"a shopkeeper buys two articles for rs . 1000 each and then sells them , making 40 % profit on the first article and 40 % loss on second article . find the net profit or loss percent ? a) 200 , b) 278 , c) 282 , d) 400 , e) 270","""profit on first article = 40 % of 1000 = 400 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : d"""
"Solve the problem systematically, showing each step clearly.","of the 65 cars on a car lot , 45 have air - bag , 30 have power windows , and 12 have both air - bag and power windows . how many of the cars on the lot have neither air - bag nor power windows ? a) 8 , b) 2 , c) 10 , d) 15 , e) 18","total - neither = all air bag + all power windows - both or 65 - neither = 45 + 30 - 12 = 63 . = > neither = 2 , hence b . answer : b"
Explain the solution process for the given equation.,"two numbers are respectively 20 % and 50 % more than a third number . what percentage is the first of the second ? a) 25 % , b) 60 % , c) 80 % , d) 55 % , e) 74 %","""required answer = (100 + x) / (100 + y) * 100 = 120 * 100 / 150 = 80 % answer is c"""
Explain the solution process for the given equation.,"here is a simple arithmetical puzzle in his own flowery , poetical language . if one - fifth of a hive of bees flew to the badamba flower , one - third flew to the slandbara , 3 times the difference of these two numbers flew to an arbour , and one bee continued to fly about , attracted on each side by the fragrant ketaki and malati , what was the total number of bees ? a) 11 , b) 15 , c) 18 , d) 17 , e) 19",b 15 the number of bees was 15
"Solve the problem systematically, showing each step clearly.","the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 5 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ? a) 1 : 2 , b) 2 : 3 , c) 3 : 4 , d) 4 : 5 , e) 5 : 6","""5 b = 7 c and so b = 7 c / 5 7 a = 2 b and so a = 2 b / 7 = 2 c / 5 a + b = 2 c / 5 + 7 c / 5 = 9 c / 5 b + c = 7 c / 5 + c = 12 c / 5 the ratio of a + b : b + c = 9 : 12 = 3 : 4 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"the area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot . what will be the length of the diagonal of the square plot ? ['a) 100 m','b) 120 m','c) 95 m','d) 80 m','e) 150 m']","given that the length of the rectangular field l = 90 m and breadth = b = 80 m . then its area lb = 90 x 80 sq . m we know that the area of square = (1 / 2) x (diagonal) 2 from the given question , we have area of square plot = area of rectangular field that is , 90 x 80 = 1 / 2 x diagonal 2 diagonal ^ 2 = 2 x 7200 = 14400 = (120) 2 diagonal = 120 m . hence b"
"Work through the equation methodically, ensuring clarity at each step.","if' a' and' b' are non - zero numbers such that their sum is 6 times the product , what is the value of 1 / a + 1 / b ? a) 5 , b) 6 , c) 7 , d) 8 , e) 12",a + b = 6 ab 1 / a + 1 / b = (b + a) / (ab) = 6 . the answer is b .
"Work through the equation methodically, ensuring clarity at each step.","in the game of dubblefud , red balls , blue balls and green balls are each worth 2 , 4 and 5 points respectively . in a certain selection of balls , the product of the point values of the balls is 16000 . if the number of blue balls in this selection equals the number of green balls , how many red balls are in the selection ? a) 1 , b) 2 , c) 3 , d) 4 , e) 5",this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z (given) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of red balls = 4 hence d
"Solve the problem systematically, showing each step clearly.","what number has a 5 : 1 ratio to the number 11 ? a) 22 , b) 50 , c) 55 , d) 52 , e) 12","""5 : 1 = x : 10 x = 55 answer : c"""
Break down and solve the equation step by step.,"a man can do a piece of work in 7 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ? a) 5 , b) 7 , c) 15 / 2 , d) 21 / 4 , e) 18 / 5","""son' s 1 day' s work = (1 / 3) - (1 / 7) = 4 / 21 the son alone can do the work in 21 / 4 days answer is d"""
Break down and solve the equation step by step.,"the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 44 years , was replaced by a new person . find the age of the new person ? a) 18 , b) 56 , c) 12 , d) 17 , e) 14","""initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = (p - 3) 10 (p - 3) = 10 p - 44 + q = > q = 14 answer : e"""
Explain the solution process for the given equation.,"a sports equipment store sold ping pong rackets for a total of $ 735 . if the average (arithmetic mean) price of a pair of rackets is $ 9.8 , how many pairs were sold ? a) 50 , b) 100 , c) 490 , d) 500 , e) 75","""average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 735 x = 75 pairs were sold . answer : e"""
"Solve the problem systematically, showing each step clearly.","when tom works alone he chops 4 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 4 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent greater than the quantifying chopped by tom ? . a) 125 % , b) 100 % , c) 25 % , d) 225 % , e) 400 %","""tom chops 8 lbs in 12 minutes tammy chopswhen tom works alone he chops 2 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 2 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent greater than the quantifying chopped by tom ? . 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n' t matter . if you multiply the time each work by x , you' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : a"""
"Work through the equation methodically, ensuring clarity at each step.","bella is taking a trip in her car from new york (point a) chicago , illinois (point b) . she is traveling at an average speed of 50 miles per hour , if the total distance from point a to point b is 790 miles , in approximately how long will bella reach her destination ? a) 10 hours , b) 12.50 hours , c) 15.80 hours , d) 25 hours , e) 1 day","answer is (c) . if she is traveling at a speed of 50 miles per hour and her trip is a total of 790 miles , 790 miles divided by 50 miles per hours would equal 15.80 hours , just shy of 16 hours ."
Break down and solve the equation step by step.,"the least number which when divided by 2 , 3 , 5 and 6 leaves a remainder 3 , but when divided by 9 leaves no remainder , is a) 16 , b) 63 , c) 73 , d) 83 , e) none of these","""explanation : l . c . m of 2 , 3 , 5 , 6 = 30 therefore required number is of the form 30 k + 3 . least value of k for which (30 k + 3) is divisible by 9 is k = 2 therefore required number = (30 x 2 + 3) = 63 . answer : b"""
Explain the solution process for the given equation.,"john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 19 , what was the price before the first discount ? a) $ 45.10 , b) $ 34.31 , c) $ 28.44 , d) $ 67.54 , e) $ 33.77","""let x be the price before the first discount . the price after the first discount is x - 25 % x (price after first discount) a second discount of 25 % of the discounted price after which the final price is 19 (x - 25 % x) - 25 % (x - 25 % x) = 19 solve for x x = $ 33.77 correct answer e"""
"Solve the problem systematically, showing each step clearly.","in the biology lab of ` ` jefferson'' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10800 petri dishes . how many germs live happily in a single dish ? a) 100 , b) 200 , c) 500 , d) 1000 , e) 5000",5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c
"Work through the equation methodically, ensuring clarity at each step.","by selling 8 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ? a) 8 , b) 9 , c) 2 , d) 6 , e) 4","""40 % - - - 8 160 % - - - ? 40 / 160 * 12 = 2 answer : c"""
"Solve the problem systematically, showing each step clearly.","village x has a population of 68000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ? a) 15 , b) 19 , c) 11 , d) 18 , e) 13","let the population of two villages be equal after p years then , 68000 - 1200 p = 42000 + 800 p 2000 p = 26000 p = 13 answer is e ."
Explain the solution process for the given equation.,"if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 200 % of j ? a) 0.35 , b) 3.5 , c) 35 , d) 350 , e) 3500","first of all , let us write the information in form of equations and numbers 125 j = 5 k or 5 j = k (i) 150 k = 50 l or 3 k = l (ii) 175 l = 75 m or 7 l = 3 m (iii) we need to find a relation between j and m from (i) and (ii) , 15 j = l multiplying this by 7 , 105 j = 7 l = 3 m hence , 35 j = m now , we are asked : 20 % of m is equal to what percent of 200 % of j assume j = 1 , hence m = 35 20 % of m = 7 and 200 % of j = 2 20 % of m = 3.5 (200 % of j) = (350 / 100) * (200 % of j) hence 20 % of m = 350 % of 200 % of j . option d"
"Solve the problem systematically, showing each step clearly.","if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 2 ] ] ? a) 3 , b) 9 , c) 12 , d) 19 , e) 25","these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 2 ] ] = 2 ^ 2 + 2 * 2 + 4 = 12 . option c"
"Solve the problem systematically, showing each step clearly.","the compound ratio of 1 : 4 , 3 : 2 and 4 : 5 ? a) 1 : 9 , b) 1 : 7 , c) 1 : 2 , d) 3 : 10 , e) 1 : 4","""1 / 4 * 3 / 2 * 4 / 5 = 3 / 10 = 3 : 10 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a pair of articles was bought for $ 720 at a discount of 10 % . what must be the marked price of each of the article ? a) $ 300 , b) $ 500 , c) $ 350 , d) $ 400 , e) $ 600","""s . p . of each of the article = 720 / 2 = $ 360 let m . p = $ x 90 % of x = 360 x = 360 * 100 / 90 = $ 400 answer is d"""
Provide a detailed solution to the given mathematical problem.,"two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.15 km respectively . the time taken by the slower train to cross the faster train in seconds is ? a) 65 sec , b) 30 sec , c) 48 sec , d) 33 sec , e) 12 sec","""relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.15 = 1.25 km = 1250 m . required time = 1250 * 3 / 125 = 30 sec . answer : b"""
Provide a detailed solution to the given mathematical problem.,"how many two - element subsets of < 1 , 23 , 45 , 67 > are there that do not contain the pair of elements 2 and 4 ? a) 11 , b) 12 , c) 14 , d) 15 , e) 20",7 c 2 - 1 = 20 answer is e
"Solve the problem systematically, showing each step clearly.","the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 20 kmph ? a) 21.21 , b) 20.25 , c) 32.25 , d) 75.75 , e) 62.61",distance covered in 1 min = (20 * 1000) / 60 = 333.33 m circumference of the wheel = (2 * (22 / 7) * . 70) = 4.4 m no of revolution per min = 333.33 / 4.4 = 75.75 answer : d
Break down and solve the equation step by step.,"what is the least common multiple of 5,40 , 36,50 a) 3698 , b) 874 , c) 3692 , d) 1800 , e) 3214","""the given numbers are 5,40 , 36,50 thus the l . c . m is 5 * 2 * 2 * 1 * 2 * 9 * 5 = 1800 the answer is d"""
"Solve the problem systematically, showing each step clearly.","if 13 = 13 w / (1 - w) , then (5 w) 2 = a) 1 / 4 , b) 5 , c) 1 , d) 2 , e) 3","""13 - 13 w = 13 w 26 w = 13 w = 1 / 2 5 w = 5 / 2 5 w * 2 = 5 / 2 * 2 = 5 answer : b"""
Explain the solution process for the given equation.,"what is the total number of integers between 2 and 38 that are divisible by 4 ? a) 8 , b) 9 , c) 7 , d) 6 , e) 11","""4 , 6 , 8 , . . . , 32,36 this is an equally spaced list ; you can use the formula : n = (largest - smallest) / (' space') + 1 = (36 - 4) / (4) + 1 = 32 / 4 + 1 = 8 + 1 = 9 answer is b"""
"Solve the problem systematically, showing each step clearly.","a and b complete a work in 8 days . a alone can do it in 12 days . if both together can do the work in how many days ? a) 4.8 days , b) 3.8 days , c) 3.65 days , d) 3.77 days , e) 5.75 days","""1 / 8 + 1 / 12 = 5 / 24 24 / 5 = 4.8 days answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","there has been successive increases of 25 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ? a) 23 % , b) 27 % , c) 31 % , d) 35 % , e) 39 %","""let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.25 * p = x * p y = x / (1.1 * 1.25) which is about 0.73 x which is a decrease of about 27 % . the answer is b ."""
Break down and solve the equation step by step.,"65 % of x = 20 % of 487.50 . find the value of x ? a) 100 , b) 150 , c) 160 , d) 180 , e) 199","65 % of x = 20 % of 487.50 then , 65 / 100 * x = 20 / 100 * 4875 / 10 x = 150 answer is b"
Provide a detailed solution to the given mathematical problem.,"a number , x is chosen at random from the set of positive integers less than 10 . what is the probability that (7 / x) > x ? a) 1 / 5 , b) 7 / 9 , c) 1 / 3 , d) 2 / 3 , e) 2 / 9","""number x has to be chosen from numbers 1 - 9 (7 / x) > x = > 7 > x ^ 2 = > x ^ 2 - 7 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 9 answer e"""
Provide a detailed solution to the given mathematical problem.,"what is the perimeter of a square with area p ^ 2 / 16 ? ['a) 3 p / 4','b) 3 p ^ 2 / 4','c) p','d) 3 p ^ 2','e) 4 p / 3']","area of square , (side) ^ 2 = (p / 4) ^ 2 therefore side of the square = p / 4 perimeter of square = 4 * side = 4 * (p / 4) = p answer is c ."
"Work through the equation methodically, ensuring clarity at each step.","a car is running at a speed of 120 kmph . what distance will it cover in 12 sec ? a) 396 m , b) 267 m , c) 180 m , d) 200 m , e) 250 m","""speed = 120 kmph = 120 * 5 / 18 = 33 m / s distance covered in 12 sec = 33 * 12 = 396 m answer is a"""
"Solve the problem systematically, showing each step clearly.","if there are 4 peanuts in a box and mary puts 4 more peanuts inside , how many peanuts are in the box ? a) 8 , b) 9 , c) 10 , d) 11 , e) 12","""4 + 4 = 8 correct answer is a) 8"""
Explain the solution process for the given equation.,"the speed of a car is 90 km in the first hour and 60 km in the second hour . what is the average speed of the car ? a) 12 , b) 75 , c) 88 , d) 54 , e) 15","""s = (90 + 60) / 2 = 75 kmph answer : b"""
Explain the solution process for the given equation.,"if 15 people contributed a total of $ 30.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is a) $ 1.00 , b) $ 16 , c) $ 5.00 , d) $ 6.00 , e) $ 20.00","""b for me 14 people with 1 $ each - > maximum = 16"""
Break down and solve the equation step by step.,"how many times digit 6 is used while writing numbers from 100 to 1400 ? a) 648 , b) 350 , c) 252 , d) 225 , e) 26","""there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90' 6 s' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 350 . hence b ."""
"Work through the equation methodically, ensuring clarity at each step.","there is enough provisions for 600 men in an army camp for 25 days . if there were 100 men less , how long will the provision last ? a) 10 days , b) 50 days , c) 100 days , d) 150 days , e) 200 days","""exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 100 * d 2 d 2 = 600 * 25 / 100 = 150 days . answer : d"""
Break down and solve the equation step by step.,"a walks at 30 kmph and 30 hours after his start , b cycles after him at 50 kmph . how far from the start does b catch up with a ? a) 1200 km , b) 1500 km , c) 2000 km , d) 2250 km , e) 3600 km","""suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 50 = 30 x = 2250 km answer is d"""
"Work through the equation methodically, ensuring clarity at each step.","every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 72 , how many more green disks than blue disks are in the bag ? a) 20 , b) 28 , c) 30 , d) 35 , e) 40","""let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 72 - - > x = 4 . g - b = 8 x - 3 x = 5 x = 20 . the answer is a ."""
"Solve the problem systematically, showing each step clearly.","a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 6 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ? a) 20 , b) 22 , c) 26 , d) 24 , e) 30","""total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 and will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = (total) - (restriction) = 27 - 1 = 26 . answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.7 % , what fraction of the products was checked by worker y ? a) 2 / 3 , b) 5 / 6 , c) 7 / 8 , d) 4 / 5 , e) 5 / 8","x : 0.5 % is 0.2 % - points from 0.7 % . y : 0.8 % is 0.1 % - points from 0.7 % . therefore the ratio of products checked by y : x is 2 : 1 . thus , worker y checked 2 / 3 of the products . the answer is a ."
Break down and solve the equation step by step.,"pens , pencils and markers in a jenna' s desk are in the ratio of 2 : 2 : 5 . if there are 10 pens , the number of markers in jenna' s desk is : a) 30 , b) 22 , c) 20 , d) 25 , e) 100","explanation : let pens = 2 x , pencils = 2 x & markers = 5 x . now , 2 x = 10 hence x = 5 . number of markers = 5 x which is 25 . answer : d"
Provide a detailed solution to the given mathematical problem.,"a goods train runs at the speed of 72 km / hr and crosses a 210 m long platform in 26 sec . what is the length of the goods train ? a) 382 , b) 782 , c) 278 , d) 310 , e) 881","""speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , (x + 210) / 26 = 20 x = 310 m . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a library has an average of 660 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is : a) 250 , b) 276 , c) 280 , d) 310 , e) none","""since the month begins with sunday , to there will be five sundays in the month average required = (660 x 5 + 240 x 25) / 30) = 310 answer : option d"""
Break down and solve the equation step by step.,"find the average of all the numbers between 6 and 34 which are divisible by 6 . a) 18 , b) 20 , c) 24 , d) 30 , e) 21","""solution average = ((12 + 18 + 24 + 30) / 5) = 84 / 4 = 21 . answer e"""
"Work through the equation methodically, ensuring clarity at each step.","the h . c . f . of two numbers is 38 and the other two factors of their l . c . m . are 12 and 10 . the larger of the two numbers is : a) 678 , b) 456 , c) 234 , d) 476 , e) 432",""": explanation : clearly , the numbers are (38 x 12) and (38 x 10) . { \ color { blue } \ therefore } larger number = (38 x 12) = 456 . answer : b) 456"""
"Solve the problem systematically, showing each step clearly.","if (a - b - c + d = 18) and (a + b - c - d = 6) , what is the value of (b - d) ^ 2 ? a) 4 . , b) 8 . , c) 12 . , d) 16 . , e) 36 .","""eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 6 (1) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 12 (2) simplify - b + d = 6 b - d = - 6 (b - d) ^ 2 = (- 6) ^ 2 = 36 my answer : e"""
Provide a detailed solution to the given mathematical problem.,"a 270 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train . a) 210 m , b) 220 m , c) 230 m , d) 240 m , e) 250 m","""relative speeds = (120 + 80) km / hr = 200 km / hr = (200 * 5 / 18) m / s = (500 / 9) m / s let length of train be xm x + 270 / 9 = 500 / 9 x = 230 ans is 230 m answer : c"""
Explain the solution process for the given equation.,"if 5 machines can produce 20 units in 10 hours , how long would it take 10 to produce 60 units ? a) 9 , b) 10 , c) 15 , d) 25 , e) 30","""5 machines would produce 60 units in 30 hours . increasing the amount of machines by 2 would mean dividing 30 hours by 2 . 30 / 2 = 15 answer : c"""
Break down and solve the equation step by step.,"what is the probability of getting atmost one head when two unbiased coin are tossed ? a) 3 / 4 , b) 3 / 2 , c) 4 / 3 , d) 1 / 2 , e) 2 / 6","""here s = { hh , ht , th , tt } let ee = event of getting one head e = { tt , ht , th } p (e) = n (e) / n (s) = 3 / 4 option a"""
Break down and solve the equation step by step.,"what is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive ? a) 190 , b) 195 , c) 200 , d) 205 , e) 210","""we' re asked for the average of all of the multiples of 10 from 10 to 400 , inclusive . to start , we can figure out the total number of terms rather easily : 1 (10) = 10 2 (10) = 20 . . . 40 (10) = 400 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with' bunching' : 10 + 400 = 410 20 + 390 = 410 30 + 380 = 410 etc . since there are 40 total terms , this pattern will create 20' pairs' of 410 . thus , since the average = (sum of terms) / (number of terms) , we have . . . (20) (410) / (40) = 410 / 2 = 205 final answer : d"""
Provide a detailed solution to the given mathematical problem.,"a , b and c can do a piece of work in 9 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ? a) 4.12 days , b) 4.52 days , c) 3.52 days , d) 2.52 days , e) 4.92 days",1 / 9 + 1 / 14 + 1 / 28 = 55 / 252 = > 252 / 55 days = > 4.52 days answer : b
Explain the solution process for the given equation.,"a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 18 , what is the total amount ? a) 70 , b) 105 , c) 178 , d) 177 , e) 169","""x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 18 35 - - - ? = > 70 answer : a"""
Explain the solution process for the given equation.,"two good train each 100 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one . a) 1.2 sec , b) 2.4 sec , c) 4.8 sec , d) 9.6 sec , e) none","""sol . relative speed = (45 + 30) km / hr = (75 x 5 / 18) m / sec = (125 / 6) m / sec . distance covered = (100 + 100) m = 1000 m . required time = (200 x 6 / 125) sec = 9.6 sec . answer d"""
Explain the solution process for the given equation.,"an article is bought for rs . 600 and sold for rs . 450 , find the loss percent ? a) 16 % , b) 18 % , c) 19 % , d) 20 % , e) 25 %","""600 - - - - 150 100 - - - - ? = > 16 2 / 3 % answer : e"""
"Solve the problem systematically, showing each step clearly.","a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 150 kg . what is the maximum weight of the crates on a single trip ? a) 1250 , b) 625 , c) 600 , d) 750 , e) 375","""max no . of crates = 5 . max weight = 150 kg max . weight carried = 5 * 150 = 750 kg = d"""
Provide a detailed solution to the given mathematical problem.,"mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 17 candidates . she plans to have one working interview with 3 of the 17 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ? a) 720 , b) 420 , c) 300 , d) 30 , e) 333","""420 . answer b"""
Explain the solution process for the given equation.,"a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 12 more blue balls than white balls , and six times as many red balls as blue balls , how many white balls does the box has ? a) 8 , b) 10 , c) 2 , d) 14 , e) 16","""x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 12 more blue balls than white balls . . . equation # 2 : y = 12 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 6 y solve equation # 2 for z : z = y - 12 now , we can replace both x and z with y in equation # 1 6 y + y + (y - 12) = 100 8 y - 12 = 100 5 y = 112 y = 14 there are 14 blue balls . this is 12 more than the number of white balls , so z = 2 . that' s the answer . just as a check , x = 84 , and 84 + 14 + 2 = 100 . answer = 2 , (c)"""
"Solve the problem systematically, showing each step clearly.","at present the ratio between the ages of arun and deepak is 5 : 7 . after 6 years , arun' s age will be 36 years . what is the age of deepak at present ? a) 35 years , b) 25 years , c) 42 years , d) 39 years , e) 40 years","""let the present ages of arun and deepak be 5 x years and 7 x years respectively 5 x + 6 = 36 5 x = 30 x = 6 deepak' s age = 7 x = 42 years answer is c"""
"Work through the equation methodically, ensuring clarity at each step.","the average weight of 8 person' s increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ? a) 56 kg , b) 80 kg , c) 85 kg , d) data inadequate , e) none of these","""b 80 kg total weight increased = (8 x 2.5) kg = 20 kg . weight of new person = (60 + 20) kg = 80 kg ."""
Provide a detailed solution to the given mathematical problem.,"what is the square root of 625 , divided by 5 ? a) 9 , b) 36 , c) 5 , d) 6 , e) 1","square root is a number times itself square root of 625 = 25 , 25 / 5 = 5 (c) 5"
Explain the solution process for the given equation.,"the ratio between the length and the breadth of a rectangular park is 1 : 4 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park (in sq . m) is ? ['a) 124545 m','b) 134561 m','c) 156787 m','d) 15450 m','e) 102400 m']","perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 1 x metres and breadth = 4 x metres . then , 2 (1 x + 4 x) = 1600 or x = 160 . length = 160 m and breadth = 640 m . area = (160 x 640) m 2 = 102400 m e"
Break down and solve the equation step by step.,"in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 6 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? a) 116 , b) 146 , c) 152 , d) 162 , e) 170","""the probability of survival for each of the first 3 months of life is 1 - 1 / 6 = 5 / 6 , so of 200 newborn 200 * 5 / 6 * 5 / 6 * 5 / 6 = ~ 116 is expected to survive . answer : a ."""
Provide a detailed solution to the given mathematical problem.,"the length of a rectangle is increased by 25 % and its breadth is decreased by 20 % . what is the effect on its area ? ['a) 10000','b) 10008','c) 10005','d) 10004','e) 10001']",100 * 100 = 10000 125 * 80 = 10000 no change answer : a
"Solve the problem systematically, showing each step clearly.","a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation g of the mean , what percent of the distribution is less than m + g ? a) 16 % , b) 32 % , c) 48 % , d) 84 % , e) 92 %","""16 % ________________________________________________ m + g 34 % ________________________________________________ m 34 % ________________________________________________ m - g 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - g and 16 % lie above m + g now below m + g = 16 + 34 + 34 = 84 % hence d"""
"Work through the equation methodically, ensuring clarity at each step.","the average of 25 results is 24 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ? a) 740 , b) 228 , c) 690 , d) 780 , e) 458","""solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x (let) now , 12 * 14 + 12 * 17 + x = 25 * 24 or , x = 228 . answer : option b"""
"Work through the equation methodically, ensuring clarity at each step.","if the given two numbers are respectively 7 % and 14 % of a third number , then what percentage is the first of the second ? a) 20 % , b) 25 % , c) 18 % , d) 50 % , e) none of these","""here , l = 7 and m = 14 therefore , first number = l / m x 100 % of second number = 7 / 14 x 100 % of second number = 50 % of second number answer : d"""
Break down and solve the equation step by step.,"if n is a positive integer and n ^ 3 is a multiple of 550 , what is the least possible value of n ? a) 8 , b) 27 , c) 81 , d) 110 , e) 125","""cube of a number entails having 3 copies of the original prime factors . since 550 is a factor of n ^ 3 the least possible value of n is 5 (11) 2 = 110 the answer is d ."""
"Solve the problem systematically, showing each step clearly.","the maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : a) 91 , b) 40 , c) 80 , d) 90 , e) none of these","""solution required number of student = h . c . f of 1080 and 920 = 40 . answer b"""
"Work through the equation methodically, ensuring clarity at each step.","the length of the bridge , which a train 145 metres long and travelling at 45 km / hr can cross in 30 seconds , is : a) 200 m , b) 230 m , c) 245 m , d) 250 m , e) 270 m","""let the length of the bridge : l the equation now is l + 145 / 12.5 m / s (45 km / hr or 12.5 m / s) = 30 solving , l = 230 m answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","excluding stoppages , the speed of a bus is 80 kmph and including stoppages , it is 60 kmph . for how many minutes does the bus stop per hour ? a) 12 min , b) 20 min , c) 25 min , d) 30 min , e) 15 min","""due to stoppages , it covers 20 km less . time taken to cover 20 km = (20 / 80 x 60) min = 15 min answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","in a group of 60 people , 35 have visited iceland and 23 have visited norway . if 31 people have visited both iceland and norway , how many people have visited neither country ? a) 30 , b) 31 , c) 32 , d) 33 , e) 34","this is an example of a standard overlapping sets question . it has no' twists' to it , so you' ll likely find using the overlapping sets formula to be a fairly easy approach . if you' re not familiar with it , then here is the formula : 60 = 35 + 23 - 31 + (# in neither group) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
"Work through the equation methodically, ensuring clarity at each step.","what is the units digit of 13 ^ 4 * 17 ^ 2 * 29 ^ 3 ? a) 9 , b) 7 , c) 5 , d) 3 , e) 1","""3 ^ 1 = 3 3 ^ 2 = 9 3 ^ 3 = 7 3 ^ 4 = 1 , it is first digit 7 ^ 2 = 9 , it is second digit 9 ^ 3 = 9 , it is third digit 1 * 9 * 9 = 1 answer : e"""
Break down and solve the equation step by step.,"a certain bus driver is paid a regular rate of $ 18 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ? a) 36 , b) 40 , c) 44 , d) 48 , e) 52","""for 40 hrs = 40 * 18 = 720 excess = 976 - 720 = 252 for extra hours = . 75 (18) = 13.5 + 18 = 31.5 number of extra hrs = 252 / 31.5 = 8 total hrs = 40 + 8 = 48 answer d 48"""
"Work through the equation methodically, ensuring clarity at each step.","the average of 10 consecutive integers is 16 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ? a) 10.5 , b) 11 , c) 11.5 , d) 12 , e) 12.5","the total subtracted is (9 + 8 + . . . + 1) = (9 * 10) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is c ."
Break down and solve the equation step by step.,"in a kilometer race , a beats b by 80 meters or 10 seconds . what time does a take to complete the race ? a) 167 sec , b) 190 sec , c) 176 sec , d) 115 sec , e) 123 sec","""time taken by b run 1000 meters = (1000 * 10) / 80 = 125 sec . time taken by a = 125 - 10 = 115 sec . answer : d"""
Break down and solve the equation step by step.,"a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 10 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ? a) 3 / 8 , b) 9 / 10 , c) 1 / 2 , d) 3 / 5 , e) 3 / 4","""x * 6 / 100 * 1 + (20000 - x) * 10 / 100 * 1 = 1440 6 x - 8 x = 144000 - 200000 = > - 2 x = - 4000 = > x = 2000 so 18000 / 20000 = 9 / 10 answer - b"""
Provide a detailed solution to the given mathematical problem.,"by weight , liquid x makes up 0.5 percent of solution p and 1.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ? a) 1.3 % , b) 1.2 % , c) 1.1 % , d) 1.0 % , e) 0.9 %",the number of grams of liquid x is 0.5 (200) / 100 + 1.5 (800) / 100 = 1 + 12 = 13 grams . 13 / 1000 = 1.3 % the answer is a .
Break down and solve the equation step by step.,"what is the remainder when 2 ^ 20 is divided by 10 ? a) 0 , b) 2 , c) 4 , d) 6 , e) 8","""2 ^ 20 = 2 ^ 10 x 2 ^ 10 and 2 ^ 10 = 1024 4 * 4 = 16 , so the unit digit of this multiplication is 6 the remainder is 6 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days , a) 6 days , b) 3 days , c) 4 days , d) 2 days , e) 5 days","""the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c"""
Explain the solution process for the given equation.,"the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ? a) 5.2 minutes , b) 5.21 minutes , c) 5.25 minutes , d) 5.28 minutes , e) 6 minutes","let both of them meet after tt min 4500 m are covered by suresh in 60 m . in tt min he will cover 4500 t 604500 t 60 likewise , in tt min suresh' s wife will cover 3750 t 603750 t 60 given , 4500 t 60 + 3750 t 60 = 7264500 t 60 + 3750 t 60 = 726 tt = 5.28 minutes option (d) is correct"
"Work through the equation methodically, ensuring clarity at each step.","calculate 469157 x 9999 = ? a) 4586970843 , b) 4686970743 , c) 4691100843 , d) 4586870843 , e) none","""answer 469157 x 9999 = 469157 x (10000 - 1) = 4691570000 - 469157 = 4691100843 . option : c"""
"Solve the problem systematically, showing each step clearly.","a candidate got 40 % of the votes polled and he lost to his rival by 2000 votes . how many votes were cast ? a) 10000 , b) 2028 , c) 2775 , d) 5496 , e) 6851","""40 % - - - - - - - - - - - l 60 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - 2000 100 % - - - - - - - - - ? = > 10000 answer : a"""
"Solve the problem systematically, showing each step clearly.","the average (arithmetic mean) of the even integers from 0 to 40 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 20 inclusive ? a) 5 , b) 8 , c) 10 , d) 15 , e) 20","""the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 (1 + 2 + . . . + n / 2) = 2 (n / 2) (n / 2 + 1) / 2 = (n / 2) (n / 2 + 1) the average is (n / 2) (n / 2 + 1) / (n / 2 + 1) = n / 2 the average of the even numbers from 0 to 40 is 40 / 2 = 20 the average of the even numbers from 0 to 20 is 20 / 2 = 10 the answer is c ."""
"Work through the equation methodically, ensuring clarity at each step.","carol and jordan draw rectangles of equal area . if carol' s rectangle measures 12 inches by 15 inches and jordan' s rectangle is 6 inches long , how wide is jordan' s rectangle , in inches ? ['a) 24','b) 26','c) 28','d) 30','e) 32']",area of first rectangle is 12 * 15 = 180 hence area of second would be 6 x = 180 x x = 30 answer is d
Break down and solve the equation step by step.,"sony and johnny caught 40 fishes . sony caught 4 times as many as johnny . how many fishes did johnny catch ? a) 12 , b) 16 , c) 34 , d) 38 , e) 8",s + j = 40 s = 4 * j j = 8 answer : e
Break down and solve the equation step by step.,"ravi can do a piece of work in 15 days while prakash can do it in 30 days . in how many days will they finish it together ? a) 11 days , b) 9 days , c) 8 days , d) 12 days , e) 10 days","""1 / 15 + 1 / 30 = 3 / 30 10 / 1 = 10 days answer : e"""
Provide a detailed solution to the given mathematical problem.,"if the price of a certain computer increased 30 percent from y dollars to 351 dollars , then 2 y = a) 540 , b) 570 , c) 619 , d) 649 , e) 700","""before price increase price = y after 30 % price increase price = y + (30 / 100) * y = 1.3 y = 351 (given) i . e . y = 351 / 1.3 = $ 270 i . e . 2 y = 2 * 270 = 540 answer : option a"""
Explain the solution process for the given equation.,"bottle r contains 250 capsules and costs $ 6.25 . bottle t contains 100 capsules and costs $ 3.0 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ? a) $ 0.25 , b) $ 0.12 , c) $ 0.05 , d) $ 0.003 , e) $ 0.005","""cost per capsule in r is 6.25 / 250 = 0.625 / 25 = 0.025 cost per capsule in t is 3.00 / 100 = 0.03 the difference is 0.005 the answer is e"""
Break down and solve the equation step by step.,"machine p and machine q are each used to manufacture 550 sprockets . it takes machine p 10 hours longer to produce 550 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ? a) 5 , b) 15 , c) 55 , d) 95 , e) 125","""p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 550 / x = 550 / 1.1 x + 10 1.1 (550) = 550 + 11 x 11 x = 55 x = 5 the answer is a ."""
Break down and solve the equation step by step.,"in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 14 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ? a) 320 $ , b) 380 $ , c) 525 $ , d) 456 $ , e) 480 $","""total cost = (1.75 * 14) + (0.65 * 14 * 55) = 24.5 + 500.5 = > 525 hence answer will be (c) 525"""
"Solve the problem systematically, showing each step clearly.","how many positive integers less than 160 are there such that they are multiples of 13 or multiples of 12 but not both ? a) 18 , b) 19 , c) 20 , d) 23 , e) 25","""for 13 : 13 . . . 160 = 13 * 12 for 12 : 12 . . . 156 = 12 * 13 but there is one integer 13 * 12 . so n = (12 - 1) + (13 - 1) = 23 d"""
"Solve the problem systematically, showing each step clearly.","if the cost price of 60 articles is equal to the selling price of 50 articles , then what is the percent profit ? a) 10 % , b) 15 % , c) 20 % , d) 25 % , e) 30 %","""let x be the cost price of one article . let y be the selling price of one article . 50 y = 60 x y = 1.2 x the answer is c ."""
Break down and solve the equation step by step.,"the weight of a glass of jar is 20 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ? a) 1 / 5 , b) 1 / 3 , c) 2 / 5 , d) 1 / 2 , e) 2 / 3","""let weight of jar filled with beans = 100 g weight of jar = 20 g weight of coffee beans = 80 g weight of jar and remaining beans = 60 g weight of remaining beans = 40 g fraction remaining = 40 / 80 = 1 / 2 answer is d ."""
"Solve the problem systematically, showing each step clearly.","a train 300 m long can cross an electric pole in 30 sec and then find the speed of the train ? a) 76 kmph , b) 54 kmph , c) 72 kmph , d) 36 kmph , e) 91 kmph","""length = speed * time speed = l / t s = 300 / 30 s = 10 m / sec speed = 10 * 18 / 5 (to convert m / sec in to kmph multiply by 18 / 5) speed = 36 kmph answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","what is the remainder when 123456789101112131415161718192021222324252627282930313233343536373839404142434481 is divided by 45 ? a) 26 , b) 36 , c) 16 , d) 06 , e) 40","explanation : let' s call : a = 123456789101112131415161718192021222324252627282930313233343536373839404142434481 = > a = b * 100 + 81 [ with b = 1234567 . . . . . 424344 ] we have : b x 100 is divisible by 45 because : - sum of all digits in b = 1 + 2 + 3 + . . . . + 44 = (1 + 44) + (2 + 43) + . . . . + (22 + 23) (22 pairs) = 22 * 45 = > b divisible for 9 since b is divisible by 9 , b * 100 will be divisible by 9 * 5 = 45 81 divided 45 gives a remainder of 36 therefore , a divided by 45 reminder 36 answer : b"
Explain the solution process for the given equation.,"in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 6 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight a) 1 / 7 , b) 1 / 8 , c) 1 / 4 , d) 3 / 7 , e) 7 / 8","""good question . so we have a garden where all the flowers have two properties : color (green or yellow) and shape (straight or curved) . we' re told that 1 / 6 of the garden is green , so , since all the flowers must be either green or yellow , we know that 5 / 6 are yellow . we' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr (yellow and straight) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr (a and b) = p (a) * p (b) . so we multiply the two probabilities , pr (yellow) * pr (straight) = 5 / 6 * 1 / 2 = 3 / 7 , or d ."""
"Work through the equation methodically, ensuring clarity at each step.","the sale price sarees listed for rs . 400 after successive discount is 12 % and 5 % is ? a) 338 , b) 277 , c) 342 , d) 334.4 , e) 212","""400 * (88 / 100) * (95 / 100) = 334.4 answer : d"""
Break down and solve the equation step by step.,"of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ? a) 1000 , b) 1200 , c) 1400 , d) 1600 , e) 1800","""let x be the number of eggs that were laid . (2 / 5) (3 / 4) (1 / 3) x = 120 (6 / 60) x = 120 x = 1200 the answer is b ."""
Explain the solution process for the given equation.,"if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 4 ] ] ? a) 3 , b) 9 , c) 15 , d) 19 , e) 28","""[ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 4 ] ] = 4 ^ 2 + 2 * 4 + 4 = 28 . option e"""
Break down and solve the equation step by step.,"the compounded ratio of (2 : 3) , (6 : 11) and (11 : 2) is : a) 1 : 2 , b) 5 : 9 , c) 2 : 1 , d) 11 : 24 , e) none",answer : option c 2 / 3 : 6 / 11 : 11 / 2 = 2 : 1
Provide a detailed solution to the given mathematical problem.,"in a room with 9 people , 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room (assuming that friendship is a mutual relationship , i . e . if jane is paul' s friend , paul is jane' s friend) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ? a) 5 / 21 , b) 3 / 7 , c) 4 / 7 , d) 5 / 7 , e) 1","""(6 / 9) (7 / 8) + (5 / 9) (6 / 8) if you choose one of the 6 with one other friend , then you have a 7 / 8 chance of not picking their friend 2 nd . if you choose one of the 5 with 2 friends , you have a 6 / 8 chance of not picking one of their friends second . add them up . 42 / 72 + 30 / 72 72 / 72 = 1 e . 1"""
Provide a detailed solution to the given mathematical problem.,"the speed of a boat in still water is 12 kmph . what is the speed of the stream if the boat can cover 32 km downstream or 16 km upstream in the same time ? a) 5 kmph , b) 6 kmph , c) 7 kmph , d) 4 kmph , e) 10 kmph","""x = the speed of the stream (12 + x) / (12 - x) = 2 / 1 12 + x = 24 - 2 x 3 x = 12 x = 4 km / hour if the speed of the stream is 4 km / hour , then the' downstream' speed of the boat is 12 + 4 = 16 km / hour and the' upstream' speed of the boat is 12 - 4 = 8 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 8 = 16 km downstream and 2 x 16 = 32 km / hour upstream . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrement of 35 % and in 2007 there is an increment of 45 % , then find the population of city at theend of the year 2007 a) 2456789 , b) 3458009 , c) 3890043 , d) 3455048 , e) 1083875","""required population = p (1 + r 1 / 100) (1 - r 2 / 100) (1 + r 3 / 100) = p (1 + 15 / 100) (1 - 35 / 100) (1 + 45 / 100) = 1083875 e"""
Break down and solve the equation step by step.,"the calendar of the year 2080 can be used again in the year ? a) 2105 , b) 1955 , c) 1945 , d) 1935 , e) 2108","""explanation : given year 2080 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2080 + 28 = 2108 answer : e"""
Explain the solution process for the given equation.,"i flew my tiny seaplane to visit my mother . on the flight up , i flew at 130 mph . on the way home , i flew 88 mph . what was my average speed for the trip ? a) 198 mph , b) 110 mph , c) 88 mph , d) 100 mph , e) 109 mph","""(130 mph + 88 mph) / 2 = 109 mph correct answer is : e"""
Break down and solve the equation step by step.,"in the rectangular coordinate system point o has coordinates (0,0) and point b has coordinates (5,5) and if point a is equidistant from points o and b and the area of the triangle oab is 16 , which of the following are the possible coordinates of point a . ['a) (- 2,6)','b) (0,4)','c) (2 , - 6)','d) (2,6)','e) (4,0)']","area . pngsince a is equidistant from points o and b , then it must be somewhere on the green line (perpendicular bisector of ob) . (2 , - 6) and (2,6) are not on that line . if a is at (0,5) or (5,0) , then the area is 1 / 2 * 5 * 5 = 25 / 2 . thus a must be at (2,6) . answer : d ."
Provide a detailed solution to the given mathematical problem.,"the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 125 resolutions ? a) 794 m , b) 704 m , c) 454 m , d) 186 m , e) 176 m","""in one resolution , the distance covered by the wheel is its own circumference . distance covered in 125 resolutions . = 125 * 2 * 22 / 7 * 22.4 = 17600 cm = 176 m answer : e"""
Explain the solution process for the given equation.,"if the wheel is 18 cm then the number of revolutions to cover a distance of 1056 cm is ? a) 18 , b) 26 , c) 14 , d) 12 , e) 9.3","""2 * 22 / 7 * 18 * x = 1056 = > x = 9.3 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ? a) rs . 692.80 , b) rs . 820 , c) rs . 990 , d) rs . 1385 , e) none","""answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 650 x 3 rs . = 990 rs . correct option : c"""
Provide a detailed solution to the given mathematical problem.,"if a 3 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ? a) 40 % , b) 100 % , c) 150 % , d) 200 % , e) 300 %","""the area a of the large cube is 3 * 3 * 6 = 54 square cm . the area of the 27 small cubes is 27 * 6 = 54 * 3 = 3 a , an increase of 200 % . the answer is d ."""
Explain the solution process for the given equation.,"if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 92 . if $ 2000 is the total amount invested , how much is invested at 8 percent ? a) $ 600 , b) $ 700 , c) $ 800 , d) $ 900 , e) $ 1000",0.1 x = 0.08 (2000 - x) + 92 0.18 x = 252 x = 1400 then the amount invested at 8 % is $ 2000 - $ 1400 = $ 600 the answer is a .
"Solve the problem systematically, showing each step clearly.","of the 400 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ? a) 65 , b) 100 , c) 115 , d) 130 , e) 260","""240 prefer x (group 1) ; 160 prefer y (group 2) . city y needs 300 people : letall 160 who prefer y (entire group 2) be relocated there , the rest 140 will be those who prefer x from group 1 ; city x needs 100 people : 240 - 140 = 100 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 160 + 100 = 260 . answer : e ."""
Explain the solution process for the given equation.,"the area of a triangle is with base 8.4 m and height 5.8 m ? a) 11.36 m 2 , b) 10.36 m 2 , c) 18.36 m 2 , d) 19.36 m 2 , e) 24.36 m 2","""1 / 2 * 8.4 * 5.8 = 24.36 m 2 answer : e"""
Break down and solve the equation step by step.,"if x , y , and z are positive real numbers such that x + y - z = 100 , y - z + x = 120 , and z - x + y = 50 , then find the x + y + z value ? a) 100 , b) 120 , c) 150 , d) 200 , e) 160","""x + y - z = 100 , - - - - - - 1) y - z + x = 120 , - - - - - - 2) z - x + y = 50 - - - - - - 3) from (1) & (2) 2 z = 20 z = 10 from (2) & (3) 2 y = 170 y = 85 then x = 100 - 75 = 25 x + y + z = 120 correct option is b"""
Explain the solution process for the given equation.,"population is 22000 . population increases by 10 % every year , then the population after 3 years is ? a) 26630 , b) 29282 , c) 36620 , d) 26620 , e) 26820","""population after 1 st year = 22000 * 10 / 100 = 2200 = = = > 22000 + 2200 = 24000 population after 2 nd year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26620 population after 3 rd year = 26620 * 10 / 100 = 2662 = = = > 26620 + 2662 = 29282 answer : b"""
Explain the solution process for the given equation.,"joan and karl each bought a telescopes and the sum of their purchases was $ 400 . if twice of what joan paid was $ 74 more than what karl paid , what did joan pay for her telescope ? a) $ 150 , b) $ 152 , c) $ 154 , d) $ 156 , e) $ 158",j + k = 400 so k = 400 - j 2 j = k + 74 2 j = (400 - j) + 74 3 j = 474 j = 158 the answer is e .
"Solve the problem systematically, showing each step clearly.","the average age of a group of n people is 14 years old . one more person aged 34 joins the group and the new average is 16 years old . what is the value of n ? a) 7 , b) 8 , c) 9 , d) 10 , e) 11","""14 n + 34 = 16 (n + 1) 2 n = 18 n = 9 the answer is c ."""
Explain the solution process for the given equation.,"at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 19.6 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ? a) 13.7 , b) 14.0 , c) 14.3 , d) 14.6 , e) 14.9","""let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 19.6 x ^ 2 = 1.96 x = 1.4 at 4 : 00 pm , the amount of bacteria was 10 (1.4) = 14 grams . the answer is b ."""
"Solve the problem systematically, showing each step clearly.","mr . kramer , the losing candidate in a two - candidate election , received 942568 votes , which was exactly 30 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ? a) 10 % , b) 12 % , c) 15 % , d) 29 % , e) 20 %","let me try a simpler one . lets assume that candidate got 30 % votes and total votes is 100 . candidate won = 30 remaining = 70 to get 50 % , candidate requires 20 votes from 100 which is 20 % and 20 votes from 70 . 20 / 70 = 2 / 7 = . 285 = 28.5 % which is approx 29 % . hence the answer is d ."
"Solve the problem systematically, showing each step clearly.","the lcm of two numbers is 2310 and hcf is 47 . if one of the numbers is 210 . then what is the other number ? a) 715 , b) 825 , c) 330 , d) 582 , e) 517",first number * second number = lcm * hcf other number = 2310 * 47 / 210 = 11 * 47 = 517 answer : e
Explain the solution process for the given equation.,"in a 8 x 8 chess board what is the total number of squares . a) 238 , b) 204 , c) 678 , d) 169 , e) 161","ans : the total number of squares in a n x n chess board is equal to ` ` the sum of first n natural number squares'' i . e . , n (n + 1) (2 n + 1) 6 n (n + 1) (2 n + 1) 6 so substituting 8 in the above formula we get 204 answer : b"
Provide a detailed solution to the given mathematical problem.,"two trains of equal length , running with the speeds of 60 and 40 kmph , take 60 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ? a) 10 sec , b) 16 sec , c) 12 sec , d) 67 sec , e) 13 sec","""rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 60 * 100 / 18 = 1000 / 3 rs = 60 + 40 = 100 * 5 / 18 t = 1000 / 3 * 18 / 500 = 12 sec answer : c"""
Provide a detailed solution to the given mathematical problem.,"find the ratio in which rice at rs . 7.10 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg a) 2 : 0 , b) 3 : 4 , c) 2 : 1 , d) 2 : 2 , e) 2 : 8","""by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 80 = 3 : 4 answer : b"""
"Solve the problem systematically, showing each step clearly.","find the length of the longest pole that can be placed in an indoor stadium 24 m long , 18 m wide and 16 m high a) 31 , b) 32 , c) 33 , d) 34 , e) 35","""sqrt (1156) = 34 becoz max length is cuboid diagonal d = sqrt (l ^ 2 + b ^ 2 + h ^ 2) where l lenght b breadth & h height answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 72 of the area of the field . what is the length of the field ? a) 73 , b) 32 , c) 34 , d) 43 , e) 96","""explanation : a / 72 = 8 * 8 = > a = 8 * 8 * 72 x * 2 x = 8 * 8 * 72 x = 48 = > 2 x = 96 answer : option e"""
Break down and solve the equation step by step.,"product of two natural numbers is 19 . then , the sum of reciprocals of their squares is a) 290 / 289 , b) 1 / 289 , c) 290 / 90 , d) 362 / 361 , e) none of these","explanation : if the numbers are a , b , then ab = 19 , as 17 is a prime number , so a = 1 , b = 19 . 1 / a 2 + 1 / b 2 = 1 / 1 (2) + 1 / 19 (2) = 362 / 361 option d"
Explain the solution process for the given equation.,"after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 6100 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ? a) 2160 , b) 2350 , c) 2000 , d) 2300 , e) 2400","""explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 6100 = 21600 exp in % = 100 - 10 = 90 % , 21600 = 90 % saving = 10 % = 21600 x 10 / 90 = rs . 2400 answer : e"""
"Solve the problem systematically, showing each step clearly.","the present population of a town is 1000 . population increase rate is 20 % p . a . find the population of town after 2 years ? a) 1440 , b) 1220 , c) 1400 , d) 1500 , e) 1620","""p = 1000 r = 20 % required population of town = p * (1 + r / 100) ^ t = 1000 * (1 + 20 / 100) ^ 2 = 1000 * (6 / 5) ^ 2 = 1440 (approximately) answer is a"""
Provide a detailed solution to the given mathematical problem.,"rs . 6000 is lent out in two parts . one part is lent at 4 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ? a) 5 : 1 , b) 5 : 7 , c) 5 : 2 , d) 5 : 8 , e) 5 : 2","""let the amount lent at 4 % be rs . x amount lent at 10 % is rs . (6000 - x) total interest for one year on the two sums lent = 4 / 100 x + 10 / 100 (6000 - x) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 2500 amount lent at 10 % = 3500 required ratio = 5 : 7 answer : b"""
"Solve the problem systematically, showing each step clearly.","in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.1 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ? a) 68.8 , b) 73.6 , c) 75.2 , d) 77.12 , e) 81.6","""degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = (7.5 + 8.1 + 8.5) = 24 point of value of the dive = 24.1 * 3.2 = 77.12 answer d"""
"Work through the equation methodically, ensuring clarity at each step.","express a speed of 56 kmph in meters per second ? a) 10.56 mps , b) 17.56 mps , c) 97.56 mps , d) 15.56 mps , e) 18.56 mps","""56 * 5 / 18 = 15.56 mps answer : d"""
Break down and solve the equation step by step.,"a survey was sent to 90 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ? a) 2 % , b) 6 % , c) 14 % , d) 28 % , e) 63 %","""case 1 : (7 / 90) = x / 100 x = 8 % case 2 : (9 / 63) = y / 100 y = 14 % so percent increase is = (y - x) = (14 - 8) % = 6 % answer is b"""
Break down and solve the equation step by step.,"if x + (1 / x) = 5 , what is the value of t = x ^ 2 + (1 / x) ^ 2 ? a) t = 21 , b) t = 22 , c) t = 23 , d) 24 , e) 27","""squaring on both sides , x ^ 2 + (1 / x) ^ 2 + 2 (x) (1 / x) = 5 ^ 2 x ^ 2 + (1 / x) ^ 2 = 23 answer : c"""
"Solve the problem systematically, showing each step clearly.","if a man lost 4 % by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 28 % ? a) 12 , b) 13 , c) 14 , d) 15 , e) 10","""96 % - - - - 16 128 % - - - - ? 96 / 128 * 16 = 12 answer : a"""
"Solve the problem systematically, showing each step clearly.","what is the least positive integer x for which (x ^ 2) + 164 is divisible by 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , and 11 ? a) 27556 , b) 800 , c) 796 , d) 87 , e) 166","2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 so (x ^ 2) + 164 = (2 * 2 * 2 * 3 * 3 * 5 * 7 * 11) = 27720 . then (x ^ 2) = 27556 . then x = 166 , which is option e ."
"Solve the problem systematically, showing each step clearly.","a cyclist rides a bicycle 8 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 8 km / hr . what is the average speed for the entire trip ? a) 8.58 , b) 8.76 , c) 9.04 , d) 9.12 , e) 9.25","""distance = 19 km time = 8 / 11 + 11 / 8 = (64 + 121) / 88 = 185 / 88 hours average speed = (19 * 88) / 185 = 9.04 km / h the answer is c ."""
Break down and solve the equation step by step.,"300 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees a) 10 , b) 12 , c) 14 , d) 16 , e) 18","26 trees have 25 gaps between them , required distance (300 / 25) = 12 b"
"Work through the equation methodically, ensuring clarity at each step.","two trains 210 m and 260 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? a) 16.92 sec , b) 14.8 sec , c) 10.68 sec , d) 10.8 sec , e) 20.8 sec","""relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 210 + 260 = 470 m . required time = 470 * 9 / 250 = 16.92 = 16.92 sec . answer : a"""
Break down and solve the equation step by step.,"among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 15 % of listco' s sales staff . listco employs 90 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ? a) 46 , b) 42 , c) 56 , d) 32 , e) 40","""i' m going in on this one . so let' s say that we have the following so we know that l 1 = 90 and that c and l 1 = 0.15 x , we should set up a double set matrix btw but anyways , i' m just explaining the point with this problem . now we are told that 0.15 x = 30 , therefore the grand total is 200 . now we know that l 2 is 200 - 90 = 110 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 60 = 40 . thus e is the correct answer choice"""
Explain the solution process for the given equation.,"the two lines y = x and x = - 7 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ? a) 18.5 , b) 21.5 , c) 24.5 , d) 27.5 , e) 30.5","""the point of intersection is (- 7 , - 7) . the triangle has a base of length 7 and a height of 7 . area = (1 / 2) * base * height = (1 / 2) * 7 * 7 = 24.5 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"fox jeans regularly sell for $ 10 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ? a) 9 % , b) 10 % , c) 11 % , d) 12 % , e) 40 %","""x discount on pony jeans , (0.22 - x) discount on fox jeans . set the equation : 3 * 10 (0.22 - x) + 2 * 18 x = 9 - - > x = 0.4 = 40 % answer : e ."""
"Solve the problem systematically, showing each step clearly.","one ton has 2600 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ? a) 2080 , b) 1700 , c) 2350 , d) 2500 , e) 8000","""16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2600 pound = 13 * 2600 * 16 ounces . hence the answer is (13 * 2600 * 16) / 260 = 2080 . answer : a ."""
"Work through the equation methodically, ensuring clarity at each step.","in a certain neighborhood , 60 percent of the student are going to school (a) , and the rest are going to school (b) . a new school (c) is opened , if 30 percent of student of school (a) and 40 percent of student of school (b) are expected to go to the new school (c) , what percent of student are expected to go to the new school (c) ? a) 30 % , b) 34 % , c) 38 % , d) 42 % , e) 46 %","say there are total of 100 students in the neighborhood , 60 students are going to school (a) and 40 student are going to school (b) 60 * 0.3 = 18 student of school (a) are expected to go to the new school (c) 40 * 0.4 = 16 student of school (b) are expected to go to the new school (c) thus total of 18 + 16 = 34 student are expected to go to the new school (c) , which is 34 % of students . answer : b ."
Provide a detailed solution to the given mathematical problem.,"the sector of a circle has radius of 18 cm and central angle 135 o . find its perimeter ? a) 78.4 cm , b) 11.5 cm , c) 91.8 cm , d) 92.5 cm , e) 99.5 cm","""perimeter of the sector = length of the arc + 2 (radius) = (135 / 360 * 2 * 22 / 7 * 18) + 2 (18) = 42.4 + 36 = 78.4 cm answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 80 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ? a) 8 % , b) 12 % , c) 16 % , d) 20 % , e) 24 %","""let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.8 x the number of students in beginner trigonometry is 4 / 5 * (2.5 x) - 0.8 x = 1.2 x the number of students in advanced trigonometry is 0.3 x the percentage in advanced trigonometry is 0.3 x / 2.5 x = 12 % the answer is b ."""
Break down and solve the equation step by step.,"if the ratio of a to b is 2 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ? a) 4 / 15 , b) 1 / 3 , c) 2 / 15 , d) 4 / 5 , e) 7 / 6","""a : b = 2 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 2 : 15 answer c"""
Break down and solve the equation step by step.,"a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 3 m , the volume of the box (in m 3) is : a) 3780 , b) 5120 , c) 6420 , d) 8960 , e) 7960","""clearly , l = (48 - 6) m = 42 m , b = (36 - 6) m = 30 m , h = 8 m . volume of the box = (42 x 30 x 3) m 3 = 3780 m 3 . answer : option a"""
"Solve the problem systematically, showing each step clearly.","bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 7 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 19 left in his pocket . what was the value of n ? a) $ 36 , b) $ 44 , c) $ 52 , d) $ 60 , e) $ 68","""started to test answer d if he had 60 , then he spent 15 at hardware store now he was left with 45 $ he spent 7 dollars on cleaning , thus he remained with 38 $ he then spent 1 / 2 of 38 , or 19 , and was left with 19 . hence , the only option that can be right is a ."""
Break down and solve the equation step by step.,"an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ? a) 4 : 5 , b) 9 : 10 , c) 14 : 15 , d) 19 : 20 , e) 24 : 25","""let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be y and y . 2 (3 x + 2 x) = 2 (y + y) 5 x = 2 y (5 / 2) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : y * y = 6 x ^ 2 : y ^ 2 = 6 x ^ 2 : (25 / 4) * x ^ 2 = 24 : 25 the answer is e ."""
"Solve the problem systematically, showing each step clearly.","a cylinder of height h is 7 / 8 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ? a) 25 % , b) 50 % , c) 69 % , d) 80 % , e) 100 %","""basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it' s height is 3 / 5 . original cylinder 7 / 8 new cylinder 3 / 5 so 3 / 5 / 7 / 8 = 3 / 5 * 8 / 7 = 0.69 or 69 % . answer c"""
Explain the solution process for the given equation.,"what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9 - sided polygon) ? a) 1 / 2 , b) 1 / 3 , c) 1 / 4 , d) 1 / 6 , e) 1 / 9","""from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 6 = 1 / 3 . the answer is b ."""
"Solve the problem systematically, showing each step clearly.","a can finish a work in 24 days , b in 9 days and c in 12 days . b and c start the work but are forced to leave after 3 days . when a done the work ? a) 10 days , b) 12 days , c) 13 days , d) 9 days , e) 14 days","""b + c = = > 1 / 9 + 1 / 12 = 7 / 36 b , c = in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done a 24 * 5 / 12 = 10 days answer a"""
Provide a detailed solution to the given mathematical problem.,"when magnified 1000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is a) 0.005 , b) 0.002 , c) 0.001 , d) 0.0003 , e) 0.0002","it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d"
"Solve the problem systematically, showing each step clearly.","each machine of type a has 3 steel parts and 2 chrome parts . each machine of type b has 2 steel parts and 4 chrome parts . if a certain group of type a and type b machines has a total of 50 steel parts and 66 chrome parts , how many machines are in the group a) 11 , b) 21 , c) 31 , d) 61 , e) 51","""look at the below representation of the problem : steel chrome total a 3 2 50 > > no . of type a machines = 50 / 5 = 10 b 2 4 66 > > no . of type b machines = 66 / 6 = 11 so the answer is 21 i . e b . hope its clear ."""
Provide a detailed solution to the given mathematical problem.,"a train running at the speed of 142 km / hr crosses a pole in 12 seconds . find the length of the train . a) 540 , b) 288 , c) 200 , d) 340 , e) 712","""speed = 162 * (5 / 18) m / sec = 45 m / sec length of train (distance) = speed * time 45 * 12 = 540 meter answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","three unbiased coins are tossed . what is the probability of getting 1 heads and 1 tail ? a) 3 / 4 , b) 1 / 4 , c) 3 / 8 , d) 7 / 8 , e) 1 / 8","""let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { tht , hth } p (e) = n (e) / n (s) = 2 / 8 = 1 / 4 answer is b"""
Break down and solve the equation step by step.,"if 27.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ? a) 638 , b) 330 , c) 550 , d) 430 , e) 880","""students enrolled in biology are 27.5 % and therefore not enrolled are 72.5 % . so of 880 is 880 * . 225 = 638 answer is a 638"""
Explain the solution process for the given equation.,"50 percent of andrea' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ? a) 14.4 , b) 180 / 7 , c) 50.4 , d) 64.8 , e) 90","""50 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = (36 / 50) * 100 = 64.8 square feet answer : option d"""
"Solve the problem systematically, showing each step clearly.","a cube has a volume of 343 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ? a) 24 , b) 48 , c) 64 , d) 2744 , e) 100","""volume = 343 = side ^ 3 i . e . side of cube = 7 new cube has dimensions 14 , 14 , and 14 as all sides are twice of teh side of first cube volume = 14 * 14 * 14 = 2744 square feet answer : option d"""
Provide a detailed solution to the given mathematical problem.,"divide rs . 32000 in the ratio 3 : 5 ? a) 12000 , 20000 , b) 12000 , 200098 , c) 12000 , 20007 , d) 12000 , 20006 , e) 12000 , 20001","""3 / 8 * 32000 = 12000 5 / 8 * 32000 = 20000 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","find the smallest number which should be multiplied with 13225 to make it a perfect square . a) 25 , b) 5 , c) 1 , d) 23 , e) 6","""13225 = 5 * 5 * 23 * 23 required smallest number = 1 1 is the smallest number which should be multiplied with 13225 to make it a perfect square . answer : c"""
Provide a detailed solution to the given mathematical problem.,"a cube of side 1.5 meter length is cut into small cubes of side 10 cm each . how many such small cubes can be obtained ? a) 2878 , b) 3375 , c) 1000 , d) 2997 , e) 2701","""along one edge , the number of small cubes that can be cut = 150 / 10 = 15 along each edge 10 cubes can be cut . (along length , breadth and height) . total number of small cubes that can be cut = 15 * 15 * 15 = 3375 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a rectangular courtyard , the sides of which are in the ratio of 4 : 3 , cost rs . 600 for paving at 50 p per m 2 ; find the length of the diagonal of the courtyard ? ['a) 17 m','b) 45 m','c) 54 m','d) 77 m','e) 34 m']",1 m 2 - - - - 1 / 2 ? - - - - - 600 = > 1200 m 2 4 x * 3 x = 1200 = > x = 10 answer : b
"Work through the equation methodically, ensuring clarity at each step.","the mean of 50 observations was 36 . it was found later that an observation 60 was wrongly taken as 23 . the corrected new mean is ? a) 36.7 , b) 36.1 , c) 36.5 , d) 36.9 , e) 36.3","""correct sum = (36 * 50 + 60 - 23) = 1837 . correct mean = 1837 / 50 = 36.7 answer : a"""
Provide a detailed solution to the given mathematical problem.,"a group of people participate in some curriculum , 25 of them practice yoga , 18 study cooking , 10 study weaving , 4 of them study cooking only , 5 of them study both the cooking and yoga , 4 of them participate all curriculums . how many people study both cooking and weaving ? a) 1 , b) 2 , c) 3 , d) 4 , e) 5","""both cooking and weaving = 18 - (4 + 4 + 5) = 5 so , the correct answer is e ."""
Break down and solve the equation step by step.,"in a class of 35 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ? a) 3 , b) 5 , c) 8 , d) 13 , e) 15","""total # of students = 35 avg # of books per student = 2 total # of books = 35 * 2 = 70 # of student borrowed at least 3 books = 35 - 2 - 12 - 10 = 11 # of books borrowed by above 11 students = 70 - (12 * 1) + (10 * 2) = 38 considering that 10 out of above 11 students borrowed only 3 books , # of books borrowed = 10 * 3 = 30 so maximum # of books borrowed by any single student = 38 - 30 = 8 option c"""
Break down and solve the equation step by step.,"the population of a town increased from 1 , 33,400 to 1 , 93,500 in a decade . the average percent increase of population per year is : a) 4.5 % , b) 5.5 % , c) 6.5 % , d) 8.75 % , e) none","""explanation : increase in 10 years = (193500 - 133400) = 60100 . increase % = (60100 / 133400 x 100) % = 45 % . required average = (45 / 10) % = 4.5 % . answer : option a"""
Provide a detailed solution to the given mathematical problem.,"in what time will a railway train 90 m long moving at the rate of 44 kmph pass a telegraph post on its way ? a) 3 , b) 5 , c) 4.3 , d) 6.5 , e) 7.4","""t = 90 / 44 * 18 / 5 = 7.4 sec answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","in what time will a car 10 m long moving at the rate of 36 kmph pass a telegraph post on its way ? a) 8 sec , b) 1 sec , c) 9 sec , d) 6 sec , e) 2 sec",t = 10 / 36 * 18 / 5 = 1 sec answer : b
Break down and solve the equation step by step.,"the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 265 , then the mean profit for the last 15 days would be a) rs . 435 , b) rs . 350 , c) rs . 275 , d) rs . 425 , e) none of these","average would be : 350 = (265 + x) / 2 on solving , x = 435 . answer : a"
Break down and solve the equation step by step.,"a superhero flies at an incredible rate of 1000 kilometers per minute . what is her speed in miles per hour ? [ 1 km = 0.6 miles ] a) 6000 , b) 36000 , c) 60000 , d) 600 , e) 3600","to calculate the equivalent of miles in a kilometer 0.6 kilometers = 1 mile 1000 kilometers = (0.6) * 1000 = 600 miles speed in miles per minute = 600 = 600 1 hour = 60 minutes speed in miles per hour = 600 * 60 = 36,000 correct answer - b"
Provide a detailed solution to the given mathematical problem.,"divide $ 5000 among x , y in the ratio 2 : 8 . how many $ that x get ? a) $ 1000 , b) $ 1050 , c) $ 1100 , d) $ 1150 , e) $ 1200",sum of ratio terms = 2 + 8 = 10 x = 5000 * 2 / 10 = $ 1000 answer is a
Explain the solution process for the given equation.,"the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is a) 123 , b) 106 , c) 100 , d) 156 , e) 240",explanation : cash realised = rs . (106.25 - 0.25) = rs . 106 . answer : b
"Solve the problem systematically, showing each step clearly.","a train 240 m in length crosses a telegraph post in 16 seconds . the speed of the train is ? a) 77 kmph , b) 55 kmph , c) 54 kmph , d) 58 kmph , e) 76 kmph","""s = 240 / 16 * 18 / 5 = 54 kmph answer : c"""
Break down and solve the equation step by step.,"what is the greatest possible length which can be used to measure exactly the lengths 18 m , 40 m and 6 m 50 cm ? a) 20 cm , b) 23 cm , c) 25 cm , d) 10 cm , e) 28 cm","""required length = hcf of 1800 cm , 4000 cm , 650 cm = 50 cm answer is d"""
"Solve the problem systematically, showing each step clearly.","a car traveling at a certain constant speed takes 12 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ? a) 60 , b) 72 , c) 72.5 , d) 73 , e) 73.5","""many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 75 kilometers per hour is 1 / 75 hours = 3,600 / 75 seconds = 48 seconds ; time to cover this distance at regular speed is 48 + 12 = 60 seconds = 60 / 3,600 hours = 1 / 60 hours ; so , we get that to cover 1 kilometer 1 / 60 hours is needed - - > regular speed 60 kilometers per hour (rate is a reciprocal of time or rate = distance / time) . answer : a"""
"Solve the problem systematically, showing each step clearly.","if x is 20 percent greater than 88 , then x = a) 68 , b) 70.4 , c) 86 , d) 105.6 , e) 108","""x is 20 % greater than 88 means x is 1.2 times 88 (in other words 88 + 20 / 100 * 88 = 1.2 * 88) therefore , x = 1.2 * 88 = 105.6 answer : d"""
"Solve the problem systematically, showing each step clearly.","yesterday' s closing prices of 2,860 different stocks listed on a certain stock exchange were all different from today' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ? a) 484 , b) 726 , c) 1,100 , d) 1,320 , e) 1,560","""lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 2860 - - - - (1) we understand from second statement - > h = (120 / 100) l = > h = 1.2 l - - - - (2) solve eq (1) (2) to get h = 1560 . e is my answer ."""
"Solve the problem systematically, showing each step clearly.","a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 10 more than that received by b , find the total amount shared by a , b and c . a) $ 260 , b) $ 360 , c) $ 160 , d) $ 460 , e) $ 560","""a = 1 / 3 (b + c) = > c = 3 a - b - - - (1) b = 2 / 7 (a + c) = > c = 3.5 b - a - - (b) a - b = $ 10 a = 10 + b (1) = = = > c = 30 + 3 b - b = 2 b + 30 = = > 2 b - c = - 30 - - - (3) (2) = = = > c = 3.5 b - b - 10 = 2.5 b - 10 = = > 2.5 b - c = 10 - - - (4) from (4) and (3) 0.5 b = 40 b = $ 80 a = $ 90 c = 270 - 80 = $ 190 total amount = 90 + 80 + 190 = $ 360 answer : b"""
Explain the solution process for the given equation.,"the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 80 % profit ? a) 1152 , b) 230 , c) 960 , d) 780 , e) 400","""c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 180 % of rs . 640 = 180 / 100 * 640 = rs . 1152 . a"""
Explain the solution process for the given equation.,"the length of the longest tape in cm which can be used to measure exactly , the length 100 cm ; 2 m 25 cm ; and 7 m 80 cm is : a) 30 , b) 5 , c) 10 , d) 36 , e) 25","the three lengths in cm are 100 , 225 & 780 . hcf of 100 , 225 & 780 is 5 . hence , the answer is 5 cm . answer : b"
"Solve the problem systematically, showing each step clearly.","a train covers a distance of 12 km in 10 minutes . if it takes 9 seconds to pass a telegraph post , then the length of the train is a) 100 m , b) 120 m , c) 140 m , d) 160 m , e) 180 cm","""explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = (speed x time) = (20 x 9) m = 180 m answer : option e"""
Explain the solution process for the given equation.,"the difference between simple interest and compound interest on $ 1200 for one year at 10 % per annum reckoned half - yearly is : a) $ 5 , b) $ 8 , c) $ 9 , d) $ 3 , e) $ 7","""s . i = $ [ (1200 * 10 * 1) / 100 ] = $ 120 . c . i = $ [ 1200 * (1 + (5 / 100) ^ 2) - 1200 ] = $ 123 . difference = $ (123 - 120) = $ 3 . answer (d)"""
"Solve the problem systematically, showing each step clearly.","carol spends 1 / 4 of her savings on a stereo and 1 / 6 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ? a) 1 / 4 , b) 2 / 7 , c) 5 / 12 , d) 1 / 2 , e) 11 / 24","""total savings = s amount spent on stereo = (1 / 4) s amount spent on television = (1 - 1 / 6) (1 / 4) s = (5 / 6) * (1 / 4) * s = (5 / 24) s (stereo + tv) / total savings = s (1 / 4 + 5 / 24) / s = 11 / 24 answer : e"""
"Solve the problem systematically, showing each step clearly.","what is the remainder when 220 * 165 * 110 * 55 is divided by 15 ? a) 12 , b) 15 , c) 10 , d) 11 , e) 18","""oa is' c' . oe : take the remainder from each of 220 / 15 , 165 / 15 and so on . . 220 / 15 gives remainder = 10 165 / 15 gives remainder = 0 110 / 15 gives remainder = 5 55 / 15 gives remainder = 10 the net remainder is the product of above individual remainders . i . e = 10 * 0 * 5 * 10 break them into pairs 10 * 0 / 15 gives remainder 10 and 5 * 10 / 15 gives remainder 5 so 10 * 5 / 15 gives remainder 5 . answer : c"""
Explain the solution process for the given equation.,"in a class of 25 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ? a) 8 , b) 9 , c) 10 , d) 11 , e) 12","""the total number of books the students borrowed is 25 * 2 = 50 . the students who borrowed zero , one , or two books borrowed 12 * 1 + 4 * 2 = 20 books . the 7 students who borrowed at least three books borrowed 50 - 20 = 30 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 30 - 18 = 12 books . the answer is e ."""
Explain the solution process for the given equation.,"the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 11 and 12 . the larger of the two numbers is : a) 338 , b) 276 , c) 322 , d) 231 , e) 121","""clearly , the numbers are (23 * 11) and (23 * 12) . larger number = (23 * 12) = 276 . answer : b"""
Provide a detailed solution to the given mathematical problem.,"an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n (n + 1) will be divisible by 5 ? a) 1 / 9 , b) 1 / 3 , c) 1 / 2 , d) 2 / 3 , e) 2 / 5","""n (n + 1) to be divisible by 3 either n or n + 1 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 , 4 , 5 } , { 6 , 7 , 8 , 9 , 10 } , . . . , { 96 , 97 , 98 , 99,100 } there is exactly 1 numbers out of 5 satisfying the above condition . for example in { 1 , 2 , 3 , 4 , 5 } n can be : 4 or 5 . thus , the overall probability is 2 / 5 . answer : d ."""
"Solve the problem systematically, showing each step clearly.","how many pieces can a square pizza be cut into by making 6 linear cuts ? a) 20 , b) 21 , c) 22 , d) 23 , e) 24","""1 cut makes 2 pieces a second cut can make 4 pieces by cutting through both pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a sixth cut can make 22 pieces by cutting through 6 of the pieces c"""
Provide a detailed solution to the given mathematical problem.,"in an examination , the percentage of students qualified to the number of students appeared from school a is 70 % . in school b , the number of students appeared is 20 % more than the students appeared from school a and the number of students qualified from school b is 50 % more than the students qualified from school a . what is the percentage of students qualified to the number of students appeared from school b ? a) 30 % , b) 70 % , c) 80 % , d) 87.5 % , e) none","solution let number of students appeared from school a = 100 . then , number of students qualified from school a = 70 . number of students appeared from school b = 120 . number of students qualified from school b = [ 150 / 100 x 70 ] = 105 . required percentage = [ 105 / 120 x 100 ] % = 87.5 % answer d"
"Solve the problem systematically, showing each step clearly.","total 85 matches are conducted in knockout match type . how many players will be participated in that tournament ? a) 85 , b) 81 , c) 53 , d) 82 , e) 84",84 players answer : e
"Work through the equation methodically, ensuring clarity at each step.","the ratio between the number of sheep and the number of horses at the stewart farm is 6 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ? a) 18 , b) 28 , c) 48 , d) 56 , e) 60","""let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 6 x = 6 * 8 = 48 . hence c ."""
"Work through the equation methodically, ensuring clarity at each step.","population is 24000 . population increases by 10 % every year , then the population after 3 years is ? a) 26630 , b) 26640 , c) 36644 , d) 31944 , e) 26844","""population after 1 st year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26400 population after 2 nd year = 26400 * 10 / 100 = 2640 = = = > 26400 + 2640 = 29040 population after 3 rd year = 29040 * 10 / 100 = 2904 = = = > 29040 + 2904 = 31944 answer : d"""
Explain the solution process for the given equation.,"earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 360 envelopes a) 6 minutes , b) 5 minutes , c) 7 minutes , d) 3 minutes , e) 4 minutes","""earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ((36) / (3 / 2)) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 360 envelopes they will take 360 / 60 mins . i . e . , 6 mins . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","the length of the bridge , which a train 145 m long and traveling at 45 km / hr can cross in 30 sec is ? a) 230 , b) 240 , c) 245 , d) 250 , e) 255","""speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , (145 + x) / 30 = 25 / 2 x = 230 m . answer : option a"""
Provide a detailed solution to the given mathematical problem.,"how many multiples of 5 are there between 5 to 75 ? a) 9 , b) 18 , c) 17 , d) 13 , e) can not be determined","""explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i . e . the units place) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 . answer : d"""
"Solve the problem systematically, showing each step clearly.","the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years , the ratio of the number of boys to the number of girls in the class is : a) 2 : 9 , b) 2 : 3 , c) 2 : 1 , d) 2 : 2 , e) 2 : 6","""explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = (k + 1) * 15.8 < = > (16.4 - 15.8) k = (15.8 - 15.4) < = > k = 0.4 / 0.6 = 2 / 3 . required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"""
Break down and solve the equation step by step.,"if a is an integer greater than 6 but less than 17 and b is an integer greater than 3 but less than 29 , what is the range of a / b ? a) 15 / 4 , b) 13 / 2 , c) 9 / 7 , d) 1 / 5 , e) 7 / 6","""the way to approach this problem is 6 < a < 17 and 3 < b < 29 minimum possible value of a is 7 and maximum is 16 minimum possible value of b is 4 and maximum is 28 range = max a / min b - min a / max b (highest - lowest) 16 / 4 - 7 / 28 = 15 / 4 hence a"""
"Solve the problem systematically, showing each step clearly.","the maximum number of students among them 890 pens and 630 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : a) 10 , b) 910 , c) 1001 , d) 1911 , e) none of these","""explanation : required number of students = h . c . f of 890 and 630 = 10 . answer : a"""
"Solve the problem systematically, showing each step clearly.","average of 10 matches is 34 , how many runs one should should score to increase his average by 5 runs . a) a) 70 , b) b) 76 , c) c) 78 , d) d) 89 , e) e) 88","""explanation : average after 11 innings should be 39 so , required score = (11 * 39) - (10 * 34) = 429 - 340 = 89 answer : option d"""
"Solve the problem systematically, showing each step clearly.","a person can row at 9 kmph and still water . he takes 4 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ? a) 33 , b) 77 , c) 26 , d) 28 , e) 20","""let the distance between a and b be x km . total time = x / (9 + 1) + x / (9 - 1) = 4.5 = > x / 10 + x / 8 = 9 / 2 = > (4 x + 5 x) / 40 = 9 / 2 = > x = 20 km . answer : e"""
"Solve the problem systematically, showing each step clearly.","a batsman makes a score of 100 runs in the 17 th inning and thus increases his averages by 5 . what is his average after 17 th inning ? a) 39 , b) 35 , c) 20 , d) 40.5 , e) 41.5","""let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 100 then average run after 17 th inning = (16 x + 100) / 17 (16 x + 100) / 17 = x + 5 = > 16 x + 100 = 17 x + 85 = > x = 15 x = 15 ; average after 17 th inning = 15 + 5 = 20 answer : c"""
Provide a detailed solution to the given mathematical problem.,"what is the value of 4 ^ 5 + 4 ^ 4 ? a) 4 ^ 12 , b) 5 (4 ^ 4) , c) 17 (4 ^ 5) , d) 8 ^ 12 , e) 7 (4 ^ 5)","""4 ^ 5 + 4 ^ 4 = 4 ^ 4 (4 + 1) = 4 ^ 4 * 5 answer b"""
"Solve the problem systematically, showing each step clearly.","a number when divided by a divisor leaves a remainder of 21 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ? a) 12 , b) 13 , c) 34 , d) 37 , e) 59","""let the number is n , the divisor = d , i will make the two equations - n = xd + 21 2 n = yd + 11 where x and y are integers solving them : d (y - 2 x) = 34 as d is also integer and 34 is a prime number , the d should be 34 to satisfy the above equation . hence answer is' d'"""
Provide a detailed solution to the given mathematical problem.,"the number of stamps that p and q had were in the ratio of 7 : 3 respectively . after p gave q 13 stamps , the ratio of the number of p' s stamps to the number of q' s stamps was 5 : 4 . as a result of the gift , p had how many more stamps than q ? a) 10 , b) 25 , c) 40 , d) 65 , e) 90","""p started with 7 k stamps and q started with 3 k stamps . (7 k - 13) / (3 k + 13) = 5 / 4 28 k - 15 k = 117 k = 9 p has 7 (9) - 13 = 50 stamps and q has 3 (9) + 13 = 40 stamps . the answer is a ."""
Explain the solution process for the given equation.,"if a cost college rs 0.70 a companyto produce a program for yhe home coming football game . if rs 15000 was received for addvertisement in the pgm , how many copies rs 0.50 a copy must be sold to make a profit of rs 8000 a) 15000 , b) 25000 , c) 45000 , d) 32000 , e) 35000","let no . of pages be x while selling with 0.70 paise / page total cost = 0.70 * x while selling with 0.50 paise / page toatal cost = 0.50 * x now according to question - (0.70 x - 0.50 x) + 8000 = 15000 therefore , x = 35000 copies must be sold answer : e"
Break down and solve the equation step by step.,"speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 6840 km and comes back to the starting point . the total time taken by him is : a) 914.2 hours , b) 900 hours , c) 915 hours , d) 868.6 hours , e) 915 hours","""explanation : speed downstream = (16 + 2) = 18 kmph speed upstream = (16 - 2) = 14 kmph total time taken = 6840 / 18 + 6840 / 14 = 380 + 488.6 = 868.6 hours answer : option d"""
Break down and solve the equation step by step.,"how much more would rs . 20000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ? a) a) rs . 6 , 602.50 , b) b) rs . 6 , 601.50 , c) c) rs . 6 , 603.50 , d) d) rs . 6 , 604.50 , e) e) rs . 6 , 605.50","""20000 (11 / 10) 4 - 20000 (6 / 5) 2 = 6 , 602.50 answer : a"""
Break down and solve the equation step by step.,"in a class , 30 students pass in english and 20 students in math , while some students among these pass in both . how many more students do only english as compared to those doing only maths ? a) 10 , b) 15 , c) 20 , d) 25 , e) indeterminate","let us consider tht x student are tohse who passed in both english and maths . . . so first we remove x student from both of them therefore , english = 30 - x maths = 20 - x now , number of students more in english = (30 - x) - (20 - x) = 30 - x - 20 + x = 10 answer : a"
"Solve the problem systematically, showing each step clearly.","7 x + y = 19 , and x + 3 y = 1 . find the value of 2 x + y a) 20 , b) 18 , c) 11 , d) 5 , e) 50",add these two equations 8 x + 4 y = 20 divide by 2 (to get 2 x + y) answer will be d . 10
Explain the solution process for the given equation.,"6 persons in an organization including a and b were to be divided in two groups of 3 members each . the total number of groups containing both a and b is what fraction of the total number of groups which can be formed ? a) 3 / 10 , b) 1 / 70 , c) 3 / 14 , d) 1 / 10 , e) 11 / 14",the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose a and b and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : a
"Solve the problem systematically, showing each step clearly.","total dinning bill for 6 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share a) $ 30.14 , b) 40.44 , c) 34.66 , d) 32.29 , e) 33.16","""211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 6 = 40.44 answer : b"""
"Solve the problem systematically, showing each step clearly.","a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 23 per kg , then his gain percent is a) 12 % , b) 23 % , c) 14 % , d) 15 % , e) 16 %","explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . (5 x 18 + 3 x 20) = rs . 150 . selling price = rs . (8 x 23) = rs . 184 . profit = 184 - 150 = 34 so , profit % = (34 / 150) * 100 = 23 % option b"
Explain the solution process for the given equation.,"30 men can do a work in 40 days . when should 20 men leave the work so that the entire work is completed in 40 days after they leave the work ? a) 22 days , b) 10 days , c) 77 days , d) 88 days , e) 55 days","""total work to be done = 30 * 40 = 1200 let 20 men leave the work after' p' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + (20 * 40) = 1200 40 p = 400 = > p = 10 days answer : b"""
Break down and solve the equation step by step.,"one night 17 percent of the female officers on a police force were on duty . if 170 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ? a) 400 , b) 420 , c) 450 , d) 480 , e) 500",let x be the number of female police officers on the police force . the number of female police officers on duty was 85 . 0.17 x = 85 x = 500 the answer is e .
Provide a detailed solution to the given mathematical problem.,"a train 200 m long crosses a platform 200 m long in 40 sec ; find the speed of the train ? a) 94 kmph , b) 58 kmph , c) 54 kmph , d) 94 kmph , e) 36 kmph","""d = 200 + 200 = 400 t = 40 s = 400 / 40 * 18 / 5 = 36 kmph answer : e"""
Explain the solution process for the given equation.,"solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 18 percent alcohol by volume ? a) 100 , b) 150 , c) 200 , d) 250 , e) 300","""18 % is 8 % - points higher than 10 % but 12 % - points lower than 30 % . thus there should be 3 parts of solution x for 2 parts of solution y . we should add 200 ml of solution y . the answer is c ."""
Break down and solve the equation step by step.,"a recipe requires 2 1 / 2 (mixed number) cups of flour 2 3 / 4 (mixed number) cups of sugar and 1 1 / 3 (mixed number) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes john can make using this recipe ? a) 5 , b) 6 , c) 7 , d) 8 , e) 9","""less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i' d need 16.5 cups . i do n' t have that much sugar , so we' re limited to 5 cakes . no need to even do milk because we' re already at 5 . sugar will be the limiting factor . answer is a"""
Provide a detailed solution to the given mathematical problem.,"the organizers of a fair projected a 25 percent increase in attendance this year over that of last year , but attendance this year actually decreased by 20 percent . what percent of the projected attendance was the actual attendance ? a) 45 % , b) 56 % , c) 64 % , d) 75 % , e) 80 %",last year attendance = 100 (assume) ; projected attendance = 125 ; actual attendance = 80 . the actual attendance therefore was (actual) / (project) = 80 / 125 * 100 = 64 $ of the projected attendance . answer : c .
"Work through the equation methodically, ensuring clarity at each step.","if 70 % of a number exceeds 28 % of it by 39.9 , then find the number ? a) 65 , b) 67 , c) 100 , d) 95 , e) 33","""use the elimination method to find the correct option . of all the options only 95 fits 70 % of 95 = 66.5 28 % of 95 = 26.6 66.5 - 26.6 = 39.9 required number is 95 . answer : d"""
Provide a detailed solution to the given mathematical problem.,"how many integers between 2000 and 3000 that have distinct digits and increase from left to right ? a) 10 , b) 20 , c) 60 , d) 120 , e) 600","since the numbers must be distinct and increasing from left to right , the only arrangements we could come - up with are : 245 _ - - > 4 246 _ - - > 3 247 _ - - > 2 248 _ - - > 1 256 _ - - > 3 257 _ - - > 2 258 _ - - > 1 267 _ - - > 2 268 _ - - > 1 number of integers = 20 b"
Provide a detailed solution to the given mathematical problem.,"a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? a) 4.8 hr , b) 2.4 hr , c) 3.6 hr , d) 1.8 hr , e) 2.0 hr","explanation : part filled by one tap in 1 hour = 1 / 4 part emptied by second tap 1 hour = 1 / 8 net part filled by both these taps in 1 hour = 1 / 3 - 1 / 8 = 5 / 24 i . e , the cistern gets filled in 24 / 5 hours = 4.8 hrs answer : option a"
Provide a detailed solution to the given mathematical problem.,"90 % of the population of a village is 8100 . the total population of the village is ? a) 9000 , b) 24000 , c) 26682 , d) 29973 , e) 12312","""x * (90 / 100) = 8100 x = 90 * 100 x = 9000 answer : a"""
"Solve the problem systematically, showing each step clearly.","solution y is 30 percent liquid x and 70 percent water . if 4 kilograms of water evaporate from 8 kilograms of solution y and 4 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ? a) 40 % , b) 41 1 / 2 % , c) 44 % , d) 45 % , e) 46 %","""in 8 kilograms of solution y there are 0.3 * 8 = 2.4 kilograms of solution x ; after 4 kilograms of water are replaced by 4 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 4 = 1.2 kilograms of solution x are added , so in the new solution of 8 kilograms there are 2.4 + 1.2 = 3.6 kilograms of solution x , which is 3.6 / 8 * 100 = 45 % of this new solution . answer : d ."""
Explain the solution process for the given equation.,"how many trailing zeros will be there after the rightmost non - zero digit in the value of 25 ! (factorial 25) ? a) 25 , b) 8 , c) 6 , d) 5 , e) 2","explanatory answer 25 ! means factorial 25 whose value = 25 * 24 * 23 * 22 * . . . . * 1 when a number that has 5 as its factor is multiplied by an even number , it results in a trailing zero . (product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied) in 25 ! , the following numbers have 5 as their factor : 5 , 10 , 15 , 20 , and 25 . 25 is the square of 5 and hence it has two 5 s in it . in toto , it is equivalent of having six 5 s . there are at least 6 even numbers in 25 ! hence , the number 25 ! will have 6 trailing zeroes in it . choice c"
Break down and solve the equation step by step.,"nancy obtained 66 , 75 , 52 , 68 and 89 marks (out of 100) in american literature , history , home economics , physical education and art . calculate her average marks ? a) 50 , b) 80 , c) 70 , d) 60 , e) 71",explanation : average = (66 + 75 + 52 + 68 + 89) / 5 = 70 . answer : c) 70
Provide a detailed solution to the given mathematical problem.,"a train running at the speed of 60 km / hr crosses a pole in 15 seconds . what is the length of the train ? a) 187 m , b) 250 m , c) 876 m , d) 150 m , e) 267 m","""speed = (60 * 5 / 18) m / sec = (50 / 3) m / sec length of the train = (speed x time) = (50 / 3 * 15) m = 250 m . answer : b"""
Provide a detailed solution to the given mathematical problem.,"the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 15 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ? a) 28 % , b) 40 % , c) 64.8 % , d) 76.5 % , e) 72 %","""original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 15 % , price = 81 - 12.15 = 68.85 which is 68.85 / 90 * 100 of the sale price on day 1 = ~ 76.5 % answer d"""
"Solve the problem systematically, showing each step clearly.","find the average of first 4 multiples of 12 ? a) 10 , b) 12.6 , c) 22.5 , d) 30 , e) 40.8","""average = (12 + 24 + 36 + 48) / 4 = 30 answer is d"""
Provide a detailed solution to the given mathematical problem.,"what is the smallest number which when increased by 7 is divisible by 25 , 49 , 15 , and 21 ? a) 3,551 , b) 3,668 , c) 3,733 , d) 3,822 , e) 3,957","""first factor each of 25 , 49 , 15 , and 21 into primes : 25 = 5 * 5 ; 49 = 7 * 7 ; 15 = 3 * 5 ; 21 = 3 * 7 the smallest number divisible by each of the numbers is 3 * 5 * 5 * 7 * 7 = 3,675 3,675 - 7 = 3,668 thus 3,668 + 7 is the smallest number divisible by 25 , 49 , 15 , and 21 b"""
"Work through the equation methodically, ensuring clarity at each step.","running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets . a) 4 , b) 6 , c) 8 , d) 10 , e) 12","""i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / (y + 2) + 1 / y = 5 / 12 (5 / 12 is because (5 / 4) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day) solving , we have y = 4 = > x takes 6 days to doing x widgets . answer : b"""
Provide a detailed solution to the given mathematical problem.,"if w is 40 percent less than e , e is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ? a) 4 % , b) 18 % , c) 36 % , d) 40 % , e) 50 %","given w = 0.6 e , e = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer ."
Provide a detailed solution to the given mathematical problem.,"40 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ? a) 30 % , b) 40 % , c) 50 % , d) 60 % , e) 70 %","""to maximize the percentage of companies offering both , let' s assume that all 40 % of companies which offer wireless internet also offer snacks . the answer is b ."""
Break down and solve the equation step by step.,"for the past n days , the average (arithmetic mean) daily production at a company was 30 units . if today' s production of 90 units raises the average to 35 units per day , what is the value of n ? a) 30 , b) 18 , c) 10 , d) 9 , e) 3","""(average production for n days) * n = (total production for n days) - - > 30 n = (total production for n days) ; (total production for n days) + 90 = (average production for n + 1 days) * (n + 1) - - > 30 n + 90 = 35 * (n + 1) - - > n = 3 . answer : e ."""
Break down and solve the equation step by step.,"two vessels contains equal number of mixtures milk and water in the ratio 4 : 2 and 5 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ? a) 3 : 1 , b) 9 : 13 , c) 5 : 11 , d) 11 : 3 , e) 15 : 4","""the ratio of milk and water in the new vessel is = (4 / 6 + 5 / 6) : (2 / 6 + 1 / 6) = 9 / 6 : 3 / 6 = 3 : 1 answer is a"""
Break down and solve the equation step by step.,"how many internal diagonals does a heptagon (seven sided polygon) have ? a) 7 , b) 9 , c) 14 , d) 20 , e) 35","""number of diagonals in any polygon can be found using this formula : n (n - 3) / 2 here n = 7 no . of diagonals = 7 (7 - 3) / 2 = 14 ans c"""
Provide a detailed solution to the given mathematical problem.,"if each year the population of the country grows by 10 % , how many years will elapse before the population of the country doubles ? a) 3 , b) 4 , c) 5 , d) 7 , e) 8","till year 2000 , population is 100 . year 2001 : population becomes 110 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 121 . . . . . . . . . . . . . 2 year elapsed year 2003 : population becomes > 133 . . . . . . . . . . . . . 3 year elapsed year 2004 : population becomes > 146 . . . . . . . . . . . . . . . . . . 4 year elapsed year 2005 : population becomes > 160 . . . . . . . . . . . . . . . . . . 5 year elapsed year 2006 : population becomes > 176 . . . . . . . . . . . . . . . . . . 6 year elapsed year 2007 : population becomes > 193 . . . . . . . . . . . . . . . . . . 7 year elapsed year 2008 : population > 200 . . . . . . . . . . . . . . . . . . 8 year elapsed answer : e"
Explain the solution process for the given equation.,"a thief is spotted by a policeman from a distance of 160 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ? a) 350 m , b) 240 m , c) 440 m , d) 640 m , e) none of them","""relative speed of the policeman = (10 - 8) km / hr = 2 km / hr . time taken by police man to cover (160 m / 1000) x 1 / 2 hr = 2 / 25 hr . in 2 / 25 hr / s , the thief covers a distance of 8 x 2 / 25 km = 16 / 25 km = 640 m answer is d ."""
Break down and solve the equation step by step.,"in a village of 2,700 people , 900 people are over 70 years old and 1200 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a female or younger than 70 years old ? a) 7 / 8 , b) 14 / 15 , c) 29 / 30 , d) 44 / 45 , e) 131 / 135","""the number of people younger than 70 years old is 2700 - 900 = 1800 the number of females older than 70 years old is 0.6 * 1200 = 720 the number of people who are either female or younger than 70 is 1800 + 720 = 2520 . p (a person is younger than 70 or male) = 2520 / 2700 = 14 / 15 the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 30 kmh , what was the average speed of the car for the entire trip ? a) 36 kmh , b) 40 kmh , c) 42 kmh , d) 44 kmh , e) 34 kmh","""assume d / 3 = 240 (this number is convenient because it is divisible by 80 , 24 and 30) so : 240 = 80 * t 1 = 3 hrs 240 = 24 * t 2 = 10 hrs 240 = 30 * t 3 = 8 hrs t = t 1 + t 2 + t 3 = 21 hrs d = rt (240 * 3) = r * 21 r = 34 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","the average monthly salary of 20 employees in an organisation is rs . 1700 . if the manager' s salary is added , then the average salary increases by rs . 100 . what is the manager' s monthly salary ? a) rs . 6003 , b) rs . 3800 , c) rs . 1288 , d) rs . 6108 , e) rs . 6011","""explanation : manager' s monthly salary rs . (1800 * 21 - 1700 * 20) = rs . 3800 . answer : b"""
"Solve the problem systematically, showing each step clearly.","following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ? a) 11 . , b) 12 . , c) 13 . , d) 14 . , e) 14.5","""price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 9 / 1.5 = 6 total price = 8 + 6 = 14 d is the answer"""
"Solve the problem systematically, showing each step clearly.","the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along theboundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park is ? a) 163600 m , b) 178600 m , c) 153600 m , d) 163600 m , e) 173600 m","""perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 (3 x + 2 x) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = (480 x 320) m 2 = 153600 m c"""
"Work through the equation methodically, ensuring clarity at each step.","a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a bridge of 800 meter length ? a) 72 seconds , b) 27 seconds , c) 40 seconds , d) 128 seconds , e) 18 seconds","""speed = 60 km / hr = 60 * (5 / 18) m / sec = 150 / 9 m / sec total distance = 400 + 800 = 1200 meter time = distance / speed = 1200 * (9 / 150) = 72 seconds answer : a"""
Explain the solution process for the given equation.,"janet invited her boy and girl friends to her party at the ratio of 3 : 7 . if 30 % of the boys and 70 % of the girls will be coming for the party from texas , how many janet invited friends will be coming from texas . a) 62 % , b) 52 % , c) 57 % , d) 56 % , e) 58 %","let total no of janet invited friends be 100 , boys 30 and girls 70 , so total number of janet' s invited guests coming from texas for both boys and girls respectively 30 * 30 / 100 = 9 and 70 * 70 / 100 = 49 so total 58 of janet' s invited guest out of the 100 invited guests will be coming from texas . . so required % is 58 % answer : e"
Break down and solve the equation step by step.,"a is three times as fast as b . if b alone can do a piece of work in 12 days , in what time can a and b together complete the work ? a) 5 , b) 8 , c) 3 , d) 2 , e) 12","""a can do the work in 12 / 3 i . e . , 4 days . a and b' s one day' s work = 1 / 4 + 1 / 12 = (3 + 1) / 12 = 1 / 3 so a and b together can do the work in 3 days . answer : c"""
Break down and solve the equation step by step.,"a man buy a book in rs 50 & sale it rs 60 . what is the rate of profit ? ? ? a) 10 % , b) 20 % , c) 30 % , d) 25 % , e) 28 %","""cp = 50 sp = 60 profit = 60 - 50 = 10 % = 10 / 50 * 100 = 20 % answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","((1 ^ m) / (5 ^ m)) ((1 ^ 16) / (4 ^ 16)) = 1 / (2 (10) ^ 31) what is m ? a) 17 , b) 18 , c) 34 , d) 31 , e) 36","((1 ^ m) / (5 ^ m)) ((1 ^ 16) / (4 ^ 16)) = 1 / (2 (10) ^ 31) ((1 / 5) ^ m) * ((1 / 2) ^ 32) = 1 / (2 * (2 * 5) ^ 31)) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so (1 / 5) ^ m = (1 / 5) ^ 31 ((1 / 5) ^ m) * ((1 / 2) ^ 32) = 1 / [ (2 ^ 32) * (5 ^ 31) ] so , m = 31 answer d"
Explain the solution process for the given equation.,"if the personal income tax rate is lowered from 42 % to 32 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 42400 ? a) $ 3500 , b) $ 5000 , c) $ 4240 , d) $ 7000 , e) $ 10000","""saving = (42 - 32) % of 42400 = 4240 . answer : c"""
Break down and solve the equation step by step.,"two cubes of their volumes in the ratio 8 : 125 . the ratio of their surface area is : ['a) 1.5 : 5','b) 2 : 5','c) 3 : 5','d) 1 : 5','e) 4 : 5']",the ratio of their surface area is 8 : 125 2 : 5 answer is b .
Break down and solve the equation step by step.,"two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 5 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ? a) 1 : 1 , b) 2 : 3 , c) 5 : 2 , d) 4 : 3 , e) 7 : 9","""mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be (8 / 4) * 3 = 6 . so , we should take of mixture b a quantity with 5 and 1 parts , respectively . this will give us in the final mixture (5 + 5) : (3 + 1) , which means 10 : 4 , or 5 : 2 . answer c ."""
"Work through the equation methodically, ensuring clarity at each step.","a sum of money is distributed among w , x , y , z in the proportion of 1 : 6 : 2 : 4 . if x gets $ 1500 more than y , what is the w' s share ? a) $ 1500 , b) $ 150 , c) $ 375 , d) $ 200 , e) $ 450","let the shares of w , x , y , z are 1 a , 6 a , 2 a , 4 a 6 a - 2 a = 1500 4 a = $ 1500 , a = 375 w' s share = 1 a = $ 375 answer is c"
Explain the solution process for the given equation.,"the ratio of buses to cars on river road is 1 to 17 . if there are 80 fewer buses than cars on river road , how many cars are on river road ? a) 40 , b) 85 , c) 60 , d) 30 , e) 20",b / c = 1 / 17 c - b = 80 . . . . . . . . . > b = c - 80 (c - 80) / c = 1 / 17 testing answers . clearly eliminate acde put c = 85 . . . . . . . . . > (85 - 80) / 85 = 5 / 85 = 1 / 17 answer : b
Provide a detailed solution to the given mathematical problem.,"if g and d are both integers , g > d , and - 3 g > 19 , then the largest value of d would be ? a) - 5 , b) - 6 , c) - 7 , d) - 8 , e) - 10","no , your thinking is incorrect . when we know that g > d and g < - 6.33 , the largest value of g can be - 7 while if g = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . (- 11 < - 10 , - 10 < - 8 , 4 < 5 etc) . so , as per the question if d < g and g = - 7 , then d' s largest' possible' value has to be - 8 . - 10 is smaller than - 8 = d"
Provide a detailed solution to the given mathematical problem.,"what number should replace the question mark ? 10 , 30 , 14 , 25 , 18 , 20 , - - - ? a) 19 , b) 21 , c) 25 , d) 22 , e) 20","""answer : d 10 , 30 , 14 , 25 , 18 , 20 , 22 ? there are two alternate sequences : + 4 and - 5 ."""
"Solve the problem systematically, showing each step clearly.","in one hour , a boat goes 11 km along the stream and 5 km against the stream . the sped of the boat in still water (in km / hr) is : a) 3 , b) 5 , c) 8 , d) 9 , e) 10","""solution speed in still water = 1 / 2 (11 + 5) km / hr = 8 kmph . answer c"""
Break down and solve the equation step by step.,"in a can , there is a mixture of milk and water in the ratio 5 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ? a) 56 , b) 60 , c) 64 , d) 68 , e) 72","""let c be the capacity of the can . (5 / 8) * (c - 8) + 8 = (2 / 3) * c 15 c - 120 + 192 = 16 c c = 72 the answer is e ."""
Provide a detailed solution to the given mathematical problem.,"out of 470 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ? a) 80 , b) 150 , c) 100 , d) 180 , e) 220","""n (a) = 325 , n (b) = 175 , n (aub) = 470 - 50 = 420 . required number = n (anb) = n (a) + n (b) - n (aub) = 325 + 175 - 420 = 80 . answer is a"""
"Work through the equation methodically, ensuring clarity at each step.","an ant walks an average of 500 meters in 12 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ? a) 2.215 , b) 2.5 . , c) 2.775 , d) 3.2 , e) 3.5","""the ant walks an average of 500 meters in 12 minutes or , 500 meters in 1 / 5 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 12 minutes or , 0.425 km in 12 / 60 = 1 / 5 hours speed = 0.425 * 5 = 2.125 km / h ans should be 2.125 answer : a"""
"Solve the problem systematically, showing each step clearly.","in triangle pqr , the angle q = 90 degree , pq = 3 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz a) 3.6 cm , b) 2.4 cm , c) 4.8 cm , d) 2.16 cm , e) 3.2 cm","""look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 3 = 8 : 10 - - > qy = 2.4 . answer : b ."""
Break down and solve the equation step by step.,"barbata invests $ 2000 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ? a) 1200 , b) 3000 , c) 1000 , d) 3600 , e) 2400","""let the additional invested amount for 8 % interest be x ; equation will be ; 2000 + 0.05 * 2000 + x + 0.08 x = 2000 + x + 0.06 (2000 + x) 0.05 * 2000 + 0.08 x = 0.06 x + 0.06 * 2000 0.02 x = 2000 (0.06 - 0.05) x = 2000 * 0.01 / 0.02 = 1000 ans : ` ` c''"""
"Solve the problem systematically, showing each step clearly.","a , b and c can do a piece of work in 30 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ? a) 12 days , b) 16 days , c) 18 days , d) 11 days , e) 38 days","""one day work of a , b and c = 1 / 30 + 1 / 30 + 1 / 40 = 1 / 11 work done by a and b together in the last 4 days = 4 * (1 / 30 + 1 / 30) = 4 / 15 remaining work = 11 / 15 the number of days required for this initial work = 8 days . the total number of days required = 4 + 8 = 12 days . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","if the sum of two positive integers is 20 and the difference of their squares is 40 , what is the product of the two integers ? a) 108 , b) 99 , c) 128 , d) 135 , e) 143","""let the 2 positive numbers x and y x + y = 20 - - 1 x ^ 2 - y ^ 2 = 40 = > (x + y) (x - y) = 40 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 11 y = 9 product = 11 * 9 = 99 answer b"""
Break down and solve the equation step by step.,"how many digits are used to number a book containg 300 pages . a) 694 , b) 792 , c) 698 , d) 784 , e) 789",explanation : number of digits in 1 digit numbers = 1 to 9 = 9 number of digits in 2 digit numbers = 10 to 99 = 90 (2) = 180 number of digits in 3 digit numbers = 100 to 300 = 201 (3) = 603 total = 792 answer : option b
Explain the solution process for the given equation.,"the unit digit in the product (224 * 607 * 214 * 863) is : a) 2 , b) 5 , c) 6 , d) 8 , e) 10","""explanation : unit digit in the given product = unit digit in (4 * 7 * 4 * 3) = 6 answer : c"""
Provide a detailed solution to the given mathematical problem.,"what is the units digit of the expression 17 ^ 7 - 2 ? a) 1 , b) 2 , c) 3 , d) 7 , e) 9","""7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 (last digit) 7 ^ 5 = 7 (last digit) and the cycle repeats after every 4 powers therefore , last digit of 17 ^ 7 = 3 3 - 2 = 1 answer a"""
Explain the solution process for the given equation.,"jim drove 923 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ? a) 113 miles , b) 277 miles , c) 456 miles , d) 887 miles , e) 767 miles",the number of miles to drive to finish his journey is given by 1200 - 923 = 277 miles correct answer b
"Solve the problem systematically, showing each step clearly.","if the sides of a square are multiplied by sqrt (5) , the area of the original square is how many times as large as the area of the resultant square ? ['a) 5 %','b) 20 %','c) 50 %','d) 100 %','e) 120 %']","let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length sqrt (5) * x , so the area is 5 x ^ 2 . the area of the original square is 1 / 5 = 20 % times the area of the new square . the answer is b ."
Break down and solve the equation step by step.,"a train 125 m long passes a man , running at 8 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is : a) 53 , b) 50 , c) 99 , d) 288 , e) 12","speed of the train relative to man = (125 / 10) m / sec = (25 / 2) m / sec . [ (25 / 2) * (18 / 5) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = (x - 8) km / hr . x - 8 = 45 = = > x = 53 km / hr . answer : a"
Break down and solve the equation step by step.,"a man swims downstream 45 km and upstream 25 km taking 5 hours each time , what is the speed of the man in still water ? a) 17 , b) 24 , c) 7 , d) 24 , e) 20","""45 - - - 5 ds = 9 ? - - - - 1 25 - - - 5 us = 5 ? - - - - 1 m = ? m = (9 + 5) / 2 = 14 / 2 = 7 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ? a) 0.125 , b) 0.25 , c) 0.375 , d) 0.5 , e) 0.666","""p = ncm * p ^ m * q ^ (n - m) n - the total number of trials . m - the number of trials with heads . n - m - the number of trials with tails . p - probability of heads . q - probability of tails . p = 3 c 2 * (1 / 2) ^ 2 * (1 / 2) ^ 1 = 3 / 8 = 0.375 answer : c"""
Provide a detailed solution to the given mathematical problem.,"in a graduating class of 236 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ? a) 144 , b) 119 , c) 113 , d) 117 , e) 31","""greatest possible number taken both should be 144 (as it is maximum for one) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total (neither must be 0 to minimize the both) so 144 + 119 + 0 - 236 = 27 greatest - smallest is 144 - 27 = 117 so answer must be d . 117"""
"Solve the problem systematically, showing each step clearly.","sum of two numbers prime to each other is 14 and their l . c . m . is 45 . what are the numbers ? a) 6 and 5 , b) 8 and 5 , c) 9 and 5 , d) 8 and 5 , e) 3 and 5","""as two numbers are prime , satisfies all but option c will make the product of numbers i . e 45 answer : c"""
Break down and solve the equation step by step.,"a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 40 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ? a) 65 % , b) 70 % , c) 75 % , d) 85 % , e) 96 %","""find the product of the two increases : (14 / 10) * (14 / 10) which is 1.96 and a 96 % increase . e"""
Provide a detailed solution to the given mathematical problem.,"if the least common addition of two prime numbers x and y is 36 , where x < y , then the value of 4 x + y is a) 32 , b) 45 , c) 59 , d) 73 , e) 87",(x + y) = 36 and both x an y are prime . the only values of x and y can be 17 and 19 (x = 17 and y = 19) 4 x + y = 4 * 17 + 19 = 87 correct option : e
"Solve the problem systematically, showing each step clearly.","if the area of a circle is 36 pi square feet , find its circumference . a) 65 pi feet , b) 43 pi feet , c) 12 pi feet , d) 18 pi feet , e) 64 pi feet","""the area is given by pi * r * r . hence pi * r * r = 81 pi r * r = 36 ; hence r = 36 feet the circumference is given by 2 * pi * r = 2 * pi * 6 = 128 pi feet correct answer c"""
Explain the solution process for the given equation.,"a train 300 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ? a) 32 , b) 48 , c) 29 , d) 27 , e) 21","""s = (300 + 300) / 45 = 600 / 45 * 18 / 5 = 48 answer : b"""
Provide a detailed solution to the given mathematical problem.,"what is the remainder when 3 ^ 381 is divided by 5 ? a) 0 , b) 1 , c) 2 , d) 3 , e) 4",i also agree that the remainder is' 3' (using the last digit of the powers of 7) . could we have the official answer please ? d
Break down and solve the equation step by step.,"from a vessel on the first day , 1 / 3 rd of the liquid evaporates . on the second day 3 / 4 th of the remaining liquid evaporates . what fraction of the volume is present at the end of the 2 day a) 1 / 3 , b) 1 / 4 , c) 1 / 5 , d) 1 / 6 , e) 1 / 7",let x be the volume . . . after 1 st day volume remaining = (x - x / 3) = 2 x / 3 after 2 st day volume remaining = (2 x / 3) - ((2 x / 3) * (3 / 4)) = (2 x / 3) (1 - 3 / 4) = (2 x / 3) * (1 / 4) = x / 6 answer : d
"Solve the problem systematically, showing each step clearly.","there is a right angle triangle inside a circle of diameter 18 cm . inside this triangle , there is another circle of diameter 6 cm . find the perimeter of the triangle . ['a) 24 cm','b) 36 * 2 ^ 1 / 2 cm','c) 36 cm','d) 54 cm','e) 42 cm']",1) the radius of the incircle of a right triangle with legs a and b and hypotenuse c is r = (a + b - c) / 2 2) the radius of the circumcircle is half the length of the hypotenuse r = c / 2 3) thus the sum of the circumradius and the inradius is half the sum of the legs r + r = (a + b) / 2 from 2 nd rule c = 18 cm from 3 rd rule a + b = 2 * (9 + 3) = 24 cm hence perimeter a + b + c = 24 + 18 = 42 cm answer : e
"Work through the equation methodically, ensuring clarity at each step.","a store owner estimates that the average price of type a products will increase by 25 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ? a) $ 14,755 , b) $ 15,325 , c) $ 16,000 , d) $ 16,225 , e) $ 17,155","""cost of type a products next year = 1.25 * 4500 = 5625 cost of type b products next year = 1.1 * 8300 = 9130 total 5625 + 9130 = 14755 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 82 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? a) 63 . , b) 73 . , c) 81 , d) 91 , e) 108","""total students = 420 boys = 312 , girls = 108 total playing soccer = 250 82 % of 250 = 205 are boys who play soccer . girls who play soccer = 45 . total girls who do not play soccer = 108 - 45 = 63 . correct option : a"""
"Work through the equation methodically, ensuring clarity at each step.","what is the remainder when 46 * 49 is divided by 8 ? a) 1 , b) 3 , c) 4 , d) 6 , e) 7","""we can make use of the rule : remainder of { (a * b) / n } } = remainder of (a / n) * remainder of (b / n) here remainder of { 46 * 49) / 8 } } = remainder of (46 / 8) * remainder of (49 / 8) = 6 * 1 = 6 answer : d"""
Explain the solution process for the given equation.,"a and b started a business investing rs . 10,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ? a) 3 : 2 , b) 9 : 2 , c) 18 : 20 , d) 1 : 2 , e) 18 : 4","""a : b = 10000 : 20000 = 1 : 2 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 153 grams of water ? a) 16 , b) 72 , c) 112 , d) 136 , e) 142","""since the ratio , by mass , of hydrogen to oxygen is 2 : 16 , then oxygen is 16 / (2 + 16) = 8 / 9 of mass of water . therefore there are 153 * 8 / 9 = 136 grams of oxygen in 153 grams of water . answer : d ."""
Provide a detailed solution to the given mathematical problem.,"the sum of three consecutive even numbers is 24 . find the middle number of the three ? a) 14 , b) 16 , c) 18 , d) 24 , e) 34","""three consecutive even numbers (2 p - 2) , 2 p , (2 p + 2) . (2 p - 2) + 2 p + (2 p + 2) = 24 6 p = 24 = > p = 4 . the middle number is : 4 p = 16 . answer : b"""
"Solve the problem systematically, showing each step clearly.","machine t takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine t to make 40 widgets ? a) 5 , b) 6 , c) 8 , d) 10 , e) 12","i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of t is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and t reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of t . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer"
"Solve the problem systematically, showing each step clearly.","a person x working alone can complete a work in 5 days . a person y completes the same amount of work in 20 days , and a person z when working alone can complete the same amount of work in 30 days . all 3 people work together for 2 days but then x and y leave . how many more days does z need to complete the work after x and y leave ? a) 13 , b) 14 , c) 15 , d) 16 , e) 17",the fraction of work completed in two days is 2 / 5 + 2 / 20 + 2 / 30 = 17 / 30 the fraction of work remaining is 1 - 17 / 30 = 13 / 30 the number of days required for z is 13 days . the answer is a .
"Work through the equation methodically, ensuring clarity at each step.","walking 3 / 2 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ? a) 12 , b) 99 , c) 27 , d) 28 , e) 20","""speed ratio = 1 : 3 / 2 = 2 : 3 time ratio = 3 : 2 1 - - - - - - - - 3 4 - - - - - - - - - ? 12 m . answer : a"""
"Solve the problem systematically, showing each step clearly.","1907 x 1907 = ? a) a) 3623216 , b) b) 3624216 , c) c) 3624316 , d) d) 3636649 , e) e) 3625216","""1907 x 1907 = (1907) 2 = (1900 + 7) 2 = (1900) 2 + (7) 2 + (2 x 1900 x 7) = 3610000 + 49 + 26600 . = 3636649 . d)"""
Break down and solve the equation step by step.,"a pizzeria in castroville creates its own special blend of shredded cheese at a cost of $ 696.05 per kilogram . the blend includes mozzarella , at $ 504.35 per kilogram , and romano cheese , at $ 887.75 per kilogram . if the employees have already shredded 19 kilograms of mozzarella cheese , how many kilograms of romano cheese will they need to shred now ? a) 19 kg , b) 13 kg , c) 10 kg , d) 23 kg , e) 15 kg","504.35 (19) + 887.75 x = 696.05 (19 + x) solve the equation . 504.35 (19) + 887.75 x = 696.05 (19 + x) 9 , 582.65 + 887.75 x = 13 , 224.95 + 696.05 x 9 , 582.65 + 191.7 x = 13 , 224.95 191.7 x = 3 , 642.3 x = 19 . answer is a ."
"Solve the problem systematically, showing each step clearly.","how many of the positive factors of 24 , 16 and how many common factors are there in numbers ? a) 1 , b) 2 , c) 3 , d) 4 , e) 5","""factors of 24 - 1 , 2 , 3 , 4 , 8 , 12 and 24 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 4 answer d"""
"Work through the equation methodically, ensuring clarity at each step.","according to a recent student poll , 3 / 4 out of 20 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ? a) 1 / 14 , b) 4 / 49 , c) 18 / 19 , d) 45 / 49 , e) 13 / 14","""15 students are interested , 5 are not interested prob = 1 - 5 c 2 / 20 c 2 = 1 - (5 * 4 / (20 * 19)) = 1 - 1 / 19 = 18 / 19 answer : c"""
Explain the solution process for the given equation.,"a 250 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ? a) 41.1 sec , b) 20.2 sec , c) 31.8 sec , d) 50.4 sec , e) none of the above","""speed = 55 km / hr (to convert km / hr in to m / s) = 55 x 5 / 18 m / s distance = 250 m + 520 m (if questions is about train crossing a post you need to consider only the length of train ,) = 770 m time = distance / speed = 770 x 18 / (5 x 55) = 50.4 sec ans is : d"""
Provide a detailed solution to the given mathematical problem.,"a train with 120 wagons crosses john who is going in the same direction , in 36 seconds . it travels for half an hour from the time it starts overtaking the john (he is riding on the horse) before it starts overtaking the mike (who is also riding on his horse) coming from the opposite direction in 24 seconds . in how much time (in secs) after the train has crossed the mike do the john meets to mike ? a) 3576 s , b) 3589 s , c) 3596 s , d) 3598 s , e) 3576 s","""let the length of the train be l metres and speeds of the train arun and sriram be r , a and s respectively , then - - - - - - - - - - (i) and - - - - - - - - - (ii) from eq . (i) and (ii) 3 (r - a) = 2 (r + k) r = 3 a + 2 k in 30 minutes (i . e 1800 seconds) , the train covers 1800 r (distance) but the arun also covers 1800 a (distance) in the same time . therefore distance between arun and sriram , when the train has just crossed sriram = 1800 (r - a) - 24 (a + k) time required = = (3600 - 24) = 3576 s e"""
"Work through the equation methodically, ensuring clarity at each step.","the sum of 111 consecutive integers is 11211 . what is the greatest integer in the set ? a) 148 , b) 150 , c) 152 , d) 154 , e) 156","""let x be the first integer in the set , then x + 110 is the largest integer . the sum is : x + (x + 1) + (x + 2) + . . . + (x + 110) = 111 x + 110 * 111 / 2 = 111 (x + 55) then x + 55 = 101 x = 46 the largest integer in the set is 46 + 110 = 156 the answer is e ."""
Break down and solve the equation step by step.,"in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability e this college graduate has a graduate degree ? a) 1 / 11 , b) 1 / 12 , c) 1 / 13 , d) 3 / 19 , e) 3 / 43","in believe the answer is d . please see below for explanation . 0) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability e of cgd / (cg) - > 3 / 19 answer d"
"Work through the equation methodically, ensuring clarity at each step.","a small college reduced its faculty by approximately 13 percent to 195 professors . what was the original number of faculty members ? a) 182 , b) 208 , c) 224 , d) 254 , e) 302","""f x is the original number of faculty members , then after 13 % reduction in faculty members number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of faculty members is 224 correct answer - c"""
Break down and solve the equation step by step.,"when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 7 , the remainder is 6 . how many values less than 100 can n take ? a) 0 , b) 2 , c) 3 , d) 6 , e) 5","""a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 (x - 1) = 7 y . . . so (x - 1) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as (29 - 1) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 6 . . d"""
"Work through the equation methodically, ensuring clarity at each step.","a car gets 32 miles to the gallon . if it is modified to use a solar panel , it will use only 80 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ? a) 84 , b) 88 , c) 92 , d) 96 , e) 100","originally , the distance the car could go on a full tank was 12 * 32 = 384 miles . after it has been modified , the car can go 32 / 0.8 = 40 miles per gallon . on a full tank , the car can go 12 * 40 = 480 miles , thus 96 miles more . the answer is d ."
Explain the solution process for the given equation.,"in a fuel station the service costs $ 2.30 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 4 mini - vans and 2 trucks , what will be the total cost , if a mini - van' s tank is 65 liters and a truck' s tank is 120 % bigger and they are all empty ? a) $ 396 , b) $ 400 , c) $ 404 , d) $ 408 , e) $ 412","""the service cost of 4 vans and 2 trucks is 6 * 2.30 $ 13.80 the fuel in 4 vans is 4 * 65 = 260 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel (vans + trucks) = 546 liters the total fuel cost is 546 * 0.7 = $ 382.20 the total cost is $ 382.20 + $ 13.80 = $ 396 the answer is a ."""
Explain the solution process for the given equation.,"in a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ? a) 30 , b) 35 , c) 40 , d) 45 , e) 50","""make a venn diagram , and enter your data . let the number of people who like only tennis be x x + 10 + 30 = 65 x = 25 so number who like tennis = 10 + 25 = 35 answer b"""
Provide a detailed solution to the given mathematical problem.,"rajat , vikas and abhishek are submitting questions in the ratio 7 : 3 : 2 . if total number of questions submitted by them is 24 . find the number of questions submitted by vikas . a) 3 , b) 4 , c) 5 , d) 6 , e) 7",explanation : number of questions submitted by vikas = (24 * 3) / (7 + 3 + 2) = 6 answer : d
Explain the solution process for the given equation.,"how many times in a day , the hands of a clock are straight ? a) 22 , b) 24 , c) 44 , d) 48 , e) 52","""in 12 hours , the hands coincide or are in opposite direction 22 times . in 24 hours , the hands coincide or are in opposite direction 44 times a day . answer : option c"""
"Work through the equation methodically, ensuring clarity at each step.","12,21 , 48,87 , __ a) 176 , b) 186 , c) 184 , d) 174 , e) 164","""21 = 12 * 2 - 3 48 = 21 * 2 + 6 87 = 48 * 2 - 9 so next number is 87 * 2 + 12 = 186 answer : b"""
Provide a detailed solution to the given mathematical problem.,"x varies inversely as square of y . given that y = 2 for x = 1 . the value of x for y = 6 will be equal to : a) 1 / 2 , b) 1 / 3 , c) 1 / 5 , d) 1 / 9 , e) 1 / 3","""given x = k / y 2 , where k is a constant . now , y = 2 and x = 1 gives k = 4 . x = 4 / y 2 = > x = 4 / 62 , when y = 6 = > x = 4 / 36 = 1 / 9 . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","if the sum of the 4 th term and the 12 th term of an arithmetic progression is 8 , what is the sum of the first 15 terms of the progression ? a) 60 , b) 120 , c) 160 , d) 240 , e) 840","""let a = first term , d = common difference . 4 th term = a + 3 d 12 th term = a + 11 d a + 3 d + a + 11 d = 8 2 a + 14 d = 8 a + 7 d = 4 . sum of the first 15 terms = 15 / 2 (2 a + 14 d) = 15 (a + 7 d) = 15 (4) = 60 . ans (a)"""
"Work through the equation methodically, ensuring clarity at each step.","pipe a fills a tank of capacity 900 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ? a) 42 minutes , b) 14 minutes , c) 54 minutes , d) 40 minutes 20 seconds , e) none of these","""in one cycle they fill 40 + 30 - 20 = 50 liters 900 = 50 * n = > n = 18 here n = number of cycles . total time = 18 * 3 = 54 as in one cycle there are 3 minutes . thus 54 minutes answer : c"""
Provide a detailed solution to the given mathematical problem.,"in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 70 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ? a) 2 % , b) 4 % , c) 8 % , d) 10 % , e) 15 %","since we were expected to find a percentage figure - it thought that it might be easier to pick a' smart number' to represent the total number of voters (republicans and democrats) . therefore , i picked 100 (as the total number of voters) and thus 60 : 40 represents the number ratio of republicans : democrats . if 70 % of republicans (which is (60 * 0.7) = 42) and 25 % of democrats (40 * 0.25 = 10) voted for candidate x , means that out of total of 100 voters ; 52 (42 + 10) voters voted for candidate x and 48 voted for candidate y . thus we can infer that candidate x is expected to win the election by 4 (52 - 48) votes . therefore candidate x is expected to win the election by (4 / 100) votes which is equivalent to 4 % . i think the answer is b ."
"Work through the equation methodically, ensuring clarity at each step.","by weight , liquid x makes up 0.7 percent of solution p and 1.2 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ? a) 1.2 % , b) 1.1 % , c) 1.0 % , d) 0.9 % , e) 0.8 %","""the number of grams of liquid x is 0.7 (200) / 100 + 1.2 (800) / 100 = 1.4 + 9.6 = 11 grams . 11 / 1000 = 1.1 % the answer is b ."""
"Solve the problem systematically, showing each step clearly.","a cab driver 5 days income was $ 400 , $ 250 , $ 650 , $ 400 , $ 500 . then his average income is ? a) $ 400 , b) $ 420 , c) $ 440 , d) $ 460 , e) $ 480","""avg = sum of observations / number of observations avg income = (400 + 250 + 650 + 400 + 500) / 5 = 440 answer is c"""
Break down and solve the equation step by step.,"the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 8 months , find for how much time did q invest the money ? a) 11 , b) 10 , c) 18 , d) 16 , e) 12","""7 * 5 : 8 * x = 7 : 10 x = 16 answer : d"""
"Solve the problem systematically, showing each step clearly.","one pipe can fill a tank four times as fast as another pipe . if together the two pipes can fill the tank in 40 minutes , then the slower pipe alone will be able to fill the tank in ? a) 100 min , b) 150 min , c) 200 min , d) 250 min , e) 300 min","""let the slower pipe alone fill the tank in x minutes then , faster pipe will fill it in x / 4 minutes 1 / x + 4 / x = 1 / 40 5 / x = 1 / 40 x = 200 min answer is c"""
"Work through the equation methodically, ensuring clarity at each step.","if m and n are positive integers and m ^ 2 + n ^ 2 = 58 , what is the value of m ^ 3 + n ^ 3 ? a) 72 , b) 224 , c) 370 , d) 512 , e) 1,600","""you need to integers which squared are equal 58 . which could it be ? let' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 stop . the integers ca n' t be greater than 7 or we will score above 58 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 the only pair that matches is 7 ^ 2 + 3 ^ 2 = 58 . so 7 ^ 3 + 3 ^ 3 = 370 . answer c .)"""
Break down and solve the equation step by step.,"an aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 1 hours , it must travel at a speed of : a) 300 kmph , b) 360 kmph , c) 600 kmph , d) 720 kmph , e) 750 kmph","""explanation : distance = (240 x 5) = 1200 km . speed = distance / time speed = 1200 / (5 / 3) km / hr . required speed = (1200 x 3 / 5) km / hr = 720 km / hr . answer is d"""
Explain the solution process for the given equation.,"n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken for singing song , find n ['a) 11','b) 12','c) 13','d) 14','e) 15']","each of 2 present in the party = > no . of pairs possible = nc 2 possible adjacent pairs = n total required combinations = nc 2 - n time taken by each combination to sing a song = 2 min total time taken = 2 (nc 2 - n) = 28 on solving the above equation , we get n = 14 answer : d"
"Work through the equation methodically, ensuring clarity at each step.","what is the greatest positive integer n such that 3 ^ n is a factor of 54 ^ 100 ? a) 100 , b) 200 , c) 300 , d) 600 , e) 900","""54 = 3 ^ 3 * 2 . 54 ^ 100 = 3 ^ 300 * 2 ^ 100 the answer is c ."""
"Solve the problem systematically, showing each step clearly.","half a number plus 5 is 13 . what is the number ? a) 8 , b) 16 , c) 10 , d) 11 , e) 12","""let x be the number . always replace ` ` is'' with an equal sign (1 / 2) x + 5 = 13 (1 / 2) x = 13 - 5 (1 / 2) x = 8 x = 16 correct answer is b"""
"Solve the problem systematically, showing each step clearly.","a man is walking at a speed of 6 km per hour . after every km he takes rest for 6 minutes . how much time will he take to cover a distance of 12 km . a) 3 hr , b) 5 hr 42 min , c) 4 hrs . 10 min , d) 3 hr . 6 min , e) none of these","""explanation : for 12 km he takes 11 times rest . 11 x 6 = 66 minutes rest = 1 hr 6 min for 12 km , 2 hr is required + rest = 2 + 1 hr 6 m = 3 hr . 6 min answer : option d"""
"Solve the problem systematically, showing each step clearly.","s (n) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s (1) = 1 , s (2) = 14 , s (3) = 149 , s (4) = 14916 , s (5) = 1491625 , etc . how many digits w are in s (99) ? a) w = 350 , b) w = 353 , c) w = 354 , d) 356 , e) 357","""focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s (99) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"""
Break down and solve the equation step by step.,"if a large pizza has a radius that is 40 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ? a) 40 % , b) 80 % , c) 96 % , d) 112 % , e) 124 %","let the radius of medium pizza be r . then the radius of large pizza is 1.4 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * (1.4 * r) ^ 2 = 1.96 * pi * r ^ 2 , an increase of 96 % . the answer is c ."
Explain the solution process for the given equation.,"a school has received 40 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ? a) $ 200 , b) $ 177.78 , c) $ 100 , d) $ 277.78 , e) $ 77.78","""let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > (3 / 5) x people already solicited = 40 % of t = > (2 / 5) t now , as per the information given in the question : (3 / 5) x = $ 400 . (2 / 5) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e (2 / 5) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e (3 / 5) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is (2 / 5) x = (amount required) . (3 / 5) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 77.78 e"""
Explain the solution process for the given equation.,"in feb mrs bil' s earnings were 70 percent of the bil family' s total income . in june mrs bil earned 10 percent more than in may . if the rest of the family' s income was the same both months , then , in june , mrs bil' s earnings were approximately what percent of the bil family' s total income ? a) 72 , b) 34 , c) 78 , d) 37 , e) 27","lets say the family income is 100 in may , bil earned 70 family income is 30 in june , bil earned 10 % more than may , so it is (70 + 10 * 70 / 100 = 77) family income is same 30 in june bil' s income percent is 77 * 100 / 107 ~ 72 ans is a"
Break down and solve the equation step by step.,"the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 440 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office . a) 400 , b) 420 , c) 480 , d) 450 , e) 510","""let no . of non - officers be x 15 * 440 + x * 110 = (x + 15) 120 x = 480 c"""
Explain the solution process for the given equation.,"a 30 % alcohol mixture is added to a 50 % alcohol mixture to form a 10 litre mixture of 45 % alcohol . how much of the 30 % mixture was used ? a) 1.5 liters , b) 2.5 liters , c) 3.5 liters , d) 4.5 liters , e) 5.5 liters",solution a = 50 % solution solution b = 30 % solution 30 % - 45 % = 15 % solution b 50 % - 45 % = 5 % solution a so the ratio is 3 : 1 for 30 % : 50 % solutions 3 / 4 * 10 liter = 7.5 for 30 % solution and 2.5 for 50 % solution . . answer : b
"Solve the problem systematically, showing each step clearly.","two numbers are in the ratio of 5 : 7 . if 20 is subtracted from each number , they are in the ratio of 5 : 9 . what are the two numbers ? a) 35 , 49 , b) 40 , 56 , c) 45 , 63 , d) 50 , 70 , e) 55 , 77","""(5 x - 20) : (7 x - 20) = 5 y : 9 y 5 x - 20 = 5 y 7 x - 20 = 9 y 140 - 100 = 45 y - 35 y 40 = 10 y y = 4 5 x - 20 = 20 x = 8 the two numbers are 5 x and 7 x which are 40 and 56 . the answer is b ."""
Break down and solve the equation step by step.,"mother , her daughter and her grand child weighs 160 kg . daughter and her daughter (child) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ? a) 46 , b) 47 , c) 48 , d) 49 , e) 40","""mother + daughter + child = 160 kg daughter + child = 60 kg mother = 160 - 60 = 100 kg child = 1 / 5 th of mother = (1 / 5) * 100 = 20 kg so now daughter = 120 - (mother + child) = 160 - (100 + 20) = 40 kg answer : e"""
Provide a detailed solution to the given mathematical problem.,"running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 10 machines produce in 6 minutes ? a) 1344 , b) 4200 , c) 8400 , d) 50400 , e) 67200",8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 10 machine produce 560 * 6 * (10 / 8) in 6 minutes 560 * 6 * 10 / 8 = 4200 answer is b .
"Solve the problem systematically, showing each step clearly.","a train length 100 m going with speed 10 m / sec another train 150 m long going with speed 15 m / sec . the distance between two train is 50 m . then how much time second train will take to cross the first train ? a) 60 sec , b) 40 sec , c) 30 sec , d) 45 sec , e) 1 min 10 sec",net speed = 15 - 10 = 5 m / sec net distance = 100 + 150 + 50 = 300 total time = 300 / 5 = 60 sec answer a
Break down and solve the equation step by step.,"a quiz has one mcq question with a , b and c as options . and two questions with true / false answers . what is the probability of giving all 3 answers correct ? a) 1 / 12 , b) 1 / 3 , c) 1 / 4 , d) 1 / 2 , e) 1 / 6",probability of getting mcq answer correct = 1 / 3 probability of getting one true / false answer correct = 1 / 2 probability of getting all 3 answers correct = 1 / 3 * 1 / 2 * 1 / 2 = 1 / 12 answer : a
Break down and solve the equation step by step.,"a merchant has selected two items to be placed on sale , one of which currently sells for 25 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ? a) 52 % , b) 40 % , c) 30 % , d) 20 % , e) 10 %","""expensive item = $ 100 ; cheap item = $ 75 ; we must increase $ 75 to $ 100 , so by $ 25 , which is approximately 30 % increase : (100 - 75) / 75 = 1 / 3 = ~ 0.33 answer : c ."""
"Work through the equation methodically, ensuring clarity at each step.","how much time will a train of length 300 m moving at a speed of 72 kmph take to cross another train of length 500 m , moving at 36 kmph in the same direction ? a) 50 , b) 80 , c) 88 , d) 76 , e) 12","""the distance to be covered = sum of their lengths = 300 + 500 = 800 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 800 / 10 = 80 sec . answer : b"""
Break down and solve the equation step by step.,"in a certain village , 150 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long (in months) will 6000 litres of water last ? a) 8 , b) 10 , c) 6 , d) 2 , e) 4","""i find it much easier to understand with real numbers , so choose (almost) any numbers to replace m , n and p : in a certain village , m 150 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long (in months) willp 2000 litres of water last ? water required is 150 * 10 = 1500 (m * n) water available is 6000 (p) it will last 4 months (p / m * n) ans : e"""
Explain the solution process for the given equation.,"x is a positive integer less than 100 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ? a) 14 , b) 22 , c) 23 , d) 24 , e) 25","""the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , (7 k + 1) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 (1) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + (n - 1) 21 = 100 n = 14.42 or n = 14 answer : - a"""
"Solve the problem systematically, showing each step clearly.","there were two candidates in an election . winner candidate received 75 % of votes and won the election by 500 votes . find the number of votes casted to the winning candidate ? a) 228 , b) 744 , c) 750 , d) 199 , e) 231","""w = 75 % l = 25 % 75 % - 25 % = 50 % 50 % - - - - - - - - 500 75 % - - - - - - - - ? = > 750 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","divide rs . 1800 among a , b and c so that a receives 2 / 5 as much as b and c together and b receives 1 / 5 as a and c together . a' s share is ? a) 400 , b) 500 , c) 375 , d) 450 , e) 600",a + b + c = 1800 a = 2 / 5 (b + c) ; b = 1 / 5 (a + c) a / (b + c) = 2 / 5 a = 1 / 6 * 3600 = > 600 answer : e
"Solve the problem systematically, showing each step clearly.","a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 270 metres long in 20 seconds . the length of the train (in metres) is : a) 180 , b) 176 , c) 175 , d) 96 , e) none of these","""explanation : let the length of train be l m . acc . to question (270 + l) / 20 = l / 8 2160 + 8 l = 20 l l = 2160 / 12 = 180 m answer a"""
Explain the solution process for the given equation.,"a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 1.5 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? (1 meter = 100 centimeters) a) 2 , 400,000 , b) 2 , 800,000 , c) 55,000 , d) 28,000 , e) 280","""let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 1.5 gms in 400,000 cm ^ 3 , x = 1.5 * 400,000 = 600,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 600,000 + 1 , 800,000 = 2 , 400,000 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","one woman and one man can build a wall together in four hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them eight hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ? a) 5 / 7 , b) 1 , c) 10 / 7 , d) 12 / 7 , e) 24 / 7","""solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 4 - - > (1) , w + 2 g = 1 / 4 - - > (2) and m + g = 1 / 8 - - > (3) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from (1) and (2) , m = 2 g and from (3) g = 1 / 24 , m = 1 / 12 and w = 1 / 6 . so , n = 1 / (7 / 24) = 24 / 7 option , e"""
"Work through the equation methodically, ensuring clarity at each step.","in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 160 girls , the total number of students in the college is ? a) 562 , b) 356 , c) 452 , d) 416 , e) 512","""let the number of boys and girls be 8 x and 5 x then , 5 x = 160 x = 32 total number of students = 13 x = 13 * 32 = 416 answer is d"""
"Solve the problem systematically, showing each step clearly.","in traveling from a dormitory to a certain city , a student went 1 / 2 of the way by foot , 1 / 4 of the way by bus , and the remaining 6 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ? a) 35 , b) 24 , c) 14 , d) 24 , e) 12","""whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 1 / 4 x + 6 x - 1 / 2 x - 1 / 4 x = 6 x = 24 km option : d"""
Break down and solve the equation step by step.,"in a factory there are 3 types of machine m 1 , m 2 and m which produces 25 % , 35 % and 40 % of the total products respectively . m 1 , m 2 and m 3 produces 2 % , 4 % and 5 % defective products , respectively . what is the percentage of non - defective products ? a) 89 % , b) 97.1 % , c) 96.1 % , d) 86.1 % , e) none of these","solution : non - defective products , { [ (25 * 0.98) + (35 * 0.96) + (40 * 0.95) ] / 100 } * 100 = 96.1 % . answer : option c"
Break down and solve the equation step by step.,"the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 4 . if the sum of their ages is 132 , what is the difference between the ages of patrick and monica ? a) 27 , b) 48 , c) 45 , d) 72 , e) 33",ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 132 x = 3 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 3 = 33 answer e
"Solve the problem systematically, showing each step clearly.","the sum of four consecutive even numbers is 140 . what would be the smallest number ? a) 32 , b) 88 , c) 70 , d) 123 , e) 12","""let the four consecutive even numbers be 2 (x - 2) , 2 (x - 1) , 2 x , 2 (x + 1) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 (x - 2) = 32 answer : a"""
"Solve the problem systematically, showing each step clearly.","if m is an integer such that (- 2) ^ 2 m = 2 ^ (3 - m) then m = ? a) 1 , b) 2 , c) 3 , d) 5 , e) 6","""(- 2) ^ (2 m) = 4 ^ m and 2 ^ (3 - m) = 4 ^ ((3 - m) / 2) therefore , m = (3 - m) / 2 2 m = 3 - m m = 1 answer a"""
"Work through the equation methodically, ensuring clarity at each step.","the difference between two parallel sides of a trapezium is 4 cm . perpendicular distance between them is 10 cm . if the area of the trapezium is 250 cm 2 find the lengths of the parallel side ['a) 27 , 23','b) 25 , 25','c) 24 , 26','d) 23 , 29','e) 24 , 45']","explanation : let the two parallel sides of the trapezium be a cm and b cm . then , a - b = 4 - - - - - - (1) and , (1 / 2) x (a + b) x 10 = 475 = > (a + b) = ((250 x 2) / 10) = > a + b = 50 - - - - - - - (2) solving 1 and 2 , we get : a = 27 , b = 23 so , the two parallel sides are 27 cm and 23 cm . answer : option a"
Explain the solution process for the given equation.,"x ^ y + y ^ x = 2408 find the values of x ? a) 2407 , b) 2408 , c) 2409 , d) 2405 , e) 32",2407 ^ 1 + 1 ^ 2407 = 2408 answer : a
Explain the solution process for the given equation.,"a child want to buy 5 new toys . if there are 15 toys that satisfy the child' s criteria , in how many different ways can the child select the 5 new toys if the order of selection does n' t matter . a) 210 , b) 1365 , c) 3003 , d) 5005 , e) 3030",the number of ways of choosing 5 toys out of 15 are counted by = 15 c 5 ways = 3003 answer : option c
"Work through the equation methodically, ensuring clarity at each step.","a shopkeeper buys two articles for rs . 1000 each and then sells them , making 20 % profit on the first article and 20 % loss on second article . find the net profit or loss percent ? a) 200 , b) 177 , c) 188 , d) 166 , e) 129","""profit on first article = 20 % of 1000 = 200 . answer : a"""
"Solve the problem systematically, showing each step clearly.","a man two flats for $ 675958 each . on one he gains 11 % while on the other he loses 11 % . how much does he gain or lose in the whole transaction ? a) 1.21 % , b) 2.56 % , c) 3.12 % , d) 4.65 % , e) 5.12 %","""in such a case there is always a loss loss % = (11 / 10) ^ 2 = 23 / 19 = 1.21 % answer is a"""
Explain the solution process for the given equation.,"the number 219 can be written as sum of the squares of 3 different positive integers . what is the difference of these 2 different larger integers ? a) 6 , b) 2 , c) 3 , d) 5 , e) 4","""sum of the squares of 3 different positive integers = 219 13 ^ 2 + 7 ^ 2 + 1 ^ 2 = 219 now , difference of these 2 different larger integers = 13 - 7 = 6 ans - a"""
Explain the solution process for the given equation.,"a milk man has 10 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : a) 20 % , b) 15 % , c) 33.33 % , d) 18 % , e) none of these","""explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 10 liters of milk . therefore , profit percentage = 15 % . answer : b"""
Explain the solution process for the given equation.,"if the price of gasoline increases by 20 % and a driver intends to spend only 8 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ? a) 4 % , b) 5 % , c) 6 % , d) 8 % , e) 10 %","""let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . (1.2 * p) y = 1.08 (p * x) y = (1.08 / 1.2) x = 0.9 x which is a reduction of 10 % . the answer is e ."""
Explain the solution process for the given equation.,"at a certain organisation , the number of male members went up by 12 % in the year 2001 from year 2000 , and the number of females members went down by 5 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ? a) 1 : 2 , b) 1 : 3 , c) 2 : 3 , d) 3 : 2 , e) 4 : 7","""men increase by 12 % = = > 1.12 m = males in 2001 women decrease by 5 % = = > 0.95 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * (m + f) = total number of employees in 2001 obviously (males in 2001) + (females in 2001) = total number of employees in 2001 1.12 m + 0.95 f = 1.012 * (m + f) 1.12 m + 0.95 f = 1.012 m + 1.012 f 1.12 m - 1.012 m = 1.012 f - 0.95 f 0.108 m = 0.062 f m / f = (0.062) / (0.108) = 62 / 108 = 4 / 7 answer = (e)"""
Break down and solve the equation step by step.,"in what time will a train 100 meters long cross an electric pole , if its speed is 360 km / hr a) 1 second , b) 4.5 seconds , c) 3 seconds , d) 2.5 seconds , e) none of these","""explanation : first convert speed into m / sec speed = 360 * (5 / 18) = 100 m / sec time = distance / speed = 100 / 100 = 1 second answer : a"""
Break down and solve the equation step by step.,"30 ^ 10 / 90 ^ 5 = ? a) 6 ^ 5 , b) 5 ^ 6 , c) 3 ^ 6 , d) 10 ^ 5 , e) 15 ^ 3","""30 ^ 10 / 90 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . 3 ^ 6 d . 10 ^ 5 e . 15 ^ 3 - > 30 ^ 10 / 90 ^ 5 = (30 ^ 10) / (3 ^ 5) (30 ^ 5) = (30 ^ 5) / (3 ^ 5) = (3 ^ 5) (10 ^ 5) / (3 ^ 5) = 10 ^ 5 . thus , d is the answer ."""
Provide a detailed solution to the given mathematical problem.,"two airplanes fly the same exact route from atlanta to chicago . plane a flies 200 mph while plane b flies 300 mph (assume that simple model versus actual acceleration / deceleration near the airports) . if plane a took off exactly 40 minutes before plane b , after how many minutes will plane b overtake plane a ? a) 65 , b) 80 , c) 90 , d) 115 , e) 120","we can use some form of the equation d = rt [ distance = rate * time ] rate of plane a : 200 mph rate of plane b : 300 mph plane a will be in the sky 40 minutes longer than plane b (2 / 3 of an hour) time of plane a when b overtakes it : t + (2 / 3) use 2 / 3 of an hour since the rate is in hours time of plane b when b overtakes a : t at the time that b overtakes a , they will have travelled the same distance so rt is equal for each plane : 200 * (t + 2 / 3) = 300 * t 200 t + 400 / 3 = 300 t 400 / 3 = 100 t 4 / 3 = t this is 1 and a third hour , so 60 minutes + 20 minutes = 80 minutes b"
"Solve the problem systematically, showing each step clearly.","a , b and c have rs . 450 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ? a) a) 100 , b) b) 110 , c) c) 120 , d) d) 130 , e) e) 140","""a + b + c = 450 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 450 - - - - - - - - - - - - - - - - c = 100 answer : a"""
Explain the solution process for the given equation.,"there are 600 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ? a) 100 , b) 200 , c) 250 , d) 300 , e) 400","""there are 594 managers and 6 others . the 6 others would compose 2 % of the total number of people if there were 300 people in the room . thus 300 managers must leave . the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"a group of 4 investment bankers and 5 clients recently frequented the bonbon ribs restaurant . the total bill for the meal , including 20 % gratuity , came to $ 756 . on average , how much did the meal of each individual cost before gratuity ? a) $ 160 , b) $ 70 , c) $ 90 , d) $ 80 , e) $ 55","4 ibs and 5 clients - so total 9 people the bill $ 756 includes 20 % gratuity . . . so the actual cost of dinner was $ 630 now , the cost per person will be $ 630 / 9 which is $ 70 option b"
"Work through the equation methodically, ensuring clarity at each step.","if a - b = 3 and a (power 2) + b (power 2) = 21 , find the value of ab . a) 5 , b) 8 , c) 4 , d) 6 , e) 3","""2 ab = (a (power 2) + b (power 2) - (a - b) (power 2) = 21 - 9 = 12 ab = 6 . answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","worker a takes 10 hours to do a job . worker b takes 15 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ? a) 40 days , b) 40 / 9 days , c) 39 / 9 days , d) 6 days , e) 60 / 9 days","""a' s one hour work = 1 / 10 . b' s one hour work = 1 / 15 . (a + b)' s one hour work = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 . both a & b can finish the work in 6 days d"""
Break down and solve the equation step by step.,"a person is traveling at 100 km / hr and reached his destiny in 5 then find the distance ? a) 250 km , b) 300 km , c) 500 km , d) 450 km , e) 350 km","""t = 5 hr s = 100 km / hr d = t * s = 100 * 5 = 500 km answer is c"""
Break down and solve the equation step by step.,"what is the difference between the largest and the smallest number written with 7 , 7 , 0 , 7 ? a) 6893 , b) 6993 , c) 6093 , d) 693 , e) none","""7770 7077 - - - - - - - - - - - - - 693 answer : d"""
Explain the solution process for the given equation.,"a chemical supply company has 60 liters of a 25 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ? a) 12 , b) 15 , c) 20 , d) 24 , e) 30","""60 liters of a 25 % hno 3 solution means hno 3 = 15 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 15 + x = 50 % of (60 + x) or x = 30 . hence , e"""
"Work through the equation methodically, ensuring clarity at each step.","find the lowest common multiple of 25 , 35 and 50 . a) 350 , b) 420 , c) 510 , d) 320 , e) 280",lcm = 2 * 5 * 5 * 7 = 350 . answer is a
"Solve the problem systematically, showing each step clearly.","find the average of all the numbers between 40 and 80 which are divisible by 3 . a) 15 , b) 70 , c) 20 , d) 60 , e) none","""sol . average = (42 + 45 + 48 + 51 + 54 + 57 + 60 + 63 + 66 + 69 + 72 + 75 + 78 / 13) = 780 / 5 = 60 . answer d"""
"Solve the problem systematically, showing each step clearly.","arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ? a) 2 . , b) 4 . , c) 5 . , d) 7 . , e) 9 .","""ad = (a + 1) (d + 1) - 11 0 = a + d - 10 a + d = 10 a = d (as they are twin brothers) a = d = 5 c is the answer"""
Break down and solve the equation step by step.,"a classroom has equal number of boys and girls . 8 girls left to play kho - kho , leaving twice as many boys as girls in the classroom . what was the total number of girls and boys present initially ? a) 16 , b) 24 , c) 32 , d) 48 , e) 54",after 8 girls left remaining 8 girls now boys 16 are twice as many as remaining girls . initially boys = 16 and girls = 16 . answer : c
Break down and solve the equation step by step.,"nd the area of trapezium whose parallel sides are 20 cm and 15 cm long , and the distance between them is 14 cm ? a) 230 cm 2 , b) 245 cm 2 , c) 255 cm 2 , d) 260 cm 2 , e) 280 cm 2","""area of a trapezium = 1 / 2 (sum of parallel sides) * (perpendicular distance between them) = 1 / 2 (20 + 15) * (14) = 245 cm 2 answer : b"""
Provide a detailed solution to the given mathematical problem.,"if a certain toy store' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 5 of its revenue in november , then the store' s revenue in december was how many times the average (arithmetic mean) of its revenues in november and january ? a) 5 / 2 , b) 10 / 3 , c) 15 / 4 , d) 25 / 3 , e) 25 / 6","""n = 2 d / 5 j = n / 5 = 2 d / 25 the average of november and january is (n + j) / 2 = 12 d / 25 / 2 = 6 d / 25 d is 25 / 6 times the average of november and january . the answer is e ."""
Break down and solve the equation step by step.,"a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 2640 in all from both of them as interest . the rate of interest per annum is ? a) 16 % , b) 12 % , c) 74 % , d) 10 % , e) 45 %","""let the rate be r % p . a . then , (5000 * r * 2) / 100 + (3000 * r * 4) / 100 = 2640 100 r + 120 r = 2640 r = 12 % answer : b"""
"Solve the problem systematically, showing each step clearly.","an empty wooden vessel weighs 16 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled . a) 3 / 5 , b) 5 / 9 , c) 1 / 24 , d) 4 / 9 , e) 7 / 15","""an empty wooden vessel weighs 16 % of its total weight when filled with paint : vessel = 0.16 (vessel + paint) ; 16 v = v + p (so the weight of completely filled vessel is 16 v) p = 15 v (so the weight of the paint when the vessels is completely filled is 15 v) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p' = 1 / 2 * 16 v ; p' = 7 v (so the weight of the paint when the vessels is partially filled is 7 v) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p' / p = 7 v / 15 v = 7 / 15 . answer : e ."""
"Solve the problem systematically, showing each step clearly.","a regular hexagon is there . the mid points of the sides were joined and formed another hexagon . then what is the percentage reduction in area . a) 25 % , b) 35 % , c) 45 % , d) 55 % , e) 65 %",let abcdef be the regular hexagon with sides ab and ed parallel . p and q are mid points of af and ef resp . ae = root (3) * s (s is side of hexagon) then pq = (root (3) * s) / 2 mid point theorem now u know side of inner hexagon use formula area of hexagon = (3 * root (3)) 2 * s ^ 2 and find diff in area of two hexagon multiply by 100 and divide the product by area of bigger hexagon ans 25 % answer : a
Provide a detailed solution to the given mathematical problem.,"in what ratio should a variety of rice costing rs . 4.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ? a) 5 / 6 , b) 5 / 9 , c) 5 / 1 , d) 5 / 3 , e) 5 / 12","""let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = (8.75 - 7.50) / (7.50 - 4.5) = 5 / 12 answer : e"""
Provide a detailed solution to the given mathematical problem.,"a sum of money at simple interest amounts to 815 in 3 years and to 854 in 4 years . the sum is : a) 698 , b) 387 , c) 373 , d) 593 , e) 372","""a 698 s . i . for 1 year = (854 - 815) = 39 . s . i . for 3 years = (39 x 3) = 117 . principal = (815 - 117) = 698 ."""
"Work through the equation methodically, ensuring clarity at each step.","claire has a total of 92 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ? a) 39 , b) 68 , c) 54 , d) 57 , e) 60","""g + h = 92 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 92 - h or 3 (92 - h) + 4 h = 300 h = 300 - 276 = 24 then g = 92 - 24 = 68 b"""
Explain the solution process for the given equation.,"100 people are attending a newspaper conference . 40 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ? a) 21 , b) 24 , c) 28 , d) 30 , e) 32","""{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 40 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 40 + { editors } - x + 2 x - - > x = 60 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 60 - 39 = 21 . answer : a ."""
Provide a detailed solution to the given mathematical problem.,"a sum of money at simple interest amounts to rs . 1072 in 2 years and to rs . 1144 in 4 years . the sum is : a) rs . 1000 , b) rs . 850 , c) rs . 500 , d) rs . 1200 , e) rs . 900","""s . i . for 2 years = rs . (1144 - 1072) = rs . 72 . s . i . for 1 year = rs . 72 / 2 = rs . 36 . principal = rs . (1072 - 72) = rs . 1000 . answer : option a"""
"Work through the equation methodically, ensuring clarity at each step.","the average of the marks of 12 students in a class is 36 . if the marks of each student are doubled , find the new average ? a) 72 , b) 23 , c) 29 , d) 26 , e) 13","""sum of the marks for the 12 students = 12 * 36 = 432 . the marks of each student are doubled , the sum also will be doubled . the new sum = 432 * 2 = 864 . so , the new average = 864 / 12 = 72 . answer : a"""
Provide a detailed solution to the given mathematical problem.,"walking at 5 / 6 of its usual speed , a train is 10 minutes too late . what is usual time to cover the journey ? a) 70 minutes , b) 2 hours , c) 2 / 3 hours , d) 5 / 6 hours , e) 85 minutes","""et speed be s and time to cover the journey be t s * t = d (distance of journey) - - - 1 now as per the question stem we have (5 / 6) s * (t + 10) = d - - - - 2 equating value of d from (1) in (2) we get t = 50 mins or 5 / 6 hrs . answer : d"""
Provide a detailed solution to the given mathematical problem.,"a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 3000 more than d , what is b' s share ? a) a) 8239 , b) b) 2900 , c) c) 6000 , d) d) 2393 , e) e) 2009","""let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 3000 = > x = 3000 . b' s share = rs . 2 x = 2 * 3000 = rs . 6000 . answer : c"""
"Solve the problem systematically, showing each step clearly.","multiplication of 2 numbers is 9375 and the quotient , when the larger one is divided by the smalleris 15 . find the sum of the numbers ? a) 200 , b) 300 , c) 400 , d) 500 , e) 600","let the numbers be x and y . then , xy = 9375 and x = 15 . y xy = 9375 (x / y) 15 y 2 = 625 . y = 25 . x = 15 y = (15 x 25) = 375 . sum of the numbers = x + y = 375 + 25 = 400 . c"
Explain the solution process for the given equation.,"roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 6 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ? a) 22 km , b) 20 km , c) 65 km , d) 18 km , e) 36 km","distance = relative speed * time = (6 + 3) * 4 = 36 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : e"
Provide a detailed solution to the given mathematical problem.,"the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 384 meters , what is the width of the field ? a) 50 , b) 60 , c) 11 , d) 80 , e) 90","""let l be the length and w be the width . l = (7 / 5) w perimeter : 2 l + 2 w = 384 , 2 (7 / 5) w + 2 w = 384 solve the above equation to find : w = 80 m and l = 112 m . correct answer d) 80"""
Explain the solution process for the given equation.,"there are 6 more women than there are men on a local co - ed softball team . if there are a total of 24 players on the team , what is the ratio of men to women ? a) 10 / 16 , b) 9 / 15 , c) 4 / 16 , d) 6 / 10 , e) 4 / 10","""w = m + 6 w + m = 24 m + 6 + m = 24 2 m = 18 m = 9 w = 15 ratio : 9 : 15 ans : b"""
"Work through the equation methodically, ensuring clarity at each step.","if the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is ? a) 18 , b) 11.2 , c) 14 , d) 12 , e) 91","""2 * 22 / 7 * 15 * x = 1056 = > x = 11.2 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","look carefully for the pattern , and then choose which pair of numbers comes next . 28 25 5 21 18 5 14 a) 11 5 , b) 10 7 , c) 11 8 , d) 5 10 , e) 10 5","explanation : this is an alternating subtraction series with the interpolation of a random number , 5 , as every third number . in the subtraction series , 3 is subtracted , then 4 , then 3 , and so on . answer : option a"
Break down and solve the equation step by step.,"the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 6 ? a) 96 , b) 106 , c) 158 , d) 116 , e) 122","""average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 6 = 38 runs total runs = new avg x new no . of innings = 38 * 21 = 798 runs made in the 11 th inning = 798 - 640 = 158 answer : c"""
"Solve the problem systematically, showing each step clearly.","there are 9 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ? a) 24 , b) 25 , c) 28 , d) 32 , e) 36","""9 c 2 = 36 the answer is e"""
Break down and solve the equation step by step.,"if 60 % of (x - y) = 30 % of (x + y) then what percent of x is y ? a) 33 % , b) 10 % , c) 5 % , d) 15 % , e) 25 %","""60 % of (x - y) = 30 % of (x + y) (60 / 100) (x - y) = (30 / 100) (x + y) 6 (x - y) = 3 (x + y) 3 x = 9 y x = 3 y therefore required percentage = ((y / x) x 100) % = ((y / 3 y) x 100) = 33 % answer is a ."""
"Solve the problem systematically, showing each step clearly.","during a sale of 20 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies . the store still makes a profit of 10 % on this sale . what is the mark up percentage on each candy ? a) 100 % , b) 80 % , c) 75 % , d) 66 + 2 / 3 % , e) 55 %","""hi akhil , i can share the way i solved it . . let' s say marked price = m so , there' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . c"""
"Solve the problem systematically, showing each step clearly.","the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 49 . what is the rate of interest per annum ? a) 5 % , b) 6 % , c) 7 % , d) 8 % , e) 9 %",$ 49 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year' s interest is 10000 * x * x 10000 * x ^ 2 = 49 x = 0.07 the answer is c .
Provide a detailed solution to the given mathematical problem.,"from a container , 6 liters milk was drawn out and was replaced by water . again 6 liters of mixture was drawn out and was replaced by the water . thus the quantity of milk and water in the container after these two operations is 9 : 16 . the quantity of mixture is : a) 15 , b) 26 , c) 22 , d) 27 , e) 11","explanation : let quantity of mixture be x liters . suppose a container contains x units of liquid from which y units are taken out and replaced by water . after operations , the quantity of pure liquid = units , where n = no of operations . so , quantity of milk = given that , milk : water = 9 : 16 milk : (milk + water) = 9 : (9 + 16) milk : mixture = 9 : 25 answer : a) 15"
Break down and solve the equation step by step.,"how many 3 digit no' s are between 100 - 500 , where sum of two digit is 3 rd ? a) 24 , b) 54 , c) 60 , d) 84 , e) 94",total permutations possible = 18 + 16 + 14 + 12 = 60 answer : c
"Work through the equation methodically, ensuring clarity at each step.","a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 120 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello , so there are no pairs other than these 90) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ? a) 3 / 16,000 , b) 1 / 8,000 , c) 3 / 1,600 , d) 1 / 90 , e) 2 / 45","""solution provided by stanford 2012 is correct : 120 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 120 / 800 * 1 / 600 = 1 / 8,000 . answer : b ."""
Provide a detailed solution to the given mathematical problem.,"a tank is filled by 3 pipes a , b , c in 5 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ? a) 25 hr , b) 35 hr , c) 40 hr , d) 20 hr , e) 50 hr","""suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 5 7 / x = 1 / 5 x = 35 hours answer is b"""
"Work through the equation methodically, ensuring clarity at each step.","a sum of money lent out at s . i . amounts to rs . 780 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ? a) s . 684 , b) s . 500 , c) s . 540 , d) s . 740 , e) s . 840","""s . i for 5 years = (1020 - 780) = rs . 240 . s . i . for 2 years = 240 / 5 * 2 = rs . 96 . principal = (780 - 96) = rs . 684 answer : a"""
"Solve the problem systematically, showing each step clearly.","in expressing a length of 61.472 km as nearly as possible with the 3 significant digits , find the percentage error ? a) 0.35 % , b) 0.4 % , c) 0.045 % , d) 0.6 % , e) none of these",explanation : error = (61.5 - 61.472) = 0.028 required percentage = 0.028 / 61.472100 = 0.045 answer : c
Explain the solution process for the given equation.,"how many numbers from 49 to 79 are exactly divisible by 11 ? a) 5 , b) 7 , c) 9 , d) 3 , e) 12","""49 / 11 = 4 and 79 / 11 = 7 = = > 7 - 4 = 3 numbers answer : d"""
Provide a detailed solution to the given mathematical problem.,"a candidate got 25 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ? a) 7500 , b) 2028 , c) 2775 , d) 5496 , e) 8000","""25 % - - - - - - - - - - - l 75 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 50 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 8000 answer : e"""
Explain the solution process for the given equation.,"if 12 men or 20 women can do a piece of work in 27 days , then in how many days can 9 men and 12 women together do the work ? a) 10 days , b) 30 days , c) 20 days , d) 80 days , e) 40 days","""c 20 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 27 days . so , 27 women can do it in (20 * 27) / 27 = 20 days ."""
Provide a detailed solution to the given mathematical problem.,"a big container is 50 % full with water . if 20 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ? a) 80 , b) 90 , c) 100 , d) 110 , e) 120","""20 liters is 25 % of the capacity c . 20 = 0.25 c c = 80 liters . the answer is a ."""
Break down and solve the equation step by step.,"the sides of a triangle are in the ratio 3 : 5 : 7 . if the pereimeter is 60 cms , the longest side is a) 7 , b) 30 , c) 28 , d) 25 , e) 16","""3 x + 5 x + 7 x = 60 15 x = 60 x = 4 longest side = 7 * 4 = 28 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","a cylinder is inserted in a sphere d / h = 2 / 3 . find the surface area of the cylinder ? ['a) 23.12','b) 24.12','c) 25.12','d) 26.12','e) 27.12']","take r = 1 , h = 3 = 2 * 3.14 * r * r + 2 * 3.14 * r * h = 2 * 3.14 * r (r + h) = 2 * 3.14 * 1 (1 + 3) = 2 * 3.14 (4) = 25.12 answer : c"
Break down and solve the equation step by step.,"287 x 287 + 269 x 269 - 2 x 287 x 269 = ? a) 534 , b) 446 , c) 354 , d) 324 , e) none of them",= a ^ 2 + b ^ 2 - 2 ab where a = 287 and b = 269 = ( a - b ) ^ 2 = ( 287 - 269 ) ^ 2 = ( 18 ) ^ 2 = 324 answer is d
"Solve the problem systematically, showing each step clearly.","a small water pump would take 4 hours to fill an empty tank . a larger pump would take 1 / 2 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ? a ) 1 / 6 , b ) 4 / 9 , c ) 1 / 4 , d ) 5 / 9 , e ) 1 / 3","""rate of the small pump is 1 / 4 tank / hour rate of the larger pump is 1 / ( 1 / 2 ) or 2 tank / hour ; combined rate of the two pumps is 1 / 4 + 2 = 9 / 4 tank / hour , together they will fill the empty tank in 1 / ( 9 / 4 ) ) = 4 / 9 hours ( time = job / rate ) . answer : b"""
Explain the solution process for the given equation.,"what is the total number of prime numbers less than 70 ? a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21","solution prime numbers less than 70 are = 12 . 2,3 , 5,7 , 11,13 , 17,19 , 23,29 , 31,37 , 41,43 , 47,53 , 59,61 , and 67 their number is 19 . answer c"
Break down and solve the equation step by step.,"in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 22 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ? a ) 42 , b ) 48 , c ) 64 , d ) 76 , e ) 88","""200 are sophomores . the number of freshmen is 600 - 160 - 0.22 ( 800 ) = 264 the answer is c ."""
Break down and solve the equation step by step.,"the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) is close to a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.15 , e ) 2.35","""( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) = 25.4303 / 11.845 = 2.15 answer : d"""
Provide a detailed solution to the given mathematical problem.,"let p be a prime number . if n = 7 p , how many divisors does n have ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5","two . n = 7 * p , and both 7 and p are prime . so the answer is b ."
"Solve the problem systematically, showing each step clearly.","every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 2 / 5 of the juniors is equal to 1 / 3 of the seniors , what fraction of the students in the room are juniors ? a ) 3 / 20 , b ) 1 / 3 , c ) 5 / 12 , d ) 12 / 17 , e ) 5 / 11","""let total number of juniors = j total number of seniors = s ( 2 / 5 ) j = ( 1 / 3 ) s = > s = 6 / 5 j total number of students = j + s = ( 11 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 11 / 5 ) j ] = 5 / 11 answer e"""
Explain the solution process for the given equation.,"in a division sum , the remainder is 8 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is : a ) 200 , b ) 251 , c ) 250 , d ) 262 , e ) 254","""diver = ( 8 * 3 ) + 3 = 27 3 * quotient = 27 quotient = 9 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 9 ) + 8 = 251 b"""
Explain the solution process for the given equation.,"31 of the scientists that attended a certain workshop were wolf prize laureates , and 12 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ? a ) a ) 11 , b ) b ) 23 , c ) c ) 24 , d ) d ) 29 , e ) d ) 36","""lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 12 . . so total who won n = 11 + 12 = 23 . . b"""
Provide a detailed solution to the given mathematical problem.,"a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 24 inches and the width of the wall is 42 inches , what is the length of the wall , in inches ? a ) 21.4 , b ) 23.4 , c ) 25.4 , d ) 26.4 , e ) 27.4","""since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 24 ^ 2 = 576 . area of rectangle is double of that 2 * 576 = 1152 . now a = lw and we need find w so a / l = w ; 1152 / 42 = 27.4 answer ! answer : e"""
Provide a detailed solution to the given mathematical problem.,"the sum of money will be double itself in 20 years and simple interest find rate of interest ? a ) 10 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 25 %","""t = 20 years p = principle amount = x a = total amount = 2 x si = simple interest = a - p = 2 x - x = x r = 100 si / pt = 100 x / 20 x = 5 % answer is b"""
Break down and solve the equation step by step.,"bert and rebecca were looking at the price of a condominium . the price of the condominium was 110 % more than bert had in savings , and separately , the same price was also 20 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings . a ) 1 : 5 , b ) 1 : 4 , c ) 2 : 3 , d ) 4 : 7 , e ) 1 : 2","""suppose bert had 100 so price becomes 210 , this 210 = 1.2 times r' s saving . . so r' s saving becomes 175 so required ratio is 100 : 175 = 4 : 7 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a bullet train 200 m long is running with a speed of 69 kmph . in what time will it pass a man who is running at 3 kmph in the direction opposite to that in which the bullet train is going ? a ) 10 sec , b ) 15 sec , c ) 12 sec , d ) 11 sec , e ) 16 sec","""a 10 sec speed of the bullet train relative to man = ( 69 + 3 ) kmph = 72 * 5 / 18 m / sec = 60 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 200 m at ( 60 / 3 ) m / sec = ( 200 * 3 / 60 ) sec = 10 sec"""
Provide a detailed solution to the given mathematical problem.,"in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 6 % . what is population of after 2 year . a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 145","""next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 6 % so total man = 150 * . 94 = 141 women will be = 175 - 141 = 34 so population after two years = [ 135 ^ 2 + 34 ^ 2 ] ^ . 5 = 145.04 = 145 so population after two year = 145 answer : e"""
Explain the solution process for the given equation.,"the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 20,000 is made ? a ) 328897 , b ) 120000 , c ) 877888 , d ) 116000 , e ) 188871","""the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 20,000 is made = 96,000 + 20,000 = rs . 1 , 16,000 answer : d"""
"Solve the problem systematically, showing each step clearly.","a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 35 % profit on the cost of the item ? a ) 18 , b ) 21.6 , c ) 22 , d ) 22.5 , e ) 27.7","""producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 35 % of the final price - - > ( final price ) * 0.65 = $ 18 - - > ( final price ) = $ 27.7 . answer : e ."""
Break down and solve the equation step by step.,"a bag holds 4 red marbles and 5 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ? a ) 1 / 10 , b ) 1 / 6 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 4","""probability of selecting first red marble = 4 / 9 probability of selecting second red marble without replacement = 3 / 8 final probability = 4 / 9 * 3 / 8 = 1 / 6 the correct answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","if 9 - 4 / x = 7 + 8 / x , then x = a ) 15 , b ) 6 , c ) 1 , d ) 5 , e ) 12","we' re given the equation 9 - 4 / x = 7 + 8 / x . we' re asked for the value of x . the common - denominator of these 4 numbers is x , so we have to multiple 2 of the numbers to give them that denominator . . . 9 x - 4 x / x = 7 x + 8 x / x we can then eliminate that denominator , which gives us . . . . 9 x - 4 = 7 x + 8 12 = 2 x both 2 x and 12 have a common denominator of 2 , so we divide both sides by 2 for our final answer . . . 6 = x b"
"Solve the problem systematically, showing each step clearly.","if ( 5 ^ 13 ) ( 9 ^ 7 ) = 3 ( 15 ^ x ) , what is the value of x ? a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15",( 5 ^ 13 ) ( 9 ^ 7 ) = 3 ( 15 ^ x ) = > 5 ^ 13 * 3 ^ 14 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 13 * 3 ^ 14 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 13 answer d
Provide a detailed solution to the given mathematical problem.,"a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b' s share in total profit of rs . 21,000 earned at the end of 2 years from the startingof the business ? a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,300 , e ) s . 7,500","""a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b' s share = rs . 21000 x 3 / 10 = rs . 6,300 . d"""
Break down and solve the equation step by step.,"a couple married in 1980 had two children , one in 1982 and the other in 1984 . their combined ages will equal the years of the marriage in ? a ) 1986 , b ) 1985 , c ) 1987 , d ) 1988 , e ) 1989",sum of year = 1 + 9 + 8 + 0 = ( 18 ) 1 + 8 = 9 1 + 9 + 8 + 2 = ( 20 ) 2 + 0 = 2 1 + 9 + 8 + 4 = ( 13 ) 1 + 3 = 4 now 9 + 2 + 4 = ( 15 ) 1 + 5 = 6 nd option a 1 + 9 + 8 + 6 = 24 ( 2 + 4 ) = 6 answer : a
"Solve the problem systematically, showing each step clearly.","how many trailing zeroes does 49 ! + 50 ! have ? a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 22","""49 ! + 50 ! = 51 * 49 ! no of trailing 0' s = no of 5 * 2 no of 2' s = 49 / 2 + 49 / 4 + 49 / 8 + 49 / 16 + 49 / 32 = d no of 5' s = 49 / 5 + 49 / 25 = 10 = p now since p < d no of trailing 0' s = 10 answer : b"""
Explain the solution process for the given equation.,"a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 6 times the number available before the new tower was built . currently , 1 / 3 of the hospital' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital' s original wing , all of the patients in the hospital' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ? a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15","""i think e - 11 / 15 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 6 x so old = x , new = 5 x now 1 / 3 of x are occupied and 1 / 5 of 5 x are occupied which simplifies to ( 5 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 5 / 5 of x occupied in the new ward . add them up to get 4 / 3 of x there are 5 x beds in new tower so ratio is : ( 4 / 3 ) x / 5 x = 4 / 15 of x subtract that from 15 / 15 of x and you get the number of un - occupied beds to total capacity of new tower = 11 / 15 . e"""
Explain the solution process for the given equation.,"if x < y < z and y - x > 3 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ? a ) 7 , b ) 6 , c ) 8 , d ) 9 , e ) 10","""we have : 1 ) x < y < z 2 ) y - x > 3 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 3 , the least value for y - x must be 5 , the least value for x must be 2 , and , thus , the least possible value for y must be 7 ( y - 2 = 5 , y = 7 ) 2 < 7 < z , since z is odd , the least possible value for z is 9 z - x = 9 - 2 = 7 answer a"""
"Solve the problem systematically, showing each step clearly.","a work which could be finished in 11 days was finished 3 days earlier after 10 more men joined . the number of men employed was ? a ) 22 , b ) 20 , c ) 88 , d ) 71 , e ) 12","""x - - - - - - - 11 ( x + 10 ) - - - - 6 x * 11 = ( x + 10 ) 6 x = 12 \ answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","how many positive integers less than 243 are multiple of 4 but not multiples of 6 ? a ) 20 , b ) 31 , c ) 42 , d ) 40 , e ) 64","""240 / 4 = 60 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 60 - 20 = 40 answer : d"""
"Solve the problem systematically, showing each step clearly.","john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 45 miles per hour , what is v in miles per hour ? a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70","""hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 40 = > v = 40 ( option b ) ."""
Provide a detailed solution to the given mathematical problem.,"three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 264 . what is their h . c . f . ? a ) 18 , b ) 22 , c ) 24 , d ) 28 , e ) 32","""let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 264 x = 22 hcf of 2 x , 3 x and 4 x = x = 22 the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 50 students are not between 3 years old and 4 years old , how many children are in the nursery school ? a ) 150 , b ) 300 , c ) 450 , d ) 490 , e ) 620",x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 50 x / 10 = 30 x = 300 answer : b
Provide a detailed solution to the given mathematical problem.,"the speed at which a man can row a boat in still water is 18 kmph . if he rows downstream , where the speed of current is 6 kmph , what time will he take to cover 100 metres ? a ) 6.67 seconds , b ) 18 seconds , c ) 26 seconds , d ) 14.99 seconds , e ) 6 seconds","""speed of the boat downstream = 18 + 6 = 24 kmph = 24 * 5 / 18 = 6.67 m / s hence time taken to cover 100 m = 100 / 6.67 = 14.99 seconds . answer : d"""
Provide a detailed solution to the given mathematical problem.,"calculate how many seconds it eill take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 2 , 5 , 8 and 11 seconds . ? a ) 440 , b ) 420 , c ) 410 , d ) 442 , e ) 422","""lcm of 2 , 5 , 8 and 11 is 440 lcm = 440 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction r of the total distance did he cover while the sun was shining on him ? a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7","if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is r = 2 / 14 = 1 / 7 . answer : e"
Break down and solve the equation step by step.,"a woman complete a journey in 30 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km . a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 672 km .","""0.5 x / 21 + 0.5 x / 24 = 30 - - > x / 21 + x / 24 = 60 - - > x = 672 km . e"""
"Solve the problem systematically, showing each step clearly.","for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 27 , the mean is how much greater than the median ? a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7","""mean = ( x + x + 2 + x + 4 + x + 7 + x + 27 ) / 5 = ( 5 x + 40 ) / 5 = x + 8 median = x + 4 thus mean - median = x + 8 - ( x + 4 ) = 4 answer = d"""
Break down and solve the equation step by step.,"a meeting has to be conducted with 4 managers . find the number of ways in which the managers be selected from among 7 managers , if 2 managers will not attend the meeting together ? a ) 25 , b ) 20 , c ) 35 , d ) 36 , e ) 38","""we can either choose all 4 people from 5 manager who have no problems or choose 3 from the 5 and 1 from the 2 managers who have a problem sitting together so 5 c 4 + ( 5 c 3 * 2 c 1 ) this is 5 + 20 = 25 answer : a"""
"Solve the problem systematically, showing each step clearly.","a certain number when divided by 110 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9","""explanation : 110 + 25 = 135 / 15 = 9 ( remainder ) e"""
"Work through the equation methodically, ensuring clarity at each step.","a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a' s income is increased by rs . 200 when the rate to profit rises from 5 to 7 percent . find the capital of a ? a ) 3377 , b ) 2899 , c ) 2500 , d ) 2778 , e ) 10000","""a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 200 a capital = 15000 * 2 / 3 = 10000 answer : e"""
Break down and solve the equation step by step.,"how many seconds will a 400 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 46 km / hr ? a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 36","""explanation : speed of train relatively to man = ( 46 - 6 ) km / hr = 40 km / hr = ( 40 x 5 / 18 ) m / sec = 11.11 m / sec time taken to pass the man = ( 400 / 11.11 ) sec = 36 sec . answer : e"""
Break down and solve the equation step by step.,"one night 15 percent of the female officers on a police force were on duty . if 300 officers were on duty that night and half of these were female officers , how many female officers were on the police force ? a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000","""let total number of female officers in the police force = f total number of officers on duty on that night = 300 number of female officers on duty on that night = 300 / 2 = 150 ( 15 / 100 ) * f = 150 = > f = 1000 answer e"""
"Solve the problem systematically, showing each step clearly.","the distance from steve' s house to work is 40 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve' s speed on the way back from work ? a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .","""time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 40 km = > speed = 20 kmph e"""
Break down and solve the equation step by step.,"if x is real , find the maximum value of the expression - 2 x ^ 2 + 9 x + 11 . a ) 12.125 , b ) 15.125 , c ) 18.125 , d ) 21.125 , e ) 24.125","""this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 9 x + 11 = ( - 2 x + 11 ) ( x + 1 ) the roots are 11 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 2.25 the maximum value is - 2 ( 2.25 ) ^ 2 + 9 ( 2.25 ) + 11 = 21.125 the answer is d ."""
Explain the solution process for the given equation.,"milk contains 5 % water . what quantity of pure milk should be added to 10 litres of milk to reduce this 2 % ? a ) 15 litres , b ) 16 litres , c ) 17 litres , d ) 25 litres , e ) 35 litres","present ration of milk to water is 95 : 5 amount of milk is 10 litres hence , pure milk content is 9.5 litre and water content is 0.5 litres now , we should not disturb the water content so , 0.5 litres of water is equivalent to 2 % so 100 % mixture is : ( 0.5 / 2 ) * 100 = 25 litre thus , milk should be added = 25 - 10 = 15 litres of pure milk answer : a"
Provide a detailed solution to the given mathematical problem.,"the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 12 minutes is a ) 1.2 km , b ) 1.8 km , c ) 2.4 km , d ) 3.6 km , e ) 1.6 km","""b = 15 km / hr , s = 3 km / hr , downstream b + s = 15 + 3 = 18 km / hr down stream time t = 12 min , we have to change it to hours so t = 12 / 60 = 1 / 5 hrs . distance = speed * time = 18 * 1 / 5 = 3.6 km . answer : d"""
"Solve the problem systematically, showing each step clearly.","what is the angle between the hands of a clock when time is 8 : 40 ? a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 100 deg","""angle between two hands = 40 h - 11 / 2 m = 40 * 8 - 40 * 11 / 2 = 320 - 220 = 100 deg answer : e"""
Break down and solve the equation step by step.,"farm tax is levied on the 75 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is : a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) 16.667 %","""this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 75 ) = 16.667 % the correct answer is ( e ) ."""
Explain the solution process for the given equation.,"a certain taxi company charges $ 3.00 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a ) 15.6 , b ) 16.0 , c ) 17.5 , d ) 18.6 , e ) 19.1","""a certain taxi company charges $ 3.00 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 3.00 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 3.0 + $ 15.6 = $ 18.6 . answer : d ."""
"Work through the equation methodically, ensuring clarity at each step.","a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is : a ) 3348 , b ) 3898 , c ) 1200 , d ) 2881 , e ) 7881",answer : c ) 1200
"Solve the problem systematically, showing each step clearly.","a vessel of capacity 90 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ? a ) 73.9 , b ) 72.9 , c ) 73.0 , d ) 73.5 , e ) 92.2","""let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] n * t for the given problem , t = 90 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 90 - 9 ) / 90 ] 2 ( 90 ) = 72.9 litres . answer : option b"""
Break down and solve the equation step by step.,"the tax on a commodity is diminished by 30 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ? a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %","""100 * 100 = 10000 70 * 115 = 8050 10000 - - - - - - - 1950 100 - - - - - - - ? = 20 % answer : a"""
Explain the solution process for the given equation.,"if both 7 ^ 2 and 3 ^ 4 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ? a ) 120 , b ) 256 , c ) 343 , d ) 441 , e ) 512","""the number a must include at least 3 ^ 2 * 7 ^ 2 = 441 the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","sakshi invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ? a ) rs . 4000 , b ) rs . 4500 , c ) rs . 5500 , d ) rs . 6000 , e ) rs . 6500","let investment in 12 % stock be rs . x . then , investment in 15 % stock = rs . ( 12000 - x ) . 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x / 10 + 3 / 25 ( 12000 - x ) = 1360 5 x + 72000 - 6 x = 1360 x 50 x = 4000 . answer = a"
Provide a detailed solution to the given mathematical problem.,"if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 70 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 1 hours longer and at an average rate of 10 miles per hour faster on that day ? a ) 100 , b ) 120 , c ) 130 , d ) 150 , e ) 160","""case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 70 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 1 ) x = 130 ans c"""
Explain the solution process for the given equation.,"what is the ratio g of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ? ['a ) 1 / 4','b ) 3 / 8','c ) 1 / 2','d ) 3 / 5','e ) 2']","one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area g = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d )"
"Work through the equation methodically, ensuring clarity at each step.","the minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time . how much does the clock gain or lose in 12 hours ? a ) 27.273 seconds , b ) 29.273 seconds , c ) 37.273 seconds , d ) 47.273 seconds , e ) 17.273 seconds",after 60 minute rotation the minute hand will make an angle of 30 degree with hour hand . after that let the time required to make an overtake is t minute in this time angle covered by minute hand = ( 360 / 60 ) t = 6 t similarly angle covered by hour hand = ( 30 / 60 ) t = t / 2 so for overtake 6 t = 30 + t / 2 or t = 60 / 11 min = 5 min and 5 / 11 min = 5 min and 300 / 11 sec = 5 min and 27.273 sec so clock loses 27.273 seconds answer : a
Provide a detailed solution to the given mathematical problem.,"in a hostel , the number of students decreased by 8 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ? a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 9.4 %","""cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.92 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.92 * 1.2 ) = > f ( new ) = 0.906 f therefore the new cost of food must be 90.6 % of the old cost , or the cost of food must decrease by 9.4 % answer : e"""
Explain the solution process for the given equation.,"the value of a machine depreciates at 25 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ? a ) $ 258375 , b ) $ 438375 , c ) $ 128375 , d ) $ 108375 , e ) $ 158375","""the value of the machine after two years = 0.75 * 0.75 * 1 , 50,000 = $ 84,375 sp such that a profit of $ 24,000 is made = 84,375 + 24,000 = $ 1 , 08,375 d"""
Break down and solve the equation step by step.,"a milk man has 15 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : a ) 20 % , b ) 25 % , c ) 33.33 % , d ) 18 % , e ) none of these","""explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 20 % . answer : a"""
"Solve the problem systematically, showing each step clearly.","how many cubes of 2 cm edge can be cut out of a cube of 24 cm edge a ) 1136 , b ) 1728 , c ) 1216 , d ) 1484 , e ) none of these","""explanation : number of cubes = ( 24 x 24 x 24 ) / ( 2 x 2 x 2 ) = 1728 answer : b"""
Break down and solve the equation step by step.,"how many integers from 10 to 180 , inclusive , are divisible by 3 but not divisible by 7 ? a ) 45 , b ) 49 , c ) 50 , d ) 52 , e ) 56","""we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 10 to 180 , inclusive is ( 168 - 21 ) / 21 + 1 = 8 ; 57 - 8 = 49 . answer : b ."""
Break down and solve the equation step by step.,"what is the compound interest paid on a sum of rs . 1500 for the period of 2 years at 10 % per annum . a ) 230 , b ) 175 , c ) 225 , d ) 315 , e ) none of these","""solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 1500 = 1500 * ( 21 / 100 ) = 315 answer d"""
Provide a detailed solution to the given mathematical problem.,"pipe a fills a tank of capacity 950 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ? a ) 57 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these",in one cycle they fill 40 + 30 - 20 = 50 liters 950 = 50 * n = > n = 19 here n = number of cycles . total time = 19 * 3 = 57 as in one cycle there are 3 minutes . thus 57 minutes answer : a
Break down and solve the equation step by step.,"the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 20 more than the number who did not , and if receipts for registration and lunch totaled $ 50,240 , how many people paid just for registration at the meeting ? a ) 700 , b ) 800 , c ) 1,300 , d ) 1,500 , e ) 400","hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 20 more than the number who did not . that means , total number of people who registered and paid for lunch = 20 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 20 + x ) = 1440 + 72 x now , total amount received was 50240 . thus , from the above data , 50 x + 1440 + 72 x = 50240 122 x = 50240 - 1440 122 x = 48800 x = 400 . hence the correct ans is e"
"Work through the equation methodically, ensuring clarity at each step.","at what rate percent of simple interest will a sum of money double itself in 66 years ? a ) 6.54 % , b ) 4.54 % , c ) 1.51 % , d ) 1.94 % , e ) 5.54 %","""let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 66 ) = 100 / 66 = 1.51 % answer : c"""
Provide a detailed solution to the given mathematical problem.,"in a garden , 26 trees are planted at equal distances along a yard 300 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ? a ) 10 metres , b ) 20 metres , c ) 14 metres , d ) 12 metres , e ) 13 metres","""between 26 trees , there are 25 gaps length of each gap = 300 / 25 = 12 i . e . , distance between two consecutive trees = 12 answer : d"""
"Solve the problem systematically, showing each step clearly.","if two integers x , y ( x > y ) are selected from - 5 to 5 ( inclusive ) , how many cases are there ? a ) 55 , b ) 60 , c ) 65 , d ) 70 , e ) 75","""there are 11 integers from - 5 to 5 inclusive . 11 c 2 = 55 . the answer is a ."""
Provide a detailed solution to the given mathematical problem.,"john and david can finish a job together in 1 hours . if john can do the job by himself in 2 hours , what percent of the job does david do ? a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %","you can also plug in numbers . for example , bob and alice work at a donut factory and make 10 donuts which is the job ( i picked this as a smart number ) . john on his own works 10 / 2 = 5 donuts per hour . john and david work 10 / 1 = 10 donuts per hour so david works 5 donuts / hour to find out the percentage , david works 5 donuts / hr x 1 hours = 5 donuts per hour . therefore 5 donuts / 10 donuts = 1 / 2 = 50 % answer : c"
Explain the solution process for the given equation.,"a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is a ) 145 , b ) 185 , c ) 253 , d ) 370 , e ) none","solution let the number be x . then 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred' s digit is smaller than the units digit . hence , required number = 253 . answer c"
Explain the solution process for the given equation.,"excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 30 km / hr . for how many minutes does the bus stop per hour ? a ) 22 , b ) 30 , c ) 77 , d ) 20 , e ) 99","""in 1 hr , the bus covers 60 km without stoppages and 30 km with stoppages . stoppage time = time take to travel ( 60 - 30 ) km i . e 30 km at 60 km / hr . stoppage time = 30 / 60 hrs = 30 min . answer : b"""
Break down and solve the equation step by step.,"( 26.3 * 12 * 20 ) / 3 + 125 = ? a ) 2339 , b ) 2229 , c ) 4429 , d ) 5529 , e ) 2669",b 2229 ? = [ ( 26.3 * 12 * 20 ) / 3 ] + 125 ? = 2104 + 125 = 2229
Explain the solution process for the given equation.,"a test has 180 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ? a ) 29 , b ) 33 , c ) 35 , d ) 40 , e ) 42","""a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 180 . thus 5 c < = 340 and so c < = 68 . then 40 < = c < = 68 and c can have 29 possible values . the answer is a ."""
Explain the solution process for the given equation.,"a and b invests rs . 6000 and rs . 9000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ? a ) 32 : 99 , b ) 82 : 31 , c ) 24 : 45 , d ) 34 : 89 , e ) 35 : 21","""a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 9000 * 6 ) + ( 6000 * 6 ) 48000 : 90000 24 : 45 answer : c"""
Explain the solution process for the given equation.,"a candidate appearing for an examination has to secure 42 % marks to pass paper i . but he secured only 42 marks and failed by 22 marks . what is the maximum mark for paper i ? a ) 110 , b ) 120 , c ) 130 , d ) 152 , e ) 150","""he secured 42 marks nd fail by 22 marks so total marks for pass the examinatn = 64 let toal marks x x * 42 / 100 = 64 x = 152 answer : d"""
"Solve the problem systematically, showing each step clearly.","b completes a work in 8 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ? a ) 3.75 days , b ) 4.44 days , c ) 5 days , d ) 6.44 days , e ) 7 days","""1 / 8 + 1 / 10 = 9 / 40 40 / 9 = 4.44 days answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","if 21 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ? a ) 150 , b ) 170 , c ) 190 , d ) 210 , e ) 230","""if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 21 lines is 21 c 2 = 210 the answer is d ."""
"Solve the problem systematically, showing each step clearly.","what is the remainder when 43 ^ 91 is divided by 5 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","""the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 91 has the form 4 k + 3 so the units digit of 43 ^ 91 is 7 . the remainder when dividing by 5 is 2 . the answer is c ."""
Explain the solution process for the given equation.,"how many integerskgreater than 100 and less than 1200 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ? a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 100","""numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ten pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 10 * 10 = 100 hence e"""
"Solve the problem systematically, showing each step clearly.","the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 3 of that total . what was the price of the basic computer ? a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000","""let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 3 of that new total price : p = 1 / 3 * $ 3,000 = $ 1000 plug this value in the first equation : c + 1000 = $ 2,500 - - > c = $ 1,500 . answer : a ."""
"Solve the problem systematically, showing each step clearly.","if a 2 + b 2 + c 2 = 941 and ab + bc + ca = 10 , then a + b + c is a ) 44 , b ) 56 , c ) 16 , d ) 32 , e ) 31","""by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 941 and ab + bc + ca = 10 , ( a + b + c ) ^ 2 = 941 + 2 ( 10 ) = 961 = 31 ^ 2 therefore : a + b + c = 31 answer : e"""
Provide a detailed solution to the given mathematical problem.,"a merchant has 1000 kg of sugar part of which he sells at 8 % profit and the rest at 18 % profit . he gains 14 % on the whole . the quantity sold at 18 % profit is ? a ) 700 kg , b ) 500 kg , c ) 600 kg , d ) 800 kg , e ) 900 kg","""by the rule of alligation : profit of first part profit of second part so , ratio of 1 st and 2 nd parts = 4 : 6 = 2 : 3 . quantity of 2 nd kind = ( 3 / 5 x 1000 ) kg = 600 kg answer : c"""
Provide a detailed solution to the given mathematical problem.,"the total marks obtained by a student in mathematics and physics is 20 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . a ) 40 , b ) 26 , c ) 20 , d ) 28 , e ) 22","""let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 20 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 20 + 20 ) / 2 = 20 . answer : c"""
Provide a detailed solution to the given mathematical problem.,"the price of a t . v . set worth rs . 8000 is to be paid in 20 installments of rs . 750 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ? a ) 7250 , b ) 7200 , c ) 7820 , d ) 6000 , e ) 2799","""money paid in cash = rs . 750 balance payment = ( 8000 - 1000 ) = rs . 7250 answer : a"""
Provide a detailed solution to the given mathematical problem.,"a shopkeeper sold an article offering a discount of 10 % and earned a profit of 25 % . what would have been the percentage of profit earned if no discount was offered ? a ) 39 % , b ) 52 % , c ) 15 % , d ) 21 % , e ) 28 %","""let c . p . be $ 100 . then , s . p . = $ 125 let marked price be $ x . then , 90 / 100 * x = 125 x = 12500 / 90 = $ 139 now , s . p . = $ 139 , c . p . = rs . 100 profit % = 39 % . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","one side of the bottom layer of a triangular pyramid has 12 balls . how many are there in the whole pyramid ? note that the pyramid is equilateral and solid . ['a ) 286','b ) 364','c ) 504','d ) 164','e ) 165']","as there are 12 balls along one side , it means that there are 12 layers of balls . the top most layer has 1 ball . the second layer has 3 ( 1 + 2 ) balls . the third layer has 6 ( 1 + 2 + 3 ) balls . the fourth layer has 10 ( 1 + 2 + 3 + 4 ) balls . the fifth layer has 15 ( 1 + 2 + 3 + 4 + 5 ) balls . similarly , there are 21 , 28 , 36 , 45 , 55 , 66 and 78 balls in the remaining layers . hence , the total number of balls are = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 balls answer : b"
Break down and solve the equation step by step.,"if n = 2 ^ 0.25 and n ^ b = 8 , b must equal a ) 3 / 80 , b ) 3 / 5 , c ) 12 , d ) 5 / 3 , e ) 80 / 3","""25 / 100 = 1 / 4 n = 2 ^ 1 / 4 n ^ b = 2 ^ 3 ( 2 ^ 1 / 4 ) ^ b = 2 ^ 3 b = 12 answer : c"""
"Solve the problem systematically, showing each step clearly.","susan finds that she spends her free time during summer vacation between swimming , reading , and hanging out with friends in a ratio of 1 : 4 : 10 . how many hours did she spend reading if she hung out with her friends for 20 hours ? a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 10",the ratio is 1 hour swimming : 4 hours reading : 10 hours hanging out with friends . divide 20 by 10 to find 1 ` ` part'' of the ratio . 20 / 10 = 2 multiply this by 4 to find the hours spent reading . 2 * 4 = 8 the answer is d .
Explain the solution process for the given equation.,"20 ^ 10 / 120 ^ 5 = ? a ) 6 ^ 5 , b ) 5 ^ 6 , c ) ( 10 / 3 ) ^ 5 , d ) 6 ^ 3 , e ) 15 ^ 3","""20 ^ 10 / 120 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . ( 10 / 3 ) ^ 5 d . 6 ^ 3 e . 15 ^ 3 - > 20 ^ 10 / 120 ^ 5 = ( 20 ^ 10 ) / ( 6 ^ 5 ) ( 20 ^ 5 ) = ( 20 ^ 5 ) / ( 6 ^ 5 ) = ( 2 ^ 5 ) ( 10 ^ 5 ) / ( 2 ^ 5 ) ( 3 ^ 5 ) = ( 10 / 3 ) ^ 5 . thus , c is the answer ."""
Provide a detailed solution to the given mathematical problem.,"the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 6 years is a ) s . 9621 , b ) s . 6921 , c ) s . 10721 , d ) s . 6261 , e ) s . 6361","""c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 6 = rs 10721 answer : c"""
Explain the solution process for the given equation.,"an alloy weighing 48 ounces is 25 % gold . how many ounces of pure gold must be added to create an alloy that is 40 % gold ? a ) 15 , b ) 20 , c ) 12 , d ) 14 , e ) 7","an alloy of 48 oz which is 25 % gold means there is 12 oz of gold . to get to an alloy that is 40 % gold , let' s use this expression : ( 12 + x ) / ( 48 + x ) = 0.40 with x representing the amount of pure gold that must be added to get to 40 % . the expression we are using represents the new total weight of pure gold over the new total weight of the alloy and this fraction should represent 40 % or 0.4 . you will see that 12 is the correct answer , as 24 / 60 = 0.4 choose c"
"Work through the equation methodically, ensuring clarity at each step.","a and b can do a piece of work in 4 days . b and c can do it in 12 days and a and c in 16 days . working together they will complete the work in how many days ? a ) 4.05 days , b ) 5.05 days , c ) 14.76 days , d ) 8.05 days , e ) 15.05 days","""a + b = 1 / 4 b + c = 1 / 12 c + a = 1 / 16 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ( a + b + c ) = 1 / 4 + 1 / 12 + 1 / 16 = 19 / 48 a + b + c = 19 / 96 96 / 19 = 5.05 days answer : b"""
Break down and solve the equation step by step.,"how many pieces of 75 cm can be cut from a rope 57 meters long ? a ) 30 , b ) 40 , c ) 76 , d ) none , e ) can not be determined","""explanation : total pieces of 75 cm that can be cut from a rope of 57 meters long is = ( 57 meters ) / ( 75 cm ) = ( 57 meters ) / ( 0.75 meters ) = 76 answer : c"""
Provide a detailed solution to the given mathematical problem.,"the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 480 m , its area is ? a ) 150 , b ) 240 , c ) 277 , d ) 261 , e ) 281","""5 x + 12 x + 13 x = 480 = > x = 16 a = 80 , b = 192 , c = 208 s = ( 80 + 192 + 208 ) / 2 = 240 answer : b"""
Provide a detailed solution to the given mathematical problem.,"the area of an isosceles trapezoid with sides of length 5 and bases of length 6 and 12 is ? a ) 44 , b ) 42 , c ) 40 , d ) 38 , e ) 36","""isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 12 will be divided into 3 parts = 6 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 18 * 4 = 36 e"""
Provide a detailed solution to the given mathematical problem.,"a cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom . if the cistern is full , in what time will the leak empty it ? a ) 50 hours , b ) 62 hours , c ) 90 hours , d ) 75 hours , e ) 100 hours","""let the leak empty the full cistern in x hours 9 x / x - 9 = 9 + 1 x = 90 hours answer is c"""
Explain the solution process for the given equation.,"a call center has two teams . each member of team a was able to process 2 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ? a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 5 , d ) 1 / 2 , e ) 1 / 5","let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 2 calls , so total calls for team a = 10 fraction for team b = 40 / ( 40 + 10 ) = 4 / 5 = answer = c"
Explain the solution process for the given equation.,"of the 720 students at a certain university , 25 percent are seniors . if x seniors were to graduate early and leave the university and no additional students entered or left the university , what value of x would reduce the number of seniors at the university to 20 percent ? a ) 30 , b ) 36 , c ) 42 , d ) 45 , e ) 48",sol : 180 - x = 20 % of ( 720 - x ) 4 x = 180 x = 45 answer : d
"Work through the equation methodically, ensuring clarity at each step.","if 2 is the remainder when m is divided by 5 , what is the remainder when 3 m is divided by 5 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4",let' s find a number which when divided by 5 leaves remainder 2 = 5 + 2 = 7 i . e . one possible value of m = 7 value of 3 m = 3 * 7 = 21 when em is divided by 5 then remainder = rem ( 21 / 5 ) = 1 answer : option b
Provide a detailed solution to the given mathematical problem.,"two sides of a triangle have lengths x and w and meet at a right angle . if the perimeter of the triangle is 4 x , what is the ratio of x to w ? ['a ) a ) 2 : 3','b ) b ) 3 : 4','c ) c ) 4 : 3','d ) d ) 3 : 2','e ) e ) 2 : 1']","ahhhh . . . . my bad . thank you , you' re correct . 8 x = 6 w - - > x / w = 3 / 4 . actually b is the right answer ."
"Work through the equation methodically, ensuring clarity at each step.","in a two digit number it is known that its unit' s digit exceeds its 10' s digit by 4 and that the product of the given number and the sum of its digits is equal to 208 , what is the number ? a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28",xy is 2 digit no . y - x = 4 ; ( 10 x + y ) * ( 2 x + 4 ) = 208 ; sub y = x + 4 ; we get 26 answer : c
Provide a detailed solution to the given mathematical problem.,"if n is a prime number greater than 5 , what is the remainder when n ^ 2 is divided by 23 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5","""there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 5 , square it and see what would be the remainder upon division of it by 23 . n = 5 - - > n ^ 2 = 49 - - > remainder upon division 49 by 23 is 3 . answer : d ."""
Break down and solve the equation step by step.,"a retailer buys a radio for rs 225 . his overhead expenses are rs 28 . he sellis the radio for rs 300 . the profit percent of the retailer is a ) 10 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) 18.5 %","""explanation : cost price = ( 225 + 28 ) = 253 sell price = 300 gain = ( 47 / 253 ) * 100 = 18.5 % . answer : e"""
Explain the solution process for the given equation.,"a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 3300 in all from both of them as interest . the rate of interest per annum is ? a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 15 %","""let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 3300 100 r + 120 r = 3300 r = 15 % answer : e"""
"Solve the problem systematically, showing each step clearly.","an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 50 cm , find the sum of the perimeters of all the triangles . a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm","""we have 50 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 25 and continues . so we have 50,25 , 12.5 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 50 / 1 - ( 1 / 2 ) = 100 equilateral triangle perimeter is 3 a = 3 * 100 = 300 . so option e ."""
Break down and solve the equation step by step.,"when a natural number n is successively divided by 12 , 34 the remainders are 56 , 78 . what will be the sum of the remainders if the order of the division is reversed ? a ) 11 , b ) 12 , c ) 10 , d ) 2 , e ) 7","1 2 3 4 5 6 7 8 leave the top right - most number 8 start with bottom right - most number 5 8 * 3 + 7 = 31 31 * 2 + 6 = 68 68 * 1 + 5 = 73 this is the number required now , do the successive division in the reverse order the sum of the remainders is 10 hence , the correct option is c"
Explain the solution process for the given equation.,"johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 25 miles per hour . how far is it to the school ? a ) 2 miles , b ) 4 miles , c ) 6.6 miles , d ) 8 miles , e ) 10 miles","answer : c ) 6.6 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 25 / ( 5 + 25 ) = 6.6 m / hr the distance between schoolhome should be half of that . ie . 6.6 miles answer c"
Break down and solve the equation step by step.,"( x + 7 ) is a factor in x ^ 2 - mx - 35 . what is the value of m ? a ) - 3 , b ) - 2 , c ) - 4 , d ) - 5 , e ) - 6","""i solved the second degree equation and found it like this : x ^ 2 - mx - 35 ( x - 5 ) ( x + 7 ) x = 5 or x = - 7 substituting both values for x in the equation we find : x ^ 2 - mx - 35 = > ( - 7 ) ^ 2 - m ( - 7 ) = 35 = > 49 + 7 m = 35 = > 7 m = 35 - 49 = - 14 = > m = - 2 and with 5 , using a similar process we end up with : ( 5 ) ^ 2 - m ( 5 ) = 35 - 10 = 5 m m = - 2 ao , ans b"""
Break down and solve the equation step by step.,"rounded to 3 decimal places , 1.003 ^ 4 = a ) 1.004 , b ) 1.006 , c ) 1.008 , d ) 1.012 , e ) 1.016","as compared to 1 , 0.003 is a very small quantity . thus , we can write ( 1 + 0.003 ) ^ 4 is nearly equal to ( 1 + 4 * 0.003 ) = 1.012 . as the question asks for approximation to three decimal places , the further terms will anyways not come into picture . d ."
"Work through the equation methodically, ensuring clarity at each step.","the mean of 40 observations was 100 . it was found later that an observation 50 was wrongly taken as 75 the corrected new mean is a ) 125.8 , b ) 102.8 , c ) 99.375 , d ) 100.52 , e ) 122","""explanation : correct sum = ( 100 * 40 + 50 - 75 ) = 3975 . correct mean = = 3975 / 40 = 99.375 answer : c"""
Break down and solve the equation step by step.,"in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 200 girls , the total number of students in the college is a ) 420 , b ) 520 , c ) 620 , d ) 620 , e ) none of these",explanation : let the boy are 8 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 8 x + 5 x = 13 x = 13 ( 40 ) = 520 answer : b
Break down and solve the equation step by step.,"how many x ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen ? a ) 3 , b ) 16 , c ) 28 , d ) 32 , e ) 56",ways to select 3 people from 8 people ( 4 twins x 2 ) = 8 c 3 = 56 ways to select 1 twin + 1 people = 4 c 1 * 6 c 1 = 24 ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen x = 56 - 24 = 32 ans : d
"Work through the equation methodically, ensuring clarity at each step.","ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km . how many hours has been driving at 20 kmph ? a ) 3.2 hr , b ) 3.4 hr , c ) 3.6 hr , d ) 3.8 hr , e ) 4.2 hr",let see d / t = v then x / 20 + ( 400 - x ) / 70 = 8 x = 64 kmh t = 64 / 20 = 3.2 hr answer : a
Break down and solve the equation step by step.,"a can finish a work in 10 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ? a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 7 , d ) 3 / 10 , e ) none of these","""explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a' s 1 day work = 1 / 10 b' s 1 day work = 1 / 5 [ because b take half the time than a ] ( a + b )' s one day work = ( 1 / 10 + 1 / 5 ) = 3 / 10 so in one day 3 / 10 work will be done answer : d"""
Provide a detailed solution to the given mathematical problem.,"pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed z ? a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16","""let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this z we get x = 8 . b ."""
"Solve the problem systematically, showing each step clearly.","carol and jordan draw rectangles of equal area . if carol' s rectangle measures 5 inches by 24 inches and jordan' s rectangle is 3 inches long , how wide is jordan' s rectangle , in inches ? a ) 25 , b ) 43 , c ) 42 , d ) 40 , e ) 18","""area of carol' s rectangle = 24 * 5 = 120 let width of jordan' s rectangle = w since , the areas are equal 3 w = 120 = > w = 40 answer d"""
Provide a detailed solution to the given mathematical problem.,"one hour after adrienne started walking the 60 miles from x to y , william started walking from x to y as well . adrienne walks 3 miles per hour and william walks 1 mile per hour faster than adrienne . how far from x will william be when he catches up to adrienne ? a ) 8 miles , b ) 9 miles , c ) 10 miles , d ) 11 miles , e ) 12 miles","first , determine how far adrienne has walked in the one hour . she has walked three miles which means she is three miles ahead of william when he sets off . william walks at four miles / hour which means that every hour , william will get one mile closer to adrienne . if he gets one mile closer every hour , it will take him three hours to catch up to her which means he travels 3 hours * 4 miles / hour = 12 miles and she travels 4 hours * 3 miles / hour = 12 miles . he will be 12 miles from x when he catches up to her . a slightly different way to solve . . . we do n' t know how long they will walk before they catch up to one another but we do know that a walks for one hour more than j . j = t and a = t + 1 . we are looking for the distance at which they meet up which means the distance will be the same . d = r * t so , r * t ( william ) = r * t ( adrienne ) r * ( t ) = r * ( t + 1 ) 4 t = 3 t + 3 t = 3 d = r * t d = 4 * 3 d = 12 d ) 12 miles"
Provide a detailed solution to the given mathematical problem.,"for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 28 ) ? a ) 2 , b ) 7 , c ) 11 , d ) 13 , e ) 17","""f ( 28 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 the greatest prime factor in this list is 13 . the answer is d ."""
Explain the solution process for the given equation.,"how many numbers from 2 to 15 are exactly divisible by 2 ? a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8","""2 / 2 = 1 and 15 / 2 = 7 7 - 1 = 6 6 + 1 = 7 numbers . answer : d"""
"Solve the problem systematically, showing each step clearly.","the side of a square is increased by 30 % then how much % does its area increases ? a ) 52.65 , b ) 69 , c ) 50.75 , d ) 42.75 , e ) 52.75","""a = 100 a 2 = 10000 a = 130 a 2 = 16900 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 6900 100 - - - - - - - ? = > 69 % answer : b"""
Provide a detailed solution to the given mathematical problem.,"average weight of 10 people increased by 3 kg when one person of 45 kg is replaced by a new man . then weight of the new man is a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 75",explanation : total weight increased is 3 * 10 = 30 . so weight of new person is 45 + 30 = 75 answer : option e
Provide a detailed solution to the given mathematical problem.,"the first half of the 20 th century , the population of a particular country increased by 200 percent . in the second half of the century , the population increased by 300 percent . what was the percent increase for the 20 th century as a whole ? a ) 500 % , b ) 600 % , c ) 800 % , d ) 1100 % , e ) 1200 %","say initially population was 100 . what is 200 % of 100 ? it is 200 / 100 * 100 = 200 . an increase of 200 % means the new population became 100 + 200 = 300 what is 300 % of 300 ? it is 300 / 100 * 300 = 900 an increase of 300 % means the new population now is 300 + 900 = 1200 so from 100 , the population increased to 1200 i . e . an increase of 1100 . 1100 is what percent of 100 ? 1100 = x / 100 * 100 i . e . it is 1100 % d"
Break down and solve the equation step by step.,"a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after 1 year service . he served only for 9 months and receiveduniform and rs . 650 , find the priceof the uniform ? a ) rs . 90 , b ) rs . 100 , c ) rs . 120 , d ) rs . 150 , e ) rs . 160","""9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"""
"Work through the equation methodically, ensuring clarity at each step.","a train which has 600 m long , is running 60 kmph . in what time will it cross a person moving at 6 kmph in same direction ? a ) 42 sec , b ) 44 sec , c ) 46 sec , d ) 40 sec , e ) 50 sec","""time taken to cross a moving person = length of train / relative speed time taken = 600 / ( ( 60 - 6 ) ( 5 / 18 ) = 600 / 54 * ( 5 / 18 ) = 600 / 15 = 40 sec answer : d"""
Explain the solution process for the given equation.,"if the cost price of 50 articles is equal to the selling price of 35 articles , then the gain or loss percent is ? a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 43","""percentage of profit = 15 / 35 * 100 = 43 % answer : e"""
"Solve the problem systematically, showing each step clearly.","a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 64.50 , his capital is ? a ) 24,602 , b ) 28,888 , c ) 25,800 , d ) 24,628 , e ) 24,6012","""let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 64.50 32 x - 31 x = 6450 * 4 x = 25,800 . answer : c"""
Explain the solution process for the given equation.,"at what price must an article costing rs . 66.5 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ? a ) 87.5 , b ) 89.5 , c ) 82.3 , d ) 82.1 , e ) 92.4","""cp = 66.5 sp = 66.5 * ( 125 / 100 ) = 83.125 mp * ( 95 / 100 ) = 59.375 mp = 87.5 answer : a"""
Provide a detailed solution to the given mathematical problem.,"jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jack and jill will make a basket but sandy will miss ? a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 48 , d ) 1 / 96 , e ) 1 / 168","""the probability that jack and jill will make a basket but sandy will miss is 1 / 6 * 1 / 7 * 7 / 8 = 1 / 48 . the answer is c ."""
"Work through the equation methodically, ensuring clarity at each step.","divide rs . 32000 in the ratio 3 : 7 ? a ) 12000 , 20000 , b ) 9600 , 22400 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 12000 , 20001",3 / 10 * 32000 = 9600 7 / 8 * 32000 = 22400 answer : b
"Work through the equation methodically, ensuring clarity at each step.","a and b complete a work in 3 days . a alone can do it in 9 days . if both together can do the work in how many days ? a ) 3.75 days , b ) 4.75 days , c ) 3.25 days , d ) 3.15 days , e ) 2.75 days","""1 / 3 + 1 / 9 = 4 / 9 9 / 4 = 4.75 days answer : b"""
Provide a detailed solution to the given mathematical problem.,"a watch was sold at a loss of 10 % . if it was sold for rs . 210 more , there would have been a gain of 4 % . what is the cost price ? a ) s . 1000 , b ) s . 1009 , c ) s . 1007 , d ) s . 1006 , e ) s . 1500",explanation : 90 % 104 % - - - - - - - - 14 % - - - - 210 100 % - - - - ? = > rs . 1500 answer : e
Explain the solution process for the given equation.,"a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 3.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ? a ) 5729 , b ) 5040 , c ) 2889 , d ) 2870 , e ) 2799","""1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 3.5 = 5040 . answer : b"""
Explain the solution process for the given equation.,"sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2.5 % more . she would get how much ? a ) 9800 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882","""( 8000 * 3 * 2.5 ) / 100 = 600 9200 - - - - - - - - 9800 answer : a"""
Break down and solve the equation step by step.,"in 10 years , a will be twice as old as b was 10 years ago . if a is now 4 years older than b the present age of b is a ) 37 , b ) 38 , c ) 39 , d ) 34 , e ) 41",let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 4 = > 2 b - b - 4 = 30 b = 34 so the present age of b is 34 years answer : d
Explain the solution process for the given equation.,"in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 50 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ? a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 49 , e ) 47","""working backward from the day it' s covered : day 50 : fully covered day 49 : half covered so 49 days answer : d"""
Explain the solution process for the given equation.,"a jogger running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 metres long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? a ) 18 seconds , b ) 26 seconds , c ) 36 seconds , d ) 16 seconds , e ) 46 seconds",total distance ( d ) = 240 + 120 = 360 meter relative speed ( s ) = 45 - 9 = 36 kmph = 36 * 5 / 18 = 10 mps d = s * t 360 = 10 * t t = 36 seconds answer : c
"Work through the equation methodically, ensuring clarity at each step.","find the total number of prime factors in the expression ( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 33",( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 13 x 2 ^ 13 x 7 ^ 5 x 11 ^ 2 = 2 ^ 26 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 26 + 5 + 2 ) = 33 . answer is e .
Provide a detailed solution to the given mathematical problem.,"find the missing figures : 0.3 % of ? = 0.15 a ) 50 , b ) 45 , c ) 150 , d ) 450 , e ) 500","let 0.3 % of x = 0.15 . then , 0.30 * x / 100 = 0.15 x = [ ( 0.15 * 100 ) / 0.3 ] = 50 . answer is a ."
Break down and solve the equation step by step.,"in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,3 ) , ( 8,3 ) , ( 4,5 ) , ( 7,5 ) ? a ) 21 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 6 .","""delta x will give us the dimension of one side of the parallelogram = 8 - 5 = 3 unit delta y will give us the dimension of the other side of parallelogram = 5 - 3 = 2 unit area of parallelogram = 3 * 2 = 6 answer is e"""
"Solve the problem systematically, showing each step clearly.","a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.4 per box per month for the record storage , what is the total amount that the company pays each month for record storage ? a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 240 , e ) e . 200","""volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.4 = 240 answer : d"""
Provide a detailed solution to the given mathematical problem.,"two trains 110 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? a ) 10.9 , b ) 10.7 , c ) 10.3 , d ) 10.8 , e ) 9.72","""relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 110 + 160 = 270 m . required time = 270 * 9 / 250 = 243 / 25 = 9.72 sec .' answer : e"""
"Solve the problem systematically, showing each step clearly.","fresh grapes contain 70 % by weight while dried grapes contain 10 % water by weight . what is the weight of dry grapes available from 100 kg of fresh grapes ? a ) 18.33 kg , b ) 21.50 kg , c ) 25.00 kg , d ) 33.33 kg , e ) 40.39 kg","""from the question we know : 100 kg * 70 % = 70 kg of water in the fresh grapes 100 kg - 70 kg of water = 30 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 10 % of the weight of the dry graps is water and we know that 30 kg is non - water mass we can set up the following equation : x = 1 / 10 ( x ) + 30 kg 9 / 10 ( x ) = 30 kg x = 33.33 kg answer - d"""
Break down and solve the equation step by step.,"what is the sum of all 3 digit numbers that leave a remainder of' 2' when divided by 5 ? a ) 897 , b ) 98,910 , c ) 64,749 , d ) 49,700 , e ) 56,720","find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 5 seeing the options after dividing and finding the reminder of 2 my answer was b"
Explain the solution process for the given equation.,"how many 5 digit number contain number 3 ? a ) 31512 , b ) 32512 , c ) 33512 , d ) 34512 , e ) 37512","""total 5 digit no . = 9 * 10 * 10 * 10 * 10 = 90000 not containing 3 = 8 * 9 * 9 * 9 * 9 = 52488 total 5 digit number contain 3 = 90000 - 52488 = 37512 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","the manufacturing cost of a shoe is rs . 190 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains a ) s 234 , b ) s 216 , c ) s 220 , d ) s 210 , e ) s 217","""explanation : total cost of a watch = 190 + ( 500 / 100 ) = 195 . gain = 20 % = > sp = 1.2 cp = 1.2 x 195 = 234 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","what is the maximum number t of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ? ['a ) 36','b ) 32','c ) 24','d ) 21','e ) 15']","27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get t = 24 cubes . ans . c"
Explain the solution process for the given equation.,"how many multiples of 8 are there between 100 and 200 ( both are inclusive ) ? a ) 27 , b ) 4 , c ) 6 , d ) 13.5 , e ) 8","""the answer is ( 200 - 100 ) / 8 + 1 = 13.5 answer is d"""
"Solve the problem systematically, showing each step clearly.","a train passes a station platform in 36 sec and a man standing on the platform in 22 sec . if the speed of the train is 54 km / hr . what is the length of the platform ? a ) 288 , b ) 210 , c ) 881 , d ) 1277 , e ) 121","""speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 22 = 330 m . let the length of the platform be x m . then , ( x + 330 ) / 36 = 15 = > x = 210 m . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a train 140 m long is running with a speed of 50 km / hr . in what time will it pass a man who is running at 4 km / hr in the direction opposite to that in which the train is going ? a ) 8.1 , b ) 7.0 , c ) 9.33 , d ) 8 , e ) 9","""speed of train relative to man = 50 + 4 = 54 km / hr . = 54 * 5 / 18 = 15 m / sec . time taken to pass the men = 140 * 1 / 15 = 9.33 sec . answer : option c"""
"Work through the equation methodically, ensuring clarity at each step.","in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,7 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ? a ) 4 / 7 , b ) 2 / 3 , c ) 3 / 5 , d ) 3 / 7 , e ) 1 / 2","""the area of the right triangle is ( 1 / 2 ) * 4 * 7 = 14 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 14 = 4 / 7 the answer is a ."""
Explain the solution process for the given equation.,"the cash difference between the selling prices of an article at a profit of 4 % and 6 % is rs 3 . the ratio of two selling prices is a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) none of these","""explanation : let the cost price of article is rs . x required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 option b"""
"Work through the equation methodically, ensuring clarity at each step.","in what time will a train 300 meters long cross an electric pole , if its speed is 90 km / hr a ) 5 seconds , b ) 12 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these","""explanation : first convert speed into m / sec speed = 90 * ( 5 / 18 ) = 25 m / sec time = distance / speed = 300 / 25 = 12 seconds answer : b"""
Provide a detailed solution to the given mathematical problem.,"evaluate 2 + 22 + 222 + 2.22 a ) 269.72 , b ) 268.22 , c ) 248.21 , d ) 248.22 , e ) 268.21","""2 + 22 + 222 + 2.22 = 248.22 option d"""
"Solve the problem systematically, showing each step clearly.","the list price of an article is rs . 70 . a customer pays rs . 61.11 for it . he was given two successive discounts , one of them being 10 % . the other discount is ? a ) 8 % , b ) 7 % , c ) 10 % , d ) 3 % , e ) 4 %","""explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 61.11 x = 3 % d"""
Provide a detailed solution to the given mathematical problem.,"find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 a ) 26 , b ) 22 , c ) 25 , d ) 30 , e ) 29","""( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 3 = 2 ^ 22 x 7 ^ 5 x 11 ^ 3 total number of prime factors = ( 22 + 5 + 3 ) = 30 . answer is d ."""
Explain the solution process for the given equation.,"if the sum of 3 consecutive even numbers is 44 more than the average of these numbers , then the largest of these numbers is ? a ) 24 , b ) 66 , c ) 9 , d ) 7 , e ) 01","answer : 24 explanation : let the smallest of these number be x . the other two numbers are ( x + 2 ) and ( x + 4 ) . x + ( x + 2 ) + ( x + 4 ) = ( x + ( x + 2 ) + ( x + 4 ) ) / 3 + 44 3 x + 3 * ( x + 2 ) + 3 * ( x + 4 ) = x + ( x + 2 ) + ( x + 4 ) + 132 9 x + 18 = 3 x + 138 6 x = 120 x = 20 therefore , the largest number is 24 . answer : a"
Provide a detailed solution to the given mathematical problem.,"if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 5 ] ] ? a ) 39 , b ) 9 , c ) 15 , d ) 19 , e ) 25","""these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 5 ] ] = 5 ^ 2 + 2 * 5 + 4 = 39 . option a"""
Explain the solution process for the given equation.,"a professional athlete was offered a 3 - year contract to play with team k that provided for an annual salary of $ 100000 in the first year , an increase in annual salary of 20 % over the previous year for the next two years , and a bonus of $ 50000 on signing . team l offered a 3 - year contract providing for an annual salary of $ 150000 in the first year , an increase in annual salary of 20 % over the previous year for the next two years , and no signing bonus . if he accepts the offer of team l and fulfills the 3 - year contract terms , the athlete will receive how much more money by choosing team l over team k ? a ) $ 132,000 , b ) $ 50,000 , c ) $ 82,500 , d ) $ 92,000 , e ) $ 100,000","team k' s contract = $ 100,000 + $ 100,000 * 1.2 + $ 100,000 * 1.2 * 1.2 + $ 50,000 = $ 414,000 team l' s contract = $ 150,000 + $ 150,000 * 1.2 + $ 150,000 * 1.2 * 1.2 = $ 546,000 the difference = $ 132,000 . answer : a ."
Provide a detailed solution to the given mathematical problem.,"a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts six hours after a . if b and k overtake a at the same instant , how many hours after a did k start ? a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 12 , e ) e ) 5","""the table you made does n' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )"""
"Solve the problem systematically, showing each step clearly.","if a 2 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ? a ) 50 % , b ) 100 % , c ) 150 % , d ) 200 % , e ) 250 %","""the area a of the large cube is 2 * 2 * 6 = 24 square cm . the area of the 8 small cubes is 8 * 6 = 48 = 2 a , an increase of 100 % . the answer is b ."""
"Solve the problem systematically, showing each step clearly.","carina has 115 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ? a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 3","""lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 115 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 105 / 15 . = 7 b"""
"Work through the equation methodically, ensuring clarity at each step.","the sides of the triangle are in the ratio 1 / 2 : 1 / 3 : 1 / 4 and its perimeter is 104 cm . the length of the longest side is ? ['a ) 32 cm','b ) 48 cm','c ) 50 cm','d ) 28 cm','e ) 30 cm']",ratio of sides = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 largest side = 104 * 6 / 13 = 48 cm answer is b
Explain the solution process for the given equation.,"find a two digit number , given that the sum of the digits is 13 and the difference of the digits is 5 . ? a ) 74 , b ) 82 , c ) 95 , d ) 76 , e ) 94","""using elimination method find which of the options fit the description of the number . . . from the option only 94 meets this description sum of digits - - - 9 + 4 = 13 difference of digits - - - 9 - 4 = 5 answer e ."""
Provide a detailed solution to the given mathematical problem.,"a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food . a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 72","""explanation : as there is meal for 70 adults and 14 have their meal , the meal left can be catered to 56 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 56 adults = 72 children hence , the meal can be catered to 72 children . answer : e"""
"Solve the problem systematically, showing each step clearly.","in 1990 the budgets for projects q and v were $ 700,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ? a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996","""let the no of years it takes is x . 700 + 30 x = 780 - 10 x - - > 40 x = 80 and x = 2 . thus , it happens in 1992 . a ."""
Provide a detailed solution to the given mathematical problem.,"a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference ? a ) 10 feet , b ) 8 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet","""total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 2 = 8 feet answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a man can do a job in 20 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ? a ) 6.3 , b ) 6.9 , c ) 7.1 , d ) 6.1 , e ) 6.2","""1 day work of the three persons = ( 1 / 20 + 1 / 20 + 1 / 25 ) = 7 / 50 so , all three together will complete the work in 300 / 47 = 7.1 days . answer : c"""
Break down and solve the equation step by step.,"the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is : a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 368","""clearly , the numbers are ( 23 x 13 ) and ( 23 x 16 ) . larger number = ( 23 x 16 ) = 368 . answer : option e"""
"Solve the problem systematically, showing each step clearly.","if k ^ 3 is divisible by 162 , what is the least possible value of integer k ? a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 36","""k ^ 3 = 162 * x = 2 * 3 ^ 4 * x the factors of k must at minimum include 2 * 3 ^ 2 = 18 . the answer is c ."""
Break down and solve the equation step by step.,"if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value f of z - x ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10","""x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] f = z - x = x + 9 - x = 9 ans : d"""
"Solve the problem systematically, showing each step clearly.","there are 20 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? a ) 10 , b ) 30 , c ) 190 , d ) 60 , e ) 90","""20 players are there . two players play one game with one another . so 20 c 2 = 20 * 19 / 2 = 190 so option c is correct"""
"Solve the problem systematically, showing each step clearly.","john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 60 miles per hour , what is v in miles per hour ? a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70","""let distance be d . we can find the total time & equate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 60 = > v = 30 answer : a"""
Provide a detailed solution to the given mathematical problem.,"a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 1.8 kilometer long bridge , at the same speed ? a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 3 min",s = 600 / 40 = 15 mps s = 1800 / 15 = 120 sec = 2 min . answer : b
"Work through the equation methodically, ensuring clarity at each step.","at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 30 males did not bring gifts to the party , how many females did bring gifts ? a ) 18 , b ) 28 , c ) 40 , d ) 68 , e ) 70","""the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 30 are males , so remaining 90 - 30 = 60 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 60 , 100 % = 60 * 100 / 60 = 100 . ans 40 % of 100 = 40 c"""
Provide a detailed solution to the given mathematical problem.,"linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 230 , what were her original savings ? a ) $ 900 , b ) $ 800 , c ) $ 1000 , d ) $ 920 , e ) $ 1500","""if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 230 . so 1 / 4 of her savings is $ 230 . so her original savings are 4 times $ 230 = $ 920 correct answer d"""
Provide a detailed solution to the given mathematical problem.,"if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 2 years the amount to be paid is ? a ) rs . 8082 , b ) rs . 7800 , c ) rs . 8100 , d ) rs . 8112 , e ) rs . 9000","""explanation : a = 7500 ( 26 / 25 ) 2 = 8112 answer is d"""
Explain the solution process for the given equation.,"if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 28 , what is the common ratio of the g . p ? a ) 3 , b ) 1 / 3 , c ) 2 , d ) 9 , e ) 1 / 9","""28 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 28 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 28 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 27 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 27 = r ^ 3 r = 3 a"""
Break down and solve the equation step by step.,"a watch was sold at a loss of 10 % . if it was sold for rs . 540 more , there would have been a gain of 8 % . what is the cost price ? a ) 1000 , b ) 2998 , c ) 3000 , d ) 2788 , e ) 2991","""90 % 108 % - - - - - - - - 18 % - - - - 540 100 % - - - - ? = > rs . 3000 answer : c"""
Provide a detailed solution to the given mathematical problem.,"calculate how much time could be saved if the train would run at its usual speed , given that it ran at 5 / 7 of its own speed and got to its destination in 15 hours ? a ) 1.29 hrs , b ) 2.29 hrs , c ) 4.29 hrs , d ) 5.29 hrs , e ) 3.29 hrs","""new speed = 5 / 7 of usual speed new time = 5 / 7 of usual time 5 / 7 of usual time = 15 hrs usual time = 15 * 5 / 7 = 10.71 hrs time saved = 15 - 10.71 = 4.29 hrs answer is c"""
Provide a detailed solution to the given mathematical problem.,"convert 0.35 in to a vulgar fraction ? a ) 18 / 50 , b ) 16 / 50 , c ) 7 / 20 , d ) 19 / 50 , e ) none","""answer 0.35 = 35 / 100 = 7 / 20 correct option : c"""
Provide a detailed solution to the given mathematical problem.,"5 n + 2 > 17 and 7 n - 5 < 44 ; n must be between which numbers ? a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9","""5 n > 15 - - > n > 3 7 n < 49 - - > n < 7 3 < n < 7 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","the grade point average of one third of the classroom is 54 ; the grade point average of the rest is 45 . what is the grade point average of the whole class ? a ) 52 , b ) 54 , c ) 48 , d ) 58 , e ) 60","""let n = total students in class total points for 1 / 3 class = 54 n / 3 = 18 n total points for 2 / 3 class = 45 * 2 n / 3 = 30 n total points for whole class = 18 n + 30 n = 48 n 48 n total class points / n total students = 48 grade point average for total class answer : c"""
Provide a detailed solution to the given mathematical problem.,"in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? a ) 69 . , b ) 73 . , c ) 81 , d ) 91 , e ) 108","total students = 420 boys = 312 , girls = 108 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 108 - 35 = 73 . correct option : b"
"Work through the equation methodically, ensuring clarity at each step.","from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 15 percent . the enrollment on january 1 , 1993 , was 60 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ? a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 52","""1.15 x = 60 - - > 23 / 20 * x = 60 - - > x = 60 * 20 / 23 = 1200 / 23 = ~ 52 . answer : e ."""
Explain the solution process for the given equation.,"a box contains 6 pairs of shoes ( 12 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ? a ) 1 / 11 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9","the problem with your solution is that we do n' t choose 1 shoe from 12 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 11 as after taking one at random there are 11 shoes left and only one is the pair of the first one ) = 1 / 11 answer : a ."
"Solve the problem systematically, showing each step clearly.","the average of first 25 prime numbers is ? a ) 9.9 , b ) 8.8 , c ) 5.6 , d ) 11.9 , e ) 11.11","""explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 / 9 = 100 / 9 = 11.11 ( approx ) answer is e"""
"Work through the equation methodically, ensuring clarity at each step.","of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 17 boys and 43 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ? a ) 5 , b ) 4 , c ) 6 , d ) 8 , e ) 10","""venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 17 boys . so 17 - 6 - 6 = 5 boys must be neither happy nor sad . answer ( a )"""
"Work through the equation methodically, ensuring clarity at each step.","a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 10.50 less , he would have gained 30 % . find the cost of the article . a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70",let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 10.50 when c . p = ( 100 * 10.50 ) / 21 = 50 answer : c
Break down and solve the equation step by step.,"what is the least possible value of expression e = ( x - 1 ) ( x - 3 ) ( x - 4 ) ( x - 6 ) + 10 for real values of x ? a ) 1 , b ) 10 , c ) 9 , d ) 0 , e ) 8","explanation : e = ( x - 1 ) ( x - 6 ) ( x - 3 ) ( x - 4 ) + 10 e = ( x 2 - 7 x + 6 ) ( x 2 - 7 x + 12 ) + 10 let x 2 - 7 x + 6 = y e = y 2 + 6 y + 10 e = ( y + 3 ) 2 + 1 minimum value = 1 , when y = - 3 answer : a"
Provide a detailed solution to the given mathematical problem.,"in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 5.5 ) , ( 8 , 0 ) , ( 0 , - 5.5 ) , ( - 8 , 0 ) ? ['a ) 56','b ) 88','c ) 112','d ) 116','e ) 120']",ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 5.5 + 5.5 = 11 area = 1 / 2 * 16 * 11 = 88 b is the answer
"Solve the problem systematically, showing each step clearly.","a train moves at average speed of 40 kmph reaches its destination on time . what its average speed becomes 35 kmph , then it reaches its destination 15 late . find the length of the journey ? a ) 70 km , b ) 85 km , c ) 38 km , d ) 14 km , e ) 1 km",difference between timings = 15 mis = 1 / 4 hr let the length of the journey be x km . then x / 35 - x / 40 = 1 / 4 8 x - 7 x = 70 x = 70 km answer ( a )
Break down and solve the equation step by step.,"1370 , 1320 , 1070 , - 180 ? a ) - 6430 , b ) - 6530 , c ) - 6630 , d ) - 6730 , e ) - 6830","1370 , 13201070 , - 180 , ? 1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a ."
"Work through the equation methodically, ensuring clarity at each step.","if x is less than y by 45 % then y exceed x by : a ) 33.33 % , b ) 25 % , c ) 81.81 % , d ) 66.66 % , e ) none of these","""using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 45 / ( 100 - 45 ) * 100 = 81.81 % answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","the ratio between the present ages of a and b is 4.5 : 3 respectively . the ratio between a' s age 4 years ago and b' s age 4 years hence is 1 : 1 . what is the ratio between a' s age 4 years hence and b' s age 4 years ago ? a ) 3 : 4 , b ) 3 : 0 , c ) 3 : 1 , d ) 7 : 3 , e ) 3 : 7","""let the present ages of a and b be 4.5 x and 3 x years respectively . then , ( 4.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1.5 x = 8 = > x = 5.33 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 28 : 12 = 7 : 3 . answer : d"""
Break down and solve the equation step by step.,"two pipes a and b can fill a tank in 30 and 60 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ? a ) 10 , b ) 20 , c ) 30 , d ) 24 , e ) 25","""part filled by a in 1 min . = 1 / 30 part filled by b in 1 min . = 1 / 60 part filled by ( a + b ) in 1 min . = 1 / 30 + 1 / 60 = 1 / 20 . both the pipes can fill the tank in 20 minutes . answer : b"""
"Solve the problem systematically, showing each step clearly.","there are 8 stores in town that had a total of 24 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 9 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6","""9 people visited 2 stores each for 18 visits . to maximize the number of stores that one person visited , let' s assume that 2 people visited 1 store each . the number of remaining visits is 24 - 18 - 2 = 4 , which is the maximum that one person could have visited . the answer is c ."""
Explain the solution process for the given equation.,"how many positive integers less than 6,000 are there in which the sum of the digits equals 5 ? a ) 65 , b ) 62 , c ) 61 , d ) 56 , e ) 58","""basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x' s ( digits add up to the 5 ) , and 3 |' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . d"""
Provide a detailed solution to the given mathematical problem.,"if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 11.00 / day for each additional week , how much does it cost to stay for 23 days ? a ) $ 160 , b ) $ 176 , c ) $ 282 , d ) $ 302 , e ) $ 286","""total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 11 = 16 * 11 = 176 $ total charge = 126 + 176 = 302 $ answer d"""
"Work through the equation methodically, ensuring clarity at each step.","a certain number of men can finish a piece of work in 10 days . however , if there were 10 less men it will take 10 days more for the work to be finished . how many men were there originally ? a ) 10 men , b ) 30 men , c ) 40 men , d ) 20 men , e ) none of these","""let x be the number of men originally thus , 10 x = ( 10 + 10 ) ( x - 10 ) 10 x = 20 ( x - 10 ) x = 2 ( x - 10 ) x = 20 answer : d"""
Break down and solve the equation step by step.,"in a family 15 people eat only vegetarian , 8 people eat only non veg . , 11 people eat both veg and non veg . . how many people eat veg in the family ? a ) 20 , b ) 11 , c ) 23 , d ) 26 , e ) 21","""total people eat veg = only veg + both veg and non veg total = 15 + 11 = 26 answer = d"""
"Solve the problem systematically, showing each step clearly.","a math teacher has 24 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles . a ) 7 , b ) 10 , c ) 11 , d ) 12 , e ) 13","""a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 24 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 24 - 17 = 7 answer ( a )"""
Explain the solution process for the given equation.,"excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 36 kmph . for how many minutes does the bus stop per hour ? a ) 20 min , b ) 8 min , c ) 9 min , d ) 10 min , e ) 11 min","""due to stoppages , it covers 18 km less . time taken to cover 18 km = ( 18 / 54 ) x 60 = 20 min answer : a"""
Explain the solution process for the given equation.,"what is the greatest 6 - digit number when divided by 8 , 9 , and 10 leaves a remainder of 6 , 7 , and 8 respectively ? a ) 456780 , b ) 678918 , c ) 997479 , d ) 997916 , e ) 997920","when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 8 when we divide by 10 , so b is the only possible answer ."
Provide a detailed solution to the given mathematical problem.,"if x is equal to the sum of the integers from 30 to 50 , inclusive , and y is the number of even integers from 30 to 50 , inclusive , what is the value of x + y ? a ) 810 , b ) 811 , c ) 830 , d ) 850 , e ) 851","since the integers from 30 - 50 are consecutive we can use the ` ` median x # of terms formula'' to determine x . there are 21 terms and the median is 40 . this gives a total of 21 x 40 = 840 . there are 11 even integers from 30 - 50 = y . therefore , x + y = 851 . answer : e"
"Work through the equation methodically, ensuring clarity at each step.","a man has some hens and cows . if the number of heads be 50 and the number of feet equals 144 , then the number of hens will be a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28","""explanation : let number of hens = h and number of cows = c number of heads = 50 = > h + c = 48 - - - ( equation 1 ) number of feet = 144 = > 2 h + 4 c = 144 = > h + 2 c = 72 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 72 - 50 = > c = 22 substituting the value of c in equation 1 , we get h + 22 = 50 = > h = 50 - 22 = 28 i . e . , number of hens = 28 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","for how many values of q , is | | | q - 5 | - 10 | - 5 | = 2 ? ( those ls are mods ) a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8","i think its 8 | | | q - 5 | - 10 | - 5 | = 2 let | q - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so' a' has four solutions 13 , 7 , 17 and 3 for a = 13 ; q has 18 or - 8 thus has 2 for every combination hence 4 x 2 = 8 answer d"
"Work through the equation methodically, ensuring clarity at each step.","the size of a television screen is given as the length of the screen' s diagonal . if the screens were flat , then the area of a square 21 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ? a ) 2 , b ) 4 , c ) 16 , d ) 38 , e ) 76","""pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 21 ^ 2 / 2 - 17 ^ 2 / 2 = 152 / 2 = 76 ans e ."""
Provide a detailed solution to the given mathematical problem.,"if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 54 kmh , what was the average speed of the car for the entire trip ? a ) 36 kmh , b ) 40 kmh , c ) 41 kmh , d ) 44 kmh , e ) 50 kmh","""assume d / 3 = 2160 ( this number is convenient because it is divisible by 80 , 24 and 54 ) so : 2160 = 80 * t 1 = 27 hrs 2160 = 24 * t 2 = 90 hrs 2160 = 54 * t 3 = 40 hrs t = t 1 + t 2 + t 3 = 157 hrs d = rt ( 240 * 3 ) = r * 157 r = 41.27 answer : c"""
Provide a detailed solution to the given mathematical problem.,"if | 20 x - 10 | = 90 , then find the product of the values of x ? a ) - 45 , b ) 50 , c ) - 62 , d ) 35 , e ) - 20","""| 20 x - 10 | = 90 20 x - 10 = 90 or 20 x - 10 = - 90 20 x = 100 or 20 x = - 80 x = 5 or x = - 4 product = - 4 * 5 = - 20 answer is e"""
Provide a detailed solution to the given mathematical problem.,"how many even integers n , such that 20 < = n < = 180 are of the form 3 k + 4 , where k is any natural number ? a ) 24 , b ) 27 , c ) 30 , d ) 33 , e ) 36","the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 278 = 16 + 6 ( 27 ) there are 27 numbers in the list . the answer is b ."
Explain the solution process for the given equation.,"find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 13 cm . a ) 335 cm 2 , b ) 885 cm 2 , c ) 285 cm 2 , d ) 247 cm 2 , e ) 725 cm 2","""area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 13 ) = 247 cm 2 answer : d"""
Break down and solve the equation step by step.,"the length of a bridge in meters , which a train 80 - meters long and traveling at 45 km / hr can cross in 30 seconds is ? a ) 215 , b ) 235 , c ) 255 , d ) 275 , e ) 295","""45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 80 = 375 meters x = 295 meters the answer is e ."""
Explain the solution process for the given equation.,"an empty wooden vessel weighs 14 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled . a ) 6 / 13 , b ) 5 / 9 , c ) 1 / 24 , d ) 4 / 9 , e ) 2 / 5","""an empty wooden vessel weighs 14 % of its total weight when filled with paint : vessel = 0.14 ( vessel + paint ) ; 14 v = v + p ( so the weight of completely filled vessel is 14 v ) p = 13 v ( so the weight of the paint when the vessels is completely filled is 13 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p' = 1 / 2 * 14 v ; p' = 6 v ( so the weight of the paint when the vessels is partially filled is 6 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p' / p = 6 v / 13 v = 6 / 13 . answer : a ."""
Break down and solve the equation step by step.,"tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 8 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ? a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4.5 mph , e ) 0.5 mph","""( 1 mph + 8 mph ) / 2 = 4.5 mph correct option is : d"""
Explain the solution process for the given equation.,"how many 3 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 121 . a ) 90 , b ) 610 , c ) 729 , d ) 900 , e ) 1000","""take the task of building palindromes and break it intostages . stage 1 : select the hundreds digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the tens digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the units digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 3 - digit palindrome ) in ( 9 ) ( 10 ) ( 1 ) ways ( = 900 ways ) answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? a ) 2.9 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 6.7 hrs , e ) 8.6 hrs","""net part filled in 1 hour = ( 1 / 4 - 1 / 10 ) = 3 / 20 the cistern will be filled in 20 / 3 hrs i . e . , 6.7 hrs . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 637 , krishan has ? a ) s . 2890 , b ) s . 2330 , c ) s . 3757 , d ) s . 1620 , e ) s . 2680","""ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 637 : n & there n = 289 x 637 / 49 = rs . 3757 answer : c"""
"Solve the problem systematically, showing each step clearly.","a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 350 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ? a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 220","""orchestra seats - a balcony seats - b a + b = 350 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 350 = 3320 - 2800 = 520 i . e . a = 130 and b = 350 - 130 = 220 more seats in balcony than orchestra = b - a = 220 - 130 = 90 answer : option a"""
"Work through the equation methodically, ensuring clarity at each step.","the area of an isosceles trapezoid with sides of length 5 and bases of length 8 and 14 is ? a ) 22 , b ) 32 , c ) 44 , d ) 55 , e ) 56","""we can divide the trapezoid into two triangles and a rectangle sides of triangle , t 1 - - > h 1 = 5 , b 1 = 3 , s 1 = root ( 25 - 9 ) = 4 = s 2 of triangle t 2 area of triangle = ( 1 / 2 ) * 4 * 3 = 6 side of the rectangle = 8 * 4 = 32 total area of the trapezoid = 32 + 6 + 6 = 44 answer : c"""
Provide a detailed solution to the given mathematical problem.,"if 20 % of a number = 1000 , then 120 % of that number will be ? a ) 20 , b ) 120 , c ) 360 , d ) 6000 , e ) 820","""let the number x . then , 20 % of x = 1000 x = ( 1000 * 100 ) / 20 = 5000 120 % of x = ( 120 / 100 * 5000 ) = 6000 . answer : d"""
"Solve the problem systematically, showing each step clearly.","two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 26 seconds . the ratio of their speeds is ? a ) 3 / 1 , b ) 9 / 1 , c ) 3 / 3 , d ) 3 / 5 , e ) 5 / 2","""let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 26 = = > 27 x + 17 y = 26 x + 26 y = = > 1 x = 9 y = = > x / y = 9 / 1 . answer : b"""
Break down and solve the equation step by step.,"a train covers a distance of 9 km in 6 min . if it takes 5 sec to pass a telegraph post , then the length of the train is ? a ) 100 , b ) 105 , c ) 110 , d ) 120 , e ) 125","""speed = ( 9 / 6 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 25 * 5 = 125 m . answer : option e"""
"Solve the problem systematically, showing each step clearly.","a watch was sold at a loss of 12 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ? a ) s . 1000 , b ) s . 875 , c ) s . 1007 , d ) s . 1006 , e ) s . 1002","""explanation : 88 % 104 % - - - - - - - - 16 % - - - - 140 100 % - - - - ? = > rs . 875 answer : b"""
Provide a detailed solution to the given mathematical problem.,"a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ? a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59","""let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c"""
Break down and solve the equation step by step.,"a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds . what is the length of the train in meters ? a ) 400 meters , b ) 1111 meters , c ) 160 meters , d ) 850 meters , e ) none of these",train overtakes a bike means that we are talking about total length of the train . ( train' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 85 seconds distance = speed * time 36000 * 85 / 3600 = 850 meters . d is the answer .
Explain the solution process for the given equation.,"25.25 / 1500 is equal to : a ) 1.012526333 , b ) 0.012625333 , c ) 0.125263333 , d ) 0.126253333 , e ) 0.016833333","""25.25 / 2000 = 2525 / 200000 = 0.016833333 answer : e"""
Explain the solution process for the given equation.,"the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 200 liters of water , how many liters of detergent will it contain ? a ) 60 , b ) 55 , c ) 50 , d ) 45 , e ) 40","""b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 200 dnew = wnew / 5 = 200 / 5 = 40 so , answer will be e"""
"Work through the equation methodically, ensuring clarity at each step.","the difference of two numbers is 11 . one third of their sum is 7 . what are the two numbers ? a ) 21,10 , b ) 16,5 , c ) 3,14 , d ) 11,10 , e ) 7,14","""let the two numbers be x and y . equation ( i ) : x - y = 11 equation ( ii ) : ( x + y ) / 3 = 7 solve system of equations : x + y = 21 x - y = 11 ( add equations together ) - - - 2 x = 32 - - - x = 16 16 - y = 11 - - - y = 5 since x = 16 and y = 5 , answer b ( 16,5 ) is correct ."""
"Work through the equation methodically, ensuring clarity at each step.","rahim bought 65 books for rs . 1150 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ? a ) rs . 17 , b ) rs . 18 , c ) rs . 12 , d ) rs . 11 , e ) rs . 10","""average price per book = ( 1150 + 920 ) / ( 65 + 50 ) = 2070 / 115 = rs . 18 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","if the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 8 centimeters , what is the length of the rectangle , in centimeters ? a ) 4 , b ) 8 , c ) 2 , d ) 16 , e ) 18","""let length of rectangle = l 4 ^ 2 = l * 8 = > l = 16 / 8 = 2 answer c"""
Provide a detailed solution to the given mathematical problem.,"if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 10 men in 3 days ? a ) 65 mtr . , b ) 28 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 17 mtr .","""20 men is 6 days can build 112 metres 10 men in 3 days can build = 112 * ( 10 / 20 ) x ( 3 / 6 ) = 28 meters answer : b ."""
Provide a detailed solution to the given mathematical problem.,"the average age of 39 students in a group is 14 years . when teacher' s age is included to it , the average increases by one . what is the teacher' s age in years ? a ) 35 years , b ) 45 years , c ) 51 years , d ) 54 years , e ) none of these","""explanation : age of the teacher = ( 40 * 15 - 39 * 14 ) years = 54 years . answer : d"""
Provide a detailed solution to the given mathematical problem.,"the cost price of 12 articles is equal to the selling price of 10 articles . what is the profit percent ? a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %","""10 * sp = 12 * cp sp = 1.2 * cp the profit percent is 20 % . the answer is b ."""
"Solve the problem systematically, showing each step clearly.","on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.2 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ? a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 9 %","""if the interest were compounded annually instead of quarterly then in one year the interest would be 2.2 * 4 = 8.8 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 8.8 % answer : e ."""
Provide a detailed solution to the given mathematical problem.,"suppose you work for a manufacturing plant that pays you $ 12.50 an hour and $ . 16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 800 ( before payroll deductions ) ? a ) 1800 , b ) 1825 , c ) 1850 , d ) 1855 , e ) 1875","""hourly = $ 12.50 / hour totalhours = 40 piecework = $ 0.16 / widget totalpieces = ? ? ? ? total pay = ( hourly * totalhours ) + ( piecework * totalpieces ) so , put it all together : $ 800 = ( $ 12.50 * 40 ) + ( $ 0.16 * total pieces ) totalpieces = ( $ 800 - ( $ 12.50 * 40 ) ) / $ 0.16 = 1875 widgets e . 1875"""
"Work through the equation methodically, ensuring clarity at each step.","gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 16 times as heavy as water ? a ) 1 : 2 , b ) 7 : 3 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5","""g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 16 w 19 + 9 x = 16 ( x + 1 ) x = 3 / 7 ratio of gold with copper = 1 : 3 / 7 = 7 : 3 answer is b"""
Break down and solve the equation step by step.,"if a randomly selected non - negative single digit integer is added to { 2 , 3 , 5 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ? a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6","we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 5 ) / 2 = 4 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ."
"Solve the problem systematically, showing each step clearly.","two employees m and n are paid a total of $ 616 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ? a ) $ 270 , b ) $ 280 , c ) $ 290 , d ) $ 300 , e ) $ 310","""1.2 n + n = 616 2.2 n = 616 n = 280 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 4 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ? a ) 347 , b ) 480 , c ) 288 , d ) 278 , e ) 131","""let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 4 2 x / 15 - x / 8 = 4 = > x = 480 km . answer : b"""
Break down and solve the equation step by step.,"if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 11 a + 11 b ? a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4","""( i ) 9 a - 11 b = 70 ( ii ) 2 a + 22 b = - 70 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."""
"Solve the problem systematically, showing each step clearly.","a man can row downstream at the rate of 16 km / hr and upstream at 8 km / hr . find man' s rate in still water and the rate of current ? a ) 12,4 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these","""explanation : rate of still water = 1 / 2 ( 16 + 8 ) = 12 km / hr rate of current = 1 / 2 ( 16 - 8 ) = 4 km / hr answer : option a"""
"Work through the equation methodically, ensuring clarity at each step.","find the ones digit of 73 ^ 352 a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9","""the units digit of 73 ^ 352 will be the same as the units digit of 3 ^ 352 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 352 = ( multiple of 4 ) + 0 , since 3 is an odd number , the units digit of 3 ^ 352 will be 1 . answer : a ."""
Explain the solution process for the given equation.,"- 64 x 29 + 165 = ? a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 1601 , e ) none of them","""given exp . = - 64 x ( 30 - 1 ) + 165 = - ( 64 x 30 ) + 64 + 165 = - 1830 + 229 = - 1601 answer is d"""
Explain the solution process for the given equation.,"a watch was sold at a loss of 10 % . if it was sold for rs . 168 more , there would have been a gain of 4 % . what is the cost price ? a ) s : 1000 , b ) s : 1067 , c ) s : 1200 , d ) s : 1028 , e ) s : 1027","""90 % 104 % - - - - - - - - 14 % - - - - 168 100 % - - - - ? = > rs : 1200 answer : c"""
Explain the solution process for the given equation.,"how many integers are divisible by 5 between 10 ! and 10 ! + 20 inclusive ? a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10",a - 7 10 ! is divisible by 5 there are 4 numbers between 10 ! and 10 ! + 20 that are divisible by 5 . hence 5
Explain the solution process for the given equation.,"in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is a ) 3 hr . , b ) 5 hr . , c ) 2 hr . , d ) 7 hr . , e ) 1 hr .","""e 1 hr . let the duration of the flight be x hours . then , 600 / x - 600 / 0.5 x = 200 - - > 600 / x - 1200 / ( 2 x + 1 ) = 200 - - > x ( 2 x + 1 ) = 3 - - > 2 x ^ 2 + x - 3 = 0 - - > ( 2 x + 3 ) ( x - 1 ) = 0 - - > x = 1 hr ."""
Provide a detailed solution to the given mathematical problem.,"martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.60 , how many discounted tickets did he buy ? a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7","""let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.6 0.4 x = 1.6 = > x = 4 discounted tickets = 10 - x = 6 ans : d"""
"Solve the problem systematically, showing each step clearly.","a man can do a piece of work in 5 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ? a ) 13 / 2 , b ) 7 , c ) 15 / 2 , d ) 8 , e ) 9","""son' s 1 day' s work = ( 1 / 3 ) - ( 1 / 5 ) = 2 / 5 the son alone can do the work in 15 / 2 days answer is c"""
Break down and solve the equation step by step.,"a cycle is bought for rs . 670 and sold for rs . 780 , find the gain percent ? a ) 70 % , b ) 20 % , c ) 16 % , d ) 19 % , e ) 80 %","""explanation : 670 - - - - 110 100 - - - - ? = > 16 % answer : c"""
"Solve the problem systematically, showing each step clearly.","in a certain corporation , there are 300 male employees and 150 female employees . it is known that 10 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ? a ) 1 / 5 , b ) 5 / 15 , c ) 6 / 15 , d ) 3 / 10 , e ) 4 / 15",p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.1 * 300 / 450 = 30 / 450 = 1 / 15 the sum of the probabilities is 6 / 15 = 2 / 5 the answer is c .
Explain the solution process for the given equation.,"if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 10 ) , what is the value of x ? a ) 9 , b ) 11 , c ) 13 , d ) 12 , e ) 17","""( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 10 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 10 hence x = 12 . answer is d"""
"Work through the equation methodically, ensuring clarity at each step.","a worker' s daily wage is increased by 50 % and the new wage is $ 51 per day . what was the worker' s daily wage before the increase ? a ) $ 28 , b ) $ 32 , c ) $ 34 , d ) $ 35 , e ) $ 40","""let x be the daily wage before the increase . 1.5 x = $ 51 x = $ 34 the answer is c ."""
Break down and solve the equation step by step.,"the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 20 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes . a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.09","""assume the manager bought 100 tomatoes . cost price = 80 given : 20 % are damaged - - > available tomatoes to sell = 80 80 * x - 80 = 0.08 * 80 80 x - 80 = 6.4 80 x = 86.64 x = 86.64 / 80 = 87 / 80 ( approx ) = 1.0875 x is slightly under 1.0875 = 1.09 answer : e"""
Explain the solution process for the given equation.,"consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes ? a ) 56678 , b ) 16789 , c ) 17576 , d ) 35142 , e ) none of these","""explanation : the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 * 26 = 676 wayshaving chosen the first two letters , the third letter can be chosen in 26 ways . = > all the three letters can be chosen in 676 * 26 = 17576 ways . it implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter . answer : c"""
Explain the solution process for the given equation.,"x and y began business with rs . 10000 and rs . 8000 after 6 months , x advances rs . 2000 and y advances rs . 2000 more . at the end of the year , their profits amounted to rs . 2000 find the share of x and y respectively . a ) 10001000 , b ) 9001100 , c ) 1200800 , d ) 8001200 , e ) 1100 , 900","( 10 * 6 + 12 * 6 ) : ( 8 * 6 + 10 * 6 ) 11 : 9 x share = 11 / 20 * 2000 = 1100 . y share = 9 / 20 * 2000 = 900 . x and y share respectively is 1100 , 900 . answer : e"
"Solve the problem systematically, showing each step clearly.","at what price must an article costing rs . 85.5 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ? a ) 122.5 , b ) 142.5 , c ) 162.5 , d ) 182.5 , e ) 112.5","""cp = 85.50 sp = 85.5 * ( 125 / 100 ) = 106.875 mp * ( 95 / 100 ) = 106.875 mp = 112.5 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","two friends plan to walk along a 33 - km trail , starting at opposite ends of the trail at the same time . if friend p' s rate is 20 % faster than friend q' s , how many kilometers will friend p have walked when they pass each other ? a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19","""if q complete x kilometers , then p completes 1.2 x kilometers . x + 1.2 x = 33 2.2 x = 33 x = 15 then p will have have walked 1.2 * 15 = 18 km . the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"p and q started a business investing rs 10000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively . a ) 2 : 7 , b ) 2 : 6 , c ) 17 : 6 , d ) 2 : 3 , e ) 7 : 8","""explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 10000 : 15000 = 10 : 15 = 2 : 3 option d"""
"Solve the problem systematically, showing each step clearly.","in a sports club with 30 members , 16 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ? a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11","""let x play both badminton and tennis so 16 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 16 - x ) + ( 19 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a"""
"Work through the equation methodically, ensuring clarity at each step.","a $ 84.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ? a ) 15 % , b ) 20 % , c ) 25 % , d ) 29 % , e ) 80 %","""listed selling price of chair = 84.95 $ discounted selling price of chair = 59.95 $ discount = 84.95 - 59.95 = 25 $ % decrease in price of chair = ( 25 / 84.95 ) * 100 % = 29 % approx answer d"""
Break down and solve the equation step by step.,"an artist wishes to paint a circular region on a square poster that is 3 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ? a ) 1 / pi , b ) sqrt ( 2 / pi ) , c ) sqrt ( 4.5 / pi ) , d ) 2 / sqrt ( pi ) , e ) pi / 2","""area of the poster is 3 x 3 = 9 1 / 2 the area = 4.5 pi * r ^ 2 = 4.5 r ^ 2 = 4.5 / pi r = sqrt ( 4.5 / pi ) answer ( c )"""
Break down and solve the equation step by step.,"jim is able to sell a hand - carved statue for $ 670 which was a 25 % profit over his cost . how much did the statue originally cost him ? a ) $ 496.30 , b ) $ 536.00 , c ) $ 555.40 , d ) $ 574.90 , e ) $ 588.20","""670 = 1.25 * x x = 670 / 1.25 = 536 $ 536 , which is ( b ) ."""
Explain the solution process for the given equation.,"by selling 10 pens for a rupee a woman loses 18 % . how many for a rupee should he sell in order to gain 30 % ? a ) 12 , b ) 14 , c ) 45 , d ) 6 , e ) 7","""d 82 % - - - 10 130 % - - - ? 82 / 130 * 10 = 6"""
"Solve the problem systematically, showing each step clearly.","the sum of the present age of henry and jill is 41 . what is their present ages if 7 years ago henry was twice the age of jill ? a ) and 25 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these","let the age of jill 7 years ago be x , age of henry be 2 x x + 7 + 2 x + 7 = 41 x = 9 present ages will be 16 and 25 answer : a"
Break down and solve the equation step by step.,"a reduction of 15 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 1200 , what is the reduced price for kg ? a ) 43 , b ) 55 , c ) 35 , d ) 45 , e ) 40","""1200 * ( 15 / 100 ) = 180 - - - - 4 ? - - - - 1 = > rs . 45 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","at a florist shop on a certain day , all corsages sold for either $ 25 or $ 40 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store' s revenue from corsages that day would have been reduced by 40 percent . what was the store' s actual revenue from corsages that day ? a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 300","""i am doing it elaborately , hope it will help you . let , no . of corsages @ $ 25 = x , no . of corsages @ $ 40 = y and revenue = r so , 25 x + 40 y = r . . . . . . . . . ( 1 ) now , given the situation , 25 ( x + 8 ) + 40 ( y - 8 ) = r - . 4 r = > 25 x + 200 + 40 y - 320 = . 6 r = > 25 x + 40 y = . 8 r + 120 . . . . . . . . . . . . ( 2 ) so , r = . 6 r + 120 = > r = 300 the answer is e ."""
Provide a detailed solution to the given mathematical problem.,"which greatest possible length can be used to measure exactly 12 meter 15 cm , 10 meter 15 cm and 10 meter 65 cm a ) 45 cm , b ) 25 cm , c ) 4 cm , d ) 5 cm , e ) 50 cm","""explanation : convert first all terms into cm . i . e . 1215 cm , 1015 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option d"""
Explain the solution process for the given equation.,"john is building a rectangular fence around a garden . the length will be 5 feet shorter than its width . if the total area of the garden is 176 square feet , what is the length of the diagonal ( in feet ) ? ['a ) between 18 and 19','b ) between 19 and 20','c ) between 20 and 21','d ) between 21 and 22','e ) between 22 and 23']","to solve this , we first need to set up an equation for the area of the garden . if x is the width , then we have x ( x - 5 ) = 176 . by putting the equation in standard form , we get x ^ 2 - 5 x - 176 = 0 . by using the quadratic formula , we get roots of - 11 and 16 . we know that x is the width , and x - 5 is the length , so by using the roots , we get 16 as the width ( x ) , and 11 as the length ( x - 5 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 16 ^ 2 + 11 ^ 2 = 256 + 121 = 377 the square root of 377 is less than 20 , since 20 ^ 2 = 400 . going down a number , we can compute 19 ^ 2 = 361 < 377 . therefore , the length of the diagonal must be between 19 and 20 . the correct answer is b ."
Provide a detailed solution to the given mathematical problem.,"if k is an integer and 0.00010101 x 10 ^ k is greater than 1000 , what is the least possible value of k ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10","""0.00010101 * 10 ^ k > 1000 we need to move the decimal point to the right 7 places to get 1010.1 this is equivalent to multiplying by 10 ^ 7 . the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","length of a rectangular plot is 30 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ? a ) 46 m , b ) 60 m , c ) 65 m , d ) 78 m , e ) 80 m","""let breadth = x metres . then , length = ( x + 30 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 30 ) + x ] = 200 2 x + 30 = 100 2 x = 70 x = 35 . hence , length = x + 30 = 65 m c"""
Provide a detailed solution to the given mathematical problem.,"x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 32 days . how long will y take to complete the work ? a ) 10 , b ) 40 , c ) 15 , d ) 18 , e ) 20","""work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 32 days whole work will be done by y in 32 * 5 / 4 = 40 days answer is b"""
Explain the solution process for the given equation.,"a person bought 110 glass bowls at a rate of rs . 10 per bowl . he sold 100 of them at rs . 14 and the remaining broke . what is the percentage gain for a ? a ) 40 , b ) 300 / 11 , c ) 243 / 7 , d ) 279 / 11 , e ) 279 / 8","""cp = 110 * 10 = 1100 and sp = 100 * 14 = 1400 gain % = 100 * ( 1400 - 1100 ) / 1100 = 300 / 11 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a retailer buys 100 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ? a ) 110 , b ) 175 , c ) 212 , d ) 218 , e ) 220","""let the market price of each pen be $ 1 then , cost price of 100 pens = $ 36 selling price of 100 pens = 99 % of $ 100 = $ 99 profit % = ( ( 63 * 100 ) / 36 ) % = 175 % answer b"""
"Work through the equation methodically, ensuring clarity at each step.","100 white and black tiles will be used to form a 20 x 20 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ? a ) 75 , b ) 70 , c ) 85 , d ) 90 , e ) 95","""answer = b please refer diagram below 90 - 20 = 70"""
"Solve the problem systematically, showing each step clearly.","a cycle is bought for rs . 1000 and sold for rs . 2000 , find the gain percent ? a ) 11 , b ) 20 , c ) 100 , d ) 77 , e ) 12","""1000 - - - - 1000 100 - - - - ? = > 100 % answer : c"""
"Solve the problem systematically, showing each step clearly.","the area of a triangle will be when a = 3 m , b = 4 m , c = 5 m , a , b , c being lengths of respective sides ? a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1",s = ( 3 + 4 + 5 ) / 2 = 6 answer : b
"Solve the problem systematically, showing each step clearly.","a bag contains 4 white marbles and 4 black marbles . if each of 4 girls and 4 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? a ) 1 / 35 , b ) 1 / 9 , c ) 1 / 10 , d ) 1 / 20 , e ) 1 / 30","""first , total ways to select for all boys and girls , i . e 8 ! / ( 4 ! * 4 ! ) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1 = 70 then there are one two way girls can have all same colors , either white or black . the number of ways in which 4 girls can select 4 white balls = 4 c 4 = 1 the number of ways in which 4 girls can select 4 black balls = 4 c 4 = 1 therefore , total favorable outcomes / total outcomes = 2 / 70 = 1 / 35 a"""
Break down and solve the equation step by step.,"find a number such that when 15 is subtracted from 7 times the number , the result is 10 more than twice the number . a ) 1 , b ) 4 , c ) 5 , d ) 0 , e ) 3","let the number be x . then , 7 x - 15 = 2 x + 10 = > 5 x = 25 = > x = 5 . hence , the required number is 5 . answer is c ."
"Solve the problem systematically, showing each step clearly.","the average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added . if average weight of the whole group after including the additional 30 members is 40 kg , what is the average weight of the additional friends ? a ) 50 kg , b ) 60 kg , c ) 61 kg , d ) 62 kg , e ) 91 kg",let a = avg . wt . of additional 30 friends original total weight = ( 30 friends ) ( 30 kg avge ) = 900 kg ( 900 + 30 a ) / ( 30 + 30 ) = 40 kg avge a = 50 kg answer - a
"Solve the problem systematically, showing each step clearly.","in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 2,800 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 8,400 higher that m , then what percentage of apartments in the building are two - bedroom apartments ? a ) 30 % , b ) 35 % , c ) 25 % , d ) 40 % , e ) 50 %","""ratio of 2 bedroom apartment : 1 bedroom apartment = 2800 : 8400 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : c"""
Explain the solution process for the given equation.,"the present worth of $ 3600 due in 2 years at 20 % per annum compound interest is ? a ) $ 1200 , b ) $ 1850 , c ) $ 2010 , d ) $ 3200 , e ) $ 2500",present worth = 3600 / ( 1 + 20 / 100 ) ^ 2 = 3600 * 5 / 6 * 5 / 6 = $ 2500 answer is e
"Work through the equation methodically, ensuring clarity at each step.","$ 8,000 is deposited in a savings account that pays 12 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ? a ) $ 8288.55 , b ) $ 8985.10 , c ) $ 8988.80 , d ) $ 8977.14 , e ) $ 8964.95","""this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 12 / 2 = 6 % now , ca = 8000 ( 1 + 6 / 100 ) ^ 2 = $ 8988.80 hence answer is c"""
Explain the solution process for the given equation.,"a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint e , in gallons , that must be purchased in order to measure out the portions needed for the mixture ? a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4","""given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b"""
"Work through the equation methodically, ensuring clarity at each step.","2 , 3 , 6 , 15 , _ , 123 ? a ) 42 , b ) 38 , c ) 28 , d ) 29 , e ) 11",answer : a
Explain the solution process for the given equation.,"how many seconds will a 600 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ? a ) 48 , b ) 36 , c ) 26 , d ) 11 , e ) 18","""explanation : here distance d = 600 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 36 sec . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used . a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139",( 35 * 4 ) - 4 = 136 answer : b
Explain the solution process for the given equation.,"two trains a and b start simultaneously in the opposite direction from two points p and q and arrive at their destinations 16 and 9 hours respectively after their meeting each other . at what speed does the second train b travel if the first train travels at 120 km / h a ) 334 , b ) 160 , c ) 387 , d ) 278 , e ) 112",answer : b ) 160 km / h
Explain the solution process for the given equation.,"the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 5 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10","""to get 40 points as end of season we need another 35 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 option e = 10 * 3 + 5 * 1 = 35 hence option e - 10"""
Provide a detailed solution to the given mathematical problem.,"tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 6 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ? a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 2 / 5","""tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 4 / 6 ) = 1 / 2 hours peter worked for 3 / 2 hours so he painted 3 / 2 * 1 / 3 = 1 / 2 of the room . the answer is a ."""
Break down and solve the equation step by step.,"an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4000 , what will be the difference between q and r' s share ? a ) 2788 , b ) 5000 , c ) 7282 , d ) 2782 , e ) 2729","""4 - - - 4000 5 - - - ? = > 5000 answer : b"""
Provide a detailed solution to the given mathematical problem.,"a , b and c can do a piece of work in 24 , 30 and 40 days respectively . they start the work together but c leaves 4 days before the completion of the work . in how many days is the work done ? a ) 11 , b ) 5 , c ) 70 , d ) 11 , e ) 13",x / 24 + x / 30 + x / 40 = 1 x = 11 days answer : d
Break down and solve the equation step by step.,"a woman swims downstream 54 km and upstream 6 km taking 6 hours each time , what is the speed of the woman in still water ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6","""54 - - - 6 ds = 9 ? - - - - 1 6 - - - - 6 us = 1 ? - - - - 1 m = ? m = ( 9 + 1 ) / 2 = 5 answer : d"""
"Solve the problem systematically, showing each step clearly.","2 trains in same direction at 50 km / hr , 32 km / hr . a man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train ? a ) 65 meters , b ) 75 meters , c ) 85 meters , d ) 95 meters , e ) 55 meters",relative speed = 18 k / hr = 5 m / sec distance covered = length of faster train = 5 * 15 = 75 meters answer : b
Provide a detailed solution to the given mathematical problem.,"in an examination 35 % of the students passed and 455 failed . how many students appeared for the examination ? a ) 540 , b ) 400 , c ) 700 , d ) 650 , e ) 840","""let the number of students appeared be x then , 65 % of x = 455 65 x / 100 = 455 x = 455 * 100 / 65 = 700 answer is c"""
Explain the solution process for the given equation.,"in a division sum , the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is : a ) 53 , b ) 58 , c ) 51 , d ) 60 , e ) 62","""diver = ( 4 * 3 ) + 2 = 14 4 * quotient = 14 quotient = 3.5 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 3.5 ) + 4 = 53 a"""
"Solve the problem systematically, showing each step clearly.","a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 2 days . b can do the work alone in ? a ) 3 hours , b ) 6 hours , c ) 7 hours , d ) 4 hours , e ) 8 hours","""b 6 hours suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 2 6 / x = 1 / 2 = > x = 12 so , b takes 6 hours to finish the work ."""
"Solve the problem systematically, showing each step clearly.","a certain industrial loom weaves 0.132 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ? a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118","""let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.132 : 15 : : 1 : x = > 0.132 * x = 15 = > x = 15 / 0.132 = > x = 114 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","mary' s income is 60 % more than tim' s income and tim' s income is 20 % less than juan' s income . what % of juan' s income is mary' s income . a ) 128 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %",even i got 96 % j = 100 t = 100 * 0.8 = 80 m = 80 * 1.6 = 128 if mary' s income is x percent of j m = j * x / 100 x = m * 100 / j = 128 * 100 / 100 = 128 ans : a
Break down and solve the equation step by step.,"two trains 151 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? a ) 7.19 , b ) 7.18 , c ) 7.16 , d ) 7.84 , e ) 7.12","""t = ( 151 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.84 answer : d"""
Provide a detailed solution to the given mathematical problem.,"in an office , totally there are 5200 employees and 45 % of the total employees are males . 50 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ? a ) 1040 , b ) 1170 , c ) 1150 , d ) 4160 , e ) none of these","""number of male employees = 5200 * 45 / 100 = 2340 required number of male employees who are less than 50 years old = 4160 * ( 100 - 50 ) % = 2340 * 50 / 100 = 1170 . answer : b"""
"Solve the problem systematically, showing each step clearly.","sum of 24 odd numbers is ? a ) 572 , b ) 573 , c ) 574 , d ) 575 , e ) 576","""sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 24 odd numbers = 24 ^ 2 = 576 answer : e"""
"Solve the problem systematically, showing each step clearly.","income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 16000 , then find his savings ? a ) 3600 , b ) 3607 , c ) 3200 , d ) 3602 , e ) 3603","""let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 16000 = > x = 3200 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3200 . answer : c"""
Break down and solve the equation step by step.,"a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase e in sales ? a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %","""last year' s sales = $ 320 million ; this year' s sales = $ 385 million ; increase e = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."""
Provide a detailed solution to the given mathematical problem.,"if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value s of z - x ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10","""x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] s = z - x = x + 9 - x = 9 ans : d"""
Break down and solve the equation step by step.,"a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20 % while buying and by 10 % while selling . what is his percentage profit ? a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 20 % , e ) ca n' t be calculated","""the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 120 - 90 ) / 90 * 100 = 20 % answer : d ."""
"Solve the problem systematically, showing each step clearly.","the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half - yearly is ? a ) 6.99 % , b ) 6.89 % , c ) 6.08 % , d ) 6.09 % , e ) 6.19 %","""amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 3 / 100 ) 2 ] = rs . 106.09 effective rate = ( 106.09 - 100 ) = 6.09 % answer : d"""
"Solve the problem systematically, showing each step clearly.","if $ 120 invested at a certain rate of simple interest amounts to $ 160 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ? a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 250","""120 amounts to 160 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 160 120 + 120 * ( r / 100 ) * ( 3 ) = 160 = > r = 100 / 9 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) 250 answer is e ."""
"Solve the problem systematically, showing each step clearly.","an inspector rejects 10 % of the meters as defective . how many will he examine to reject 20 ? a ) a ) 100 , b ) b ) 120 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160","""then , 10 % of x = 20 ( 10 / 100 ) x = 20 x = ( 20 * 100 * ) / 10 = 200 answer is d"""
"Solve the problem systematically, showing each step clearly.","how long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length ? a ) 28 , b ) 41.25 , c ) 55 , d ) 18 , e ) 12","""t = ( 660 + 165 ) / 72 * 18 / 5 t = 41.25 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","the length of the bridge , which a train 140 meters long and travelling at 45 km / hr can cross in 30 seconds , is ? a ) 328 , b ) 279 , c ) 235 , d ) 288 , e ) 211","speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 140 + x ) / 30 = 25 / 2 = = > 2 ( 140 + x ) = 750 = = > x = 235 m . answer : c"
Break down and solve the equation step by step.,"what is 2 2 / 3 - 1 1 / 4 divided by 1 / 4 - 1 / 6 ? a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 1 , e ) 51 / 4","""2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 4 - 1 / 6 = ( 6 - 4 ) / 24 = 2 / 24 = 1 / 12 so 17 / 12 / 1 / 12 = 17 / 12 * 12 = 17 / 1 answer - d"""
Break down and solve the equation step by step.,"17 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ? a ) 34 , b ) 87 , c ) 30 , d ) 99 , e ) 77","""3 w = 2 m 17 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 17 * 21 * 8 = 14 * x * 6 x = 34 answer : a"""
Explain the solution process for the given equation.,"a merchant marks his goods up by 20 % and then offers a discount of 5 % on the marked price . what % profit does the merchant make after the discount ? a ) 8 % , b ) 6 % , c ) 21 % , d ) 14 % , e ) 17 %","""let the price be 100 . the price becomes 120 after a 20 % markup . now a discount of 5 % on 120 . profit = 114 - 100 14 % answer d"""
Break down and solve the equation step by step.,"an alloy weighing 20 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ? a ) 6 , b ) 9 , c ) 12 , d ) 76 , e ) 48","""in 24 ounces , gold is 20 * ( 70 / 100 ) = 14 ounces . now we add x ounces of pure gold to make it 90 % gold . so 14 + x = ( 24 + x ) * 90 / 100 = > x = 76 . answer is d ."""
Provide a detailed solution to the given mathematical problem.,"bird is flying 120 km / hr between b to r . two trains at b to r at 60 kmph . the distance traveled by the bird before it is killed ? a ) 90 kms . , b ) 100 kms . , c ) 110 kms . , d ) 120 kms . , e ) 130 kms .","it will depend on the distance between b and r . if distance between b and r is 120 kms , time taken by trains before collision = 120 / ( 60 + 60 ) = 1 hr distance traveled by bird in 1 hr = 120 kms . so the distance traveled by the bird before it is killed = 120 kms . answer : d"
Break down and solve the equation step by step.,"the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ? a ) 28 cm 2 , b ) 27 cm 2 , c ) 29 cm 2 , d ) 25 cm 2 , e ) 35 cm 2","""area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : d"""
Provide a detailed solution to the given mathematical problem.,"during the first two weeks of january , the total rainfall in springdale was 30 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ? a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 18 inches","""total rainfall in 2 weeks = 18 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 18 inches x = 12 and 1.5 x = 18 rainfall during second week = 18 inches option e"""
"Work through the equation methodically, ensuring clarity at each step.","what is the distance covered by a train if it travels with a speed of 150 kmh for 8 hours ? a ) 1000 km , b ) 700 km , c ) 800 km , d ) 1400 km , e ) 1200 km","""distance = time x speed distance = 150 x 8 = 1200 answer : e"""
Break down and solve the equation step by step.,"if the least common multiple of two prime numbers x and y is 77 , where x > y , then the value of 2 x + y is a ) 11 , b ) 17 , c ) 21 , d ) 29 , e ) 33","""lcm ( x , y ) = 77 and both x an y are prime . the only values of x and y can be 11 and 7 ( x = 11 and y = 7 ) 2 x + y = 2 * 11 + 7 = 29 correct option : d"""
Explain the solution process for the given equation.,"what is the probability that company g' s advertisement will be one of the first two be shown during the first commercial break ? a ) 1 / 225 , b ) 1 / 30 , c ) 1 / 15 , d ) 2 / 15 , e ) 4 / 15",g 1 / 15 + ( 14 / 15 ) * 1 / 14 = 2 / 15 d
Break down and solve the equation step by step.,"how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol ? a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 100 / 19 , e ) 39 / 4","""20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 24 % of ( 100 + x ) or 20 + x = ( 100 + x ) 6 / 25 500 + 25 x = 600 + 6 x 19 x = 100 x = 100 / 19 ans : d"""
"Work through the equation methodically, ensuring clarity at each step.","a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 6 km ? a ) 3 , b ) 5 , c ) 6 , d ) 67 , e ) 7","""m = 4 s = 2 us = 4 - 2 = 2 d = 6 t = 6 / 2 = 3 answer : a"""
Break down and solve the equation step by step.,"the average weight of 10 persons increases by 6.3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? a ) 176 kg , b ) 80 kg , c ) 185 kg , d ) 90 kg , e ) 128 kg","""solution total weight increased = ( 10 x 6.3 ) kg = 63 kg . weight of new person = ( 65 + 63 ) kg = 128 kg . answer e"""
Break down and solve the equation step by step.,"what will be the remainder when ( 27 ^ 27 ) + 27 is divided by 28 ? a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 28","""x ^ n + 1 will be divisible by x + 1 only when n is odd 27 ^ 27 + 1 will be divisible by 27 + 1 ( 27 ^ 27 + 1 ) + 26 , when divided by 28 will give 26 as remainder answer is d"""
Provide a detailed solution to the given mathematical problem.,"a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 60 % ? a ) 800 , b ) 882 , c ) 772 , d ) 652 , e ) 271","""cost price = rs . 500 profit = 60 % of 500 = rs . 300 selling price = cost price + profit = 500 + 300 = 800 answer : a"""
Explain the solution process for the given equation.,"a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 570 pounds after processing , how many pounds did it weigh before processing ? a ) 191 , b ) 355 , c ) 737 , d ) 876 , e ) 1,560","""let weight of side of beef before processing = x ( 65 / 100 ) * x = 570 = > x = ( 570 * 100 ) / 65 = 876 answer d"""
Explain the solution process for the given equation.,"5216 x 51 = ? a ) 212016 , b ) 266016 , c ) 266436 , d ) 216314 , e ) 216318","""normal way of multiplication may take time . here are one alternative . 5216 x 51 = ( 5216 x 50 ) + 5216 = ( 5216 x 100 ) / 2 + 5216 = 521600 / 2 + 5216 = 260800 + 5216 = 266016 answer is b"""
Provide a detailed solution to the given mathematical problem.,"a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 200 . find the total worth of the stock ? a ) 20029 , b ) 20000 , c ) 10000 , d ) 20027 , e ) 20026","""let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 200 = > x = 10000 answer : c"""
Explain the solution process for the given equation.,"a bicycle wheel has a diameter of 0.66 m . how many complete revolutions does it make in 1 km ? a ) 246 , b ) 448 , c ) 1408 , d ) 482 , e ) 223","""1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.66 m ) = 482.5 . hence 482 complete revolutions . answer d"""
Provide a detailed solution to the given mathematical problem.,"of the families in city x in 2001 , 25 percent owned a personal computer . the number of families in city x owning a computer in 2008 was 15 percent greater than it was in 2001 , and the total number of families in city x was 6 percent greater in 2008 than it was in 2001 . what percent of the families in city x owned a personal computer in 2008 ? a ) 27.12 % , b ) 23.12 % , c ) 25.55 % , d ) 31.22 % , e ) 56.22 %","""say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 25 number of families owning computer in 1998 = 25 * 115 / 100 = 28.75 number of families in 1998 = 106 the percentage = 28.75 / 106 * 100 = 27.12 % . answer : a"""
Provide a detailed solution to the given mathematical problem.,"in a clothing store , there are 6 different colored neckties ( red , orange , yellow , green , blue , and indigo ) and 4 different colored shirts ( red , orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ? a ) 719 / 720 , b ) 1 / 24 , c ) 2 / 233 , d ) 3 / 543 , e ) 1 / 720","4 ties and 4 shirts . . . red tie can take any of 4 shirts . . orange can take any of the remaining 3 shirts yellow any of remaining 2 . . and so on till last indigo chooses the 1 remaining . . total ways = 4 * 3 * 2 * 1 = 24 out of this 720 , only 1 way will have same colour tie and shirt . . prob = 1 / 720 b"
Explain the solution process for the given equation.,"last year sandy saved 6 % of her annual salary . this year , she made 10 % more money than last year , and she saved 9 % of her salary . the amount saved this year was what percent of the amount she saved last year ? a ) 140 % , b ) 152 % , c ) 165 % , d ) 176 % , e ) 190 %","let last year' s salary be x . last year , sandy save 0.06 x this year , sandy saved 0.09 * 1.1 x = 0.099 x 0.099 x / 0.06 x = 99 / 60 = 1.65 = 165 % the answer is c ."
Explain the solution process for the given equation.,"after decreasing 20 % in the price of an article costs rs . 200 . find the actual cost of an article ? a ) 280 , b ) 250 , c ) 260 , d ) 270 , e ) 300","""cp * ( 80 / 100 ) = 200 cp = 2.5 * 100 = > cp = 250 answer : b"""
Explain the solution process for the given equation.,"find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 100 of money ? a ) 1500 , b ) 6000 , c ) 2500 , d ) 1400 , e ) 2000","""p = 100 ( 100 / 10 ) 2 = > p = 2000 answer : e"""
Provide a detailed solution to the given mathematical problem.,"exactly 10 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ? a ) 20 % , b ) 42 % , c ) 44 % , d ) 85 % , e ) 84 %","""you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 10 % of all reporters reporters covering politics / all reporters = 10 / 70 = 1 / 7 reporters not covering politics / all reporters = 6 / 7 = 85 % = d"""
"Work through the equation methodically, ensuring clarity at each step.","in a recent head - to - head run - off election , 10,000 absentee ballets were cast . 2 / 3 of the absentee ballets were thrown out and 2 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ? a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000","""1 / 3 * 3 / 5 ( total absentee votes ) = 1 / 5 ( total votes ) = 1 / 5 * 10000 = 2000 answer is a"""
"Solve the problem systematically, showing each step clearly.","a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet . what is its area , in square feet ? a ) 76,800 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800","""you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 400 , you can deduce the following a = 240 b = 320 240 x 320 = 76,800 a is the answer ."""
Provide a detailed solution to the given mathematical problem.,"in one alloy there is 12 % chromium while in another alloy it is 10 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy . a ) 8.8 % , b ) 9 % , c ) 9.2 % , d ) 8.6 % , e ) 10.6 %","""the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.12 * 15 + 0.10 * 35 = 5.3 kg , so the percentage is 5.3 / 50 * 100 = 10.6 % . answer : e ."""
"Solve the problem systematically, showing each step clearly.","in a division , a student took 48 as divisor instead of 36 . his answer was 24 . the correct answer is - a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38","""x / 48 = 24 . x = 24 * 48 . so correct answer would be , ( 24 * 48 ) / 36 = 32 . answer : b"""
Explain the solution process for the given equation.,"an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ? a ) 720 , b ) 360 , c ) 250 , d ) 280 , e ) 290","""let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 3120 = rs . 720 answer : a"""
"Solve the problem systematically, showing each step clearly.","a part - time employee whose hourly wage was increased by 15 percent decided to reduce the number of hours worked per week so that the employee' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ? a ) 9 , b ) 13.04 , c ) 10 , d ) 11 , e ) 12","""let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.15 x now we need to find number of hours worked so that x * y = 1.15 x * z i . e z = 1 / 1.15 y % decrease = ( y - 1 / 1.15 y ) / y * 100 = 13.04 % thus my answer is b ."""
Break down and solve the equation step by step.,"sally , mark , sarah , steve and jim are inheriting the money from their grandmother . she left them $ 527500 to split equally between all of them . if the money is split equally , how much money will each person receive ? a ) $ 135875 , b ) $ 52700 , c ) $ 127900 , d ) $ 105500 , e ) $ 105000",there are 5 people inheriting the money . we have to take the total of the inheritance and divide it by 5 for each person receiving money . $ 527500 / 5 = $ 105500 . therefore the correct answer is d .
Provide a detailed solution to the given mathematical problem.,"a batsman in his 11 th inning makes a score of 69 and their by increasing his average by 1 . what is his average after the 11 th inning ? a ) 58 , b ) 59 , c ) 68 , d ) 69 , e ) 78","""10 x + 69 = 11 ( x + 1 ) x = 58 + 1 = 59 answer : b"""
Break down and solve the equation step by step.,"a train speeds past a pole in 15 sec and a platform 150 m long in 25 sec , its length is ? a ) 100 , b ) 150 , c ) 160 , d ) 225 , e ) 180","""let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 150 ) / 25 = x / 15 = > x = 225 m . answer : option d"""
"Work through the equation methodically, ensuring clarity at each step.","the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ? a ) 10 , b ) 15 , c ) 20 , d ) 15 / 2 , e ) 24",after passing the hiker the cyclist travels for 5 minutes at a rate of 10 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 6 miles . in those 5 mins the hiker travels a distance of 1 / 2 miles . so the hiker still has to cover 1 / 2 miles to meet the waiting cyclist . the hiker will need 15 / 2 mins to cover the remaining 1 / 2 miles . so the answer is d .
Explain the solution process for the given equation.,"the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 50,000 , how much profit did the business make ? a ) $ 80,000 , b ) $ 100,000 , c ) $ 120,000 , d ) $ 150,000 , e ) $ 200,000","let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 50000 p = $ 80,000 the answer is a ."
Explain the solution process for the given equation.,"in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m","""explanation : each row contains 12 plants . there are 11 gapes between the two corner trees ( 11 x 2 ) metres and 1 metre on each side is left . therefore length = ( 22 + 2 ) m = 24 m . answer : c"""
Explain the solution process for the given equation.,"sides of a rectangular park are in the ratio 3 : 2 and its area is 2400 sq m , the cost of fencing it at 50 ps per meter is ? a ) 287 , b ) 100 , c ) 125 , d ) 988 , e ) 271","""3 x * 2 x = 2400 = > x = 20 2 ( 60 + 40 ) = 200 m 200 * 1 / 2 = rs . 100 answer : b"""
"Solve the problem systematically, showing each step clearly.","8 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? a ) 144 , b ) 131 , c ) 115 , d ) 84 , e ) 45","""there are 8 business exec and in each handshake 2 business execs are involved . hence 8 c 2 = 28 also , each of 8 exec will shake hand with every 7 other chairmen for total of 56 handshake . total = 28 + 56 = 84 ans : d"""
Provide a detailed solution to the given mathematical problem.,"if 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes a ) 55 , b ) 42 , c ) 43 , d ) 44 , e ) 45","""n ( n - 1 ) / 2 = 11 * 10 / 2 = 55 answer : a"""
Provide a detailed solution to the given mathematical problem.,"what number is obtained by adding the units digits of 734 ^ 98 and 347 ^ 82 ? a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15","""the units digit of 734 ^ 98 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 82 is 9 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 82 is in the form 4 n + 2 , the units digit is 9 . then 6 + 9 = 15 . the answer is e ."""
"Work through the equation methodically, ensuring clarity at each step.","the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 75 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ? a ) 48 , b ) 51 , c ) 60 , d ) 71 , e ) 96","""the total sum of the numbers should be increased by 50 . then the average will increase by 50 / 10 = 5 . the correct average is 51 . the answer is b ."""
"Solve the problem systematically, showing each step clearly.","there are 100 students in a certain geometry class . if one half of the students are boys and one fifth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ? a ) 6 , b ) 10 , c ) 18 , d ) 24 , e ) 27",total students = 100 one half of the students are boys = 1 / 2 * 100 = 50 one fifth of the boys are under six feet tall = 1 / 5 * 50 = 10 . . . therefore number of boys in the class under six feet tall = 10 . . . answer b . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 5 of 1 / 2 of total students = 1 / 5 * 1 / 2 * 100 = 10 . . . answer b
"Work through the equation methodically, ensuring clarity at each step.","find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29","""( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 3 x 11 ^ 2 = 2 ^ 22 x 7 ^ 3 x 11 ^ 2 total number of prime factors = ( 22 + 3 + 2 ) = 27 . answer is d ."""
Break down and solve the equation step by step.,"the sum of the present ages of a , b , c is 57 years . 3 years ago their ages were in the ratio 1 : 2 : 3 . what is the present age of a ? a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12","three years ago : a : b : c = 1 : 2 : 3 let a = 1 x , b = 2 x , and c = 3 x . today : ( x + 3 ) + ( 2 x + 3 ) + ( 3 x + 3 ) = 57 x = 8 so the present age of a is x + 3 = 11 the answer is d ."
Provide a detailed solution to the given mathematical problem.,"a retailer bought a machine at a wholesale price of $ 126 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ? a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 168","my solution : wholesale price = 126 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 126 + 1 / 5 ( 126 ) x = 168 ; answer : e"
Explain the solution process for the given equation.,"the tax on a commodity is diminished by 28 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ? a ) 18 % , b ) 19 % , c ) 32 % , d ) 12 % , e ) 52 %","""100 * 100 = 10000 72 * 112 = 8064 10000 - - - - - - - 1936 100 - - - - - - - ? = 19.36 % answer : b"""
Break down and solve the equation step by step.,"what is the dividend . divisor 16 , the quotient is 6 and the remainder is 2 a ) 86 , b ) 87 , c ) 88 , d ) 89 , e ) 90","""c = d * q + r c = 16 * 6 + 2 c = 86 + 2 c = 88"""
Provide a detailed solution to the given mathematical problem.,"a survey was sent to 60 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ? a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 4 %","""case 1 : ( 7 / 60 ) = x / 100 x = 12 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 12 ) % = 2 % answer is a"""
Break down and solve the equation step by step.,"if length of rectangle is increased by 10 % , and breadth is decreased by 10 % . what will it effect on area of rectangle ? ['a ) it will have no effect','b ) 1 % increase','c ) 1 % decrease','d ) 2 % increase','e ) 2 % decrease']","let initial length = l , and breadth = b area = l * b new length = l * 110 % = [ l * 110 / 100 ] = 11 l / 10 , new breadth = 9 b / 10 new area = 11 l / 10 * 9 b / 10 = 99 / 100 lb decrease in area = [ lb - 99 / 100 lb ] = lb / 100 = % decrease = [ lb / 100 * 1 / lb * 100 ] = 1 % answer c"
Provide a detailed solution to the given mathematical problem.,"what is the smallest no . which must be added to 532869 so as to obtain a sum which is divisible by 9 ? a ) 9 , b ) 2 , c ) 1 , d ) 3 , e ) 6","""for 532869 , 5 + 3 + 2 + 8 + 6 + 9 = 33 3 must be added to 532869 to make it divisible by 9 . now , 5 + 3 + 2 + 8 + 7 + 2 = 27 = > 27 is a multiple of 9 and hence 532869 is also divisible by 9 d"""
Break down and solve the equation step by step.,"a hall 36 m long and 15 m broad is to be paved with stones , each measuring 4 dm by 5 dm . the number of stones required is : a ) 180 , b ) 2700 , c ) 18 , d ) 18000 , e ) 1.8","""area of the hall = 3600 * 1500 area of each stone = ( 40 * 50 ) therefore , number of stones = ( 3600 * 1500 / 40 * 50 ) = 2700 answer : b"""
Break down and solve the equation step by step.,"a group of n students can be divided into equal groups of 4 with 3 student left over or equal groups of 5 with 3 students left over . what is the sum of the two smallest possible values of n ? a ) 66 , b ) 46 , c ) 49 , d ) 53 , e ) 86","""4 x + 3 = 5 y + 3 . . . . . . . . . . . ie : 4 x - 5 y = 0 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x = fraction ( not possible ) if y = 4 thus x = 5 n = 23 if y = 6 thus x = not possible fraction if y = 8 thus x = 10 n = 43 23 + 43 = 66 . . . . . a"""
Break down and solve the equation step by step.,"danny and steve are running towards each other , each one from his own house . danny can reach steve' s house in 35 minutes of running , which is half the time it takes steve to reach danny' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ? a ) 17.5 minutes . , b ) 35 minutes . , c ) 52.5 minutes . , d ) 70 minutes . , e ) 105 minutes .","""danny' s time is 35 minutes . the time to reach halfway is 17.5 minutes . steve' s time is 70 minutes . the time to reach halfway is 35 minutes . the time difference is 35 - 17.5 = 17.5 minutes the answer is a ."""
Provide a detailed solution to the given mathematical problem.,"how many positive integers less than 9999 are such that the product of their digits is 210 . a ) 24 , b ) 58 , c ) 26 , d ) 34 , e ) 25","""the prime factorization of 210 is 2 * 3 * 5 * 7 . so one way to make the right kind of number is to use those four digits , in any of the 4 ! = 24 orders you can put them in . notice though that we can also get 210 as a product by multiplying 5 , 6 and 7 . so we can make some 3 - digit numbers with the right product : 3 ! = 6 of them to be exact . but we can also get the right product using the digit 1 along with the digits 5 , 6 , and 7 . again we can arrange those digits in 4 ! = 24 orders . a"""
Explain the solution process for the given equation.,"equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 8 full and other jar 1 / 6 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ? a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 2 , d ) 7 / 12 , e ) 1 / 4","""same amount of water made bigger jar 1 / 8 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 8 + 1 / 8 = 1 / 4 full . answer : e ."""
Break down and solve the equation step by step.,"if the sum of two numbers is 55 and the h . c . f and l . c . m of these numbers are 5 and 120 respectively , then the sum of the reciprocal of the numbers is equal to : a ) 55 / 601 , b ) 601 / 55 , c ) 11 / 120 , d ) 120 / 11 , e ) 120 / 13","""let the numbers be a and b . then , a + b = 55 and ab = 5 * 120 = 600 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 55 / 600 = 11 / 120 . answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","a batsman scored 210 runs which included 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets a ) 40 % , b ) 50 % , c ) 65 % , d ) 71.4 % , e ) 75 %","""number of runs made by running = 210 - ( 3 x 4 + 8 x 6 ) = 210 - ( 60 ) = 150 now , we need to calculate 60 is what percent of 120 . = > 150 / 210 * 100 = 71.4 % d"""
Explain the solution process for the given equation.,"the price of a jacket is reduced by 15 % . during a special sale the price of the jacket is reduced another 30 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ? a ) 60 , b ) 65 , c ) 69 , d ) 68.25 , e ) 67.5","1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 15 % , therefore bringing down the price to $ 85 . 3 ) again it is further discounted by 30 % , therefore bringing down the price to $ 59.5 4 ) now 59.5 has to be added byx % in order to equal the original price . 59.5 + ( x % ) 59.5 = 100 . solving this eq for x , we get x = 68.25 ans is d"
Break down and solve the equation step by step.,"for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today' s production of 115 units raises the average to 55 units per day , what is the value of n ? a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16","the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 115 - 55 = 60 n = 12 the answer is c ."
Explain the solution process for the given equation.,"in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 2,000 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 8,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ? a ) 20 % , b ) 25 % , c ) 50 % , d ) 60 % , e ) 27 %","""ratio of 2 bedroom apartment : 1 bedroom apartment = 2000 : 8000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : a"""
Provide a detailed solution to the given mathematical problem.,"amithab' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is : a ) rs . 4250 , b ) rs . 4288 , c ) rs . 4227 , d ) rs . 4218 , e ) rs . 4219","""explanation : amithab' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } { 6 } = 4250 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","a 4 - digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1 , 2 , 4 , and 6 at all . if repeated digits are allowed , what is the probability that it has at least one even digit ? a ) 23 / 24 , b ) 31 / 36 , c ) 55 / 64 , d ) 65 / 81 , e ) 75 / 121",p ( no even digits ) = 2 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 16 / 81 p ( at least one even digit ) = 1 - 16 / 81 = 65 / 81 the answer is d .
Break down and solve the equation step by step.,"the sum of digits of a two digit number is 12 , the difference between the digits is 4 . find the number a ) 84 , b ) 94 , c ) 83 , d ) 72 , e ) none","""description : = > x + y = 12 , x - y = 4 adding these 2 x = 16 = > x = 8 , y = 4 . thus the number is 84 answer a"""
"Solve the problem systematically, showing each step clearly.","venus travels around the sun at a speed of approximately 21.9 miles per second . the approximate speed is how many miles per hour ? a ) 64,420 , b ) 78,840 , c ) 83,160 , d ) 88,970 , e ) 94,320","21.9 * 3600 = 78,840 the answer is b ."
Explain the solution process for the given equation.,"at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 10 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 14 . how many cooks does the restaurant have ? a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15","""originally there were 3 k cooks and 10 k waiters . 14 k = 10 k + 12 k = 3 there are 9 cooks . the answer is c ."""
"Solve the problem systematically, showing each step clearly.","a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction w of the cookies that were placed in the other tins were placed in the green tin ? a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7","blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction w = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )"
Provide a detailed solution to the given mathematical problem.,"for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 80 color copies at print shop y than at print shop x ? a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140","""the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 80 * $ 1.50 = $ 120 the answer is a ."""
"Solve the problem systematically, showing each step clearly.","an aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of : a ) 2200 kmph , b ) 1800 kmph , c ) 1900 kmph , d ) 2100 kmph , e ) none","""explanation : distance = ( 1500 x 2 ) = 3000 km . speed = distance / time speed = 3000 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 3000 x 3 / 5 km / hr = 1800 km / hr . answer : option b"""
"Solve the problem systematically, showing each step clearly.","a lemonade stand sold only small and large cups of lemonade on tuesday . 4 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday' s total revenue was from the sale of large cups ? a ) ( a ) 7 / 16 , b ) ( b ) 7 / 15 , c ) ( c ) 10 / 21 , d ) ( d ) 7 / 31 , e ) ( e ) 1 / 2","""a simpler way i guess would be to think that in total 5 cups were sold . out of which 4 are small and 1 is large . now let the small ones cost $ 6 . so the large ones would cost $ 7 . so , 4 * 6 = 24 and 1 * 7 = 7 . total revenue was 24 + 7 = 31 and large cup sales as found above is 7 therefore answer is 7 / 31 d"""
"Solve the problem systematically, showing each step clearly.","set x consists of all two - digit primes and set y consists of all positive multiples of 6 less than 100 . if the two sets are combined into one , what will be the range of the new set ? a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 91","""set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 6 , 12 , 18 , . . . . . . . . . . . . . . . , 84 , 90 , 96 } combining two sets , say set z set z = { 6 , 11 , 12 , 13 , 17 , 18 , . . . . . . . . . . . . . . . . . . . , 83 , 84 , 89 , 90 , 96,97 } range = max value - min value range ( z ) = 97 - 6 = 91 oa e is the answer ."""
"Work through the equation methodically, ensuring clarity at each step.","in a group of 800 people , 1 / 5 play at least one instrument , 32 play two or more . what is the probability that one student play exactly one instrument ? a ) 2 / 125 , b ) 4 / 25 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5","""p ( playing 2 or more instruments ) = 32 / 800 = 1 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 1 / 25 = 4 / 25 . answer b ."""
Provide a detailed solution to the given mathematical problem.,"seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 30 percent ryegrass , what percent of the weight of this mixture is x ? a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %","""qnty . ( cheaper ) / qty . ( dearer ) = ( dearer - mean ) / ( mean - cheaper ) thus qy / qx = ( 40 - 30 ) / ( 30 - 25 ) = 2 therefore qy = 2 qx and qy + qx = 100 % ( total ) . hence qx = 33.33 % answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","on the number line , if x is halfway between - 11 and 5 , and if y is halfway between - 3 and 7 , what number is halfway between x and y ? a ) - 1.5 , b ) - 0.5 , c ) 0.5 , d ) 1.5 , e ) 2.5","""x = - 3 and y = 2 . the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"675.987 - ? + 56.84 = 289.654 a ) a ) 443.173 , b ) b ) 752.804 , c ) c ) 714.642 , d ) d ) 629.906 , e ) of these","""explanation : 443.173 answer : option a"""
Provide a detailed solution to the given mathematical problem.,"a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by c are ? a ) 11 , b ) 18 , c ) 45 , d ) 17 , e ) 12","""a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 15 / 25 * 75 = 45 answer : c"""
Explain the solution process for the given equation.,"if log 64 = 1.8061 , then the value of log 16 will be ( approx ) ? a ) 1.204 , b ) 1.9874 , c ) 1.3564 , d ) 1.2547 , e ) 1.6547","""log 64 = 1.8061 log 4 ^ 3 = 1.8061 log 4 = 0.6020 2 log 4 = 1.2040 log 4 ^ 2 = 1.2040 log 16 = 1.2040 ( approx ) answer a"""
"Solve the problem systematically, showing each step clearly.","rhoda tosses a coin 5 times . find the probability of getting exactly 4 heads . a ) 5 / 32 , b ) 6 / 32 , c ) 5 / 16 , d ) 4 / 32 , e ) 8 / 32","exactly 4 heads out of 5 would be : hhhht , hhthh , or many other combinations . therefore , no . of possible combinations are 5 ! / 4 ! * 1 ! = 5 probability = 5 / 2 ^ 5 = 5 / 32 answer : a"
"Solve the problem systematically, showing each step clearly.","salesperson a' s compensation for any week is $ 300 plus 6 percent of the portion of a' s total sales above $ 1,000 for that week . salesperson b' s compensation for any week is 8 percent of b' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ? a ) $ 21,000 , b ) $ 12,000 , c ) $ 15,000 , d ) $ 4,500 , e ) $ 4,000","""sometime , setting up an equation is an easy way to go with : 300 + 0.06 ( x - 1000 ) = 0.08 x x = 12,000 ans : b"""
Provide a detailed solution to the given mathematical problem.,"a train 160 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ? a ) 443 m , b ) 354 m , c ) 340 m , d ) 350 m , e ) 250 m","""c 340 c = ( 72 * 5 / 18 ) * 25 - 160 = 340"""
Break down and solve the equation step by step.,"naomi drives to the beauty parlor in 60 minutes . on the way back , her average speed is half the average speed as it was to the way to the parlor . how much time will it take naomi to travel two round trips to the beauty parlor ? a ) 3 hours . , b ) 4 hours . , c ) 4 hours and 20 minutes . , d ) 5 hours and 50 minutes , e ) 6 hours .","s 1 = 2 s 2 since , speed is inversely proportional to time we have , s 1 / s 2 = 2 / 1 = t 2 / t 1 therefore , the time taken for one trip = 60 + 120 = 180 minutes total = 180 * 2 = 360 minutes = 6 hours answer : e"
"Work through the equation methodically, ensuring clarity at each step.","last year a worker saved 15 % of her annual salary . this year , she made 20 % more money than last year and she saved 25 % of her salary . the amount she saved this year was what percent of the amount she saved last year ? a ) 120 % , b ) 140 % , c ) 160 % , d ) 180 % , e ) 200 %","""let x be the worker' s salary last year . last year , she saved 0.15 x . this year , she saved 0.25 ( 1.2 x ) = 0.3 x 0.3 x / 0.15 x = 200 % the answer is e ."""
"Work through the equation methodically, ensuring clarity at each step.","the sum of 4 consecutive even numbers is 140 . what would be the largest number ? a ) 33 , b ) 38 , c ) 70 , d ) 123 , e ) 12","let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x + 1 ) = 38 . answer : b"
"Solve the problem systematically, showing each step clearly.","if the difference between the compound interest & simple interest of a certain sum of money is rs . 72 at 12 % p . a . per two year . find the sum ( in rs . ) ? a ) 200 / 15 , b ) 200 / 17 , c ) 220 / 17 , d ) 240 / 17 , e ) 260 / 17",200 / 17 c . i = a - p a = p ( 1 + 12 / 100 ) ^ 2 s . i = p * 2 * 12 / 100 c . i - s . i = 72 given substitute and solve p = 200 / 17 answer : b
"Solve the problem systematically, showing each step clearly.","the diagonal of the floor of a rectangular closet is 7 feet . the shorter side of the closet is 4 feet . what is the area of the closet in square feet ? ['a ) 20 sq . ft','b ) 27 sq . ft','c ) 37 sq . ft','d ) 47 sq . ft','e ) 57 sq . ft']",other side = 15 2 - 9 2 2 2 ft = 225 - 81 4 4 ft = 144 4 ft = 6 ft . area of closet = ( 6 x 4.5 ) sq . ft = 27 sq . ft . b )
"Solve the problem systematically, showing each step clearly.","in the coordinate plane a slope of the line k is 3 times the y - intercept of the line k . what is the x - intercept of the line k ? a ) - 4 , b ) 4 , c ) - 1 / 4 , d ) - 1 / 3 , e ) 2","as y = 3 mx + m , from 0 = 3 mx + m we get x = - 1 / 3 . hence , the correct answer choice is d ."
Break down and solve the equation step by step.,"in a tree , 3 / 7 of the birds are robins while the rest are bluejays . if 1 / 3 of the robins are female and 3 / 5 of the bluejays are female , what fraction of the birds in the tree are male ? a ) 11 / 35 , b ) 14 / 35 , c ) 18 / 35 , d ) 31 / 70 , e ) 37 / 70","""the fraction of birds that are male robins is ( 2 / 3 ) ( 3 / 7 ) = 2 / 7 . the fraction of birds that are male bluejays is ( 2 / 5 ) ( 4 / 7 ) = 8 / 35 . the total fraction of male birds is 2 / 7 + 8 / 35 = 18 / 35 . the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 11 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ? a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 63","""i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 11 = 63 answer e"""
Break down and solve the equation step by step.,"a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 5 gallons of water and 10 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ? a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175","""nope , 150 . i can only get it by following pr' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 10 gallons salt is added and 5 gallons of water is added . so salt now becomes - > ( 0.2 x + 10 ) and water - - > ( 0.6 x + 5 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 10 ) = ( 0.6 x + 5 ) / 2 = 0.4 x + 20 = 0.6 x + 5 = > 0.2 x = 15 solving , x = 75 answer : b"""
Break down and solve the equation step by step.,"the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 432 meters , what is the width of the field ? a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90","""let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 432 , 2 ( 7 / 5 ) w + 2 w = 432 solve the above equation to find : w = 90 m and l = 126 m . correct answer e ) 90"""
"Solve the problem systematically, showing each step clearly.","on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets rain cloud , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ? a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 5 , e ) 1 / 4","if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : c"
"Solve the problem systematically, showing each step clearly.","find the sum lend at c . i . at 5 p . c per annum will amount to rs . 341 in 2 years ? a ) 221 , b ) 309 , c ) 400 , d ) 288 , e ) 171","""explanation : 341 = p ( 21 / 20 ) 2 p = 309.29 answer : b"""
"Solve the problem systematically, showing each step clearly.","the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits x of the larger integer ? a ) x = 2 , b ) x = 5 , c ) x = 8 , d ) 10 , e ) 11","really hard . but let' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) ."
"Work through the equation methodically, ensuring clarity at each step.","there are 2 white plates , 6 green plates , 8 red plates , 4 pink plates , and 10 purple plates in the cabinet . what is the least number of plates that you have to pull out to make sure that you will have a matching pair ? ( assume that all the plates are identical except for the color ) a ) 2 , b ) 4 , c ) 12 , d ) 7 , e ) 6","since there are 5 colors , if you take 5 plates , you could still have 1 plate per color and not have a match . therefore , upon taking the 6 th plate , you will definitely have a match since the 6 th plate will form at least a pair with the 1 st 5 so 5 + 1 = 6 answer is e"
Break down and solve the equation step by step.,"in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 11 , 0 ) , ( 0 , - 3.5 ) , ( - 11 , 0 ) ? a ) 56 , b ) 77 , c ) 112 , d ) 116 , e ) 120","""area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 11 + 11 = 22 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 22 * 7 = 77 b is the answer"""
"Work through the equation methodically, ensuring clarity at each step.","virginia , adrienne , and dennis have taught history for a combined total of 102 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ? a ) 23 , b ) 32 , c ) 35 , d ) 43 , e ) 44","""let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 102 = > 3 d = 102 + 27 = 129 = > d = 43 answer d"""
Break down and solve the equation step by step.,"one week , a certain truck rental lot had a total of 26 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 14 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ? a ) 18 , b ) 16 , c ) 12 , d ) 24 , e ) 4","""n - not rented trucks ; r - rented trucks n + r = 26 n + r / 2 = 14 r = 24 d"""
Explain the solution process for the given equation.,"a man' s speed with the current is 16 km / hr and the speed of the current is 3.2 km / hr . the man' s speed against the current is a ) 9 , b ) 9.6 , c ) 11 , d ) 12 , e ) 13","""man' s rate in still water = ( 16 - 3.2 ) km / hr = 12.8 km / hr . man' s rate against the current = ( 12.8 - 3.2 ) km / hr = 9.6 km / hr . answer : b"""
Break down and solve the equation step by step.,"find the last digit in the product 287 x 287 + 269 x 269 - 2 x 287 x 269 ? a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 4","explanation : given exp . = a 2 + b 2 - 2 ab , where a = 287 and b = 269 = ( a - b ) 2 = ( 287 - 269 ) 2 = ( 182 ) = 324 answer is e"
Provide a detailed solution to the given mathematical problem.,"a candidate who gets 40 % of the marks fails by 40 marks . but another candidate who gets 60 % marks gets 20 marks more than necessary for passing . find the number of marks for passing ? a ) 100 marks , b ) 200 marks , c ) 160 marks , d ) 371 marks , e ) 827 marks","""40 % - - - - - - - - - - - - 40 60 % - - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - - - - 60 40 % - - - - - - - - - - - - - - ? 120 + 40 = 160 marks answer : c"""
Provide a detailed solution to the given mathematical problem.,"a reduction of 40 % in the price of bananas would enable a man to obtain 66 more for rs . 40 , what is reduced price per dozen ? a ) 1.91 , b ) 2.91 , c ) 4.91 , d ) 3.91 , e ) 5.91","""40 * ( 40 / 100 ) = 16 - - - 66 ? - - - 12 = > rs . 2.91 answer : b"""
Break down and solve the equation step by step.,"in the manufacture of a certain product , 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ? a ) 0.125 % , b ) 0.32 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %","""percent of defective produced = 8 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 8 / 100 ) * 100 % = ( 32 / 10000 ) * 100 % = ( 32 / 100 ) % = . 32 % answer b"""
Provide a detailed solution to the given mathematical problem.,"each side of a rectangle is increased by 100 % . by what percentage does the area increase ? a ) 300 % , b ) 400 % , c ) 500 % , d ) 200 % , e ) 600 %",original area = a * b where a and b are sides after increase in side increase in area will be = ( ( ( 2 a * 2 b ) - ( a * b ) ) * 100 ) / ( a * b ) = 300 % answer : a
"Solve the problem systematically, showing each step clearly.","in how many v ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ? a ) 720 , b ) 864 , c ) 900 , d ) 936 , e ) 1296",total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4 ! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value v = ( 1 ) - ( 2 ) = 1296 - 360 = 936 . d
"Work through the equation methodically, ensuring clarity at each step.","excluding stoppages , the speed of a train is 54 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ? a ) a ) 13.55 , b ) b ) 14.55 , c ) c ) 15.55 , d ) d ) 16.55 , e ) e ) 17.55","""explanation : t = 14 / 54 * 60 = 15.55 answer : option c"""
"Work through the equation methodically, ensuring clarity at each step.","the average of 10 numbers is 23 . if each number is increased by 2 , what will the new average be ? a ) 36 , b ) 25 , c ) 72 , d ) 29 , e ) 22","""sum of the 10 numbers = 230 if each number is increased by 2 , the total increase = 2 * 10 = 20 the new sum = 230 + 20 = 250 the new average = 250 / 10 = 25 . answer : b"""
Explain the solution process for the given equation.,"if 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ? a ) 110 , b ) 130 , c ) 150 , d ) 170 , e ) 190","if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 20 lines is 20 c 2 = 190 the answer is e ."
Break down and solve the equation step by step.,"by investing rs . 1620 in 8 % stock , michael earns rs . 135 . the stock is then quoted at a ) 46 , b ) 96 , c ) 35 , d ) 87 , e ) 13","""to earn rs . 135 , investment = rs . 1620 . to earn rs . 8 , investment = rs . 96 . market value of rs . 100 stock = rs . 96 . answer : b"""
Provide a detailed solution to the given mathematical problem.,"if price of t . v set is reduced by 18 % , then its sale increases by 72 % , find net effect on sale value a ) 41 , b ) 45 , c ) 46 , d ) 47 , e ) 48","""- a + b + ( ( - a ) ( b ) / 100 ) = - 18 + 72 + ( - 18 * 72 ) / 100 = - 18 + 72 - 13 = 41 answer : a"""
Explain the solution process for the given equation.,"an error 6 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is a ) 12.04 % , b ) 14.14 % , c ) 12.36 % , d ) 12.26 % , e ) 15.5 %","""100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 106 x 106 ) cm 2 . ( a 2 - a 1 ) = [ ( 106 ) 2 - ( 100 ) 2 ] = ( 106 + 100 ) x ( 106 - 100 ) = 1236 cm 2 . percentage error = 12.36 % d"""
"Work through the equation methodically, ensuring clarity at each step.","a car was driving at 80 km / h for 40 minutes , and then at 60 km / h for another 40 minutes . what was its average speed ? a ) 113.33 . , b ) 103.33 , c ) 93.33 , d ) 83.33 , e ) 73.33","""driving at 80 km / h for 40 minutes , distance covered = 80 * 2 / 3 = 53.33 km driving at 90 km / h for 40 minutes , distance covered = 90 * 2 / 3 = 60 km average speed = total distance / total time = 113.33 / 1 = 113.33 km / h answer : 113.33 km / h"""
"Work through the equation methodically, ensuring clarity at each step.","running at the same constant rate , 15 identical machines can produce a total of 45 bags per minute . at this rate , how many bags could 150 such machines produce in 8 minutes ? a ) 9,00 , b ) 1,800 , c ) 2,700 , d ) 3,600 , e ) 4,800","""let' s take the approach that uses the answer choices to eliminate wasted time . 45 / 15 = 3 bags per minute per machine . 150 machines = 450 per minute . 8 minutes worth = 3600 bags . looking at the answers it is clear . . . we can only choose ( d ) . the correct answer is d ."""
"Solve the problem systematically, showing each step clearly.","in a school 10 % of the boys are same in number as 1 / 3 th of the girls . what is the ratio of boys to the girls in the school ? a ) 5 : 2 , b ) 2 : 3 , c ) 10 : 3 , d ) 3 : 7 , e ) 2 : 5","""10 % of b = 1 / 3 g 10 b / 100 = g / 3 b = 10 g / 3 b / g = 10 / 3 b : g = 10 : 3 answer is c"""
"Solve the problem systematically, showing each step clearly.","a train can travel 50 % faster than a car . both start from point a at the same time and reach point b 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . the speed of the car is : a ) 120 kmph , b ) 150 kmph , c ) 50 kmph , d ) 80 kmph , e ) 75 kmph","""let speed of the car be x kmph . then , speed of the train = 150 / 100 x = 3 / 2 x kmph . 75 / x - 75 / ( 3 / 2 ) x = 125 / 10 x 60 75 / x - 50 / x = 5 / 24 x = 25 x 24 / 5 = 120 kmph . answer : a"""
Break down and solve the equation step by step.,"a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5.2 hours , then the distance covered at 40 kmph is a ) 130 km , b ) 120 km , c ) 100 km , d ) 124 km , e ) none of these","""let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5.2 or , x / 40 + ( 250 - x ) / 60 = 5.2 or , ( 3 x + 500 - 2 x ) / / 120 = 5.2 or 500 + x = 624 x = 124 answer : d"""
Explain the solution process for the given equation.,"if q and t are positive integers , qt + q + t can not be a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9",let qt + t + q = x add 1 on both sides : qt + t + q + 1 = x + 1 tq + 1 ) + q + 1 = x + 1 ( q + 1 ) ( t + 1 ) = x + 1 minimum value of ( q + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > qt + t + s can not be 6 answer : b
Explain the solution process for the given equation.,"at a local appliance manufacturing facility , the workers received a 30 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ? a ) 83 % , b ) 80 % , c ) 23 % , d ) 17 % , e ) 12 %","""let' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 130 = 1300 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 130 = 7.67 so he can reduce his work by 2.33 hours . which is > 23 % . answer c"""
"Work through the equation methodically, ensuring clarity at each step.","a cylindrical can has a radius of 4 centimeters and a height of 24 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ? a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi","""they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 4 * 24 = 192 pi answer is d ."""
"Solve the problem systematically, showing each step clearly.","the number of timeshare condos available at sunset beach is 3 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 400 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ? a ) 60 , b ) 90 , c ) 120 , d ) 100 , e ) 240","""let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 3 / 5 x = 400 hence , x = 250 . so , number of timeshare condos available at playa del mar = 250 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 3 / 5 x = 2 / 5 x = 2 / 5 ( 250 ) = 100 the correct answer is d"""
"Solve the problem systematically, showing each step clearly.","the sale price sarees listed for rs . 278 after successive discount is 18 % and 19 % is ? a ) 321 , b ) 276 , c ) 342 , d ) 265 , e ) 198","""explanation : 278 * ( 88 / 100 ) * ( 81 / 100 ) = 198 answer : e"""
Provide a detailed solution to the given mathematical problem.,"if x is equal to the sum of the integers from 50 to 70 , inclusive , and y is the number of even integers from 50 to 70 , inclusive , what is the value of x + y ? a ) 1211 , b ) 1231 , c ) 1251 , d ) 1271 , e ) 1291","""x = 50 + 51 + . . . + 70 = 21 ( 60 ) = 1260 y = 11 x + y = 1271 the answer is d ."""
Break down and solve the equation step by step.,"the market value of a certain machine decreased by 30 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ? a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 2,400 , e ) $ 800","""market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 30 / 100 ) = 8000 - 2400 = $ 5600 market value in 1984 = market value in 1983 - ( 30 % of $ 8000 ) = 5600 - 2400 = $ 3200 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","two trains 140 m and 200 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? a ) 10.9 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 12.24 sec","""relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 200 = 340 m . required time = 340 * 9 / 250 = 12.24 sec . answer : e"""
"Solve the problem systematically, showing each step clearly.","30 men can do a work in 40 days . when should 15 men leave the work so that the entire work is completed in 40 days after they leave the work ? a ) 87 days , b ) 10 days , c ) 15 days , d ) 44 days , e ) 22 days","total work to be done = 30 * 40 = 1200 let 15 men leave the work after' p' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 15 * 40 ) = 1200 40 p = 600 = > p = 15 days answer : c"
"Solve the problem systematically, showing each step clearly.","if 40 honey bees make 40 grams of honey in 40 days , then 1 honey bee will make 1 gram of honey in how many days ? a ) 1 , b ) 3.5 , c ) 40 , d ) 49 , e ) 30","""explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 40 : : 40 : x honey 40 : 1 = > 1 x 40 x x = 40 x 1 x 40 = > x = 40 . answer : c"""
Break down and solve the equation step by step.,"find the probability that a leap year chosen at random will have 53 sundays a ) 2 / 7 , b ) 2 / 6 , c ) 2 / 5 , d ) 2 / 3 , e ) 2 / 4","""a leap year has 366 day which is 52 full weeks + 2 odd days . now these two odd days may be ( sun + mon ) , ( mon + tue ) , . . . . ( sat + sun ) . now there are total 7 ways . of which sunday appeared two times . so answer 2 / 7 answer : a"""
Explain the solution process for the given equation.,"a reduction of 20 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ? a ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 41 , e ) s . 32","""800 * ( 20 / 100 ) = 160 - - - - 5 ? - - - - 1 = > rs . 32 answer : e"""
"Solve the problem systematically, showing each step clearly.","a bus started its journey from mumbai and reached pune in 44 min with its average speed of 50 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ? a ) 38 min , b ) 36 min , c ) 31 min , d ) 40 min , e ) 49 min","""sol . distance between ramgarh and devgarh = ( 50 * 44 ) / 60 = 110 / 3 average speed of the bus is increased by 5 km / hr then the speed of the bus = 55 km / hr required time = 110 / 3 * 60 / 55 = 40 min d"""
Provide a detailed solution to the given mathematical problem.,"a train starts full of passengers . at the first station , it drops one - third of the passengers and takes 280 more . at the second station , it drops one - half of the new total and takes 12 more . on arriving at the third station , it is found to have 248 passengers . find the number of passengers in the beginning . a ) 240 , b ) 248 , c ) 280 , d ) 288 , e ) 290","let x be no . of passengers at beginning at , 1 st station is drops 1 / 3 rd so remaining 2 / 3 rd are in train only plus 280 i . e . , 2 x / 3 + 280 at 2 nd stop 1 / 2 of new total and 12 more i . e . , ( 2 x / 3 + 280 ) / 2 + 12 = 248 on solving above equation we get x as 288 answer : d"
"Solve the problem systematically, showing each step clearly.","5 is added to a certain number , the sum is multiplied by 5 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 60 . what is the number ? a ) 21 , b ) 20 , c ) 2 , d ) 30 , e ) 45","""let number is x . when 5 added to it , = ( x + 5 ) 5 multiplied to sum , = 5 * ( x + 5 ) now , = [ { 5 * ( x + 5 ) } / 5 ] and , = [ { 5 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 5 * ( x + 5 ) } / 5 ] - 5 = half of 60 [ ( 5 x + 25 ) / 5 ) = 30 + 5 5 x + 25 = 35 * 5 x + 5 = 7 * 1 x + 5 = 7 x = 7 - 5 x = 2 so , required number is : 2 . answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","set a consists of all the prime numbers between 62 and 85 . what is the range of set a ? a ) 12 , b ) 13 , c ) 16.6 , d ) 16 , e ) 23","the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 83 lowest number = 67 range = highest - lowest = 83 - 67 = 16 option d"
"Work through the equation methodically, ensuring clarity at each step.","the weight of a glass of jar is 10 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ? a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 5 / 9","""let weight of jar filled with beans = 100 g weight of jar = 10 g weight of coffee beans = 90 g weight of jar and remaining beans = 60 g weight of remaining beans = 50 g fraction remaining = 50 / 90 = 5 / 9 answer is e ."""
Explain the solution process for the given equation.,"if an average hard drive had a capacity of 0.3 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ? a ) 3072 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536","""0.3 * 2 ^ 10 = 0.3 * 1024 = 307.2 the answer is a ."""
Provide a detailed solution to the given mathematical problem.,"a train running at the speed of 60 km / hr crosses a pole in 30 sec . what is the length of the train ? a ) 535 m , b ) 178 m , c ) 186 m , d ) 168 m , e ) 500 m","""speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 30 = 500 m answer : e"""
"Solve the problem systematically, showing each step clearly.","rs 70000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 8000 find money given by 10 % ? a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000","""let first parrt is x and second part is y then x + y = 70000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 8000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 80000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 80000 = 70000 + y so y = 10000 then x = 70000 - 10000 = 60000 first part = 60000 answer : d"""
"Solve the problem systematically, showing each step clearly.","a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 3 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ? a ) 12 : 15 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2","""the ratio of economy to luxury cars is 5 : 3 - - > e : l = 5 : 3 = 20 : 12 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 12 : 15 . answer : a ."""
Explain the solution process for the given equation.,"1904 x 1904 = ? a ) 3623216 , b ) 3624216 , c ) 3624316 , d ) 3625116 , e ) 3625216","""1904 x 1904 = ( 1904 ) 2 = ( 1900 + 4 ) 2 = ( 1900 ) 2 + ( 4 ) 2 + ( 2 x 1900 x 4 ) = 3610000 + 16 + 15200 . = 3625216 . e )"""
Explain the solution process for the given equation.,"reduce 368 / 598 to the lowest terms a ) 30 / 25 , b ) 28 / 13 , c ) 28 / 29 , d ) 8 / 13 , e ) none of these","explanation : we can do it easily by in two steps step 1 : we get the hcf of 368 and 598 which is 46 step 2 : divide both by 46 , we will get the answer 8 / 13 answer : option d"
"Solve the problem systematically, showing each step clearly.","a , b and c are employed to do apiece of work for rs . 529 . a and c are supposed to finish 19 / 23 of the work together . how much shall be paid to b ? a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 16","c 12 12 men can complete a work in 18 days . six days after they started working , 4 more men joined them . how many days will all of them together complete the remaining work ?"
Break down and solve the equation step by step.,"if | 5 x - 15 | = 100 , then find the sum of the values of x ? a ) 1 , b ) - 2 , c ) 6 , d ) - 3 , e ) 4","""| 5 x - 15 | = 100 5 x - 15 = 100 or 5 x - 15 = - 100 5 x = 115 or 5 x = - 85 x = 23 or x = - 17 sum = 23 - 17 = 6 answer is c"""
Explain the solution process for the given equation.,"what is the area of a square field whose diagonal of length 14 m ? a ) 160 sq m , b ) 140 sq m , c ) 200 sq m , d ) 400 sq m , e ) 180 sq m","""d 2 / 2 = ( 14 * 14 ) / 2 = 140 answer : b"""
"Solve the problem systematically, showing each step clearly.","a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 40 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ? a ) 1 : 20 , b ) 1 : 10 , c ) 17 : 8 , d ) 17 : 4 , e ) 17 : 60","first of all , let' s consider 1 liter of the stuff he is going to sell - - - naive customers think it' s pure milk , but we know it' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 40 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.40 = $ 36 cost = 36 / 1.4 = 360 / 12 = $ 25.71 if he wants a 40 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 25.71 . well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that' s 25.71 / 33 = 60 / 77 of a liter . if milk is 60 / 77 of the liter , then water is 17 / 77 of the liter , and the ratio of water to milk is 17 : 60 . answer choice ( e )"
"Solve the problem systematically, showing each step clearly.","the cyclist going at a constant rate of 20 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 60 miles per hour . the motor - cyclist stops to wait for the cyclist 10 minutes after passing her , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ? a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 40","""for the 10 minutes the motor - cyclist continues to overtake the cyclist , she is going at 40 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 20 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 40 / 20 * 10 or 20 minutes answer is ( b )"""
Explain the solution process for the given equation.,"if x is a positive integer with fewer than 3 digits , what is the probability r that x * ( x + 1 ) is a multiple of either 4 or 5 ? a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99","""interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability r that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."""
Explain the solution process for the given equation.,"a jar contains only red , yellow , and orange marbles . if there are 3 red , 7 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22","""i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 5 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 5 ) , which indeed is 5 / 22 . e"""
Explain the solution process for the given equation.,"in the first 10 overs of a cricket game , the run rate was only 4.6 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ? a ) 4.25 , b ) 5.9 , c ) 6.25 , d ) 7 , e ) 7.5","""required run rate = 282 - ( 4.6 x 10 ) = 236 236 / 40 = 5.9 b )"""
Explain the solution process for the given equation.,"two airplanes take off from one airfield at noon . one flies due east at 204 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ? a ) 166 , b ) 408 , c ) 400 , d ) 483 , e ) 566",b in two hours : the plane flying east will be 408 miles away from airport . the other plane will be 566 miles away from airport . 566 / 408 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 408 miles apart . b
"Solve the problem systematically, showing each step clearly.","a pump can fill a tank with water in 4 hours . because of a leak , it took 20 hours to fill the tank . the leak can drain all the water of the tank in ? a ) 1 , b ) 3 , c ) 5 , d ) 4 , e ) 2","p - - > pump , l - - - > leak pipe - - - - - - - - - - p - - - - - - - - - l - - - - - - - - - - - - ( p - l ) - - time - - - - - - - - - 4 - - - - - - - - - x - - - - - - - - - - - - - 20 * rate - - - - - - - - - 5 - - - - - - - - - x - - - - - - - - - - - - - 1 work - - - - - - - 20 - - - - - - - - - 20 - - - - - - - - - - - 20 time required to empty the tank if leakage present = 20 / ( ( 5 ) - 1 ) = ( 20 ) / ( 4 ) = 5 ans - c"
Break down and solve the equation step by step.,"the ratio of 2 numbers is 10 : 20 and their h . c . f . is 100 . their l . c . m . is ? a ) 1100 , b ) 3000 , c ) 2100 , d ) 1000 , e ) 2000","""let the numbers be 10 x and 20 x their h . c . f . = 100 so the numbers are 10 * 100 , 20 * 100 = 1000 , 2000 l . c . m = 2000 answer is e"""
Provide a detailed solution to the given mathematical problem.,"what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 6 ? a ) 5 , b ) 12 , c ) 10 , d ) 20 , e ) 30","""what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 6 ? 9 ^ 6 = ( 3 ^ 2 ) ^ 6 = 3 ^ 12 b . 12"""
Provide a detailed solution to the given mathematical problem.,"in shop there are 10 bulbs , a total of 4 are defective . if a customer buys 4 bulbs selected at random from the box , what is the probability that neither bulbs will be defective ? a ) 2 / 19 , b ) 3 / 29 , c ) 4 / 15 , d ) 1 / 15 , e ) 1 / 2","first , there are 6 c 4 ways you can select 6 good bulbs from 4 good ones . second , there are 10 c 4 ways you select 4 bulbs from 10 ones in the box . then , the probability that neither bulb will be defective is : 6 c 4 / 10 c 4 = 15 / 210 = 1 / 15 answer is d"
Explain the solution process for the given equation.,"shekar scored 76 , 65 , 82 , 67 and 95 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ? a ) 65 , b ) 77 , c ) 75 , d ) 85 , e ) 90",explanation : average = ( 76 + 65 + 82 + 67 + 95 ) / 5 = 385 / 5 = 77 hence average = 77 answer : b
Break down and solve the equation step by step.,"the population of a town increased from 1 , 24,300 to 1 , 62,400 in a decade . the average percent increase of population per year is : a ) 4.37 % , b ) 4 % , c ) 2.3 % , d ) 3.75 % , e ) none","""explanation : increase in 10 years = ( 162400 - 124300 ) = 87500 . increase % = ( 38100 / 162400 x 100 ) % = 23 % . required average = ( 23 / 10 ) % = 2.3 % . answer : option c"""
"Solve the problem systematically, showing each step clearly.","double of quarter of 4 percent written as a decimal is : a ) 0.003 , b ) 0.0005 , c ) 0.25 , d ) 0.02 , e ) none of these",explanation : solution : ( 2 ) * ( 1 / 4 ) * 4 % = 2 * ( 1 / 4 * 1 / 100 ) = 0.02 . answer : d
"Solve the problem systematically, showing each step clearly.","5 times a number equals one 100 . the number is a ) 50 , b ) 10 , c ) 15 , d ) 25 , e ) 20","since five times the number equals one hundred , then the number equals one hundred divided by five . therefore the number is 100 / 5 = 20 . correct answer e"
"Work through the equation methodically, ensuring clarity at each step.","a bus covers a distance of 12 km in 5 min . if it takes 5 sec to pass a telegraph post , then the length of the bus is ? a ) 120 m , b ) 180 m , c ) 240 m , d ) 200 m , e ) 280 m",speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the bus = 40 * 5 = 200 m . answer : d
"Solve the problem systematically, showing each step clearly.","how many integers between 323,700 and 458,600 have tens digit 1 and units digit 3 ? a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,349","""there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 323,700 and 458,600 is 458,600 - 323,700 = 134,900 - one number per each hundred gives 134,900 / 100 = 1,349 numbers . answer : e ."""
Explain the solution process for the given equation.,"it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill one sixteenth of the dish ? a ) 16 days , b ) 26 days , c ) 27 days , d ) 28 days , e ) 29 days","the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . the answer is b ."
Break down and solve the equation step by step.,"| 9 - 4 | - | 12 - 14 | = ? a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4","""| 9 - 4 | - | 12 - 14 | = | 5 | - | - 2 | = 5 - 2 = 3 correct answer a"""
"Work through the equation methodically, ensuring clarity at each step.","a train 100 m in length crosses a telegraph post in 12 seconds . the speed of the train is ? a ) 16 kmph , b ) 30 kmph , c ) 54 kmph , d ) 18 kmph , e ) 19 kmph","""s = 100 / 12 * 18 / 5 = 30 kmph answer : b"""
Explain the solution process for the given equation.,"when a student joe , weighing 40 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ? a ) 5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg","""after two persons leave the group the average remains the same . that means the weight of the two persons = 40 + 30 = 70 so , the average the two persons = 35 that gives the answer 40 - 35 = 5 answer a"""
Explain the solution process for the given equation.,"there were two candidates in an election . winner candidate received 54 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ? a ) 776 , b ) 1944 , c ) 2199 , d ) 2157 , e ) 2125","""w = 54 % l = 46 % 54 % - 46 % = 8 % 8 % - - - - - - - - 288 54 % - - - - - - - - ? = > 1944 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 5 % . what is the approximate interest he pays annually ? a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000","since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 5 % quarterly rate . so the bank charges 5 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 5 % of 10,000 = $ 2000 as our answer . but since , the interest is compounded , it will be a bit more than $ 2000 . option ( c ) looks correct . answer : c"
Explain the solution process for the given equation.,"a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 55 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ? a ) 37 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .","""20 % of 2 litres = 0.4 litres 55 % of 6 litres = 3.3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % a"""
"Solve the problem systematically, showing each step clearly.","from a pack of 52 cards , 1 card is drawn at random . what is the probability that a heart is drawn ? a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 13 , e ) 3 / 26","""the total number of cards is 52 . the number of hearts is 13 . p ( heart ) = 13 / 52 = 1 / 4 the answer is c ."""
Break down and solve the equation step by step.,"an investment compounds annually at an interest rate of 34.1 % what is the smallest investment period by which time the investment will more than triple in value ? a ) 3 , b ) 4 , c ) 6 , d ) 9 , e ) 12",assume initial amount is x annual interest is 34.1 % so after 1 year the amount will become x * ( 100 + 34.1 ) / 100 = > x * 4 / 3 now we need to find n for x * ( 4 / 3 ) ^ n = 3 x ; or in other words n = 4 answer : b
Provide a detailed solution to the given mathematical problem.,"what is value of ( ( 2 ^ 5 ) * ( 9 ^ 2 ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) = ? a ) 1 / 6 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 4",= > ( ( 2 ^ 5 ) * ( ( 3 ^ 2 ) ^ 2 ) / ( ( 2 ^ 3 ) ^ 2 ) * ( 3 ^ 5 ) ) = > ( ( 2 ^ 5 ) * ( 3 ^ 4 ) ) / ( ( 2 ^ 6 ) * ( 3 ^ 5 ) ) = > 1 / ( 2 * 3 ) = > 1 / 6 option a is answer
Explain the solution process for the given equation.,"at a speed of 50 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 15 gallon tank of gasoline and travels for 5 hours at 50 miles per hour , the amount of gasoline used would be what fraction of a full tank ? a ) 3 / 25 , b ) 11 / 36 , c ) 5 / 9 , d ) 2 / 3 , e ) 25 / 36",gas used = ( 5 hours ) * ( 50 miles / hour ) * ( 1 gallon / 30 miles ) = 8 + 1 / 3 gallons portion used = ( 8 + 1 / 3 ) / 15 = 5 / 9 ans c
"Work through the equation methodically, ensuring clarity at each step.","a woman complete a journey in 25 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km . a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 560 km .",0.5 x / 21 + 0.5 x / 24 = 25 - - > x / 21 + x / 24 = 50 - - > x = 560 km . e
Explain the solution process for the given equation.,"the ratio of the incomes of rajan and balan is 7 : 6 and the ratio of their expenditure is 6 : 5 . if at the end of the year , each saves $ 1000 then the income of rajan is ? a ) $ 7600 , b ) $ 7000 , c ) $ 8000 , d ) $ 9000 , e ) $ 5000",let the income of rajan and balan be $ 7 x and $ 6 x let their expenditures be $ 6 y and $ 5 y 7 x - 6 y = 1000 - - - - - - - 1 ) 6 x - 5 y = 1000 - - - - - - - 2 ) from 1 ) and 2 ) x = 1000 rajan' s income = 7 x = 7 * 1000 = $ 7000 answer is b
Explain the solution process for the given equation.,"each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , forty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 72 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ? a ) 24 % , b ) 16 % , c ) 11 % , d ) 7 % , e ) 5 %","let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.4 i + 0.8 f = 0.72 ( i + f ) 0.08 f = 0.32 i f = 4 i this means that for every 1 incandescent bulb , there are 4 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.4 i / ( 0.4 i + 0.8 f ) = 0.4 i / ( 0.4 i + 0.8 * 4 i ) = 0.4 i / 3.6 i = 1 / 9 which is about 11 % . the answer is c ."
Provide a detailed solution to the given mathematical problem.,"a shipment of 250 smartphones contains 76 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ? a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3","""probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = ( 76 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 75 ( we already picked one ) defective phones is = ( 75 / 249 ) combined probability of series of events = product of the probabilities = ( 76 / 250 ) * ( 75 / 249 ) 76 / 250 is close to ( 7 / 23 ) and ( 75 / 249 ) = ( 25 / 83 ) so answer is ( 7 / 23 ) * ( 25 / 83 ) = ( 1 / 11 ) so , answer will be c"""
Break down and solve the equation step by step.,"every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 3200 ? a ) 8100 , b ) 3388 , c ) 7767 , d ) 4050 , e ) 2288","""3200 * 9 / 8 * 9 / 8 = 4050 answer : d"""
Provide a detailed solution to the given mathematical problem.,"two years ago , john put $ 5000 into a savings account . at the end of the first year , his account had accrued $ 500 in interest bringing his total balance to $ 5500 . the next year , his account balance increased by 10 % . at the end of the two years , by what percent has john' s account balance increased from his initial deposit of $ 5000 ? a ) 19 % , b ) 21 % , c ) 20 % , d ) 22 % , e ) 25 %",investment 5000 dollars 1 st year total gained = 500 total amount end of first year = 5500 second year account increased by 10 % = 5500 * 0.1 = 550 therefore total amount by second year end = 6050 so total percentage increase in money = ( 6050 - 5000 ) * 100 / 5000 = 21 % correct answer b = 21 %
Explain the solution process for the given equation.,"the hour hand of a watch rotates 30 degrees every hour . how many complete rotations does the hour hand make in 6 days ? a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16","explanation : there are 360 degrees in a complete circle , so 360 / 30 = 12 hours to make one full circle . in 6 days there are 24 hours x 6 = 144 hours total . the total number of rotations will be 144 / 12 = 12 . answer : ( c )"
Explain the solution process for the given equation.,"if 70 honey bees make 70 grams of honey in 70 days , then 1 honey bee will make 1 gram of honey in how many days ? a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 70","""explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 70 : : 70 : x honey 70 : 1 = > 1 x 70 x x = 70 x 1 x 70 = > x = 70 . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","the remainder when q = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . + 3 ^ 200 is divided 13 . a ) 12 , b ) 7 , c ) 0 , d ) 5 , e ) 3","q = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . . . . . . . . . + 3 ^ 200 is a geometric progression having common ratio as' 3' and number of terms as' 201' . since sum to n terms in gp = a ( r ^ n - 1 ) / ( r - 1 ) where a = first term and r = common ration hence , 1 * ( 3 ^ 201 - 1 ) / ( 3 - 1 ) rem of ( 3 ^ 201 - 1 ) / 2 divided by 13 3 ^ 201 - 1 / 26 wkt , 3 ^ 3 = 27 = 26 + 1 { ( 26 + 1 ) ^ 67 - 1 } / 26 { 1 - 1 } / 26 = > 0 . c"
Break down and solve the equation step by step.,"a river 7 m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ? a ) 54996.5 , b ) 32296.5 , c ) 34996.5 , d ) 34996.5 , e ) 31255.5","""rate of water flow - 4 kmph - - 4000 / 60 - - 66.66 m / min depth of river - - 7 m width of river - - 75 m vol of water per min - - 66.66 * 7 * 75 - - - 34996.5 answer c"""
Break down and solve the equation step by step.,"the sum of the ages of 4 children born at the intervals of 3 years each is 36 years . what is the age of the youngest child ? a ) 22 , b ) 18 , c ) 4.5 , d ) 99 , e ) 38","""let x = the youngest child . each of the other four children will then be x + 3 , x + 6 , x + 9 we know that the sum of their ages is 36 so , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) = 36 therefore the youngest child is 4.5 years old answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","find the area of a parallelogram with base 26 cm and height 14 cm ? a ) 287 cm 2 , b ) 887 cm 2 , c ) 364 cm 2 , d ) 368 cm 2 , e ) 668 cm 2","""area of a parallelogram = base * height = 26 * 14 = 364 cm 2 answer : c"""
Explain the solution process for the given equation.,"in 3 annual examinations , of which the aggregate marks of each was 500 , a student secured average marks 45 % and 55 % in the first and the second yearly examinations respectively . to secure 40 % average total marks , it is necessary for him in third yearly examination to secure marks : a ) 100 , b ) 350 , c ) 400 , d ) 450 , e ) 500",total marks : 1500 for three exams 40 % of 1500 = 600 first exam marks = 45 % of 500 = 225 second exam marks = 55 % of 500 = 275 let x be the third exam marks 225 + 275 + x = 600 x = 100 answer : a
"Solve the problem systematically, showing each step clearly.","the simple interest on a certain sum of money for 2 years at 10 % per annum is half the compound interest on $ 100 for 2 years at 5 % per annum . the sum placed on simple interest is ? a ) $ 602.5 , b ) $ 625.8 , c ) $ 710.6 , d ) $ 745 , e ) $ 790.3","""c . i . = 100 * ( 1 + 5 / 100 ) ^ 2 - 100 = 100 * 21 / 20 * 21 / 20 - 100 = $ 120.5 sum = 120.5 * 100 / 2 * 10 = $ 602.5 answer is a"""
"Solve the problem systematically, showing each step clearly.","in a division , a student took 72 as divisor instead of 36 . his answer was 24 . the correct answer is - a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38","""x / 72 = 24 . x = 24 * 72 . so correct answer would be , ( 24 * 72 ) / 36 = 48 . answer : c"""
Provide a detailed solution to the given mathematical problem.,"a 12 % stock yielding 10 % is quoted at : a ) rs . 83.33 , b ) rs . 110 , c ) rs . 112 , d ) rs . 120 , e ) rs . 140",income of rs 10 on investment of rs 100 income of rs 12 on investment of ? = ( 12 * 100 ) / 10 = 120 answer : d
Provide a detailed solution to the given mathematical problem.,"the ratio between the sale price and the cost price of an article is 7 : 5 . what is the ratio between the profit and the cost price of that article ? a ) 2 : 8 , b ) 2 : 1 , c ) 2 : 2 , d ) 2 : 4 , e ) 2 : 5","""explanation : let c . p . = rs . 5 x and s . p . = rs . 7 x . then , gain = rs . 2 x required ratio = 2 x : 5 x = 2 : 5 answer : e"""
Explain the solution process for the given equation.,"a two - digit number is such that the product of the digits is 8 . when 18 is added to the number , then the digits are reversed . the number is : a ) 32 , b ) 24 , c ) 12 , d ) 7 , e ) 45","""answer : option b let the ten' s and unit' s digit be x and 8 / x respectively . then , ( 10 x + 8 / x ) + 18 = 10 * 8 / x + x 9 x 2 + 18 x - 72 = 0 x 2 + 2 x - 8 = 0 ( x + 4 ) ( x - 2 ) = 0 x = 2 so , ten' s digit = 2 and unit' s digit = 4 . hence , required number = 24 ."""
Explain the solution process for the given equation.,"a person can swim in still water at 6 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 14 km ? a ) 3.5 , b ) 4.5 , c ) 5 , d ) 9 , e ) 6","""m = 6 s = 2 us = 6 - 2 = 4 d = 42 t = 14 / 4 = 3.5 answer : a"""
Provide a detailed solution to the given mathematical problem.,"for any non - zero a and b that satisfy | ab | = ab and | a | = a | b - 4 | + | ab - b | = ? a ) ab - 4 , b ) 2 b - ab - 4 , c ) ab + 4 , d ) ab - 2 b + 4 , e ) 4 - ab","| ab | = ab and | a | = - a = > b is also negative . so | b - 4 | + | ab - b | = ( b - 4 ) + ab - b ( as ab is positive and - b is positive , so expression is totally positive ) = b - 4 + ab - b = ab - 4 answer - a"
Break down and solve the equation step by step.,"an engineer undertakes a project to build a road 10 km long in 150 days and employs 30 men for the purpose . after 50 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time . a ) 22 , b ) 30 , c ) 15 , d ) 18 , e ) 20","""30 workers working already let x be the total men required to finish the task in next 100 days 2 km done hence remaining is 8 km also , work has to be completed in next 100 days ( 150 - 50 = 100 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 50 ) / ( 2 * 100 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : b"""
Break down and solve the equation step by step.,"of 70 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92","""total = 90 thrower = 37 rest = 90 - 37 = 33 left handed = 33 / 3 = 11 right handed = 22 if all thrower are right handed then total right handed is 37 + 22 = 59 so c . 59 is the right answer"""
"Work through the equation methodically, ensuring clarity at each step.","martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 19.20 , how many discounted tickets did he buy ? a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 2","""let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 19.2 0.4 x = 3.2 = > x = 8 discounted tickets = 10 - x = 2 ans : e"""
"Work through the equation methodically, ensuring clarity at each step.","a train covers a distance of 12 km in 5 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ? a ) 120 m , b ) 180 m , c ) 240 m , d ) 220 m , e ) 280 m","""speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the train = 40 * 6 = 240 m . answer : c"""
Provide a detailed solution to the given mathematical problem.,"a and b start walking towards each other at 6 pm at speed of 6 kmph and 4 kmph . they were initially 50 km apart . at what time do they meet ? a ) 8 pm , b ) 6 pm , c ) 11 pm , d ) 10 pm , e ) 5 pm","""time of meeting = distance / relative speed = 50 / 4 + 6 = 50 / 10 = 5 hrs after 6 pm = 11 pm answer is c"""
Explain the solution process for the given equation.,"a rectangular grass field is 75 m * 55 m , it has a path of 3.2 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ? a ) s . 1350 , b ) s . 1327 , c ) s . 1328 , d ) s . 1364 , e ) s . 1927","""area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 3.2 * 2 ) 2 * 2.5 = > 682 682 * 2 = rs . 1364 answer : d"""
Provide a detailed solution to the given mathematical problem.,"if 25 / 999 = 0.002 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ? a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2","""0 . [ u ] 25 [ / u = 0.002002002002 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 2 . since 81 is multiple of 3 , the 81 st digit is 2 . answer e"""
Provide a detailed solution to the given mathematical problem.,"the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 294 sq . cm , what is the length of the rectangle ? a ) 15 cm , b ) 18 cm , c ) 21 cm , d ) 24 cm , e ) 27 cm","""2 l + 2 w = 5 w l = 3 w / 2 w * l = 294 3 w ^ 2 / 2 = 294 w ^ 2 = 196 w = 14 l = 3 ( 14 ) / 2 = 21 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"peter invested a certain sum of money in a simple interest bond whose value grew to $ 300 at the end of 3 years and further to $ 400 at the end of another 5 years . what was the rate of interest in which he invested his sum ? a ) 12 % , b ) 12.5 % , c ) 6.67 % , d ) 6.25 % , e ) 8.33 %","answer initial amount invested = $ x amount at the end of year 3 = $ 300 amount at the end of year 8 ( another 5 years ) = $ 400 therefore , the interest earned for the 5 year period between the 3 rd year and 8 th year = $ 400 - $ 300 = $ 100 as the simple interest earned for a period of 5 years is $ 100 , interest earned per year = $ 20 . therefore , interest earned for 3 years = 3 * 20 = $ 60 . hence , initial amount invested x = amount after 3 years - interest for 3 years = 300 - 60 = $ 240 . rate of interest = ( interest per year / principal ) * 100 = 20 / 240 * 100 = 8.33 % choice is ( e )"
"Solve the problem systematically, showing each step clearly.","p software has coding line 5 % more than n , n software has coding line 4 / 20 more than m . m software has 80 lines of coding . find p lines . a ) 101 , b ) 107 , c ) 108 , d ) 109 , e ) 110","""m s / w has 80 line of code n s / w has = 80 + 80 * 4 / 20 = 96 line of code p s / w 5 % more n' code 96 + 4.8 = 100.8 or 101 line of code answer : a"""
Explain the solution process for the given equation.,"if a / b = 1 / 2 , b / c = 5 , c / d = 2 / 3 , d / e = 1 / 6 and e / f = 2 / 3 , then what is the value of abc / def ? a ) 50 / 729 , b ) 20 / 456 , c ) 45 / 752 , d ) 13 / 452 , e ) 45 / 741","""say a = 2 . then : a / b = 1 / 2 - - > b = 4 ; b / c = 5 - - > c = 4 / 5 ; c / d = 2 / 3 - - > d = 6 / 5 ; d / e = 1 / 6 - - > e = 36 / 5 ; e / f = 2 / 3 - - > f = 54 / 2 . abc / def = ( 2 * 4 * 4 / 5 ) / ( 6 / 5 * 36 / 5 * 54 / 5 ) = 50 / 729 . answer : a ."""
Provide a detailed solution to the given mathematical problem.,"n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 n is divided by 4 ? a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 5","""explanation : let n = 4 q + 3 . then 2 n = 8 q + 6 = 4 ( 2 q + 1 ) + 2 . thus , when 2 n is divided by 4 , the remainder is 2 . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a straight line in the xy - plane has y - intercept of 49 . on this line the x - coordinate of the point is 71 and y - coordinate is 12 then what is the slope of the line ? a ) 0.5 , b ) 0.51 , c ) - 0.52 , d ) 0.31 , e ) - 0.49","""eq of line = y = mx + c c = 49 x = 71 y = 12 substitute given : m = ( y - c ) / x = ( 12 - 49 ) / 71 = - 37 / 71 = - 0.52 correct option is c"""
"Work through the equation methodically, ensuring clarity at each step.","the average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results ? a ) 34 , b ) 25 , c ) 48 , d ) 50 , e ) none",answer sum of 70 result = sum of 40 result + sum of 30 result . = 40 x 30 + 30 x 40 = 2400 / 70 correct option : a
"Solve the problem systematically, showing each step clearly.","a gambler bought $ 3000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ? a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400","in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 3,000 - $ 880 = $ 2,120 . answer : b ."
Break down and solve the equation step by step.,"jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much w does she have in her account after two years ? a ) $ 10079.44 , b ) w = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11","""ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"""
Explain the solution process for the given equation.,"( 3192 + 6160 ) / 28 a ) 380 , b ) 350 , c ) 334 , d ) 310 , e ) none of these","""explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9352 ) / 28 = 334 option c"""
"Work through the equation methodically, ensuring clarity at each step.","in what time will a train 200 metres long cross an electric pole , if its speed be 124 km / hr ? a ) 4.8 sec , b ) 5.9 sec , c ) 5.0 sec , d ) 5.4 sec , e ) 5.8 sec","""solution speed = ( 124 x 5 / 18 ) m / sec = 34.44 m / sec time taken = ( 200 / 34.44 ) sec = 5.8 sec . answer e"""
Provide a detailed solution to the given mathematical problem.,"in the coordinate plane , points ( x , 8 ) and ( 20 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x * y = a ) 120 , b ) 100 , c ) 135 , d ) 140 , e ) 160","line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 8 ) = ( 32 , 8 ) and ( 20 , y ) = ( 20,5 ) - - > x * y = 32 * 5 = 160 . answer : e"
Explain the solution process for the given equation.,"find the simple interest on rs . 64,000 at 16 2 / 3 % per annum for 9 months . a ) s . 8500 , b ) s . 8000 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500","""p = rs . 64000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 64,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8000 answer is b ."""
Explain the solution process for the given equation.,"the ratio 10 : 20 expressed as percent equals to a ) 50 % , b ) 80 % , c ) 40 % , d ) 90 % , e ) 100 %","""explanation : actually it means 10 is what percent of 20 , which can be calculated as , ( 10 / 20 ) * 100 = 10 * 5 = 50 answer : option a"""
"Work through the equation methodically, ensuring clarity at each step.","a trader bought a car at 40 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ? a ) 8 % , b ) 62 % , c ) 2 % , d ) 9 % , e ) 22 %","""original price = 100 cp = 60 s = 60 * ( 180 / 100 ) = 112 100 - 108 = 8 % answer : a"""
Break down and solve the equation step by step.,"on selling 11 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is : a ) s . 45 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 120","""( c . p . of 11 balls ) - ( s . p . of 11 balls ) = ( c . p . of 5 balls ) c . p . of 6 balls = s . p . of 11 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 6 = rs . 120 . answer : option e"""
Provide a detailed solution to the given mathematical problem.,"a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1989 on her 32 nd birthday first be eligible to retire under this provision ? a ) 2008 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007","""she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1989 + 19 = 2008 . answer : a ."""
Break down and solve the equation step by step.,"what is the compound interest on rs . 9500 at 6 % p . a . compounded half - yearly for 1 1 / 2 years . a ) 810.91 , b ) 840.91 , c ) 880.91 , d ) 887.91 , e ) 980.91","""compound interest : a = p ( 1 + r / n ) nt a = 10 , 380.91 c . i . > > 10 , 380.91 - 9500 > > rs . 880.91 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","if the sides of a triangle are 30 cm , 40 cm and 50 cm , what is its area ? a ) 400 , b ) 500 , c ) 550 , d ) 600 , e ) 700","""the triangle with sides 30 cm , 40 cm and 50 cm is right angled , where the hypotenuse is 50 cm . area of the triangle = 1 / 2 * 40 * 30 = 600 cm 2 answer : option d"""
"Work through the equation methodically, ensuring clarity at each step.","the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 50,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 400,000 , e ) $ 540,000","""the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 50,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 50000 * 2 ^ 3 = 400000 hence , the answer is d ."""
"Solve the problem systematically, showing each step clearly.","it takes 40 identical printing presses 15 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ? a ) 16 , b ) 18 , c ) 20 , d ) 21 , e ) 24",40 printing presses can do 1 / 15 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 15 = 1 / 20 of the job each hour . the answer is c .
"Solve the problem systematically, showing each step clearly.","a walks at 30 kmph and 30 hours after his start , b cycles after him at 55 kmph . how far from the start does b catch up with a ? a ) 1200 km , b ) 1980 km , c ) 2000 km , d ) 2500 km , e ) 3600 km","""suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 55 = 30 x = 1980 km answer is b"""
Break down and solve the equation step by step.,"what is the measure of the angle w made by the diagonals of the any adjacent sides of a cube . a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90","""c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c"""
"Solve the problem systematically, showing each step clearly.","i sold a book at a profit of 10 % . had i sold it for $ 150 more , 15 % would have been gained . find the cost price ? a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540","""115 % of cost - 110 % of cost = $ 150 5 % of cost = $ 150 cost = 150 * 100 / 5 = $ 3000 answer is c"""
Provide a detailed solution to the given mathematical problem.,"a gold purification process cycle , is able to remove 1 / 16 of impurities in gold . if we have a 10 grams of gold ore dust containing 16 / 24 pure gold . how much impurities would have been removed from that old after 4 cycles of purification using that method ? a ) 0.72 , b ) 0.74 , c ) 0.76 , d ) 0.78 , e ) 0.82","x is the initial quantity of impurities in that gold . after a cycle of purification the quantity of impurities left would be x 1 = x - 1 / 16 x i . e . x 1 = 15 / 16 x same thing for x 2 , x 3 , x 4 , respectively representing the quantity of impurities left after 2 , 3 , 4 cycles of purification . so we have : x 1 = 15 / 16 x x 2 = 15 / 16 x 1 x 3 = 15 / 16 x 2 x 4 = 15 / 16 x 3 by multiplying both ends of the equations we get : x 1 * x 2 * x 3 * x 4 = ( 15 / 16 ) ^ 4 x * x 1 * x 2 * x 3 simplification leaves us with : x 4 = ( 15 / 16 ) ^ 4 x x 4 is the quantity of impurities left after four cycles . so the cumulative quantity of impurities ( q 4 ) which has been removed after 4 cycles is : q 4 = x - x 4 = x - ( 15 / 16 ) ^ 4 x i . e . q 4 = x ( 1 - ( 15 / 16 ) ^ 4 ) in this case , given x was : x = ( 1 - 16 / 24 ) * 10 g = 3.33 g ( remember we had 16 / 24 pure gold ) so we have q 4 = 3.33 * ( 1 - ( 15 / 16 ) ^ 4 ) = 3.33 * ( 1 - ( 50625 / 65536 ) ) = 3.33 * ( 14911 / 65536 ) = 0.757 rounded gives q 4 = 0.76 answer : c"
Explain the solution process for the given equation.,"what is the sum of the greatest common factor and the lowest common multiple of 45 and 125 ? a ) 1920 , b ) 2201 , c ) 3240 , d ) 1130 , e ) 3840","""prime factorization of the given numbers 45 = 3 ^ 2 125 = 5 ^ 3 greatest common factor = 5 lowest common multiple = 3 ^ 2 * 5 ^ 2 * 5 = 1125 sum = 5 + 1125 = 1130 answer d"""
"Solve the problem systematically, showing each step clearly.","annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 25 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ? a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100","""annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 25 minutes , sam rides 5 km so sam will be 3 km ahead . it will take annie 60 minutes to catch sam . the answer is c ."""
Break down and solve the equation step by step.,"in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 72 . what is the total number of students in the school ? a ) 72 , b ) 80 , c ) 120 , d ) 40 , e ) 150","""explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 72 + 2 / 3 of 72 80 / 100 x = 120 x = 150 . answer : option e"""
Break down and solve the equation step by step.,"if 10 typists can type 30 letters in 30 minutes , then how many letters will 40 typists working at the same rate complete in 1 hour ? a ) 200 , b ) 210 , c ) 205 , d ) 225 , e ) 240","""no . of letters typing by 10 typists in 30 minutes = 30 no . of letters typing by 10 typists in 60 minutes = 30 * 2 = 60 no . of letters typing by 40 typists in 60 minutes = 60 / 10 * 40 = 240 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","in a company , 50 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ? a ) 85 % , b ) 80 % , c ) 75 % , d ) 70 % , e ) 65 %","""the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 50 % of all employees are women , so non - union women are 50 % - 18 % = 32 % 40 % of all employees are non - union . the percent of non - union employees who are women is 32 % / 40 % = 80 % the answer is b ."""
Break down and solve the equation step by step.,"the average of 6 no .' s is 2.80 . the average of 2 of them is 2.4 , while the average of the other 2 is 2.3 . what is the average of the remaining 2 no' s ? a ) 2.3 , b ) 2.6 , c ) 3.6 , d ) 3.7 , e ) 4.6",sum of the remaining two numbers = ( 2.80 * 6 ) - [ ( 2.4 * 2 ) + ( 2.3 * 2 ) ] = 16.80 - ( 4.8 + 4.6 ) = 16.80 - 9.40 = 7.40 required average = ( 7.4 / 2 ) = 3.7 answer : d
"Solve the problem systematically, showing each step clearly.","find the value of m 62519 x 9999 = m ? a ) 724533811 , b ) 625127481 , c ) 545463251 , d ) 725117481 , e ) 677899932","""62519 x 9999 = 62519 x ( 10000 - 1 ) = 62519 x 10000 - 62519 x 1 = 625190000 - 62519 = 625127481 b"""
Explain the solution process for the given equation.,"a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 900 grams . find the profit percent . a ) 12.11 , b ) 11.11 , c ) 13.11 , d ) 14.11 , e ) 15.11","""explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 900 100 + g / 100 + 0 = 1000 / 900 100 + g = 10 / 9 * 100 g = 11.11 answer : b"""
Explain the solution process for the given equation.,"some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 45 % . what fraction of the original paint was replaced ? a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5","""45 % is 20 % - points above 25 % and 5 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 1 : 4 . 1 / 5 of the original paint was replaced . the answer is b ."""
Break down and solve the equation step by step.,"a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 5 m , the volume of the box ( in m 3 ) is : a ) 4940 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960","""clearly , l = ( 48 - 10 ) m = 38 m , b = ( 36 - 10 ) m = 26 m , h = 8 m . volume of the box = ( 38 x 26 x 5 ) m 3 = 4940 m 3 . answer : option a"""
Provide a detailed solution to the given mathematical problem.,"what should be added to 4750 so that it may become a perfect square ? a ) 11 , b ) 15 , c ) 16 , d ) 17 , e ) 18","""69 x 69 = 4761 4761 - 4750 = 11 if added to 11 get perfect square answer = a"""
Provide a detailed solution to the given mathematical problem.,"in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 175 girls , the total number of students in the college is ? a ) 562 , b ) 356 , c ) 455 , d ) 416 , e ) 512","""let the number of boys and girls be 8 x and 5 x then , 5 x = 175 x = 35 total number of students = 13 x = 13 * 35 = 455 answer is c"""
Provide a detailed solution to the given mathematical problem.,"the instructions state that cheryl needs 5 / 11 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 25 / 55 square yards left that she did not use . what is the total amount of square yards of material cheryl used ? a ) 1 / 12 , b ) 1 / 9 , c ) 1 2 / 3 , d ) 2 / 3 , e ) 2 1 / 9","""total bought = 5 / 11 + 2 / 3 left part 25 / 55 - - - > 5 / 11 so used part 5 / 11 + 2 / 3 - 5 / 11 = 2 / 3 ans d"""
"Work through the equation methodically, ensuring clarity at each step.","which number should replace both the asterisks in ( * / 18 ) x ( * / 162 ) = 1 ? a ) 27 , b ) 36 , c ) 54 , d ) 72 , e ) 90",let ( y / 18 ) x ( y / 162 ) = 1 y ^ 2 = 18 x 162 = 18 x 18 x 9 y = ( 18 x 3 ) = 54 the answer is c .
Provide a detailed solution to the given mathematical problem.,"shopkeeper rise price by 35 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ? a ) 5.275 % , b ) 4.275 % , c ) 3.275 % , d ) 6.275 % , e ) 7.275 %","""let d initial price be 100 35 % rise now price = 135 / 100 * 100 = 135 10 % discount then price = 135 * 90 / 100 = 121.5 15 % discount then price = 121.5 * 85 / 100 = 103.275 so gain = 103.275 - 100 = 3.275 gain % = gain * 100 / cp = = > 3.275 * 100 / 100 = 3.275 % answer : c"""
Provide a detailed solution to the given mathematical problem.,"divide rs . 800 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a' s share is ? a ) s . 800 , b ) s . 200 , c ) s . 600 , d ) s . 500 , e ) s . 900","""a + b + c = 800 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 800 = > 200 answer : b"""
Break down and solve the equation step by step.,"the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 46 ) is : a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0","""step 1 : ( 35 ) ^ ( 87 ) can be broken up into ( 5 ) ^ 87 x ( 7 ) ^ 87 . each power of 7 ends in a units digit of either a 7 , 9,3 or 1 . each power of 5 ends in a 5 . when you multiply 5 by any odd number you will end up with a units digit of 5 . step 2 : ( 93 ) ^ ( 46 ) can be broken up into ( 3 ) ^ 46 x ( 31 ) ^ 46 . each power of 31 ends in a units digit of 1 . each power of 3 ends in a units digit of either 3 , 9,7 and 1 . since there is a pattern here where every 4 th power of 3 ends in a units digit of 3 , the 46 th power of 3 would end in a units digit of 9 . when you multiply 1 by 9 you end up with a units digit of 9 . therefore , the units digit we are looking for is 5 + 9 = 14 . units digit will be 4 . answer b ."""
"Solve the problem systematically, showing each step clearly.","a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 115 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ? a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 13.03 %","""typical dosage is dose : weight : : 2 : 15 . now if weight is 115 : ( 115 / 15 ) ) then typical dosage would be 2 * 7.67 = 15.33 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 15.33 ) * 100 = 13.03 % e is the answer ."""
Explain the solution process for the given equation.,"find large number from below question the difference of 2 no' s is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder a ) 1236 , b ) 1356 , c ) 1470 , d ) 1556 , e ) 1635","""let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"""
"Work through the equation methodically, ensuring clarity at each step.","the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is : a ) 23 , b ) 19 , c ) 22 , d ) 20 , e ) 14","""let the total number of workers be x . then , 8000 x = ( 10000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 28000 = x = 14 . answer : e"""
Break down and solve the equation step by step.,"if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 7 m of the same rod ? a ) 22.8 kg , b ) 26.6 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these","""explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 7 : : 42.75 : x = > 11.25 x x = 7 x 42.75 = > x = ( 7 x 42.75 ) / 11.25 = > x = 26.6 answer : b"""
Provide a detailed solution to the given mathematical problem.,"two circular frames are kept one above the other . frame x has a diameter of 16 cm and frame y has a diameter of 12 cm . what fraction of the surface of frame x is not covered by frame y ? ['a ) 3 / 5','b ) 7 / 16','c ) 12 / 16','d ) 24 / 12','e ) 2 / 3']","the questions asks us to find the surface which is not covered by the frame y i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the frame y = pi * r ^ 2 , where r = 6 = > pi * 36 area of the frame x = pi * 64 surface not covered by the frame y = pi * 64 - pi * 36 = pi * 28 fraction of frame x' s surface is not covered by a frame y = pi * 28 / total area of the frame x = 28 / 64 = 7 / 16 answer is b"
Provide a detailed solution to the given mathematical problem.,"the average weight of 6 person' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? a ) 76 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these","""explanation : total weight increased = ( 6 x 2.5 ) kg = 15 kg . weight of new person = ( 65 + 15 ) kg = 80 kg . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","if x + y = - 10 , and x = 25 / y , what is the value of x ^ 2 + y ^ 2 ? a ) 55 , b ) 65 , c ) 50 , d ) 75 , e ) 85","""x ^ 2 + y ^ 2 should make you think of these formulas : ( x + y ) ( x + y ) = x ^ 2 + y ^ 2 + 2 xy we already know ( x + y ) = - 10 and x * y = 25 ( x + y ) ( x + y ) = ( - 10 ) ( - 10 ) = x ^ 2 + y ^ 2 + 2 * ( 25 ) x ^ 2 + y ^ 2 = 100 - 50 = 50 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","a sum amounts to rs . 8820 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ? a ) s . 4000 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 8000","""ci = 8820 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 8820 = p [ 21 / 20 ] ^ 2 8820 [ 20 / 21 ] ^ 2 8000 answer : e"""
Provide a detailed solution to the given mathematical problem.,"a batsman makes a score of 90 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning . a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56","""let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 90 = 11 x x = 90 - 50 = 40 answer is a"""
Explain the solution process for the given equation.,"what percent of 120 are 90 ? a ) 25 % , b ) 50 % , c ) 75 % , d ) 33 % , e ) 30 %","""explanation : ( ? % / 100 ) * 120 = 90 ? = 75 % answer is c"""
"Solve the problem systematically, showing each step clearly.","in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.36 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ] a ) 0.33 , b ) 0.44 , c ) 0.48 , d ) 44 , e ) 48","""a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 36 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 36 = 48 cents . answer : e ."""
"Solve the problem systematically, showing each step clearly.","a shopkeeper has 280 kg of apples . he sells 35 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total . a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %","""if the total quantity was 100 then 35 x 20 % + 60 x 30 % = 25 this profit will remain same for any total quantity unless the % of products remains the same . hence' b' is the answer"""
Provide a detailed solution to the given mathematical problem.,"a train 120 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ? a ) 7.2 sec , b ) 9.3 sec , c ) 12 sec , d ) 15.2 sec , e ) 18 sec",speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 120 m at 50 / 3 m / sec = 120 * 3 / 50 sec = 7.2 sec answer : a .
"Work through the equation methodically, ensuring clarity at each step.","solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 50 milliliters of solution x to create a solution that is 25 percent alcohol by volume ? a ) 150 , b ) 500 / 3 , c ) 400 , d ) 480 , e ) 600","""we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 50 then y = 150 answer : a"""
"Solve the problem systematically, showing each step clearly.","a water tank , having the shape of a rectangular prism of base 100 square centimeters , is being filled at the rate of 1 liter per minute . find the rate at which the height of the water in the water tank increases . express your answer in centimeters per minute . ['a ) 30 cm','b ) 10 cm','c ) 50 cm','d ) 90 cm','e ) 70 cm']",the volume of a rectangular prism is given by area of base ? height the rate at which the tank is being filled is 1 liter per minute which we need to convert 1 liter = 1 dm 3 but 1 dm = 10 cm . hence 1 liter = ( 10 cm ) 3 = 1000 cm 3 the height h of the water is related to the volume by volume = area of base * h in one minute the volume increases by 1 liter or 1000 cm 3 and the height increases by h = volume / area of base = 1000 cm 3 / 100 cm 2 = 10 cm correct answer b
Break down and solve the equation step by step.,"an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 40 meters . how many times did the ball bounce ? a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 9","""division of total distance travelled will be 16 + 16 + 8 ans : 2"""
"Solve the problem systematically, showing each step clearly.","an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 2,395 , what was the total number of pairs of contact lenses that she sold ? a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19","""( x + 5 ) * 150 + x * 85 = 2395 = > x = 7 total lens = 7 + ( 7 + 5 ) = 19 answer e"""
"Solve the problem systematically, showing each step clearly.","a computer manufacturer produces a certain electronic component at a cost of $ 100 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 24,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 100 components a month , what is the lowest price it can sell them for such that the costs do n' t exceed the revenues ? a ) 278 , b ) 366 , c ) 349 , d ) 335 , e ) 295","""$ 24500 is a fixed cost each component is $ 104 ( $ 100 to produce , $ 4 to ship ) manufacturer will be producing and selling 100 components so therefore the equation to find price would be 100 * p = 24500 + ( 100 * 100 ) + ( 100 * 4 ) p = ( 24500 + 10000 + 400 ) / 100 p = 349 answer : c"""
Break down and solve the equation step by step.,"there are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed . a ) 26 , b ) 32 , c ) 35 , d ) 30 , e ) 45","""explanation : hcf ( 408 , 216 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 216 / 24 = 17 + 9 = 26 answer : a"""
Break down and solve the equation step by step.,"david spends $ 350 buying his favorite dolls . if he buys only small lemonhead dolls , which are $ 2 cheaper than the large lemonhead dolls , he could buy 20 more dolls than if he were to buy only large lemonhead dolls . how much does a large lemonhead doll cost ? a ) $ 5 , b ) $ 7 , c ) $ 6 , d ) $ 8 , e ) $ 9","if large doll costs $ 5 , then he can buy 350 / 5 = 70 large dolls and 350 / 3 = 116 small dolls . difference is more than 20 . discard . if large doll costs $ 7 , then he can buy 350 / 7 = 50 large dolls and 350 / 5 = 70 small dolls . difference is 20 , which is we wanted . answer b ."
Provide a detailed solution to the given mathematical problem.,"each of the integers from 1 to 14 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ? a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 8","""out of the 14 integers : 7 are odd and 7 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 7 odd numbers first 2 . 8 th number will be the first even number so we need to withdraw at least 8 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 8 . ( e )"""
Break down and solve the equation step by step.,"a shopkeeper sold 10 articles at the cost price of 12 articles . then find the profit % or lost % a ) - 10 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %",here 10 articles selling price = 12 articles cost price so the difference = 12 - 10 = 2 % of profit = 2 * 100 / 10 = 20 % correct option is d
Provide a detailed solution to the given mathematical problem.,"if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 24 , what is the value of r - p ? a ) 28 , b ) 10 , c ) 30 , d ) 40 , e ) 5","""arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 48 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 28 hence , the correct answer is a"""
Explain the solution process for the given equation.,"ages of two persons differ by 18 years . if 4 years ago , the elder one was 4 times as old the younger one , find their present age a ) 6,24 , b ) 9,27 , c ) 10,28 , d ) 18,36 , e ) 19,37","explanation : let the age of younger person be x , then elder person' s age is ( x + 18 ) = > 4 ( x - 4 ) = ( x + 18 - 4 ) [ 4 years before ] = > 4 x - 16 = x + 14 = > x = 10 . so elder person' s age is x + 18 = 28 answer : option c"
"Work through the equation methodically, ensuring clarity at each step.","in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many r eggs does the plant process per day ? a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000","""straight pluggin in for me . as usual , i started with c and got the answer . lets' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there r = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c ."""
Provide a detailed solution to the given mathematical problem.,"a rectangular swimming pool is 8 feet by 20 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 540 square feet . what is the width of the deck ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""let the width = w total area of the pool and deck = ( 2 w + 8 ) ( 2 w + 20 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 12 * 24 has unit digit 8 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 13 * 25 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 14 * 26 has unit digit 4 . . . . . . . . . . . hold d ) 4 feet . . . . . . . . . . . . 16 * 28 has unit digit 8 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 18 * 30 has unit digit 0 . . . . . . . . . . . eliminate answer : e w = 5"""
"Work through the equation methodically, ensuring clarity at each step.","when positive integer n is divided by 4 , the remainder is 2 . when n is divided by 7 , the remainder is 5 . how many values less than 100 can n take ? a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 3 . . c"""
"Work through the equation methodically, ensuring clarity at each step.","if the price of a certain computer increased 20 percent from d dollars to 351 dollars , then 2 d = a ) 540 , b ) 585 , c ) 619 , d ) 649 , e ) 700","""before price increase price = d after 30 % price increase price = d + ( 20 / 100 ) * d = 1.2 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 292,5 i . e . 2 d = 2 * 292.5 = 585 answer : option b"""
Explain the solution process for the given equation.,"if | 4 x + 6 | = 36 , then find the sum of the values of x ? a ) - 3 , b ) 4 , c ) 3 , d ) - 5 , e ) 6","""| 4 x + 6 | = 36 4 x + 6 = 36 or 4 x + 6 = - 36 4 x = 30 or 4 x = - 42 x = 7.5 or x = - 10.5 sum = 7.5 - 10.5 = - 3 answer is a"""
"Work through the equation methodically, ensuring clarity at each step.","a 180 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ? a ) 320 meter , b ) 225 meter , c ) 230 meter , d ) 235 meter , e ) none of these","""explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 180 / 9 = 500 / 9 = > x + 180 = 500 = > x = 320 so the length of the train is 320 meters option a"""
"Solve the problem systematically, showing each step clearly.","a box contains 12 pairs of shoes ( 24 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ? a ) 1 / 190 , b ) 1 / 23 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9","""the problem with your solution is that we do n' t choose 1 shoe from 24 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 23 ( as after taking one at random there are 23 shoes left and only one is the pair of the first one ) = 1 / 23 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","of 30 applicants for a job , 12 had at least 4 years' experience , 18 had degrees , and 3 had less than 4 years' experience and did not have a degree . how many of the applicants had at least 4 years' experience and a degree ? a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5","""d . 7 30 - 3 = 27 27 - 12 - 18 = - 7 then 7 are in the intersection between 4 years experience and degree . answer d"""
Break down and solve the equation step by step.,"how many multiples of 8 are less than 1600 , and also multiples of 64 ? a ) 25 , b ) 28 , c ) 62 , d ) 83 , e ) 89",the lcm of 8 and 64 is 64 . divide 1600 / 64 = 25 . xxx . so a is your answer .
"Work through the equation methodically, ensuring clarity at each step.","a goods train runs at the speed of 72 km / hr and crosses a 300 m long platform in 26 sec . what is the length of the goods train ? a ) 382 , b ) 782 , c ) 278 , d ) 270 , e ) 220","""speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 300 ) / 26 = 20 x = 220 m . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","how many of the positive factors of 33 are not factors of 45 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","""factors of 33 - 1 , 3 , 11 , 33 , factors of 45 - 1 , 3 , 5 , 9 , 15 , 45 , comparing both , we have three factors of 33 which are not factors of 45 - 11 , 33 , the answer is c"""
Provide a detailed solution to the given mathematical problem.,"a person is traveling at 25 km / hr and reached his destiny in 5 hr find the distance ? a ) 100 km , b ) 95 km , c ) 135 km , d ) 80 km , e ) 125 km",speed = 25 km / hr time = 5 hr distance = 25 * 5 = 125 km answer is e
Break down and solve the equation step by step.,"what is the sum of the greatest common factor and the lowest common multiple of 12 and 16 ? a ) 19 , b ) 22 , c ) 52 , d ) 36 , e ) 38","""prime factorization of the given numbers 12 = 2 ^ 2 * 3 48 = 2 ^ 4 * 3 greatest common factor = 4 lowest common multiple = 48 sum = 4 + 48 = 52 answer c"""
Explain the solution process for the given equation.,"a company has two models of computers , model x and model y . operating at a constant rate , a model x computer can complete a certain task in 60 minutes and a model y computer can complete the same task in 30 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model x computers were used ? a ) 18 , b ) 16 , c ) 15 , d ) 17 , e ) 20","""let' s say 1 work is processing 60 gb of data . model x : 1 gb per min model y : 2 gb per min working together , 1 x and 1 y = 3 gb per min so , 20 times as many computers would work at 60 gb per min . so no . of x = 20 answer is e"""
"Work through the equation methodically, ensuring clarity at each step.","a snail , climbing a 20 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ? a ) 12 , b ) 16 , c ) 17 , d ) 20 , e ) 21","""total transaction in two days = 4 - 2 = 2 feet in 16 days it will climb 16 feet on the 17 th day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 17 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","how many books each of volume 100 meter cube can be packed into a crate of volume 4000 meter cube ? ['a ) 100','b ) 120','c ) can not be determined','d ) 180','e ) 200']","gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 4000 m 3 can be 400 * 10 or 40 * 100 or just 4000 * 1 we do n' t know , so we cant calculate answer : c"
Provide a detailed solution to the given mathematical problem.,"2 minute is taken to travel the diagonal of square field at 3 km / hour . calculate the area of field ? ['a ) 25 are','b ) 30 are','c ) 50 are','d ) 60 are','e ) 45 are']","speed of man = [ 3 * 5 / 18 ] m / sec . = 5 / 6 m / sec . , distance travel in 2 minute = { 5 / 6 * 2 * 60 } m . = 100 m . diagonal of square field = 100 m area of field = 1 / 2 * diagonal ^ 2 = [ 1 / 2 * 100 * 100 ] sq . m = 5000 sq . m = 5000 / 100 = 50 are ( 1 are = 100 sq . m ) answer c"
Provide a detailed solution to the given mathematical problem.,"a man whose bowling average is 12.4 , takes 4 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ? a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57","""12.4 * x + 26 = ( 4 + x ) 12 solve equation x = 55 answer : c"""
Provide a detailed solution to the given mathematical problem.,"solve the given equation 9 ^ y = 3 ^ 12 , what is y ? a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6","3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e"
Break down and solve the equation step by step.,"arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 35 % profit ? a ) 16.39 , b ) 16.33 , c ) 16.35 , d ) 17.01 , e ) 16.32",c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 135 % of rs . 630 = 135 / 100 * 630 = rs . 850.50 . s . p . per kg = 850.50 / 50 = rs . 16.38 = 16.30 . answer : d
"Solve the problem systematically, showing each step clearly.","a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 3 hours to fill the tank . the leak can drain all the water in ? a ) 10 hr , b ) 14 hr , c ) 12 hr , d ) 9 hr , e ) 15 hr","""work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 leak will empty the tank in 14 hrs answer is b"""
Provide a detailed solution to the given mathematical problem.,"the l . c . m . of two numbers is 36 . the numbers are in the ratio 2 : 3 . then sum of the number is : a ) 28 , b ) 30 , c ) 40 , d ) 53 , e ) 54","""let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 36 or x = 6 . the numbers are 12 and 18 . hence , required sum = ( 12 + 18 ) = 30 . answer : option b"""
"Solve the problem systematically, showing each step clearly.","how many odd prime numbers are there less than 50 ? a ) 15 , b ) 1 , c ) 2 , d ) 14 , e ) 17","""odd prime number less than 50 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 there is 14 the odd prime number answer is d"""
Break down and solve the equation step by step.,"yearly subscription to professional magazines cost a company $ 940.00 . to make a 30 % cut in the magazine budget , how much less must be spent ? a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 658","""total cost 940 940 * 30 / 100 = 282 so the cut in amount is 282 the less amount to be spend is 940 - 282 = 658 answer : e"""
Explain the solution process for the given equation.,"a rectangle having length 100 cm and width 40 cm . if the length of the rectangle is increased by fifty percent then how much percent the breadth should be decreased so as to maintain the same area . a ) 25 % , b ) 33.33 % , c ) 40 % , d ) 75 % , e ) none of these","""explanation : solution : ( 50 / ( 100 + 50 ) * 100 ) % = 33.33 % answer : b"""
Explain the solution process for the given equation.,"seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 31 % ryegrass , what percent of the weight of the mixture is from mixture x ? a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %","""31 % is 6 % - points above 25 % and 9 % - points below 40 % . thus the ratio of mixture y to mixture x is 3 : 2 . the percent of mixture x is 2 / 5 = 40 % . the answer is c ."""
Explain the solution process for the given equation.,"a paper is in a square form whose one side is 20 cm . two semi circles are drawn on its opposites as diameters . if these semi circles are cut down what is the area of the remaining paper ? ['a ) 8.76','b ) 8.79','c ) 8.75','d ) 8.74','e ) 8.72']",( 5 * 3.5 ) / 2 = 8.75 answer : c
Break down and solve the equation step by step.,"what is the probability of getting only 1 head in a single throw of four fair coins ? a ) 1 / 2 , b ) 3 / 8 , c ) 1 / 4 , d ) 1 / 5 , e ) 5 / 8","""one possible case is httt . p ( httt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 there are 4 c 1 = 4 possible cases . p ( 1 head ) = 4 * 1 / 16 = 1 / 4 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 245 , what is the difference between the ages of patrick and monica ? a ) 27 , b ) 48 , c ) 80 , d ) 72 , e ) 18","""ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 245 x = 5 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 5 = 80 answer c"""
Explain the solution process for the given equation.,"in a basketball game , tim scored 20 points more than joe , but only half as many points as ken . if the 3 players scored a combined total of 100 points , how many points did tim score ? a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 45","let joe scored point = x then tim scored = x + 20 ken scored = 2 * ( x + 20 ) = 2 x + 40 as given , x + x + 20 + 2 x + 40 = 100 points 4 x + 60 = 100 x = 100 - 60 / 4 = 10 so tim scored = x + 20 i . e ) 10 + 20 = 30 answer : d"
Break down and solve the equation step by step.,"if f ( x ) = 1 / x and x is a natural number , what can not be the answer for f ( f ( x ) ) ? a ) 1 / 7 , b ) 3 , c ) 12 / 3 , d ) 6 / 6 , e ) 1","answer a is impossible because the invers of 1 / x is x , and the only way to have something other than a natural number is to input something other than a natural number . with the specification that only natural numbers may be used 1 / 7 is not a possibility for f ( f ( x ) )"
Provide a detailed solution to the given mathematical problem.,"john can row at 5 kmph and still water . he takes 5 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ? a ) 28 km , b ) 12 km , c ) 16 km , d ) 30 km , e ) 20 km",let the distance between a and b be x km . total time = x / ( 5 + 1 ) + x / ( 5 - 1 ) = 5 = > x / 6 + x / 4 = 4 = > ( 2 x + 3 x ) / 12 = 5 = > x = 12 km . answer : b
"Work through the equation methodically, ensuring clarity at each step.","two good train each 650 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one . a ) 12.4 sec , b ) 24.3 sec , c ) 62.4 sec , d ) 60.1 sec , e ) none","""sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 650 + 650 ) m = 1300 m . required time = ( 1300 x 6 / 125 ) sec = 62.4 sec . answer c"""
Provide a detailed solution to the given mathematical problem.,"if x = 6 ^ 36 and x ^ x = 6 ^ k , what is k ? a ) 6 ^ 36 , b ) 6 ^ 38 , c ) 6 ^ 72 , d ) 6 ^ 216 , e ) 6 ^ 432","""solution : we know that x = 6 ^ 36 which implies x ^ x = ( 6 ^ 36 ) ^ ( 6 ^ 36 ) = 6 ^ ( 36 * 6 ^ 36 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 6 ^ ( 6 ^ 2 * 6 ^ 36 ) = 6 ^ ( 6 ^ ( 2 + 36 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 6 ^ ( 6 ^ 38 ) given that x ^ x = 6 ^ k so 6 ^ ( 6 ^ 38 ) = 6 ^ k since the base is same the exponent will also be same therefore k = 6 ^ 38 answer : b"""
Break down and solve the equation step by step.,"the perimeter of one face of a cube is 40 cm . its volume will be : a ) 125 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 1000 cm 3 , e ) none of these","""explanation : edge of cude = 40 / 4 = 10 cm volume = a * a * a = 10 * 10 * 10 = 1000 cm cube option d"""
Break down and solve the equation step by step.,"calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10 % of its volume is occupied by concrete ? a ) 6000 , b ) 5400 , c ) 3800 , d ) 4700 , e ) 2500","""explanation : let' b' be the nuber of bricks . = > 10 x 4 / 100 x 5 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x b = > 10 x 20 x 90 = 15 x 2 x b = > b = 6000 answer is a"""
Explain the solution process for the given equation.,"a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 1000 more than d , what is b' s share ? a ) 4000 , b ) 5000 , c ) 2000 , d ) 1000 , e ) 6000","""let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 1000 x = 1000 . b' s share = rs . 2 x = rs . ( 2 x 1000 ) = rs . 2000 . answer is c ."""
Provide a detailed solution to the given mathematical problem.,"if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 6.2 ] + [ - 3.4 ] + [ 12.7 ] ? a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3","""you are asked what the closest lesser integer value to [ x ] is . [ - 6.2 ] = - 7.0 [ - 3.4 ] = - 4.0 [ 12.7 ] = 12.0 therefore , answer is : - 7.0 - 4.0 + 12.0 = - 1.0 option a ."""
Break down and solve the equation step by step.,"a man can row his boat with the stream at 16 km / h and against the stream in 8 km / h . the man' s rate is ? a ) 4 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph","""ds = 16 us = 8 s = ? s = ( 16 - 8 ) / 2 = 4 kmph answer : a"""
Break down and solve the equation step by step.,"robert is travelling on his cycle and has calculated to reach point a at 2 p . m . if he travels at 10 km / hr ; he will reach there at 12 noon if he travels at 15 km / hr . at what speed must he travel to reach a at 1 p . m . ? a ) 17 kmph , b ) 19 kmph , c ) 15 kmph , d ) 12 kmph , e ) 16 kmph","d 12 kmph let the distance traveled be x km . then , x / 10 - x / 15 = 2 3 x - 2 x = 60 = > x = 60 km . time taken to travel 60 km at 10 km / hr = 60 / 10 = 6 hrs . so , robert started 6 hours before 2 . p . m . i . e . , at 8 a . m . required speed = 60 / 5 = 12 kmph ."
Explain the solution process for the given equation.,"a bag contains 7 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ? a ) 4 / 13 , b ) 6 / 13 , c ) 8 / 21 , d ) 11 / 21 , e ) 17 / 42","""the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 7 c 2 = 21 the number of ways to draw two white balls is 7 c 2 = 21 p ( two balls of the same colour ) = 42 / 91 = 6 / 13 the answer is b ."""
Explain the solution process for the given equation.,"600 x 223 + 600 x 77 = ? a ) 180000 , b ) 138800 , c ) 658560 , d ) 116740 , e ) none of them","""= 600 x ( 223 + 77 ) ( by distributive law ) = 600 x 300 = 180000 answer is a"""
"Solve the problem systematically, showing each step clearly.","the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 5 ) , how many units is p from the y - axis ? a ) 2.5 , b ) 5 , c ) 7.5 , d ) 10 , e ) 12","""the x - axis is 5 units from the point p . thus the y - axis is 10 units from the point p . the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"a train 300 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ? a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 19 sec","""speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 300 m at 50 / 3 m / sec = 300 * 3 / 50 sec = 18 sec answer : d ."""
Explain the solution process for the given equation.,"a person travels equal distances with speed of 3 km / hr , 4 km / hr and 5 km / hr and takes a total of 47 minutes . find the total distane a ) 3 km , b ) 4 km , c ) 6 km , d ) 9 km , e ) 5 km","explanation : let the distance be 3 x km , then , x / 3 + x / 4 + x / 5 = 47 / 60 47 x / 60 = 47 / 60 x = 1 so total distance = 3 * 1 = 3 km option a"
Explain the solution process for the given equation.,"a 7 - digit combination lock on a safe has zero exactly 3 times , does not have the digit 1 at all . what is the probability that exactly 3 of its digits are odd ? a ) 9 / 16 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 6","remaining number of digits after three' 0' digits = 4 constraint - no more' 0' and no more' 1' well , these four digits can be odd or even 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 ways to choose 3 odd digits out of total 4 digits = 4 c 3 = 4 4 * 1 / 16 = 1 / 4 d is the answer hi ! since we are talking about remaining 4 digits . each digit can either be odd or even ( total ways to select = 2 . desired outcome = 1 ) so let' s say we want to choose first 3 digits as odd digits and last digit as even . the probability will be : - 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 but out of remaining 4 digit , any 3 can be odd and one even as there are no constraints in the question . therefore , total ways of choosing 3 odd digits out of 4 total digits = 4 c 3 so , the probability = 4 * 1 / 16 = 1 / 4 answer is d"
"Work through the equation methodically, ensuring clarity at each step.","the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .","""let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 20 ) / 2 = 40 . answer : a"""
Break down and solve the equation step by step.,"two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ? a ) 122,195 , b ) 121,199 , c ) 120,192 , d ) 102,192 , e ) 126,109","""( 5 x - 30 ) : ( 8 x - 30 ) = 5 : 9 x = 24 = > 120,192 answer : c"""
"Solve the problem systematically, showing each step clearly.","a and b can do a work in 12 days , b and c in 15 days , c and a in 20 days . if a , b and c work together , they will complete the work in : a ) 5 days , b ) 7 5 / 6 days , c ) 10 days , d ) 15 2 / 3 days , e ) none of these","""( a + b )' s 1 day' s work = 1 / 12 , ( b + c )' s 1 day' s work = 1 / 15 ; ( a + c )' s 1 day' s work = 1 / 20 adding , we get : 2 ( a + b + c )' s 1 day' s work = ( 1 / 12 + 1 / 15 + 1 / 20 ) = 12 / 60 = 1 / 5 ( a + b + c )' s 1 day' s work = 1 / 10 so , a , b and c together can complete the work in 10 days . correct option : c"""
Break down and solve the equation step by step.,"machine m , n , o working simultaneously machine m can produce x units in 3 / 4 of the time it takes machine n to produce the same amount of units . machine n can produce x units in 2 / 7 the time it takes machine o to produce that amount of units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ? a ) 1 / 2 , b ) 7 / 13 , c ) 4 / 13 , d ) 8 / 29 , e ) 6 / 33","now ultimately the speed of every machine is given with respect to mach o . so lets assume the speed of o , say 12 hrs to make x units ( assuming 6 because we can see we will need to divide by 3 and 4 mach o makes x units in 12 hrs so , mach n = 2 / 7 of o = 2 / 7 * 12 = 24 / 7 hrs to make x units and mach m = 3 / 4 of n = 3 / 4 * 24 / 7 = 1 / 6 hrs to make x units no they are running simultaneously . lets see how much each mach makes in 1 hr mach o = x / 12 units mach n = 7 / 24 units mach m = x / 6 units in 1 hr , together they make - x / 12 + 7 / 24 + x / 6 = 13 / 24 so what ratio of this has mach n made ? ( 7 / 24 ) / ( 13 / 24 ) = 7 / 13 ans : b = 7 / 13"
"Solve the problem systematically, showing each step clearly.","one computer can upload 100 megabytes worth of data in 5 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 40 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ? a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 13","""since the first computer can upload 100 megabytes worth of data in 5 seconds then in 5 * 8 = 40 seconds it can upload 8 * 100 = 800 megabytes worth of data , hence the second computer in 40 seconds uploads 1300 - 800 = 500 megabytes worth of data . the second computer can upload 100 megabytes of data in 8 seconds . answer : b ."""
Provide a detailed solution to the given mathematical problem.,"a box contains 1 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ? a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3","""my complicated version of your simple approach let the 5 black balls be bbbbb and 1 red balls be r they can be arranged in 6 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 5 ! x 1 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 4 black ( bbbb ) and 1 red ( r ) they can be arranged in ( 5 ! ) / ( 4 ! x 1 ! ) hence required probability = [ ( 6 ! ) / ( 5 ! x 1 ! ) ] / [ ( 5 ! ) / ( 4 ! x 1 ! ) ] = 6 / 5 c"""
"Work through the equation methodically, ensuring clarity at each step.","sandy is younger than molly by 20 years . if the ratio of their ages is 7 : 9 , how old is sandy ? a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70","""let sandy' s age be 7 x and let molly' s age be 9 x . 9 x - 7 x = 20 x = 10 sandy is 70 years old . the answer is e ."""
Explain the solution process for the given equation.,"the current of a stream runs at the rate of 4 kmph . a boat goes 12 km and back to the starting point in 2 hours , then find the speed of the boat in still water ? a ) a ) 17.33 , b ) b ) 2 , c ) c ) 18 , d ) d ) 16 , e ) e ) 13.21","""s = 4 m = x ds = x + 4 us = x - 4 12 / ( x + 4 ) + 12 / ( x - 4 ) = 2 x = 13.21 answer : e"""
"Solve the problem systematically, showing each step clearly.","the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 10 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ? a ) 32.5 , b ) 35 , c ) 48 , d ) 65 , e ) 67.5","""1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 67.5 . 4 ) now 67.5 has to be added by x % in order to equal the original price . 67.5 + ( x % ) 67.5 = 100 . solving this eq for x , we get x = 48.1 answer is c ."""
"Work through the equation methodically, ensuring clarity at each step.","a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 20 sec . what is the length of the platform ? a ) 389 m , b ) 350 m , c ) 285 m , d ) 299 m , e ) 219 m","""speed = 300 / 20 = 15 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 15 = > x = 285 m . answer : c"""
Provide a detailed solution to the given mathematical problem.,"find the 21 th term of an arithmetic progression whose first term is 3 and the common difference is 5 . a ) 100 , b ) 102 , c ) 103 , d ) 150 , e ) 46","""n th term of a . p = a + ( n - 1 ) * d = 3 + ( 21 - 1 ) * 5 , = 3 + 100 = 103 . answer : c"""
Provide a detailed solution to the given mathematical problem.,"three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 138 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ? a ) 18 square meters , b ) 19 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters","""total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 138 = 200 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : b ."""
"Solve the problem systematically, showing each step clearly.","bob is attempting to feed his pets . he feeds his pets as follows : - no dog receives more food than any other dog - no cat receives any less food than any other cat - the cats , as a group , receive exactly as much food as a single dog if bob has 7 dogs and 4 cats , approximately what percentage of the food bag does a cat receive ? a ) 25.0 % , b ) 8.3 % , c ) 3.1 % , d ) 2.7 % , e ) 1.0 %","c . each cat gets 1 / 4 as much food as a dog . a dog gets 1 / 8 of the food . 1 / 4 of 1 / 8 is 1 / 32 , which is about 3.1 % , so the answer is c ."
"Solve the problem systematically, showing each step clearly.","in an it company , there are a total of 120 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ? a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 75","""you could pick 70 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 75 . e"""
"Solve the problem systematically, showing each step clearly.","on a sum of money , the simple interest for 2 years is rs . 660 , while the compound interest is rs . 696.30 , the rate of interest being the same in both the cases . the rate of interest is a ) 10 % , b ) 11 % , c ) 12 % , d ) 10.5 % , e ) none","""solution difference in c . i and s . i for 2 years = rs ( 696.30 - 660 ) = rs . 36.30 . s . i for one years = rs 330 . s . i on rs . 330 for 1 year = rs . 36.30 rate = ( 100 x 36.30 / 330 x 1 ) % = 11 % . answer b"""
"Work through the equation methodically, ensuring clarity at each step.","a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 10 % . what was its profit on the items sold in february ? a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 40 %","""assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.9 * 150 x = 135 x hence total profit = 35 % option c"""
"Solve the problem systematically, showing each step clearly.","exactly 30 % of the reporters for a certain wire service cover local politics in country x . if 25 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ? a ) 20 % , b ) 42 % , c ) 60 % , d ) 80 % , e ) 84 %","let' s assume there are 100 reporters - - > 30 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 30 ( # of reporters who cover local politics ) : 0.75 x = 30 - - > x = 40 , hence 40 reporters cover politics and the rest 100 - 40 = 60 reporters do not cover politics at all . answer : c ."
Break down and solve the equation step by step.,"on dividing number by 357 , we get 39 as remainder . on dividing the same number by 17 , what will be the remainder ? a ) 0 , b ) 3 , c ) 5 , d ) 11 , e ) 13","""let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x 2 = ( 5 k + 3 ) 2 = ( 25 k 2 + 30 k + 9 ) = 5 ( 5 k 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . answer : c"""
Break down and solve the equation step by step.,"how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 6 a ) 5 , b ) 305 , c ) 365 , d ) 405 , e ) 495","560 , 562 , 564 , 566 , and 568 , so total 5 . hence option a ."
Break down and solve the equation step by step.,"two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 40 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ? a ) 4 : 5 , b ) 9 : 25 , c ) 5 : 4 , d ) 25 : 9 , e ) can not be determined from the information provided","""same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 20 / speed b since the times are same , 50 pi / speed a = 40 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 4 correct option : c"""
Break down and solve the equation step by step.,"find the amount on rs . 5000 in 2 years , the rate of interest being 10 % per first year and 12 % for the second year ? a ) 3377 , b ) 6160 , c ) 5460 , d ) 1976 , e ) 1671",5000 * 110 / 100 * 112 / 100 = > 6160 answer : b
"Work through the equation methodically, ensuring clarity at each step.","what is the normal price of an article sold at $ 36 after two successive discounts of 10 % and 20 % ? a ) $ 45 , b ) $ 48 , c ) $ 50 , d ) $ 54 , e ) $ 56","""0.8 * 0.9 * cost price = $ 36 cost price = $ 50 the answer is c ."""
"Solve the problem systematically, showing each step clearly.","in an exam , amar scored 64 percent , bhavan scored 36 percent and chetan 44 percent . the maximum score awarded in the exam is 900 . find the average mark scored by all the 3 boys ? a ) 384 , b ) 432 , c ) 207 , d ) 269 , e ) 208",average mark scored by all the three boys = [ 64 / 100 ( 900 ) + 36 / 100 ( 900 ) + 44 / 100 ( 900 ) ] / 3 = 432 answer : b
"Solve the problem systematically, showing each step clearly.","how many integerskgreater than 100 and less than 800 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ? a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90","""numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be six pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 6 * 10 = 60 hence b ."""
Break down and solve the equation step by step.,"if the sides of a cube are in the ratio 4 : 3 . what is the ratio of their diagonals ? a ) 4 : 3 , b ) 4 : 8 , c ) 4 : 1 , d ) 4 : 2 , e ) 4 : 7","""a 1 : a 2 = 4 : 3 d 1 : d 2 = 4 : 3 answer : a"""
Provide a detailed solution to the given mathematical problem.,"a can do a piece of work in 40 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ? a ) 24 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days","""10 / 40 + 10 / 30 + 10 / x = 1 x = 24 days answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 4 if each digit can be used only once in each number ? a ) 1776 , b ) 1887 , c ) 1998 , d ) 2332 , e ) 2554","""there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 444 ) = 1998 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"a house wife saved $ 4 in buying an item on sale . if she spent $ 28 for the item , approximately how much percent she saved in the transaction ? a ) 8 % , b ) 13 % , c ) 10 % , d ) 11 % , e ) 12 %","""actual price = 28 + 4 = $ 32 saving = 4 / 32 * 100 = 13 % approximately answer is b"""
Explain the solution process for the given equation.,"a can do a job in 10 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ? a ) 2 / 5 , b ) 8 / 15 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13","""a' s 1 day work = 1 / 10 b' s 1 day work = 1 / 20 a + b 1 day work = 1 / 10 + 1 / 20 = 3 / 20 a + b 4 days work = 3 / 20 * 4 = 3 / 5 remaining work = 1 - 3 / 5 = 2 / 5 answer is a"""
Explain the solution process for the given equation.,"the price for a loaf of bread in april was $ 1.17 , in may the price was $ 1.30 , and in june the price was $ 1.05 . if 2 / 3 as much bread was sold in april as in may , and twice as much was sold in june as in april , what was the average price for a loaf of bread sold during the 3 - month period ? a ) $ 1.13 , b ) $ 1.14 , c ) $ 1.15 , d ) $ 1.16 , e ) $ 1.17",let x be the number of loaves sold in may . then 2 x / 3 loaves were sold in april and 4 x / 3 loaves were sold in june . the average price was ( 2 x / 3 ) ( 117 ) + 130 x + ( 4 x / 3 ) ( 105 ) / ( 2 x / 3 + x + 4 x / 3 ) = ( 78 + 130 + 140 ) / ( 3 ) = 348 / 3 = $ 1.16 the answer is d .
Explain the solution process for the given equation.,"two numbers are respectively 20 % and 50 % more than a third number . the ratio of the two numbers is a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 6 : 5 , e ) 7 : 5","""explanation : let the third number be x . first number ( 120 / 100 ) * x = 6 x / 5 second number ( 150 / 100 ) * x = 3 x / 2 ratio = 6 x / 5 : 3 x / 2 = > 4 : 5 option c"""
"Work through the equation methodically, ensuring clarity at each step.","a cistern is filled by a tap in 3 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how long will it take the leak to empty it ? a ) 11 , b ) 12 , c ) 29 , d ) 28 , e ) 29",2 / 7 - 1 / x = 1 / 4 x = 28 answer : d
Break down and solve the equation step by step.,"what is the remainder when ( 71 ) ( 73 ) is divided by 8 ? a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7","""( 71 ) ( 73 ) = ( 72 - 1 ) ( 72 + 1 ) = 72 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e ."""
Provide a detailed solution to the given mathematical problem.,"in what ratio must tea at rs . 65 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 6 per kg ? a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none","""required ratio = 500 : 500 = 1 : 1 answer a"""
"Solve the problem systematically, showing each step clearly.","company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 9 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ? a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 9 / 19","""# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 9 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 9 / 5 = 9 - - > total time for both of them would be 10 + 9 = 19 - - > deluxe / total = 9 / 19 . answer : e ."""
Explain the solution process for the given equation.,"find the annual income derived by investing $ 6800 in 40 % stock at 136 . a ) 550 , b ) 2000 , c ) 250 , d ) 3000 , e ) 400","""by investing $ 136 , income obtained = $ 40 . by investing $ 6800 , income obtained = $ [ ( 40 / 136 ) * 6800 ] = $ 2000 . answer b ."""
"Work through the equation methodically, ensuring clarity at each step.","a train 1600 m long can cross a pole in 40 sec and then find the speed of the train ? a ) 140 , b ) 142 , c ) 144 , d ) 146 , e ) 148","""length = speed * time speed = l / t s = 1600 / 40 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : c"""
Provide a detailed solution to the given mathematical problem.,"if a ^ 2 + b ^ 2 = 177 and ab = 54 then find the value of a + b / a - b ? a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9","""( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 117 + 2 * 24 = 225 a + b = 15 ( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 117 - 2 * 54 a - b = 3 a + b / a - b = 15 / 3 = 5 answer is c ."""
"Work through the equation methodically, ensuring clarity at each step.","if 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days , the time taken by 15 men and 20 boys in doing the same type of work will be ? a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8","""let 1 men' s 1 day work = x and 1 boy' s 1 day work = y . then , 6 x + 8 y = 1 / 10 and 26 x + 48 y = 1 / 2 solving these two equations , we get : x = 1 / 100 and y = 1 / 200 ( 15 men + 20 boys )' s 1 day work = ( 15 / 100 + 20 / 200 ) = 1 / 4 15 men and 20 boys can do the work in 4 days . answer : a"""
Explain the solution process for the given equation.,"if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the first part is ? a ) a ) 426 , b ) b ) 526 , c ) c ) 247 , d ) d ) 204 , e ) e ) 297",given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 6 / 19 = rs . 247 answer : c
Break down and solve the equation step by step.,"a number is doubled and 9 is added . if resultant is trebled , it becomes 81 . what is that number a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 15","""explanation : = > 3 ( 2 x + 9 ) = 81 = > 2 x + 9 = 27 = > x = 9 answer : option a"""
Provide a detailed solution to the given mathematical problem.,"a container holds 4 quarts of alcohol and 4 quarts of water . how many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume ? a ) 4 / 3 , b ) 5 / 3 , c ) 7 / 3 , d ) 8 / 3 , e ) 10 / 3","let the number of quarts that should be added to get the required ratio = x so total quarts of water = ( x + 4 ) but the original number of quarts of alcohol remains the same , so we have : 4 / ( x + 4 ) = 3 / 5 cross - multiply : now we have 20 = 3 x + 12 = > 3 x = 20 - 12 = > x = 8 / 3 answer - d"
"Solve the problem systematically, showing each step clearly.","a 260 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ? a ) 240 mts , b ) 270 mts , c ) 260 mts , d ) 250 mts , e ) none of these","explanation : relative speed = 120 + 80 = 200 km / hr . = 200 x 5 / 18 = 500 / 9 m / sec . let the length of the other train be l mts . then , ( l + 260 ) / 9 = 500 / 9 = > l = 240 mts . answer is a"
Break down and solve the equation step by step.,"the time taken by mr . dhoni to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 72 kmph , find the speed of the stream ? a ) 24 kmph , b ) 25 kmph , c ) 26 kmph , d ) 30 kmph , e ) 28 kmph",the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 72 / 3 = 24 kmph . answer : a
Explain the solution process for the given equation.,"the mean of 50 observations was 36 . it was found later that an observation 29 was wrongly taken as 23 . the corrected new mean is : a ) 36.1 , b ) 36.5 , c ) 36.22 , d ) 36.12 , e ) 36.18","""explanation : correct sum = ( 36 * 50 + 29 - 23 ) = 1806 . correct mean = = 1806 / 50 = 36.12 answer : d ) 36.12"""
Break down and solve the equation step by step.,"a bicycle wheel has a diameter of 0.51 m . how many complete revolutions does it make in 1 km ? a ) 246 , b ) 448 , c ) 1408 , d ) 710 , e ) 624",1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.51 m ) = 624.5 . hence 624 complete revolutions . answer e
"Solve the problem systematically, showing each step clearly.","excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 20 km / hr . for how many minutes does the bus stop per hour ? a ) 22 , b ) 88 , c ) 77 , d ) 40 , e ) 99","""in 1 hr , the bus covers 60 km without stoppages and 20 km with stoppages . stoppage time = time take to travel ( 60 - 20 ) km i . e 40 km at 60 km / hr . stoppage time = 40 / 60 hrs = 40 min . answer : d"""
"Solve the problem systematically, showing each step clearly.","to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 15 hours a day ? a ) 23 , b ) 22 , c ) 21 , d ) 20 , e ) 19.2","""man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 15 = 300 therefore number of days = 5760 / 300 = 19.2 days ans = e"""
Break down and solve the equation step by step.,"how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 15 km / hr ? a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180","""15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 500 / ( 25 / 6 ) = 120 seconds the answer is b ."""
Explain the solution process for the given equation.,"1,000 ^ 2 + 1,001 ^ 2 = a ) 6 , 030,053 , b ) 6 , 002,001 , c ) 6 , 030,055 , d ) 6 , 030,056 , e ) 6 , 030,057","""interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 total - > * 1 answer b ."""
Break down and solve the equation step by step.,"two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 3 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ? a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 6 , e ) 2 / 10","""suppose the water in each jug is l liters cx x ( 1 / 3 ) = l cx = 3 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 3 l = 1 / 6 answer will be d"""
Provide a detailed solution to the given mathematical problem.,"14 men can complete a piece of work in 22 days . in how many days can 18 men complete that piece of work ? a ) 23 days , b ) 26 days , c ) 17 days , d ) 29 days , e ) 20 days","""c 17 days 14 * 22 = 18 * x = > x = 17 days"""
Provide a detailed solution to the given mathematical problem.,"a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 8.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ? a ) 16.5 % , b ) 9 % , c ) 35 % , d ) 55 % , e ) 65 %","""the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.085 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 85 f - - > s = 10 f - - > f / s = 1 / 10 - - > f / ( s + f ) = 1 / ( 1 + 10 ) = 1 / 11 = 0.09 . answer : b ."""
"Solve the problem systematically, showing each step clearly.","sue' s trail mix is 30 % nuts and 70 % dried fruit . jane' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane' s trails mix contains 48 % nuts , what percent of the combined mixture is dried fruit ? a ) 20 % , b ) 24 % , c ) 28 % , d ) 32 % , e ) 36 %","""48 % is 18 % - points above 30 % and 12 % - points below 60 % . so the ratio of sue' s mix to jane' s mix is 2 : 3 . 2 / 5 * 70 % = 28 % the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"what is the sum of all the numbers between 1 and 16 , inclusive ? a ) 190 , b ) 200 , c ) 185 , d ) 166 , e ) 213","""all you have to do is add 1 + 2 + 3 + 4 . . . + 14 + 15 + 16 , which is 190 . final answer : a"""
"Solve the problem systematically, showing each step clearly.","if the sides of a triangle are 28 cm , 26 cm and 12 cm , what is its area ? a ) 120 cm 2 , b ) 156 cm 2 , c ) 178 cm 2 , d ) 189 cm 2 , e ) 176 cm 2","""the triangle with sides 28 cm , 26 cm and 12 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 12 = 156 cm 2 answer : b"""
Explain the solution process for the given equation.,"hree number are in the ratio of 3 : 4 : 5 and their l . c . m . is 2400 . their h . c . f . is : a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80","let the numbers be 3 x , 4 x and 5 x . then , their l . c . m . = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 x 40 ) , ( 4 x 40 ) and ( 5 x 40 ) . hence , required h . c . f . = 40 . answer : a"
Provide a detailed solution to the given mathematical problem.,"ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent . overall he make a . ? a ) 277 , b ) 209 , c ) 121 , d ) 200 , e ) 128","""let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . answer : d"""
Provide a detailed solution to the given mathematical problem.,"how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 60 m long and 16 1 / 2 m board ? a ) 99 , b ) 18 , c ) 16 , d ) 198 , e ) 15","""60 * 33 / 2 = 5 / 2 * 2 * x = > x = 198 answer : d"""
Break down and solve the equation step by step.,"a pupil' s marks were wrongly entered as 79 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is : a ) 30 , b ) 80 , c ) 20 , d ) 68 , e ) 26","""let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 79 - 45 ) = > x / 2 = 34 = > x = 68 . answer : d"""
Break down and solve the equation step by step.,"a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 250 more than a : a ) 2348 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771","""explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b' s earnings - a' s earnings = \ inline \ frac { 2 xy } { 100 } = 250 total earning = \ inline \ frac { 58 xy } { 100 } = 7250 answer : b ) rs . 7250"""
"Work through the equation methodically, ensuring clarity at each step.","in an it company , there are a total of 100 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ? a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 65","""you could pick 50 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 55 . c"""
Provide a detailed solution to the given mathematical problem.,"if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 20,000 is invested at the same interest rate , what is the interest from the investment ? a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 1000 , e ) $ 900","- > 250 / 5,000 = 5 % and 20,000 * 5 % = 1000 . thus , d is the answer ."
"Solve the problem systematically, showing each step clearly.","the price of a certain painting increased by 30 % during the first year and decreased by 20 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ? a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 104 %","""easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.20 = 130 * 0.80 = 104 hence required answer = ( 104 / 100 ) * 100 % = 104 % answer is e ."""
Break down and solve the equation step by step.,"if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 222 responses are needed , what is the minimum number of questionnaires that should be mailed ? a ) 280 , b ) 370 , c ) 460 , d ) 550 , e ) 640","""let x be the minimum number of questionnaires to be mailed . 0.6 x = 222 x = 370 the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"the number of the members of a club is more than 50 and less than 80 . when 5 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ? a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8","""the number of members is 7 k + 5 = 8 j + 5 the only number in this range which satisfies this is 61 . 61 / 9 = 6 ( 9 ) + 7 the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","in a neighborhood having 90 households , 11 did not have either a car or a bike . if 18 households had a both a car and a bike and 44 had a car , how many had bike only ? a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10","""{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 18 + 11 - - > { bike } = 53 - - > # those who have bike only is { bike } - { both } = 53 - 18 = 35 . answer : b ."""
"Work through the equation methodically, ensuring clarity at each step.","five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8,10 seconds respectively . in 60 minutes , how many times do they toll together ? a ) 41 , b ) 10 , c ) 31 , d ) 16 , e ) 17","l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 60 min they will toll 30 times . as they have initially tolled once , the answer will be 30 + 1 = 31 . answer : c"
"Work through the equation methodically, ensuring clarity at each step.","in the next cricket world cup t - 20 , team t has decided to score 200 runs only through 4 s and 6 s . in how many ways can the team t score these 200 runs ? a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18","team t can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6' s . so the number of fours scored forms an ap 2 , 5 , 8 , . . . 50 with a common difference of 3 . number of ways of scoring 200 only through 4' s and 6' s = ( 50 - 2 ) / 3 + 1 = 17 answer : d alternate solution : 4 x + 6 y = 200 - - > 2 x + 3 y = 100 x = ( 100 - 3 y ) / 2 - - > 100 - 3 y should be even . this is possible when 3 y is even . there are 17 even multiples of 3 between 0 and 100 . answer : d"
Provide a detailed solution to the given mathematical problem.,"find the number of shares that can be bought for rs . 8200 if the market value is rs . 28 each with brokerage being 2.5 % . a ) 237 , b ) 270 , c ) 177 , d ) 285.7 , e ) 111","""explanation : cost of each share = ( 28 + 2.5 % of 28 ) = rs . 28.7 therefore , number of shares = 8200 / 28.7 = 285.7 answer : d"""
Explain the solution process for the given equation.,"a and b can finish a work in 7 days and 8 days respectively . if both do work one day and leave one day . and a start the work then in how much days work will finish ? a ) 52 / 7 , b ) 8 , c ) 14 / 2 , d ) 6 , e ) 43 / 6","( a + b ) work in 2 days = [ 1 / 7 + 1 / 8 ] = 15 / 56 ( a + b ) work in 6 days = 45 / 56 now , the turn of a , work of a in 1 day = 1 / 7 . till now completed work = [ 45 / 56 + 1 / 7 ] = 53 / 56 , remaining work = [ 1 - 53 / 56 ] = 3 / 56 now , turn of b , 1 / 8 work b do in 1 day so , 3 / 56 part of work b do = [ 8 * 3 / 56 ] = 3 / 7 days total time taken = 6 + 1 + 3 / 7 = 52 / 7 days answer a"
"Work through the equation methodically, ensuring clarity at each step.","length of a rectangular plot is 16 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ? a ) 58 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m","""let breadth = x metres . then , length = ( x + 16 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 16 ) + x ] = 200 2 x + 16 = 100 2 x = 84 x = 42 . hence , length = x + 16 = 58 m a"""
"Work through the equation methodically, ensuring clarity at each step.","solve this 6 + 7 = 12 8 + 9 = 16 5 + 6 = 10 7 + 8 = 14 then , 3 + 3 = ? ? a ) 11 , b ) 12 , c ) 5 , d ) 14 , e ) 18",5 answer : c
"Solve the problem systematically, showing each step clearly.","a meeting has to be conducted with 4 managers . find the number of ways in which the managers may be selected from among 8 managers , if there are 2 managers who refuse to attend the meeting together . a ) 48 , b ) 55 , c ) 58 , d ) 62 , e ) 70","""the total number of ways to choose 4 managers is 8 c 4 = 70 we need to subtract the number of groups which include the two managers , which is 6 c 2 = 15 . 70 - 15 = 55 the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"stacy and heather are 25 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? . a ) 9.0 mile , b ) 13.0 mile , c ) 11.0 mile , d ) 10.2 mile , e ) 12 mile","ss - stacy' s speed = 6 m / hr sh - heather' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 25 - 2.4 = 22.6 time taken = distance / speed = 22.6 / 11 = 2.05 hrs heather will cover = 5 * 2.4 = 10.2 miles . answer d"
"Work through the equation methodically, ensuring clarity at each step.","divide $ 600 among a , b in the ratio 1 : 2 . how many $ that a get ? a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600",sum of ratio terms = 1 + 2 = 3 a = 600 * 1 / 3 = $ 200 answer is e
Break down and solve the equation step by step.,"how many multiples of 5 are there between 10 and 89 , 10 and 89 inclusive ? a ) 17 , b ) 16 , c ) 18 , d ) 19 , e ) 20","""5 multiples are . . . 10,15 , 20,25 , 30,35 , 40,45 , 50,55 , 60,65 , 70,75 , 80,85 , . . . , . . . , the answer is = 16 answer is b"""
Provide a detailed solution to the given mathematical problem.,"in a class of students , 1 / 2 of the number of girls is equal to 1 / 3 of the total number of students . what is the ratio of boys to girls in the class ? a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 3 / 4","""( 1 / 2 ) g = ( 1 / 3 ) ( b + g ) 3 g = 2 b + 2 g g = 2 b b / g = 1 / 2 . the answer is a ."""
"Work through the equation methodically, ensuring clarity at each step.","there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 50 % a ) 40.8 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 22.75","""60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 50 / 100 = 50.40 so x = 40.8 answer : a"""
Provide a detailed solution to the given mathematical problem.,"in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 600 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? a ) 438 , b ) 446 , c ) 452 , d ) 462 , e ) 470","""number of newborns that can die in first month = 1 / 10 * 600 = 60 survived = 540 number of newborns that can die in second month = 1 / 10 * 540 = 54 survived = 486 number of newborns that can die in third month = 1 / 10 * 486 = 48 survived = 438 answer : a"""
"Solve the problem systematically, showing each step clearly.","a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 5 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ? a ) 3 / 8 , b ) 1 / 2 , c ) 9 / 16 , d ) 5 / 7 , e ) 3 / 4","the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 5 / 8 * c : ( b + c ) / 2 = ( 5 / 8 ) * c b = ( 1 / 4 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 4 * c ) / 2 = ( 1 / 8 ) * c median = ( a + c ) / 2 = ( 1 / 8 * c + c ) / 2 = ( 9 / 8 ) * c / 2 = ( 9 / 16 ) * c ( answer c )"
Break down and solve the equation step by step.,"city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 5 : 30 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ? a ) 5 : 00 , b ) 7 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00",train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 5 : 30 pm + 2 hrs = 7 : 30 pm answer : b . 7 : 30
Break down and solve the equation step by step.,"if a : b is 3 : 4 and b : c is 4 : 5 then a : c is equal to a ) 1 : 3 , b ) 3 : 5 , c ) 3 : 4 , d ) 3 : 7 , e ) 1 : 5",the two ratios given are having the same number 4 for b in both the ratios . hence - a : b = 3 : 4 b : c = 4 : 5 = > a : c = 3 : 5 answer b
"Solve the problem systematically, showing each step clearly.","there are 660 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? a ) 75 , b ) 110 , c ) 125 , d ) 175 , e ) 225","""female = x male = 660 - x x / 2 + 660 - x / 4 = 1 / 3 * ( 660 ) = 220 x = 220 x / 2 = 110 is supposed to be the answer m is missing something correct option b"""
Break down and solve the equation step by step.,"10 women can complete a work in 9 days and 10 children take 12 days to complete the work . how many days will 6 women and 7 children take to complete the work ? a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 2","""1 women' s 1 day work = 1 / 90 1 child' s 1 day work = 1 / 120 ( 6 women + 7 children )' s 1 day work = ( 6 / 90 + 7 / 120 ) = 1 / 8 6 women and 7 children will complete the work in 8 days . d"""
Break down and solve the equation step by step.,"the cross - section of a cannel is a trapezium in shape . if the cannel is 20 m wide at the top and 12 m wide at the bottom and the area of cross - section is 800 sq m , the depth of cannel is ? a ) 76 , b ) 50 , c ) 27 , d ) 80 , e ) 25","""1 / 2 * d ( 20 + 12 ) = 800 d = 50 answer : b"""
Break down and solve the equation step by step.,"for integers x , y , and z , if ( 3 ^ x ) ( 4 ^ y ) ( 5 ^ z ) = 13107 , 200000 and x + y + z = 16 , what is the value of xy / z ? a ) undefined , b ) 0 , c ) 3 , d ) 5 , e ) 7","the number 13,107 , 200,000 is not divisible by 3 . ( we can verify this by adding the digits of the number to see that the sum is not a multiple of 3 . ) thus x = 0 and xy / z = 0 . the answer is b ."
Provide a detailed solution to the given mathematical problem.,"a certain sum of money is divided among a , b and c so that for each rs . a has 80 paisa , b has 65 paisa and c 40 paisa . if c' s share is rs . 40 , find the sum of money ? a ) rs . 185 , b ) rs . 410 , c ) rs . 285 , d ) rs . 385 , e ) rs . 475","""a : b : c = 80 : 65 : 40 = 16 : 13 : 8 8 - - - - 40 37 - - - - ? = > rs . 185 answer : a"""
Provide a detailed solution to the given mathematical problem.,"a grocer has a sale of rs . 5400 , rs . 9000 , rs . 6300 , rs . 7200 and rs . 4500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ? a ) s . 1200 , b ) s . 5400 , c ) s . 5400 , d ) s . 4999 , e ) s . 5000","""total sale for 5 months = rs . ( 5400 + 9000 + 6300 + 7200 + 4500 ) = rs . 32400 . required sale = rs . [ ( 5600 x 6 ) - 32400 ] = rs . ( 33600 - 32400 ) = rs . 1200 . option a"""
Explain the solution process for the given equation.,"when processing flower - nectar into honey bees' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 20 % water ? a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.6 kg , e ) none of these","""explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 80 % ( 100 - 20 ) . therefore 0.5 x amount of flower - nectar = 0.80 x amount of honey = 0.80 x 1 kg therefore amount of flower - nectar needed = ( 0.80 / 0.51 ) kg = 1.6 kgs answer : d"""
"Solve the problem systematically, showing each step clearly.","the speed at which a woman can row a boat in still water is 120 kmph . if she rows downstream , where the speed of current is 60 kmph , what time will he take to cover 500 metres ? a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12",speed of the boat downstream = 120 + 60 = 180 kmph = 180 * 5 / 18 = 50 m / s hence time taken to cover 500 m = 500 / 50 = 10 seconds . answer : c
"Work through the equation methodically, ensuring clarity at each step.","a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 1 / 6 as much as the small cups , what fraction of tuesday' s total revenue was from the sale of large cups ? a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 1 / 10","""let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 1 / 6 * 6 = $ 1 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 1 = $ 4 ; fraction of total revenue from large cups : 4 / ( 36 + 4 ) = 1 / 10 . answer : e ."""
Provide a detailed solution to the given mathematical problem.,"a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area t covered by the two roads ? a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625","""area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads t = 1000 + 600 - 25 = 1575 answer : option c"""
Provide a detailed solution to the given mathematical problem.,"harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 5 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ? a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 11","""the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 5 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 5 x = 11 x august tips as a fraction of total tips = 5 x / 11 x = 5 / 11 . so e"""
"Solve the problem systematically, showing each step clearly.","in a stockpile of products produced by 3 machines m 1 , m 2 and m 3 , 40 % and 30 % were manufactured by m 1 and m 2 respectively . 3 % of the products of m 1 are defective , 1 % of products of m 2 defective , while 93 % of the products of m 3 iii are not defective . what is the percentage of defective in the stockpile ? a ) 3 % , b ) 5 % , c ) 2.5 % , d ) 4 % , e ) 3.6 %","explanation : let there be 100 products in the stockpile . 40 % and 30 % were manufactured by m 1 and m 2 respectively . so , 30 % are manufactured by m 3 . products from m 1 = 40 , from m 2 = 30 and from m 3 = 30 . number of defective products from m 1 = 0.03 x 40 = 1.2 , from m 2 = 0.01 x 30 = 0.3 and from m 3 = 0.07 x 30 = 2.1 therefore , total number of defective products = 3.6 answer : e"
Break down and solve the equation step by step.,"when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 8 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 15 ? a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20","""when positive integer n is divided by 3 , the remainder is 1 i . e . , n = 3 x + 1 values of n can be one of { 1 , 4 , 7 , 10 , 13 , 16 , 19 , 22 . . . . . . . . . . . . . . 49 , 52 , 59 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 8 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 13 , 21 , 29 , 37 , 45 , 53 , 61 . . . . . . . . } combining both the sets we get n = { 13 , 37 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 15 or 15 x in case of n = 13 p = 2 so for min value of p , we take min value of n . b is the answer ."""
"Solve the problem systematically, showing each step clearly.","in 1996 , the property tax of a community is increased by 6 % over the 1995 tax . an additional surcharge of $ 200 is also added for a special project . if the petersons' 1996 tax totals $ 2108 , find their property tax for the year 1995 a ) 1600 , b ) 1800 , c ) 1900 , d ) 2000 , e ) 2500",tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b
"Solve the problem systematically, showing each step clearly.","in what time will a train 300 m long cross an electric pole , it its speed be 144 km / hr ? a ) 2.5 sec , b ) 9.7 sec , c ) 3.5 sec , d ) 2.9 sec , e ) 7.5 sec","""speed = 144 * 5 / 18 = 40 m / sec time taken = 300 / 40 = 7.5 sec . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","a number when divided by a divisor leaves a remainder of 25 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ? a ) 12 , b ) 13 , c ) 35 , d ) 38 , e ) 59","""let the number is n , the divisor = d , i will make the two equations - n = xd + 25 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 38 as d is also integer and 38 is a prime number , the d should be 38 to satisfy the above equation . hence answer is' d'"""
Provide a detailed solution to the given mathematical problem.,"the average length of 6 strings is 80 cm . if the average length of one third of the strings is 70 cm , what is the average of the other strings ? a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .",edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third strings is 70 . that means out 6 / 3 = 2 strings . let the avg length of two strings be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining strings . imo correct option is b .
"Solve the problem systematically, showing each step clearly.","in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 37 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ? a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47","""working backward from the day it' s covered : day 37 : fully covered day 36 : half covered so 36 days answer : a"""
Break down and solve the equation step by step.,"5 pieces of wood have an average length of 128 cm and a median length of 140 cm . what is the maximum possible length , in cm , of the shortest piece of wood ? a ) a ) 90 , b ) b ) 100 , c ) c ) 110 , d ) d ) 130 , e ) e ) 140","c . 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3 rd piece ( sorted in increasing length ) length = 140 ( median ) for sum of first 2 wood length to become max , last two should be least . let 4 th , 5 th wood also have length 140 each . total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220 / 2 = 110 answer c"
Break down and solve the equation step by step.,"a can do a piece of work in 12 days and b can do a piece of work in 18 days how many days will the work be completed if both of them work together ? a ) 15 , b ) 7.2 , c ) 7.7 , d ) 7.4 , e ) 8","""a' s 1 day work = 1 / 12 , b' s 1 day work = 1 / 18 ; ( a + b ) 1 day work = 1 / 12 + 1 / 18 = 5 / 36 ; they can finish the work in = 36 / 5 = 7.2 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","simplify : 896 x 896 - 204 x 204 a ) 761200 , b ) 761400 , c ) 761800 , d ) 761500 , e ) none of them","""( 896 ) ^ 2 - ( 204 ) ^ 2 = ( 896 + 204 ) ( 896 - 204 ) = 1100 x 692 = 761200 . answer is a ."""
Explain the solution process for the given equation.,"a large box contains 15 small boxes and each small box contains 20 chocolate bars . how many chocolate bars are in the large box ? a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 300 , e ) e ) 690","""the only thing you have to do is a simple multiply we have : 15 * 20 = 300 correct answer is : d ) 300"""
Explain the solution process for the given equation.,"a train 125 m long passes a man , running at 2 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ? a ) 36 , b ) 50 , c ) 28 , d ) 47 , e ) 29","""speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 2 ) km / hr . x - 2 = 45 = = > x = 47 km / hr answer : d"""
"Solve the problem systematically, showing each step clearly.","excluding the stoppages , the speed of a bus is 64 km / hr and including the stoppages the speed of the bus is 48 km / hr . for how many minutes does the bus stop per hour ? a ) 15 min , b ) 10 min , c ) 12 min , d ) 20 min , e ) 18 min","""speed of the bus without stoppage = 64 km / hr speed of the bus with stoppage = 48 km / hr difference in speed = 16 km / hr so , the time taken in the stoppages = time taken to cover 16 km = ( 16 / 64 ) hr = 1 / 4 hr = 15 min answer : a"""
"Solve the problem systematically, showing each step clearly.","during a certain two - week period , 70 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ? a ) a / 14 , b ) 5 a / 7 , c ) 7 a / 5 , d ) 14 a , e ) 35 a","""total movies = 100 . comedies = 70 . action + drama = 30 . since there were 5 times as many dramas as action movies , then action + 5 * action = 30 - - > action = a = 5 . comedies = 70 = 14 a . answer : d ."""
"Solve the problem systematically, showing each step clearly.","john left home and drove at the rate of 35 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ? a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .","""the total distance d traveled by john is given by d = 35 * 2 + 3 * 55 = 235 miles . answer a"""
Explain the solution process for the given equation.,"in a factory , there are 80 % technicians and 20 % non - technicians . if the 80 % of the technicians and 20 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ? a ) 62 % , b ) 68 % , c ) 52 % , d ) 22 % , e ) 42 %","""total = 100 t = 80 nt = 20 80 * ( 20 / 100 ) = 24 80 * ( 20 / 100 ) = 24 16 + 16 = 32 = > 100 - 32 = 68 % answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","carol and jordan draw rectangles of equal area . if carol' s rectangle measures 5 inches by 24 inches and jordan' s rectangle is 12 inches long , how wide is jordan' s rectangle , in inches ? a ) 25 , b ) 23 , c ) 22 , d ) 20 , e ) 10","""area of carol' s rectangle = 24 * 5 = 120 let width of jordan' s rectangle = w since , the areas are equal 12 w = 120 = > w = 10 answer e"""
Break down and solve the equation step by step.,"exactly 12 % of the reporters for a certain wire service cover local politics in country x . if 40 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ? a ) 20 % , b ) 42 % , c ) 44 % , d ) 80 % , e ) 84 %","""let' s assume there are 100 reporters - - > 12 reporters cover local politics . now , as 40 % of the reporters who cover all politics do not cover local politics then the rest 60 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 60 % of them equal to 12 ( # of reporters who cover local politics ) : 0.6 x = 12 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."""
Break down and solve the equation step by step.,"the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 57 kmph , find the speed of the stream ? a ) 15 , b ) 17 , c ) 19 , d ) 18 , e ) 16","""the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 57 / 3 = 19 kmph . answer : c"""
Explain the solution process for the given equation.,"albert buys 4 horses and 9 cows for rs . 13,400 . if he sells the horses at 10 % profit and the cows at 20 % profit , then he earns a total profit of rs . 1880 . the cost of a horse is : a ) rs . 2007 , b ) rs . 2000 , c ) rs . 2089 , d ) rs . 2067 , e ) rs . 2098","""let c . p . of each horse be rs . x and c . p . of each cow be rs . y . then , 4 x + 9 y = 13400 - - ( i ) and , 10 % of 4 x + 20 % of 9 y = 1880 2 / 5 x + 9 / 5 y = 1880 = > 2 x + 9 y = 9400 - - ( ii ) solving ( i ) and ( ii ) , we get : x = 2000 and y = 600 . cost price of each horse = rs . 2000 . answer : b"""
"Solve the problem systematically, showing each step clearly.","if 9 engines consume 24 metric tonnes of coal , when each is working 8 hoursa day , how much coal will be required for 8 engines , each running 13 hours a day , it is being given that 3 engines of former type consume as much as 4 engines of latter type ? a ) 23 , b ) 25 , c ) 26 , d ) 28 , e ) 30","explanation : let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal consumed ( direct proportion ) more working hours , more coal consumed ( direct proportion ) less rate of consumption , less coal consumed ( direct proportion ) number of engines 9 : 8 working hours 8 : 13 } : : 24 : x rate of consumption ( 1 / 3 ) : ( 1 / 4 ) ( 9 * 8 * ( 1 / 3 ) * x ) = ( 8 * 13 * ( 1 / 4 ) * 24 ) < = > 24 x = 624 < = > x = 26 . answer : c"
"Work through the equation methodically, ensuring clarity at each step.","a room of 6 m 20 cm long and 5 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor . a ) 88900 , b ) 87700 , c ) 88970 , d ) 88000 , e ) 89000","""explanation : area of the room = 620 * 574 sq cm size of largest square tile = h . c . f of 620 cm and 574 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 620 * 574 ) / ( 2 * 2 ) = 88970 answer : c ) 88970"""
"Work through the equation methodically, ensuring clarity at each step.","how many six - digit numbers that do not contain the digits 5 or 8 are there ? a ) 483224 , b ) 156444 , c ) 229376 , d ) 816416 , e ) 316544","""we can have 7 digits ( 1 , 2,3 , 4,6 , 7,9 ) for the first place ( hundred thousand' s place ) . and similarly 8 digits for ten thousands , thousands , hundred' s , tenth' s and unit digit . ( 0,1 , 2,3 , 4,6 , 7,9 ) so in total 7 * 8 * 8 * 8 * 8 * 8 = 229376 hence c"""
Explain the solution process for the given equation.,"which number need to add to 956734 to get a number exactly divisible by 412 ? a ) 345 , b ) 342 , c ) 343 , d ) 342 , e ) 341","""956734 / 412 = 2322 and reminder = 70 . 412 - 70 = 342 so , the next number divisible by 412 is 342 places in front of 956734 which means 342 + 956734 = 957076 342 should be added to 956734 b"""
"Work through the equation methodically, ensuring clarity at each step.","in measuring the sides of a rectangle , one side is taken 10 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements . a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 4.5 % , e ) 2.6 %","""say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 110 * 95 = 10,450 , which is 4.5 % greater than the actual area . answer : d ."""
"Work through the equation methodically, ensuring clarity at each step.","when tossed , a certain coin has an equal probability of landing on either side . if the coin is tossed 5 times , what is the probability that it will land on the same side each time ? a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32","""on the first toss , the coin will land on one side or the other . on the second toss , the probability of landing on the same side is 1 / 2 . on the third toss , the probability of landing on the same side is 1 / 2 . on the fourth toss , the probability of landing on the same side is 1 / 2 . on the fifth toss , the probability of landing on the same side is 1 / 2 . p ( same side all five times ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 . the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years , arun' s age will be 26 years . what is the age of deepak at present ? a ) 15 , b ) 21 , c ) 23 , d ) 12 , e ) 25",let the present ages of arun and deepak be 4 x years and 3 x years respectively 4 x + 6 = 26 4 x = 20 x = 5 deepak' s age = 3 x = 15 years answer is a
"Work through the equation methodically, ensuring clarity at each step.","how many positive integers less than 5,000 are evenly divisible by neither 13 nor 21 ? a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349","""integers less than 5000 divisible by 13 5000 / 13 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 13 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 13 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4349 answer e ."""
"Work through the equation methodically, ensuring clarity at each step.","the sum of present age of abe and the age before 7 years is 35 . find the present age of abe . what will be his age after 7 years ? a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29","present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 35 2 x - 7 = 35 2 x = 35 + 7 x = 42 / 2 x = 21 z = x + 7 = 21 + 7 = 28 answer : d"
Explain the solution process for the given equation.,"the price of a t . v . set worth rs . 12000 is to be paid in 20 installments of rs . 1200 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ? a ) 29997 , b ) 10800 , c ) 27098 , d ) 19000 , e ) 2799",money paid in cash = rs . 1200 balance payment = ( 12000 - 1200 ) = rs . 10800 . answer : b
Explain the solution process for the given equation.,"find the cost of fencing around a circular field of diameter 70 m at the rate of rs . 1 a meter ? a ) 288 , b ) 132 , c ) 220 , d ) 592 , e ) 261","""2 * 22 / 7 * 35 = 220 220 * 1 = rs . 220 answer : c"""
"Solve the problem systematically, showing each step clearly.","a car travels at a speed of 75 miles per hour . how far will it travel in 5 hours ? a ) 425 miles , b ) 625 miles , c ) 325 miles , d ) 375 miles , e ) 625 miles","""during each hour , the car travels 65 miles . for 5 hours it will travel 75 + 75 + 75 + 75 + 75 = 5 * 65 = 375 miles correct answer d"""
Break down and solve the equation step by step.,"find the average of first 15 natural numbers . a ) 10 , b ) 120 , c ) 15 , d ) 8 , e ) 16","explanation : sum of first n natural numbers = n ( n + 1 ) / 2 hence , sum of first 15 natural numbers = ( 15 x 16 ) / 2 = 120 therefore , required average of = 120 / 15 = 8 answer : d"
"Work through the equation methodically, ensuring clarity at each step.","david has $ 1800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ? a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200",suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b
Provide a detailed solution to the given mathematical problem.,"find ( 7 x + 8 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ? a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29",x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 8 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 8 y ) / ( 3 y - 2 y ) = > 29 y / y = 29 answer : e
Explain the solution process for the given equation.,"a student got 71 % in math and 81 % in history . to get an overall average of 75 % , how much should the student get in the third subject ? a ) 63 % , b ) 75 % , c ) 77 % , d ) 79 % , e ) 81 %","""71 + 81 + x = 3 * 75 x = 73 the answer is a ."""
Provide a detailed solution to the given mathematical problem.,"if | 5 x - 10 | = 100 , then find the sum of the values of x ? a ) 1 , b ) - 2 , c ) 3 , d ) - 3 , e ) 4","""| 5 x - 10 | = 100 5 x - 10 = 100 or 5 x - 10 = - 100 5 x = 110 or 5 x = - 90 x = 22 or x = - 18 sum = 21 - 18 = 3 answer is c"""
Break down and solve the equation step by step.,"the average of 11 results is 20 . the average of first 5 of them is 15 and that of last 5 is 22 . find the 6 th result ? a ) 35 , b ) 50 , c ) 100 , d ) 120 , e ) 150","""6 th result = sum of 11 results - sum of 10 results = 11 * 20 - 5 * 15 - 5 * 22 = 220 - 75 - 110 = 35 answer is a"""
Explain the solution process for the given equation.,"9 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? a ) 144 , b ) 131 , c ) 99 , d ) 90 , e ) 45","there are 9 business exec and in each handshake 2 business execs are involved . hence 9 c 2 = 36 also , each of 9 exec will shake hand with every 7 other chairmen for total of 63 handshake . total = 36 + 63 = 99 ans : c"
Explain the solution process for the given equation.,"tom , working alone , can paint a room in 20 hours . peter and john , working independently , can paint the same room in 10 hours and 5 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ? a ) 5 / 7 , b ) 7 / 8 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 5","""let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 20 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 10 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 5 * t part of the job : 1 / 20 * ( t + 4 ) + 1 / 10 * ( t + 2 ) + 1 / 5 * t = 1 - - > multiply by 20 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 20 - - > t = 2 ; hence peter has done 1 / 10 * ( 2 + 2 ) = 4 / 10 = 2 / 5 answer : c"""
"Solve the problem systematically, showing each step clearly.","richard traveled the entire 60 miles trip . if he did the first 2 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ? a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 32 mph , e ) 55 mph","average speed = sum of distance / sum of time . if he travelled the first 2 miles at 24 miles / hr , it would take 0.083 hr . for the remaining trip , if he went at 48 miles / 1 hr , it would take 1 hour . then , the average speed is 60 miles / ( 0.083 + 1 ) hrs = 55 miles / 1 hr . therefore , the answer is e ."
Provide a detailed solution to the given mathematical problem.,"the cricket team of 11 members is 28 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ? a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28","""let the average age of the whole team be x years . 11 x - ( 28 + 31 ) = 9 ( x - 1 ) = > 11 x - 9 x = 50 = > 2 x = 50 = > x = 25 . so , average age of the team is 25 years . d"""
"Solve the problem systematically, showing each step clearly.","if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } is used exactly once , in how many ways can the digits be arranged ? a ) 4830 , b ) 5040 , c ) 5250 , d ) 5460 , e ) 5680","""7 ! = 5040 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","14 is what percent of 70 ? a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 500 %","""14 = x * 70 / 100 x = 20 % ans ; d"""
Break down and solve the equation step by step.,"if 25 % of a number is subtracted from a second number , the second number reduces to its 4 - sixth . what is the ratio of the first number to the second number ? a ) 5 : 3 , b ) 4 : 3 , c ) 6 : 3 , d ) 3 : 4 , e ) 5 : 4",explanation : let the numbers be p & q q - p / 4 = 4 q / 6 = > q - 4 q / 6 = p / 4 = > 2 q / 6 = p / 4 = > p / q = 4 / 3 answer b
"Work through the equation methodically, ensuring clarity at each step.","express a speed of 66 kmph in meters per second ? a ) 10.33 mps , b ) 17 mps , c ) 97 mps , d ) 17.33 mps , e ) 18.33 mps","""66 * 5 / 18 = 18.33 mps answer : e"""
"Solve the problem systematically, showing each step clearly.","how many liters of oil at rs . 40 per liter should be mixed with 240 liters of a second variety of oil at rs . 60 per liter so as to get a mixture whose cost is rs . 52 per liter ? a ) 120 , b ) 150 , c ) 160 , d ) 180 , e ) 200",8 : 12 = 2 : 3 if 240 lrs of the 2 nd variety taken then the 1 st variety should be taken as 160 lr answer c
"Solve the problem systematically, showing each step clearly.","a train 500 m long , running with a speed of 180 km / hr will pass a tree in ? a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 10 sec , e ) 12 sec",speed = 180 * 5 / 18 = 50 m / sec time taken = 500 * 1 / 50 = 10 sec answer : d
"Solve the problem systematically, showing each step clearly.","a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ? a ) 20 , b ) 25 , c ) 27 , d ) 22 , e ) 91","""let the son' s present age be x years . then , man' s present age = ( x + 22 ) years . ( x + 22 ) + 2 = 2 ( x + 2 ) x + 24 = 2 x + 4 = > x = 20 . answer : a"""
"Solve the problem systematically, showing each step clearly.","the difference between simple and compound interest on rs . 1200 for one year at 10 % per annum reckoned half - yearly is ? a ) rs . 7 , b ) rs . 3 , c ) rs . 8 , d ) rs . 1 , e ) rs . 4","""s . i . = ( 1200 * 10 * 1 ) / 100 = rs . 120 c . i . = [ 1200 * ( 1 + 5 / 100 ) 2 - 1200 ] = rs . 123 difference = ( 123 - 120 ) = rs . 3 . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","the guests at a football banquet consumed a total of 319 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ? a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164","""to minimize one quantity maximize other . 159 * 2 ( max possible amount of food a guest could consume ) = 318 pounds , so there must be more than 159 guests , next integer is 160 . answer : a ."""
"Solve the problem systematically, showing each step clearly.","a hemispherical bowl is made of 0.5 cm thick steel . inner radius of the bowl is 4 cm . the volume of steel used in making the bowl is ['a ) 55.83 cm 3','b ) 56.83 cm 3','c ) 113.67 cm 3','d ) 58.83 cm 3','e ) none of these']",inner r = 4 outer r = 4.5 formula = 2 / 3 * 22 / 7 ( r ^ 2 - r ^ 2 ) ( 2 / 3 ) * ( 22 / 7 ) * ( 4.5 * 4.5 * 4.5 - 4 * 4 * 4 ) = 56.83 answer : b
"Solve the problem systematically, showing each step clearly.","a man walks at a rate of 10 mph . after every ten miles , he rests for 8 minutes . how much time does he take to walk 50 miles ? a ) 300 , b ) 318 , c ) 322 , d ) 324 , e ) 332","""to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 8 = 32 minutes . total time = 300 + 32 = 332 minutes . answer : e ."""
"Work through the equation methodically, ensuring clarity at each step.","if 20 % of a number = 400 , then 120 % of that number will be ? a ) 20 , b ) 120 , c ) 360 , d ) 2400 , e ) 2820","""let the number x . then , 20 % of x = 400 x = ( 400 * 100 ) / 20 = 2000 120 % of x = ( 120 / 100 * 2000 ) = 2400 . answer : d"""
Provide a detailed solution to the given mathematical problem.,"a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 25 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s ) a ) 8250 , b ) 9350 , c ) 10,450 , d ) 11,550 , e ) 12,650","""the distance the sound traveled to the man is 25 * 330 = 8250 meters the answer is a ."""
Break down and solve the equation step by step.,"kim can do a work in 3 days while david can do the same work in 2 days . both of them finish the work together and get rs . 150 . what is the share of kim ? a ) 77 , b ) 60 , c ) 99 , d ) 26 , e ) 21",kim' s wages : david' s wages = kim' s 1 day work : david' s 1 day work = 1 / 3 : 1 / 2 = 2 : 3 kim' s share = 2 / 5 * 150 = rs . 60 answer : b
Break down and solve the equation step by step.,"a car ferry can hold up to 60 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 5 tons ? a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20","""the weight of one car and one truck is 5.75 tons . 60 / 5.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is e ."""
Break down and solve the equation step by step.,"a white paper 2 inches wide is placed around a rectangular black paper with dimensions 8 inches by 12 inches . what is the area of the white paper , in square inches ? ['a ) 96','b ) 196','c ) 128','d ) 144','e ) 168']","this question is an example of a' punch out' question - we have to find the area of everything , then' punch out' the part that we do n' t want . we' re told that a white paper 2 inches wide is placed around a rectangular black paper with dimensions 8 inches by 12 inches . we' re asked for the area of the frame , in square inches . area of a rectangle = ( length ) ( width ) so the area of the black paper is . . . ( 8 ) ( 12 ) = 96 the white paper' adds' 2 inches to the top , bottom , left and right' sides' of the picture , so the area of everything is . . . ( 8 + 2 + 2 ) ( 12 + 2 + 2 ) = ( 12 ) ( 16 ) = 196 when we' punch out' the area of the black paper , we' ll be left with the area of the white paper : 192 - 96 = 96 final answer : b"
Break down and solve the equation step by step.,"on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent r of thatbeforejuly 1 last year ? a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %",the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before r = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b
Explain the solution process for the given equation.,"what is the remainder when 54487 ^ ( 42787035 ) is divided by 5 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","""we need to find the units digit of the number . the units digit of powers of seven repeats 7 , 9 , 3 , and 1 cyclically . since 42787035 has the form 4 a + 3 , the units digit is 3 . then the remainder when dividing by 5 is 3 . the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","2.505 / 10.02 = a ) 0.35 , b ) 0.3505 , c ) 0.25 , d ) 0.351 , e ) 0.3527","""2.505 / 10.02 2505 / 1002 = 2.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.25 . answer : c"""
Provide a detailed solution to the given mathematical problem.,"set a contains all the even numbers between 8 and 50 inclusive . set b contains all the even numbers between 108 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ? a ) 2200 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325","""set a contains 8 , 10 , 12 . . . 50 set b contains 108 , 110 , 112 . . . 150 number of terms in each set = 22 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 22 = 2200 answer a"""
"Solve the problem systematically, showing each step clearly.","nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ? a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40","""b its is . let price = x ( x - 1 ) 8 = 6 x x = 4 hence total money = 6 * 4 = 24"""
Provide a detailed solution to the given mathematical problem.,"a circle is inscribed in a triangle of side 6 cm . and a square is inscribed in the circle . what is the area of square ? ['a ) 4 cm ^ 2','b ) 6 cm ^ 2','c ) 5 cm ^ 2','d ) 7 cm ^ 2','e ) 8 cm ^ 2']",the radius of the incircle in a equilateral triangle is a / 2 ( sqrt ) 3 where a = side of triangle = 6 cm so the diameter of the circle would be the diagonal of square so diagonal = 2 * a / 2 ( sqrt ) 3 = a / ( sqrt ) 3 so area of square = 1 / 2 * ( diagonal ) ^ 2 = 6 * 6 / 2 * 3 = 6 cm ^ 2 answer : b
Break down and solve the equation step by step.,"after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6840 . find the actual price of the good . a ) rs . 6000 , b ) rs . 9000 , c ) rs . 10800 , d ) rs . 10000 , e ) rs . 9980","""let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6840 1 = 6840 / 68.4 100 = ( 6840 * 100 ) / 68.4 = rs . 10,000 . answer : option d"""
Provide a detailed solution to the given mathematical problem.,"in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 11 and 200 , then the least and greatest integer on the card would be a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 14 , e ) 5 and 14","""given : 11 < x ( x + 1 ) < 200 . now , it' s better to test the answer choices here rather than to solve : if x = 3 then x ( x + 1 ) = 12 > 11 - - > so , the least value is 4 . test for the largest value : if x = 15 then x ( x + 1 ) = 15 * 16 = 240 > 200 - - > discard b . answer : a ."""
"Work through the equation methodically, ensuring clarity at each step.","in the formula a = ( 2 r ) ^ 3 , if r is halved , then a is multiplied by ? a ) 64 , b ) 1 / 8 , c ) 1 , d ) 8 , e ) 1 / 64",say r = 2 = > a 1 = 64 when r = 1 ; v 2 = 8 v 2 = 1 / 8 * v 1 . answer : b
Provide a detailed solution to the given mathematical problem.,"the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 2 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? a ) s . 4528 , b ) s . 1812 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521","""area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 2 = rs . 1812 answer : b"""
Break down and solve the equation step by step.,"there are 399 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ? a ) 152 , b ) 209 , c ) 57 , d ) 231 , e ) 181","""given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 399 = 231 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a bus trip of 360 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ? a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55","""the time is the distance / speed . the time difference is 1 hour . 360 / v - 360 / ( v + 5 ) = 1 360 ( v + 5 ) - 360 v = ( v ) ( v + 5 ) 1800 = ( v ) ( v + 5 ) 40 * 45 = ( v ) ( v + 5 ) v = 40 mph the answer is b ."""
Break down and solve the equation step by step.,"a certain hobby shop sold model cars for $ 5.00 each and model trains for $ 8.00 each . if a customer purchased both cars and trains from the store for a total of $ 31.00 , what total number of cars and trains did the customer purchase ? a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7","we can take numbers , as price of car 5 , 8 for train and 31 total for ease . now we can determine quickly that total number should range between 31 / 8 < = n < = 31 / 5 , so ans should be between 3 and 7 . now solving the expression 5 a + 8 b = 31 decreasing 31 in multiple of 5 and checking divisibility of that number by 8 . this way we get 3 cars , 2 trains we get $ 31.00 total 3 * 5 + 2 * 8 = 31 hence total number is 3 + 2 = 5 ans c"
Provide a detailed solution to the given mathematical problem.,"5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ? a ) 4400 , b ) 3500 , c ) 8700 , d ) 9000 , e ) 8000","""x * ( 95 / 100 ) * ( 85 / 100 ) = 3553 x = 4400 answer a"""
"Work through the equation methodically, ensuring clarity at each step.","in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 16 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ? a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 128 %","""0,128 r = x / 100 * 0.1 r answer e"""
"Work through the equation methodically, ensuring clarity at each step.","the amount of time that three people worked on a special project was in the ratio of 3 to 5 to 6 . if the project took 140 hours , how many more hours did the hardest working person work than the person who worked the least ? a ) 32 hours , b ) 40 hours , c ) 35 hours , d ) 30 hours , e ) 36 hours","""let the persons be a , b , c . hours worked : a = 3 * 140 / 14 = 30 hours b = 5 * 140 / 14 = 50 hours c = 6 * 140 / 14 = 60 hours c is the hardest worker and a worked for the least number of hours . so the difference is 60 - 30 = 30 hours . answer : d"""
Provide a detailed solution to the given mathematical problem.,"the tax on a commodity is diminished by 22 % and its consumption increased by 11 % . the effect on revenue is ? a ) 8 , b ) 6 , c ) 5 , d ) 4 , e ) 2","""100 * 100 = 10000 88 * 111 = 9768 - - - - - - - - - - - 10000 - - - - - - - - - - - 232 100 - - - - - - - - - - - ? = > 2 % decrease answer : e"""
"Solve the problem systematically, showing each step clearly.","what is the tenth digit to the right of the decimal point , in the decimal expansion of ( 1 / 5 ) ^ 10 a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8","actually 1 / 5 = 0.2 = 2 * 10 ^ - 1 so 2 ^ 10 * 10 ^ - 10 2 has sequence 24 , 86 . hence digit will be 4 answer is c"
"Solve the problem systematically, showing each step clearly.","if the sum of the first n positive integers is s , what is the sum of the first n positive integers divisible by 5 , in terms of s ? a ) s / 2 , b ) s , c ) 2 s , d ) 2 s + 2 , e ) 5 s","""answer is e given sum of 1 2 3 . . . . . n = s sum of 5 , 10 , 15 . . . . 5 n = 5 [ sum ( 1 2 3 . . . . n ) ] = 5 s"""
"Work through the equation methodically, ensuring clarity at each step.","a can do a work in 12 days . b can do the same work in 24 days . if both a & b are working together in how many days they will finish the work ? a ) 3 , b ) 5 , c ) 8 , d ) 2 , e ) 6","""a rate = 1 / 12 b rate = 1 / 24 ( a + b ) rate = ( 1 / 12 ) + ( 1 / 24 ) = 1 / 8 a & b finish the work in 8 days correct option is c"""
"Work through the equation methodically, ensuring clarity at each step.","a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck' s tank is completely filled . if the truck' s tank has a radius of 4 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ? a ) 1.6 , b ) 1 , c ) 0.4 , d ) 0.16 , e ) 0.016","""the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 16 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 160 / 10,000 = 16 / 1000 = 0.016 ft the answer is e ."""
"Solve the problem systematically, showing each step clearly.","if 20 men can build a water fountain 56 metres long in 21 days , what length of a similar water fountain can be built by 35 men in 3 days ? a ) 10 m , b ) 14 m , c ) 17 m , d ) 19 m , e ) 20 m","""explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 21 : 3 : : 56 : x therefore ( 20 x 21 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 420 = 14 hence , the required length is 14 m . answer : b"""
Break down and solve the equation step by step.,"what is the remainder when 7 ^ 498 is divided by 5 ? a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0","""7 ^ 0 = 1 7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = . . . 1 7 ^ 5 = . . . . 7 7 ^ 6 = . . . . . . 9 and so on in a recurring pattern of 1,7 , 9,3 , 1,7 , 9,3 . . . . 498 / 4 = 124 ( with a remainder 2 ) so the last number is a 9 . so when 7 ^ 498 is divided by 5 the remainder is 4 , ans = a"""
"Solve the problem systematically, showing each step clearly.","x starts a business with rs . 54000 . y joins in the business after 9 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ? a ) 1 : 2 , b ) 2 : 1 , c ) 8 : 3 , d ) 3 : 5 , e ) 8 : 1","""explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 54000 * 12 : 27000 * 3 = 54 * 12 : 27 * 3 = 2 * 4 : 1 = 8 : 1 . answer : option e"""
"Work through the equation methodically, ensuring clarity at each step.","the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ? a ) 20 years , b ) 22 years , c ) 24 years , d ) 25 years , e ) 27 years","""age of the 15 th student = [ 15 * 15 - ( 14 * 4 + 16 * 9 ) ] = ( 225 - 200 ) = 25 years . answer : d"""
"Solve the problem systematically, showing each step clearly.","a and b invests rs . 3000 and rs . 7000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year' s profit ? a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 14 , d ) 9 : 9 , e ) 9 : 5","""( 3 * 6 + 6 * 6 ) : ( 7 * 12 ) 54 : 84 = > 9 : 14 . answer : c"""
"Solve the problem systematically, showing each step clearly.","the radius of a semi circle is 6.5 cm then its perimeter is ? a ) 32.7 , b ) 32.4 , c ) 33.4 , d ) 32.8 , e ) 32.1","""36 / 7 r = 6.5 = 33.4 answer : c"""
Break down and solve the equation step by step.,"if 1 tic equals 4 tacs and 5 tacs equal 8 tocs , what is the ratio of one tic to one toc ? a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 32 / 5 , e ) 1 / 15","""tic = 4 * tac and 5 * tac = 8 * toc ; 5 * tic = 20 * tac and 20 * tac = 32 * toc - - > 5 * tic = 32 * toc - - > tic / toc = 32 / 5 . answer : d ."""
"Work through the equation methodically, ensuring clarity at each step.","a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 104 million in sales ? a ) 8 % , b ) 15 % , c ) 45 % , d ) 42 % , e ) 56 %","""( 9 / 104 ) / ( 3 / 20 ) = 30 / 54 = 57,6 % it means that 9 / 108 represents only 57,6 % . therefore a decrease of 42 % . answer d"""
Explain the solution process for the given equation.,"a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 650 sq . feet , how many feet of fencing will be required ? a ) 34 , b ) 40 , c ) 85 , d ) 88 , e ) none","""explanation we have : l = 20 ft and lb = 650 sq . ft . so , b = 32.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 65 ) ft = 85 ft . answer c"""
Break down and solve the equation step by step.,"a can do a piece of work in 40 days ; b can do the same in 40 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ? a ) 20 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days","""10 / 40 + 10 / 40 + 10 / x = 1 x = 20 days answer : a"""
Provide a detailed solution to the given mathematical problem.,"gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ? a ) 3 : 2 , b ) 1 : 2 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3","""g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 8 w 10 + 5 x = 8 ( x + 1 ) x = 2 / 3 ratio of gold with copper = 1 : 2 / 3 = 3 : 2 answer is a"""
"Solve the problem systematically, showing each step clearly.","a one - foot stick is marked in 1 / 3 and 1 / 4 portion . how many total markings will there be , including the end points ? a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5","""lcm of 12 = 12 1 / 3 marking are ( table of 4 ) 0 . . . . . . 4 . . . . . . 8 . . . . . 12 ( total = 4 ) 1 / 4 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 ( total = 5 ) overlapping markings are 0 . . . . . . . . 12 ( total = 2 ) total markings = 4 + 5 - 2 = 7 answer = c"""
"Work through the equation methodically, ensuring clarity at each step.","some of 10 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 15 % . what fraction of the original paint was replaced ? a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 5","""let total paint = 1 let amount replaced = x 10 ( 1 - x ) + 20 x = 15 x = 1 / 2 answer : c"""
Break down and solve the equation step by step.,"a train 90 m long is running at 20 kmph . in how much time will it pass a platform 80 m long ? a ) 15.6 seconds , b ) 24.6 seconds , c ) 28.6 seconds , d ) 13.6 seconds , e ) 35.6 seconds",distance travelled = 90 + 80 m = 170 m speed = 20 * 5 / 8 = 25 / 2 m time = 170 * 2 / 25 = 13.6 seconds answer : d .
Explain the solution process for the given equation.,"a cricket bat is sold for $ 900 , making a profit of $ 150 . the profit percentage would be a ) 24 % , b ) 20 % , c ) 30 % , d ) 36 % , e ) 40 %",150 / ( 900 - 150 ) = 150 / 750 = 0.2 = 20 % . answer : b
"Solve the problem systematically, showing each step clearly.","if taxi fares were $ 10.00 for the first 1 / 5 mile and $ 1.00 for each 1 / 5 mile there after , then the taxi fare for a 10 - mile ride was a ) $ 55.10 , b ) $ 59.20 , c ) $ 59.40 , d ) $ 59.00 , e ) $ 55.00","""in 10 miles , initial 1 / 5 mile charge is $ 10 rest of the distance = 10 - ( 1 / 5 ) = 49 / 5 rest of the distance charge = 49 ( 1.00 ) = $ 49.00 ( as the charge is 1.00 for every 1 / 5 mile ) = > total charge for 4 miles = 10 + 49.00 = 59.00 answer is d"""
"Solve the problem systematically, showing each step clearly.","a man can row upstream at 8 kmph and downstream at 13 kmph . the speed of the stream is ? a ) 3 kmph , b ) 2.5 kmph , c ) 3.5 kmph , d ) 4.3 kmph , e ) 5 kmph","""speed of stream = 1 / 2 ( 13 - 8 ) = 2.5 kmph answer is b"""
Explain the solution process for the given equation.,"a shopkeeper forced to sell at cost price , uses a 850 grams weight for a kilogram . what is his gain percent ? a ) 17.65 % , b ) 9 % , c ) 11.11 % , d ) 12 % , e ) none of these","""shopkeeper sells 850 g instead of 1000 g . so , his gain = 1000 - 850 = 150 g . thus , % gain = ( 150 * 100 ) / 850 = 17.65 % . answer : option a"""
"Work through the equation methodically, ensuring clarity at each step.","a monkey ascends a greased pole 20 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ? a ) 30 th minute , b ) 31 st minute , c ) 37 th minute , d ) 32 nd minute , e ) 33 th minute","""the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 10 meters . i mean this will continue for first 18 * 2 = 36 mins . he would have reached 18 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 36 + 1 = 37 mins . so , asnwer will be c"""
Provide a detailed solution to the given mathematical problem.,"if k and w are the dimensions of a rectangle that has area 20 and if k and w are integers such that k > w , what is the total number of possible values of k ? ['a ) two','b ) three','c ) four','d ) five','e ) six']","kw = 20 = 20 * 1 = 10 * 2 = 5 * 4 - - > k can take 3 values , answer : b"
"Solve the problem systematically, showing each step clearly.","the l . c . m of two numbers is 495 and their h . c . f is 5 . if the sum of the numbers is 10 , then their difference is : a ) 10 , b ) 46 , c ) 70 , d ) 90 , e ) 100","""let the numbers be x and ( 100 - x ) . then , x ( 100 - x ) = 5 * 495 x 2 - 100 x + 2475 = 0 ( x - 55 ) ( x - 45 ) = 0 x = 55 or 45 the numbers are 45 and 55 . required difference = 55 - 45 = 10 . answer : a"""
"Solve the problem systematically, showing each step clearly.","in a caravan , in addition to 60 hens , there are 35 goats and 6 camels with some keepers . if the total number of feet be 193 more than the number of heads in the caravan , the number of keepers is a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25","explanation : let number of keepers be x . then , total number of feet = 2 x 60 + 4 x 35 + 4 x 6 + 2 x = 2 x + 284 . total number of heads = 60 + 35 + 6 + x = 101 + x . therefore ( 2 x + 284 ) = ( 101 + x ) + 193 or x = 10 . answer : b"
"Work through the equation methodically, ensuring clarity at each step.","a and b can do a work in 8 days , b and c can do the same work in 12 days . a , b and c together can finish it in 6 days . a and c together will do it in ? a ) 8 , b ) 4 , c ) 6 , d ) 12 , e ) 10","( a + b + c )' s 1 day work = 1 / 6 ; ( a + b )' s 1 day work = 1 / 8 ( b + c )' s 1 day work = 1 / 12 ( a + c )' s 1 day work = ( 2 * 1 / 6 ) - ( 1 / 8 + 1 / 12 ) = ( 1 / 3 - 5 / 24 ) = 1 / 8 so , a and c together will do the work in 8 days . answer a"
Break down and solve the equation step by step.,"a batsman makes a score of 50 runs in the 17 th inning and thus increases his averages by 2 . what is his average after 17 th inning ? a ) 39 , b ) 18 , c ) 42 , d ) 40.5 , e ) 41.5","""let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 50 then average run after 17 th inning = ( 16 x + 50 ) / 17 ( 16 x + 50 ) / 17 = x + 2 = > 16 x + 50 = 17 x + 34 = > x = 16 x = 16 ; average after 17 th inning = 16 + 2 = 18 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","the greater of two numbers is twice the less , and the sum of the numbers is 96 . what are the numbers ? a ) 64 , b ) 68 , c ) 70 , d ) 79 , e ) 80",let x = the less number 2 x = the greater number the sum of the numbers is 96 x + 2 x = 96 3 x = 96 x = 32 2 x = 64 option a
"Solve the problem systematically, showing each step clearly.","circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 5 more revolutions than gear p ? a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 15","""gear q makes 30 more revolutions each 60 seconds . the time to make 5 = 30 / 6 more revolutions is 60 / 6 = 10 seconds . the answer is c ."""
Break down and solve the equation step by step.,"there are 7 baskets numbered from 1 to 7 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ? a ) 90 , b ) 120 , c ) 250 , d ) 720 , e ) 910","""each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 = 7 * 8 / 2 = 28 apples . the total number of apples taken by 10 children is 10 * 28 = 280 the number of apples left in the end is 1000 - 280 = 720 apples . the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"in a certain village , 20 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 2000 litres of water last ? a ) 5 , b ) 2 , c ) 10 , d ) 1 , e ) 12","i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 20 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 20 * 10 = 200 ( m * n ) water available is 2000 ( p ) it will last 10 months ( p / m * n ) ans : c"
Provide a detailed solution to the given mathematical problem.,"natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 1.5 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ? a ) 1.065 , b ) 1.125 , c ) 1.225 , d ) 1.375 , e ) 1.425","""let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 1.5 km / hour x / 3 = 1.5 x = 4.5 km the average speed while climbing = distance / time = 4.5 / 4 = 1.125 km / h the answer is b ."""
"Solve the problem systematically, showing each step clearly.","if jack walked 4 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ? a ) 3.2 , b ) 4.5 , c ) 6 , d ) 6.25 , e ) 15",distance walked in 1 hour and 15 mins = 4 miles speed per hour = distance / time = 4 / ( 5 / 4 ) = 3.2 miles per hour answer a
Explain the solution process for the given equation.,"a 6 % stock yields 8 % . the market value of the stock is ? a ) rs . 11 , b ) rs . 75 , c ) rs . 17 , d ) rs . 16 , e ) rs . 22","""for an income of rs . 8 , investment = rs . 100 . for an income of rs 6 , investment = rs . \ inline \ left ( \ frac { 100 } { 8 } \ times 6 \ right ) = rs . 75 market value of rs . 100 stock = rs . 75 . answer : b"""
Explain the solution process for the given equation.,"the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ? a ) 187.89 cm , b ) 182.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm","""calculated average height of 35 boys = 184 cm . wrong total height of 35 boys = 184 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm + 106 cm ) / 35 = 184 cm - 60 / 35 cm = 184 cm - 1.71 cm = 182.29 cm . answer : b"""
Break down and solve the equation step by step.,"what is the unit digit of ( 8 ! * 4 ! / 8 ! * 3 ! ) ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","""( 8 ! * 4 ! / 8 ! * 3 ! ) = ( 4 ! / 3 ! ) = 24 / 6 = 4 units digit of the above product will be equal to 4 answer e"""
"Work through the equation methodically, ensuring clarity at each step.","a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates z apply to what fraction of a week ? a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10",number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates z / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c
"Work through the equation methodically, ensuring clarity at each step.","mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 47 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ? a ) 10 % , b ) 6 % , c ) 15 % , d ) 17 % , e ) 20 %","""let me try a simpler one . lets assume that candidate got 47 % votes and total votes is 100 . candidate won = 47 remaining = 53 to get 50 % , candidate requires 3 votes from 100 which is 3 % and 3 votes from 53 . 3 / 53 = . 056 = 5.6 % which is approx 6 % . hence the answer is b ."""
Explain the solution process for the given equation.,"worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ? a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9","""one day work of a = 1 / 8 one day work of b = 1 / 10 so one day work of a and b together = 1 / 8 + 1 / 10 = 9 / 40 so total days required = 40 / 9 answer : b"""
Explain the solution process for the given equation.,"a set consists of 18 numbers , all are even or multiple of 5 . if 6 numbers are even and 12 numbers are multiple of 5 , how many numbers is multiple of 10 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5","{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 18 = 6 + 12 - { both } + 0 ; { both } = 0 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : a ."
"Solve the problem systematically, showing each step clearly.","together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours r would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ? a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .","""say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job r in 44 hours . answer : c ."""
"Work through the equation methodically, ensuring clarity at each step.","what is the remainder when 135 ^ 77 is divided by 7 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","""( 15 ^ 77 * 9 ^ 77 ) / 7 ; ( 15 ^ 77 ) / 7 * ( 9 ^ 77 ) / 7 ; 1 * 2 ^ 77 / 7 ; ( ( 2 ^ 3 ) ^ 25 * 2 ^ 2 ) / 7 ; 1 * 4 = 4 answer : e"""
Break down and solve the equation step by step.,"the average weight of 8 person' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what might be the weight of the new person ? a ) 65 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these","""a 65 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 64 + 20 ) kg = 65 kg ."""
Break down and solve the equation step by step.,"machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 2800 envelopes . a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 60 / 7","""you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 2800 envelopes b will take 2800 / 1400 hrs = 2 hrs so the answer is choice a"""
Break down and solve the equation step by step.,"we run a business that rents out canoes and kayaks . a canoe rental costs $ 9 per day , and a kayak rental costs $ 12 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 432 in revenue . how many more canoes than kayaks were rented out ? a ) 10 , b ) 9 , c ) 8 , d ) 7 , e ) 6","""let x be the number of canoes . then 3 x / 4 is the number of kayaks . 9 x + ( 3 x / 4 ) * 12 = 432 9 x + 9 x = 432 18 x = 432 x = 24 ( canoes ) 3 x / 4 = 18 ( kayaks ) there were 24 - 18 = 6 more canoes rented out . the answer is e ."""
Explain the solution process for the given equation.,"if x is to be chosen at random from the integers between 1 to 5 , inclusive , and y is to be chosen at random from the integers between 7 and 10 , inclusive , what is the probability that x + y will be even ? a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6",x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 2 / 5 * 2 / 4 = 1 / 5 p ( x and y are both odd ) = 3 / 5 * 2 / 4 = 3 / 10 p ( x + y is even ) = 1 / 5 + 3 / 10 = 1 / 2 the answer is a .
Explain the solution process for the given equation.,"the difference of two numbers is 1465 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ? a ) a ) 270 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310","""let the smaller number be x . then larger number = ( x + 1465 ) . x + 1465 = 6 x + 15 5 x = 1450 x = 290 smaller number = 290 . c )"""
Provide a detailed solution to the given mathematical problem.,"there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the p measure in inches of the width of the foil covered prism ? a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10","""if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = p = 10 ans e ."""
Break down and solve the equation step by step.,"there are 2 red chips and 4 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ? a ) a ) 10 , b ) b ) 12 , c ) c ) 50 , d ) d ) 60 , e ) e ) 100","""using anagram method : 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ b _ b _ b _ b so . . 6 ! / number of repeated letters ( 2 ! ) ( 4 ! ) = 10 ans : e"""
"Work through the equation methodically, ensuring clarity at each step.","how many times are the hands of a clock at right angle in 5 days ? a ) 202 , b ) 220 , c ) 210 , d ) 212 , e ) 222","in 1 day , they are at right angles 44 times . in 5 days , they are at right angles 220 times . answer : option b"
Break down and solve the equation step by step.,"a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 2 rows or 7 rows or 9 rows , then no tree will be left . find the least number of trees required a ) 22 , b ) 60 , c ) 126 , d ) 76 , e ) 21","""explanation : the least number of trees that are required = lcm ( 2 , 7 , 9 ) = 126 answer : c"""
Break down and solve the equation step by step.,"julian owes his classmate jenny 20 dollars . if he borrows 8 dollars how much will he owe her ? a ) 28 , b ) 12 , c ) - 28 , d ) 12 , e ) 0",add how he has already borrowed and how much he is going to borrow - 20 + - 8 correct answer c ) - 28
Break down and solve the equation step by step.,"mixture contains alcohol and water in the ratio 4 : 3 . if 6 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture . a ) 10 , b ) 6.8 , c ) 27 , d ) 22 , e ) 29","""let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 24 x = 4 ( 3 x + 5 ) 12 x = 20 x = 1.7 quantity of alcohol = ( 4 x 1.7 ) litres = 6.8 litres . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.3 years , the ratio of the number of boys to the number of girls in the class is a ) 7 : 3 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 5 : 6","""explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) < = > k = 0.5 / 0.6 = 5 / 6 . required ratio = 5 / 6 : 1 = 5 : 6 . answer : e"""
Break down and solve the equation step by step.,"if 4 is the remainder when m is divided by 10 , what is the remainder when 4 m is divided by 10 ? a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0","""we can put m = 10 * k + 4 . so 4 * m = 40 * k + 16 - - - > 40 * k + 16 = 10 * ( 4 * m + 1 ) + 6 - - - > the remainder is 6 . the answer is , therefore , ( c ) ."""
Break down and solve the equation step by step.,"8.008 / 1.001 a ) 0.008 , b ) 8 , c ) 0.8 , d ) 80 , e ) 800","""answer is 8 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 1001 = 8 answer b"""
Explain the solution process for the given equation.,"if the ratio of a to b is 8 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ? a ) 8 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6","""a : b = 8 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 8 : 15 answer a"""
Break down and solve the equation step by step.,"the perimeter of one face of a cube is 24 cm . its volume will be : a ) 216 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these","""explanation : edge of cude = 24 / 4 = 6 cm volume = a * a * a = 6 * 6 * 6 = 216 cm cube option a"""
Break down and solve the equation step by step.,"a car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 60 km / hour . at what speed , in km / hr , is the car traveling ? a ) 70 , b ) 72 , c ) 74 , d ) 75 , e ) 55","""time to cover 1 kilometer at 80 kilometers per hour is 1 / 60 hours = 3,600 / 60 seconds = 60 seconds ; time to cover 1 kilometer at regular speed is 60 + 5 = 65 seconds = 65 / 3,600 hours = 1 / 55 hours ; so , we get that to cover 1 kilometer 1 / 55 hours is needed - - > regular speed 55 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e"""
Break down and solve the equation step by step.,"the ratio 2 : 10 expressed as percent equals to a ) 50 % , b ) 30 % , c ) 25 % , d ) 20 % , e ) 90 %","""explanation : actually it means 2 is what percent of 10 , which can be calculated as , ( 2 / 10 ) * 100 = 2 * 10 = 20 answer : option d"""
Provide a detailed solution to the given mathematical problem.,"a manufacturer produces a certain men' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 20 % longer than the smallest size , how long , in inches , is the shoe in size 15 ? a ) 8.6 , b ) 9.8 , c ) 10.4 , d ) 11.2 , e ) 12.6","""let x be the length of the size 8 shoe . then 0.2 x = 9 / 5 x = 9 inches the size 15 shoe has a length of 9 + 7 / 5 = 10.4 inches the answer is c ."""
Break down and solve the equation step by step.,"a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 15 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ? a ) $ 204 , b ) $ 216 , c ) $ 220 , d ) $ 230 , e ) $ 240","""wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 15 emlpoyee paid = . 85 * 240 = 204 $ answer a"""
"Solve the problem systematically, showing each step clearly.","a coin is tossed 6 times . what is the probability of getting exactly 5 heads ? a ) 3 / 8 , b ) 3 / 16 , c ) 5 / 16 , d ) 3 / 32 , e ) 7 / 64","""the number of possible outcomes is 2 ^ 6 = 64 there are 6 ways to get exactly 5 heads . p ( exactly 5 heads ) = 6 / 64 = 3 / 32 the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a blank ? a ) 2 / 3 , b ) 6 / 7 , c ) 5 / 7 , d ) 8 / 7 , e ) 4 / 3",total draws = prizes + blanks = 10 + 25 = 35 probability of getting a blank = 25 / 35 = 5 / 7 correct option is c
Break down and solve the equation step by step.,"what is the least number should be added to 1056 , so the sum of the number is completely divisible by 28 ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 8","""( 1056 / 28 ) gives remainder 20 20 + 8 = 28 , so we need to add 8 e"""
Provide a detailed solution to the given mathematical problem.,"we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 550 . how many green hats did we buy ? a ) a ) 36 , b ) b ) 40 , c ) c ) 41 , d ) d ) 42 , e ) e ) 44","""let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 550 . 6 ( 85 - g ) + 7 g = 550 . 510 - 6 g + 7 g = 550 . g = 550 - 510 = 40 . the answer is b ."""
Explain the solution process for the given equation.,"the smallest number which when diminished by 3 is divisible by 21 , 2836 and 45 is . . . a ) 829 , b ) 869 , c ) 859 , d ) 4320 , e ) 427",427 answer : e
Provide a detailed solution to the given mathematical problem.,"at 15 : 00 there were 21 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ? a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30",initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d
Explain the solution process for the given equation.,"there are 3 girls and 6 boys . how many kids are there ? a ) 10 , b ) 19 , c ) 20 , d ) 9 , e ) 12",d
Explain the solution process for the given equation.,"20 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ? a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 60","20 % of employees are women with fair hair . 40 % of fair - haired employees are women . so , 20 % * employees = 40 % * fair haired employees ( because both are equal to the number of fair haired women employees ) ( 1 / 2 ) * employees = fair haired employees answer ( c )"
"Solve the problem systematically, showing each step clearly.","a no . when divided by 223 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ? a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 15","""223 + 43 = 266 / 17 = 11 ( remainder ) d"""
Provide a detailed solution to the given mathematical problem.,"an article is bought for rs . 1280 and sold for rs . 900 , find the loss percent ? a ) 28 % , b ) 29 % , c ) 16 % , d ) 26 % , e ) 32 %","""1280 - - - - 380 100 - - - - ? = > 29 % answer : b"""
Provide a detailed solution to the given mathematical problem.,"a certain telescope increases the visual range at a particular location from 90 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ? a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 66 2 / 3 %","""original visual range = 90 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 90 ) / 90 * 100 % = 2 / 3 * 100 % = 66.67 % answer e"""
Break down and solve the equation step by step.,"if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is ? a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48","""q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"""
Break down and solve the equation step by step.,"b completes a work in 9 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ? a ) 3.75 days , b ) 4.73 days , c ) 5.75 days , d ) 6.75 days , e ) 7.73 days","""1 / 9 + 1 / 10 = 19 / 90 90 / 19 = 4.73 days answer : b"""
Explain the solution process for the given equation.,"the moon revolves around the earth at a speed of approximately 0.9 kilometers per second . this approximate speed is how many kilometers per hour ? a ) 60 , b ) 61.2 , c ) 3240 , d ) 3,600 , e ) 3,672","""moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.9 * 3600 = 3240 kilometers per hour . option c is correct"""
"Work through the equation methodically, ensuring clarity at each step.","the radius of a semi circle is 35 cm then its perimeter is ? a ) 32.8 , b ) 180 , c ) 32.1 , d ) 32.2 , e ) 32.9","""diameter 70 cm 1 / 2 * 22 / 7 * 70 + 70 = 180 answer : b"""
"Solve the problem systematically, showing each step clearly.","calculate how many days it will take for 5 boys to paint a 30 m long fence if 2 boys can paint a 20 m long fence in 3 days , a ) 6.80 days , b ) 4.80 days , c ) 3.80 days , d ) 2 days , e ) 1.80 days","""the length of wall painted by one boy in one day = 20 / 2 * 1 / 3 = 3.33 m no . of days required to paint 50 m cloth by 8 boys = 30 / 5 * 1 / 3.33 = 1.80 days . e"""
"Work through the equation methodically, ensuring clarity at each step.","the mean of 50 observations is 200 . but later he found that there is decrements of 9 from each observations . what is the the updated mean is ? a ) 165 , b ) 185 , c ) 190 , d ) 191 , e ) 199","""191 answer is d"""
"Solve the problem systematically, showing each step clearly.","a , b , c can complete a piece of work in 18 , 6,12 days . working together , they complete the same work in how many days ? a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 36 / 11 , e ) 24 / 7","""a + b + c 1 day work = 1 / 18 + 1 / 6 + 1 / 12 = 11 / 36 a , b , c together will complete the job in 36 / 11 days answer is d"""
Explain the solution process for the given equation.,"a man gains 50 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be . a ) 130 % , b ) 300 % , c ) 150 % , d ) 160 % , e ) 170 %","explanation : let the c . p . = x , then s . p . = ( 150 / 100 ) x = 3 x / 2 new s . p . = 2 ( 3 x / 2 ) = 3 x / 1 profit = 3 x / 1 - x = 3 x / 1 profit % = ( profit / c . p . ) * 100 = > ( 3 x / 1 ) * ( 1 / x ) * 100 = 300 % option b"
Explain the solution process for the given equation.,"when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 86.12 , what is the value of y ? a ) 96 , b ) 87 , c ) 75 , d ) 25 , e ) 12","""by the definition of a remainder , the remainder here is equal to 9 / y . the remainder in decimal form is given as . 12 therefore , 9 / y = . 12 solve for y and get 75 . c"""
Explain the solution process for the given equation.,"if 16 ^ y = 4 ^ 16 , what is y ? a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 16","""16 ^ y = 4 ^ 2 y = 4 ^ 16 2 y = 16 y = 8 the answer is c ."""
Explain the solution process for the given equation.,"if the sum and difference of two numbers are 10 and 19 respectively , then the difference of their square is : a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 190","let the numbers be x and y . then , x + y = 10 and x - y = 19 x 2 - y 2 = ( x + y ) ( x - y ) = 10 * 19 = 190 . answer : e"
Explain the solution process for the given equation.,"what percent of 60 is 25 ? a ) 60 % , b ) 50 % , c ) 42 % , d ) 25 % , e ) 10 %","""the phrasing of the question is difficult for some students . ` ` what percent of 60 is 25 ?'' is the same question as ` ` 25 is what percent of 60 ?'' many students find this later way of phrasing the question easier to work with . if x is y percent of z , then x / z = y / 100 ; for example , 10 is 50 % of 20 ; x = 10 , y = 50 , and z = 20 similarly , if you wanted to know what percent of 100 is 50 , you would intuitively know that it is 50 % since it is 50 / 100 or 50 per cent ( literally , per 100 ) . applying this logic to the problem at hand : 25 / 60 = . 42 = 42 % thus , 25 is 42 % of 60 if this way of solving the problem is difficult to conceptualize , consider another approach . it should be clear that 30 is 50 % ( or 1 / 2 ) or 60 . since 25 is less than 30 , 25 must be less than 50 % of 60 . this means that any answer that is not less than 50 % is wrong . since 25 % is 1 / 4 and 1 / 4 of 60 is 15 ( since 15 * 4 = 60 ) , 25 % is too small . by process of elimination , the answer is 42 % answer c"""
Explain the solution process for the given equation.,"3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 17 , 28 and 35 , 45 what is the minimum possible range in scores of the 3 test - takers ? a ) a 17 , b ) b ) 28 , c ) c ) 35 , d ) d ) 45 , e ) e ) 80","it is finding the minimum range between all their scores , if all test taker scores are between 0 and maximum range we will have : a - 0 and 17 b - 0 and 28 c - 0 and 35 d - 0 and 45 therefore the minimum range is 45 , it cant be any lower however you play with the numbers . d"
"Solve the problem systematically, showing each step clearly.","if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 50 , how much more remains to be paid ? a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950","""95 % remains to be paid so the remaining amount is 19 * 50 = $ 950 . the answer is e ."""
"Work through the equation methodically, ensuring clarity at each step.","a certain sky blue paint contains 10 percent blue pigment and 90 percent red pigment by weight . a certain green paint contains 70 percent blue pigment and 30 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ? a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5","10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 9 = 4.5 grams of red pigment"
Break down and solve the equation step by step.,"two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many w hours will it take if jim types the report and mary edits it immediately after he is done ? a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8","""break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many w hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."""
Explain the solution process for the given equation.,"if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is ? a ) 127 , b ) 688 , c ) 200 , d ) 121 , e ) 123","""let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","how many of the integers between 25 and 95 are even ? a ) 35 , b ) 90 , c ) 11 , d ) 10 , e ) 9","""number start between 25 to 95 is 70 numbers half of them is even . . which is 35 answer : a"""
Break down and solve the equation step by step.,"bullock likes to keep a spare tyre in his car every time . on a certain day , he travels 1 , 60,000 km and just to make the most of all the tyres , he changes the tyres between his journey such that each tyre runs the same distance . what is the distance traveled by each tyre ? a ) 70,000 , b ) 60,000 , c ) 128,000 , d ) 90,000 , e ) 10,000","the distance traveled by each tyre : 4 / 5 * 1 , 60 , 000 km = 128,000 km . c"
Provide a detailed solution to the given mathematical problem.,"mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 30 ft how many poles do he need ? ['a ) 20','b ) 30','c ) 40','d ) 50','e ) 60']",if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 20 feet hence no of poles = 600 / 20 = 30 answer : b
"Solve the problem systematically, showing each step clearly.","how many 3 - digit numerals begin with a digit that represents a odd prime and end with a digit that represents a prime number ? a ) 16 , b ) 80 , c ) 160 , d ) 120 , e ) 240","""prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 3 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 4 ways total = 3 * 10 * 4 = 120 ans : d"""
Explain the solution process for the given equation.,"in what time will a train 100 meters long cross an electric pole , if its speed is 36 km / hr a ) 8.5 seconds , b ) 10 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds","""first convert speed into m / sec speed = 36 * ( 5 / 18 ) = 10 m / sec time = distance / speed = 100 / 10 = 10 seconds answer : b"""
Break down and solve the equation step by step.,"danny can divide his herd into 5 equal parts and also to 6 equal parts , but not to 9 equal parts . what could be the number of cows danny has in his herd ? a ) 120 , b ) 155 , c ) 180 , d ) 336 , e ) 456",danny can divide his herd into 5 equal parts and also to 6 equal parts = > no of cows = multiple of 5 and 6 = multiple of 30 . only option a and c qualify . now 2 nd condition : but not to 9 equal parts : so it should not be a multiple of 9 . answer : a
Provide a detailed solution to the given mathematical problem.,"compound interest of rs . 6000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) . a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 945 , e ) none of the above","""10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 6000 [ 1 + ( 5 / 100 ) ] ^ 3 - 6000 = 6000 [ ( 21 / 20 ) ^ 3 - 1 ] = 6000 ( 9261 - 8000 ) / 8000 = 6 * 1261 / 8 = 945 answer : d"""
"Solve the problem systematically, showing each step clearly.","find the least number of complete years in which a sum of money put out at 13 % compound interest will be more than double of itself ? a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9","""6 years answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","what is the unit digit in 7 ^ 105 ? a ) 9 , b ) 7 , c ) 3 , d ) 8 , e ) 5","""unit digit in 7 ^ 105 = unit digit in [ ( 7 ^ 4 ) ^ 26 x 7 ] but , unit digit in ( 7 ^ 4 ) ^ 26 = 1 unit digit in 7 ^ 105 = ( 1 x 7 ) = 7 . answer b ) 7 ."""
Explain the solution process for the given equation.,"you and your friend spent a total of $ 17 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ? a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 10 , e ) $ 5","""my lunch = l , my friends lunch = l + 3 ( l ) + ( l + 3 ) = 17 l + l + 3 - 3 = 17 - 3 2 l = 14 l = 7 my friends lunch l + 3 = 7 + 3 = $ 10 , the answer is d"""
Provide a detailed solution to the given mathematical problem.,"patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils . the cost of 90 pencils is how many times the selling price of 90 pencils ? a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.2 , e ) 1.44","""say the cost price of 90 pencils was $ 90 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 90 - 90 p = 40 p - - > p = 9 / 13 . ( cost price ) / ( selling price ) = 1 / ( 9 / 13 ) = 13 / 9 = 1.44 . answer : e ."""
Explain the solution process for the given equation.,"indu gave bindu rs . 6500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ? a ) 12.8 , b ) 20 , c ) 10.4 , d ) 11.6 , e ) 15","""6500 = d ( 100 / 4 ) 2 d = 10.4 answer : c"""
Provide a detailed solution to the given mathematical problem.,"two pipes a and b can separately fill a cistern in 45 minutes and 60 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ? a ) 90 min , b ) 100 min , c ) 72 min , d ) 75 min , e ) 130 min","""1 / 40 - ( 1 / 45 + 1 / 60 ) = - 1 / 72 third pipe can empty in 72 minutes answer : c"""
"Solve the problem systematically, showing each step clearly.","a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 4 hours . how many hours in total will it take the crow to finish a quarter of the nuts ? a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8","""in one hour , the crow eats 1 / 20 of the nuts . ( 1 / 4 ) / ( 1 / 20 ) = 5 hours the answer is b ."""
Explain the solution process for the given equation.,"what is the smallest number which when diminished by 24 , is divisible 5 , 10 , 15 and 20 ? a ) 276 , b ) 84 , c ) 88 , d ) 90 , e ) 342","""required number = ( lcm of 5 , 10 , 15 and 20 ) + 24 = 60 + 24 = 84 option b"""
"Solve the problem systematically, showing each step clearly.","two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one . a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) 65 sec","""explanation : relative speed = = ( 45 + 30 ) km / hr = 75 x 5 / 18 m / sec = 125 / 6 m / sec we have to find the time taken by the slower train to pass the driver of the faster train and not the complete train . so , distance covered = length of the slower train . therefore , distance covered = 500 m . required time = 500 x 6 / 125 = 24 sec . answer is b"""
"Solve the problem systematically, showing each step clearly.","if x is 40 percent greater than 88 , then x = a ) 68 , b ) 70.4 , c ) 123.2 , d ) 105.6 , e ) 108","""x = 88 * 1.4 = 123.2 so the answer is c ."""
Explain the solution process for the given equation.,"a milk man has 20 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : a ) 22 , b ) 25 , c ) 27 , d ) 29 , e ) 11","""explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = \ inline \ frac { 5 } { 20 } \ times 100 = 25 % % [ profit % = \ inline \ frac { profit } { cost \ : price } \ times 100 ] answer : b ) 25 %"""
"Work through the equation methodically, ensuring clarity at each step.","3 distinct single - digit numbers . a , b , c are in gp . if abs ( x ) for real x is the absolute value of x ( x if x is + ve or 0 and - x if x is - ve ) , then the number of different possible values of abs ( a + b + c ) is a ) 5 , b ) 6 , c ) 3 , d ) 4 , e ) 7","a , b , c may be ( 1 , 2,4 ) & ( 4 , 2,1 ) ( 1 , 3,9 ) & ( 9 , 3,1 ) ( 2 , 4,8 ) & ( 8 , 4,2 ) ( 4 , 6,9 ) & ( 9 , 6,4 ) find abs ( a + b + c ) for these 8 gps 7,13 , 15,19 so , we get 4 different values answer : d"
"Work through the equation methodically, ensuring clarity at each step.","by selling 11 pencils for a rupee a man loses 30 % . how many for a rupee should he sell in order to gain 30 % ? a ) 8 , b ) 7 , c ) 6 , d ) 11 , e ) 9","""70 % - - - 12 130 % - - - ? 70 / 130 * 11 = 6 answer : d"""
Break down and solve the equation step by step.,"the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the width and the length of the garden . a ) 80 , b ) 90 , c ) 100 , d ) 70 , e ) 110","""let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width'' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 answer c"""
Break down and solve the equation step by step.,"the current of a stream runs at the rate of 3 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ? a ) a ) 7.24 , b ) b ) 2 , c ) c ) 8.5 , d ) d ) 6.67 , e ) e ) 3","""s = 3 m = x ds = x + 3 us = x - 3 6 / ( x + 3 ) + 6 / ( x - 3 ) = 2 x = 7.24 answer : a"""
Break down and solve the equation step by step.,"a watch was sold at a loss of 5 % . if it was sold for rs . 500 more , there would have been a gain of 5 % . what is the cost price ? a ) 1000 , b ) 2998 , c ) 2778 , d ) 2788 , e ) 2991","""95 % 105 % - - - - - - - - 10 % - - - - 500 100 % - - - - ? = > rs . 5000 answer : d"""
"Solve the problem systematically, showing each step clearly.","how many factors does 16 ^ 2 have ? a ) 2 , b ) 8 , c ) 4 , d ) 25 , e ) 26","""36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 2 * 2 = 4 answer c ."""
Provide a detailed solution to the given mathematical problem.,"the sum of present age of abe and the age before 7 years is 27 . find the present age of abe . what will be his age after 7 years ? a ) 25 , b ) 24 , c ) 27 , d ) 28 , e ) 29","""present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 27 2 x - 7 = 27 2 x = 27 + 7 x = 34 / 2 x = 17 z = x + 7 = 17 + 7 = 24 answer : b"""
Break down and solve the equation step by step.,"there are 5 chess amateurs playing in villa' s chess club tournament . if each chess amateur plays with exactly 16 other amateurs , what is the total number of chess games possible to be played in the tournament ? a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120","""each person is one participant of 4 games . so there are in all 16 * 5 = 80 instances of one participant games . but each game has 2 participants so total number of games = 80 / 2 = 40 c"""
"Work through the equation methodically, ensuring clarity at each step.","united telephone charges a base rate of $ 9.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ? a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes","lets take number of minutesx . given that , 9 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 60 minutes ans e"
Break down and solve the equation step by step.,"in a certain warehouse , 90 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ? a ) 8 , b ) 64 , c ) 168 , d ) 102 , e ) 144","""if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 90 % of the packages weigh less than 75 pounds so , 90 % oft = number of packages that weigh less than 75 pounds 90 % of 240 = 216 , so 216 packages weigh less than 75 pounds of those 216 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 216 - 48 = 168 = c"""
Explain the solution process for the given equation.,"a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . metre a ) rs 680 , b ) rs 780 , c ) rs 880 , d ) rs 480 , e ) rs 980","""area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 80 = 68000 p in rs = 68000 / 100 = rs 680 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","in a division sum , the quotient is 120 , the divisor 456 and the remainder 333 , find the dividend ? a ) 55287 , b ) 29887 , c ) 27768 , d ) 55053 , e ) 17191","""explanation : 120 * 456 + 333 = 55053 answer : d"""
Explain the solution process for the given equation.,"4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 6 mat - weavers in 6 days ? a ) 25 , b ) 9 , c ) 39 , d ) 61 , e ) 16","""let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 6 : : 4 : x days 4 : 6 4 * 4 * x = 6 * 6 * 4 x = ( 6 * 6 * 4 ) / ( 4 x 4 ) x = 9 . answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","find the area of a parallelogram with base 36 cm and height 24 cm ? a ) 760 , b ) 284 , c ) 288 , d ) 864 , e ) 820","""area of a parallelogram = base * height = 36 * 24 = 864 cm 2 answer : d"""
"Solve the problem systematically, showing each step clearly.","how many integers are between 8 and 122 / 7 , inclusive ? a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 16","122 / 7 = 17 . xx we are not concerned about the exact value of 122 / 7 as we just need the integers . the different integers between 8 and 122 / 7 would be 8 , 9 , 10 , 11 , 12,13 , 14,15 , 16,17 total number of integers = 10 option b"
Provide a detailed solution to the given mathematical problem.,"p and q started a business investing rs 85000 and rs 10000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively . a ) 17 : 5 , b ) 17 : 3 , c ) 17 : 6 , d ) 17 : 2 , e ) 17 : 8","""explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 85000 : 10000 = 85 : 10 = 17 : 2 option d"""
Provide a detailed solution to the given mathematical problem.,"what least number must be subtracted from 3830 so that the remaining number is divisible by 15 ? a ) 3 , b ) 1 , c ) 5 , d ) 11 , e ) 15","""on dividing 3830 by 15 , we get remainder = 5 . required number be subtracted = 5 answer : c"""
Explain the solution process for the given equation.,"little john had $ 5.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ? a ) $ 2.15 , b ) $ 2.05 , c ) $ 2.45 , d ) $ 2.25 , e ) $ 2.85","""john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 5.10 - 3.05 = $ 2.05 answer : b"""
"Solve the problem systematically, showing each step clearly.","the sale price sarees listed for rs . 400 after successive discount is 30 % and 20 % is ? a ) 297 , b ) 879 , c ) 342 , d ) 762 , e ) 224","""400 * ( 70 / 100 ) * ( 80 / 100 ) = 224 answer : e"""
Break down and solve the equation step by step.,"if two sides of a triangle have lengths 3 and 8 , which of the following could be the perimeter of the triangle ? i . 9 ii . 15 iii . 19 ['a ) none','b ) i only','c ) ii only','d ) iii only','e ) i , ii , and iii']","the length of any side of a triangle must be larger than the positive difference of the other two sides , but smaller than the sum of the other two sides . therefore : ( 8 - 3 ) < { third side } < ( 8 + 3 ) . 5 < { third side } < 11 . perimeter = { third side } + 8 + 3 = { third side } + 11 . 16 < { perimeter } < 22 . answer d"
Provide a detailed solution to the given mathematical problem.,"a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 3 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ? a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 24",let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 3 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 3 ) = 8 x . the fraction of sensors which have been upgraded is x / ( x + 8 x ) = x / 9 x = 1 / 9 the answer is d .
"Work through the equation methodically, ensuring clarity at each step.","in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number t and the smallest possible number of students that could have taken both geometry and biology ? a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31","""official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number t of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."""
"Solve the problem systematically, showing each step clearly.","how many positive integers less than 14 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ? a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 8","""the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 - > the number = 5 , 8 , 11 - - > 3 numbers when a = 2 , b = 1 , 2,3 - > . . . . - - > 3 numbers when a = 3 , b = 1,2 , 3,4 - - > . . . . - - > 2 numbers total number is already 8 . look at the answer there is no number greater than 8 - - > we dont need to try any more answer must be e"""
Break down and solve the equation step by step.,"the moon revolves around the earth at a speed of approximately 1.03 kilometers per second . this approximate speed is how many kilometers per hour ? a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,708 , e ) 3,672","""moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.03 * 3600 = 3708 kilometers per hour . option d is correct"""
"Work through the equation methodically, ensuring clarity at each step.","two trains 180 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? a ) 10.7 , b ) 10.9 , c ) 10.24 , d ) 12.24 , e ) 18.8","""relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 180 + 160 = 340 m . required time = 340 * 9 / 250 = 12.24 sec . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","if two positive numbers are in the ratio 1 / 8 : 1 / 5 , then by what percent is the second number more than the first ? a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 65 %","""given ratio = 1 / 8 : 1 / 5 = 5 : 8 let first number be 5 x and the second number be 8 x . the second number is more than first number by 3 x . required percentage = 3 x / 5 x * 100 = 60 % . answer : c"""
Break down and solve the equation step by step.,"in how many ways can an answer key for a quiz be written if the quiz contains 4 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ? a ) 512 , b ) 656 , c ) 740 , d ) 896 , e ) 972","""there are 2 ^ 4 = 16 possibilities for the true - false answers . however we need to remove two cases for tttt and ffff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 14 * 64 = 896 . the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 4 x + 2 = 0 ? a ) 8 , b ) 10 , c ) 2 , d ) 16 , e ) 24","""a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 4 / 1 = - 4 ab = 2 / 1 = 2 hence a / b + b / a = [ ( - 4 ) 2 - 2 ( 2 ) ] / 2 = 4 / 2 = 2 . c )"""
Provide a detailed solution to the given mathematical problem.,"find the simple interest on rs . 68,000 at 16 2 / 3 % per year for 9 months . a ) 7500 , b ) 6500 , c ) 8500 , d ) 9500 , e ) none of them","""p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is c ."""
Provide a detailed solution to the given mathematical problem.,"a row of ants comprised of 102 ants . a man walked upon it and all except 42 were crushed beneath his foot . how many ants are left alive ? a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45","solution : all except 42 were crushed means that all the ants except 42 were crushed beneath the man' s foot . hence , 42 ants are alive now answer b"
Provide a detailed solution to the given mathematical problem.,"the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 14","""solution let the toatl number of workers be x . then 8000 x = ( 10000 x 7 ) + 6000 ( x - 7 ) x = 14 . answer e"""
Explain the solution process for the given equation.,"efrida and frazer who live 13 miles apart , meet at a restaurant that is directly north of efrida' s home and directly east of frazer' s home . if the restaurant is two miles closer to efrida' s home , than to frazer' s home , how many miles is the restaurant from frazer' s home ? a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11","""it' s a simple geometry problem . look at the diagram below : answer : e ."""
"Solve the problem systematically, showing each step clearly.","if the ratio of a to b is 11 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ? a ) 4 / 15 , b ) 11 / 15 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6","""a : b = 11 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 11 : 15 answer b"""
Explain the solution process for the given equation.,"a can do a half of certain work in 60 days and b one third of the same in 35 days . they together will do the whole work in . a ) 56 days , b ) 420 days , c ) 46 days , d ) 560 days , e ) 96 days","""a = 120 days b = 105 days 1 / 120 + 1 / 105 = 45 / 2520 = 1 / 56 = > 56 days answer : a"""
Provide a detailed solution to the given mathematical problem.,"what is the minimum percentage increase in the mean of set f { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ? a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %","mean of f is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of f , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( 4 - 2 ) / 2 * 100 = 100 % . answer : d ."
Break down and solve the equation step by step.,"a man walks at a rate of 10 mph . after every ten miles , he rests for 5 minutes . how much time does he take to walk 50 miles ? a ) 300 , b ) 318 , c ) 320 , d ) 324 , e ) 330","to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 5 = 20 minutes . total time = 300 + 20 = 320 minutes . answer : c ."
Provide a detailed solution to the given mathematical problem.,"if the sides of a triangle are 39 cm , 32 cm and 10 cm , what is its area ? a ) 120 , b ) 772 , c ) 288 , d ) 160 , e ) 2848","""the triangle with sides 39 cm , 32 cm and 10 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 32 * 10 = 160 cm 2 answer : d"""
"Solve the problem systematically, showing each step clearly.","there are 12 slate rocks , 16 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ? a ) 3 / 32 , b ) 7 / 64 , c ) 11 / 105 , d ) 15 / 127 , e ) 19 / 134",12 / 36 * 11 / 35 = 11 / 105 the answer is c .
"Solve the problem systematically, showing each step clearly.","john had a stock of 1400 books in his bookshop . he sold 62 on monday , 62 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ? a ) 81.57 % , b ) 36.5 % , c ) 80.67 % , d ) 56.5 % , e ) 80.57 %","""let n be the total number of books sold . hence n = 62 + 62 + 60 + 48 + 40 = 272 let m be the books not sold m = 1400 - n = 1400 - 272 = 1128 percentage books not sold / total number of books = 1128 / 1200 = 0.81 = 80.57 % correct answer e"""
Explain the solution process for the given equation.,"a retailer buys a radio for rs 225 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is a ) 10 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) none of these","""explanation : cost price = ( 225 + 15 ) = 240 sell price = 300 gain = ( 60 / 240 ) * 100 = 25 % . answer : c"""
"Solve the problem systematically, showing each step clearly.","find the compound interest on $ 46,000 at 20 % per annum for 9 months , compounded quarterly a ) 2532.05 , b ) 2552.32 , c ) 2524.34 , d ) 7250.75 , e ) 9012.55","""principal = $ 46000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 46000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 53250.75 ci . = $ ( 53250.75 - 46000 ) = $ 7250.75 answer d ."""
"Solve the problem systematically, showing each step clearly.","a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds ? a ) 5 / 6 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 2 , e ) 3 / 5","""the searchlight completes one revolution every 30 seconds . the probability that the man' s area will be lit up is 10 / 30 = 1 / 3 . the probability that he will stay in the dark is 1 - 1 / 3 = 2 / 3 the answer is c ."""
Break down and solve the equation step by step.,"what is the value of 4 ^ 5 + 4 ^ 7 ? a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 7 ( 4 ^ 5 )","""4 ^ 5 + 4 ^ 7 = 4 ^ 5 ( 1 + 4 ^ 2 ) = 4 ^ 5 * 17 answer c"""
"Work through the equation methodically, ensuring clarity at each step.","a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 15 heads and 43 legs . how many cats does the ship host ? a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8","""sa' s + co + ca + cats = 15 . sa' s + 1 + 1 + cats = 15 or sa' s + cats = 13 . sa' s ( 2 ) + 2 + 1 + cats * 4 = 43 sa' s * 2 + cats * 4 = 40 or sa' s + cats * 2 = 20 or 13 - cats + cat * 2 = 20 then cats = 7 d"""
Explain the solution process for the given equation.,"a reduction of 25 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ? a ) 2.8 , b ) 2.3 , c ) 2.5 , d ) 3.3 , e ) 2.9","""100 * ( 25 / 100 ) = 25 - - - 10 ? - - - 1 = > rs . 2.5 100 - - - 75 ? - - - 2.5 = > rs . 3.3 answer : d"""
Explain the solution process for the given equation.,"if p is the product of the integers from 1 to 35 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ? a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19","""35 ! has 3 , 6 , 9 , . . . . 30 , 33 as factors , which are 11 multiples of 3 . we need to add 4 more to these 11 because of 9 , 18 , and 27 . the greatest integer of k is 15 . the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"diana took out a charge account at the general store and agreed to pay 6 % simple annual interest . if she charges $ 60 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ? a ) $ 62.40 , b ) $ 62.80 , c ) $ 63.20 , d ) $ 63.60 , e ) $ 64.00","""1.06 * $ 60 = $ 63.60 the answer is d ."""
"Solve the problem systematically, showing each step clearly.","find the least number which when divided by 18,32 , 48,52 leaves remainder 14,28 , 44,48 respectively . a ) 2845 , b ) 3250 , c ) 3740 , d ) 4150 , e ) 5140","""the difference of 18 - 14 = 4 , 32 - 28 = 4 , 48 - 44 = 4 , 52 - 48 = 4 lcm of 18,32 , 48,52 = 3744 required number = 3744 - 4 = 3740 answer is c"""
Provide a detailed solution to the given mathematical problem.,"a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 9 the total number of progressives in the entire country , what fraction of the country is traditionalist ? a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5","let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 9 the total number of traditionalists is 6 p / 9 = 2 p / 3 . the total population is p + 2 p / 3 = 5 p / 3 p / ( 5 p / 3 ) = 3 / 5 the answer is e ."
Explain the solution process for the given equation.,"a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18900 . a' s share is ? a ) 6300 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 1261","""x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18900 = 6300 answer : a"""
Explain the solution process for the given equation.,"the length of the bridge , which a train 160 metres long and travelling at 45 km / hr can cross in 30 seconds , is ? a ) 255 , b ) 267 , c ) 245 , d ) 277 , e ) 215","""speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 160 + x ) / 30 = 25 / 2 = > 2 ( 160 + x ) = 750 = > x = 215 m . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","when the positive integer a is divided by 11 , the quotient is b and the remainder 3 . when a is divided by 19 , the remainder is also 3 . what is the remainder when b is divided by 19 ? a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0","any number which when divided by divisor d 1 , d 2 , etc . leaving same remainderrtakes the form ofk + r where k = lcm ( d 1 , d 2 ) in this case the divisors are 1119 and remainder is 3 . so lcm ( 11,19 ) = 209 so n = 209 + 3 = 212 also a = d 1 q + 3 ; which means d 1 q = 209 d 1 = 11 therefore q = 19 and ( b divided by 19 ) 19 / 19 leaves remainder 0 . answer is e"
"Solve the problem systematically, showing each step clearly.","a part of certain sum of money is invested at 9 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ? a ) 4 : 6 , b ) 4 : 9 , c ) 5 : 3 , d ) 4 : 1 , e ) 4 : 2","""15 : 9 = 5 : 3 answer : c"""
Provide a detailed solution to the given mathematical problem.,"a fruit seller had some apples . he sells 40 % apples and still he has 420 . originally he had how many apples ? a ) 400 , b ) 500 , c ) 700 , d ) 450 , e ) 650",suppose originally he had x apples then ( 100 - 40 ) % of x = 420 60 x / 100 = 420 x = 700 answer is c
Provide a detailed solution to the given mathematical problem.,"what will be the compound interest on a sum of rs . 26000 after 3 years at the rate of 12 % p . a . ? a ) s . 10123.22 , b ) s . 10823.20 , c ) s . 10123.20 , d ) s . 10123.29 , e ) s . 10528.13","""explanation : amount = [ 26000 * ( 1 + 12 / 100 ) 3 ] = 26000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 36528.13 - 26000 ) = rs . 10528.13 answer : e"""
Provide a detailed solution to the given mathematical problem.,"elvin' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin' s total telephone bill for january was $ 48 and elvin' s total telephone bill for february was 90 $ . if elvin' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin' s fixed monthly charge for internet service ? a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 6 , e ) $ 28","""bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 48 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 90 i . e . x + y = 48 and 2 x + y = 90 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 90 - 48 i . e . x = 42 i . e . fixed monthly charge , y = 6 answer : option d"""
Explain the solution process for the given equation.,"john and david work at a hospital with 4 other workers . for an internal review , 2 of the 4 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ? a ) 1 / 14 , b ) 1 / 20 , c ) 1 / 13 , d ) 1 / 7 , e ) 1 / 6","""probability that john and david will both be chosen out of 8 workers = ( 2 / 4 ) * ( 1 / 3 ) = 1 / 6 answer e"""
Provide a detailed solution to the given mathematical problem.,"the average weight of 9 person' s increases by 5.5 kg when a new person comes in place of one of them weighing 86 kg . what might be the weight of the new person ? a ) 72 kg , b ) 77.5 kg , c ) 135.5 kg , d ) data inadequate , e ) none of these","""total weight increased = ( 9 x 5.5 ) kg = 49.5 kg . weight of new person = ( 86 + 49.5 ) kg = 135.5 kg . answer : option c"""
Break down and solve the equation step by step.,"the maximum number of students among them 1048 pens and 828 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : a ) 4 , b ) 8 , c ) 16 , d ) 1911 , e ) none of these","""explanation : required number of students = h . c . f of 1048 and 828 = 4 . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 53900 . how many times did he participate in the competition ? a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11","""53900 = 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 7 times . the answer is a ."""
Provide a detailed solution to the given mathematical problem.,"if the ratio of two number is 5 : 7 and lcm of the number is 320 then what is the number . a ) 15 , b ) 9 , c ) 10 , d ) 11 , e ) 35","""product of two no = lcm * hcf 5 x * 7 x = 320 * x x = 9 answer : b"""
"Solve the problem systematically, showing each step clearly.","two numbers are in the ratio of 5 : 9 . if 25 be subtracted from each , they are in the ratio of 35 : 59 . find the numbers ? a ) 150,170 , b ) 150,270 , c ) 50,270 , d ) 180,270 , e ) 150,290","""( 5 x - 25 ) : ( 9 x - 25 ) = 35 : 59 x = 30 = > 150,270 answer : b"""
"Solve the problem systematically, showing each step clearly.","69 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ? a ) 20 , b ) 23 , c ) 24 , d ) 25 , e ) 26","""according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 69 x 12 x 5 = 30 x 6 x x x = 23 hence , the number of days = 23 . answer : b"""
Explain the solution process for the given equation.,"find large number from below question the difference of two numbers is 1000 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder a ) 1345 , b ) 1197 , c ) 1540 , d ) 1600 , e ) 1635","""let the smaller number be x . then larger number = ( x + 1365 ) . x + 1000 = 6 x + 15 5 x = 985 x = 197 large number = 197 + 1365 = 1197 b"""
"Work through the equation methodically, ensuring clarity at each step.","if k is the greatest positive integer such that 4 ^ k is a divisor of 16 ! then k = a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7","""16 / 4 = 4 16 / 16 = 1 4 + 1 = 5 k = 5 answer : c"""
Break down and solve the equation step by step.,"the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 9 minutes , then the area of the park ( in sq . m ) is : a ) 153601 , b ) 153600 , c ) 153602 , d ) 153603 , e ) 194400","""perimeter = distance covered in 9 min . = ( 12000 / 60 ) x 9 m = 1800 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1800 or x = 180 . length = 540 m and breadth = 360 m . area = ( 540 x 360 ) m 2 = 194400 m 2 . answer : e"""
"Solve the problem systematically, showing each step clearly.","a big container is 40 % full with water . if 28 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ? a ) 68 , b ) 72 , c ) 76 , d ) 80 , e ) 84","""28 liters is 35 % of the capacity c . 28 = 0.35 c c = 28 / 0.35 = 80 liters . the answer is d ."""
Explain the solution process for the given equation.,"jar x is 1 / 5 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ? a ) 2 / 5 , b ) 3 / 5 , c ) 7 / 10 , d ) 7 / 20 , e ) 9 / 20","""let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 5 + p / 4 = 9 / 20 the answer is e ."""
Provide a detailed solution to the given mathematical problem.,"a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ? a ) 42 , b ) 70 , c ) 140 , d ) 196 , e ) 315","""ans : 196 7 c 1 * 8 c 2 answer d )"""
Explain the solution process for the given equation.,"what is the greater of the two numbers whose product is 2560 , given that the sum of the two numbers exceeds their difference by 32 ? a ) a ) 90 , b ) b ) 100 , c ) c ) 160 , d ) d ) 70 , e ) of these","""let the greater and the smaller number be g and s respectively . gs = 2560 g + s exceeds g - s by 32 i . e . , g + s - ( g - s ) = 32 i . e . , 2 s = 32 = > s = 16 g = 2560 / s = 160 . answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","median w of price of the car is 52000 . which could be the median of the other two . 35000 , 44000 , x , y , 57000 . a ) 38000 , b ) 47000 , c ) 48000 , d ) 51000 , e ) 56000","median of the car is 52000 therefore 52000 is the middle number . assuming y > = x , x will have to be the median value i . e . 52000 . therefore the remaining value would have to be between 52000 and 57000 inclusive . the only answer choice that fits is w = 56000 . e"
"Solve the problem systematically, showing each step clearly.","a pair of articles was bought for $ 360 at a discount of 10 % . what must be the marked price of each of the article ? a ) $ 200 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600","""s . p . of each of the article = 360 / 2 = $ 180 let m . p = $ x 90 % of x = 360 x = 180 * 100 / 90 = $ 200 answer is a"""
Break down and solve the equation step by step.,"how many multiples of 4 are there between 1 and 100 , inclusive ? a ) 25 , b ) 22 , c ) 23 , d ) 30 , e ) 36","""25 multiples of 4 between 1 and 100 inclusive . from 4 * 1 upto 4 * 25 , ( 1,2 , 3,4 , . . . , 25 ) . hence , 25 multiples ! correct option is a"""
"Work through the equation methodically, ensuring clarity at each step.","what is the smallest no . that should be added to 236 to make it exactly divisible by 9 ? a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9","""if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 2 + 3 + 6 = 11 , the next multiple of 9 is 18 . 7 must be added to 236 to make it divisible by 9 d"""
Explain the solution process for the given equation.,"speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7380 km and comes back to the starting point . the total time taken by him is : a ) 914.2 hours , b ) 937.1 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours","""explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7380 / 18 + 7380 / 14 = 410 + 527.1 = 937.1 hours answer : option b"""
"Work through the equation methodically, ensuring clarity at each step.","p , q and r have rs . 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ? a ) rs . 3200 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these","""let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","if the selling price of 50 articles is equal to the cost price of 25 articles , then the loss or gain percent is : a ) 45 % , b ) 23 % , c ) 20 % , d ) 60 % , e ) 50 %","""c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 25 . loss % = 25 / 50 * 100 = 50 % answer e"""
Break down and solve the equation step by step.,"how many of the positive factors of 24 are not factors of 25 a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5","""factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 25 - 1,5 , 25 comparing both , we have 1 factor of 24 which are not factors of 25 - 1 answer : d"""
Explain the solution process for the given equation.,"in the quadratic equation x 2 - bx + 20 = 0 , if the product of two roots is 20 , what is the sum of the two roots ? a ) 20 , b ) 12 , c ) 16 , d ) 14 , e ) 18","explanation : the sum of the roots of the quadratic equation ax 2 + ax + c = 0 are ( - b / a ) and the product of the roots are ( c / a ) . thus , in the equation x 2 - ax + 20 = 0 , where a = 1 , b = - a and c = 20 . we get , product of the roots = 20 sum of the roots = - ( - 12 ) / 1 = 12 answer : b"
"Solve the problem systematically, showing each step clearly.","if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 25 , what is the value of r - p ? a ) 20 , b ) 10 , c ) 30 , d ) 40 , e ) 5","""arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 50 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 30 hence , the correct answer is c"""
"Solve the problem systematically, showing each step clearly.","find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 a ) 26 , b ) 32 , c ) 25 , d ) 27 , e ) 29","""( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 5 = 2 ^ 22 x 7 ^ 5 x 11 ^ 5 total number of prime factors = ( 22 + 5 + 5 ) = 32 . answer is b ."""
Explain the solution process for the given equation.,"sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 70 ps per meter is ? a ) 287 , b ) 369 , c ) 175 , d ) 279 , e ) 361","""3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.70 = rs . 175 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ? a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25","""percent of students who are 25 years old or older is 0.4 * 48 + 0.3 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 34 = 66 . answer : b ."""
"Work through the equation methodically, ensuring clarity at each step.","if the price of a certain computer increased 30 percent from d dollars to 377 dollars , then 2 d = a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 580","""before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 377 ( given ) i . e . d = 377 / 1.3 = $ 290 i . e . 2 d = 2 * 290 = 580 answer : option e"""
Provide a detailed solution to the given mathematical problem.,"john was 19 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty' s age is now 7 / 8 of john' s . how old is betty ? a ) 21 , b ) 26 , c ) 28 , d ) 30 , e ) 32","""assume betty' s age on marriage = x years . john' s age on marriage = 19 john' s age after 5 years = 24 years . betty' s age after 5 years = x + 5 given : x + 5 = 7 / 8 ( 24 ) = 21 therefore betty' s current age = 21 option a"""
Explain the solution process for the given equation.,"the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew , who weight 53 kg is replaced by a new man . find the weight of the new man . a ) 59 kg , b ) 62 kg , c ) 74 kg , d ) 85 kg , e ) 71 kg","""total weight increased = 1.8 * 10 = 18 kg weight of the new man = 53 + 18 = 71 kg answer is e"""
Provide a detailed solution to the given mathematical problem.,"if 5 < x < 8 < y < 13 , then what is the greatest possible positive integer difference of x and y ? a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7","""let x = 5.1 and y = 12.1 greatest possible difference = 12.1 - 5.1 = 7 answer e"""
"Work through the equation methodically, ensuring clarity at each step.","of the 14,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ? a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %","""the number of employees is not reqd . . . 1 / 2 of 2 / 7 are shunted out so 1 / 7 left . . . there are another 5 equal parts ( 5 / 7 ) . . so total remaining parts = 6 , in which 1 part is journeyman . . . . therefore % = 1 / 6 * 100 = 16.67 % answer : b"""
Break down and solve the equation step by step.,"a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 55 % . staff are allowed a further 50 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ? a ) 0.275 d , b ) 0.225 d , c ) 0.265 d , d ) 0.245 d , e ) 0.205 d","""effective discount = a + b + ab / 100 = - 55 - 50 + ( - 55 ) ( - 50 ) / 100 = 77.5 sale price = d * ( 1 - 77.5 / 100 ) sale price = . 225 * d answer ( b )"""
Explain the solution process for the given equation.,"a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 4 . what is the ratio of luxury cars to sport utility vehicles ? a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 10 : 12 , e ) 1 : 2","""the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 15 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 4 - - > e : s = 5 : 4 = 15 : 12 . thus , l : s = 10 : 12 . answer : d ."""
Explain the solution process for the given equation.,"the original price of a suit is $ 150 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ? a ) $ 130 , b ) $ 136 , c ) $ 144 , d ) $ 150 , e ) $ 160","""0.8 * ( 1.2 * 150 ) = $ 144 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed r of the train . a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61","""let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = r ans = c"""
Break down and solve the equation step by step.,"a number is doubled and 9 is added . if resultant is trebled , it becomes 51 . what is that number a ) 4 , b ) 10 , c ) 12 , d ) 14 , e ) 15","""explanation : = > 3 ( 2 x + 9 ) = 51 = > 2 x + 9 = 17 = > x = 4 answer : option a"""
Break down and solve the equation step by step.,"find the number of different prime factors of 12800 a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6","""explanation : l . c . m of 12800 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 2 , 5 number of different prime factors is 2 . answer : option b"""
"Solve the problem systematically, showing each step clearly.","there are 2 sections a and b in a class , consisting of 36 and 24 students respectively . if the average weight of section a is 30 kg and that of section b is 30 kg , find the average of the whole class ? a ) 30 kg , b ) 37 kg , c ) 42 kg , d ) 55.12 kg , e ) 29.78 kg","""total weight of 36 + 44 students = 36 * 30 + 24 * 30 = 1800 average weight of the class is = 1800 / 60 = 30 kg answer is a"""
"Solve the problem systematically, showing each step clearly.","a man can row upstream at 26 kmph and downstream at 40 kmph , and then find the speed of the man in still water ? a ) 22 , b ) 37 , c ) 30 , d ) 33 , e ) 18","""us = 26 ds = 40 m = ( 40 + 26 ) / 2 = 33 answer : d"""
Explain the solution process for the given equation.,"an aeroplane covers a certain distance of 590 kmph in 8 hours . to cover the same distance in 2 3 / 4 hours , it must travel at a speed of a ) 1780 , b ) 1716 , c ) 1890 , d ) 1980 , e ) 1450",speed of aeroplane = 590 kmph distance travelled in 8 hours = 590 * 8 = 4720 km speed of aeroplane to acver 4720 km in 11 / 4 = 4720 * 4 / 11 = 1716 km answer b .
"Solve the problem systematically, showing each step clearly.","in a river flowing at 2 km / hr , a boat travels 56 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time . a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 21 hours , e ) none of these","""explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 56 km total time taken = time taken downstream + time taken upstream = ( 56 / 8 ) + ( 56 / 4 ) = 21 hr . answer : option d"""
"Solve the problem systematically, showing each step clearly.","a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1406 ? a ) s . 109 , b ) s . 108 , c ) s . 100 , d ) s . 95 , e ) s . 102","""3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1406 74 x = 1406 = > x = 19 5 x = 95 rs . answer : d"""
Provide a detailed solution to the given mathematical problem.,"a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18300 . a' s share is ? a ) 8876 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 6100","""x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18300 = 6100 answer : e"""
"Solve the problem systematically, showing each step clearly.","an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2800 , what will be the difference between q and r' s share ? a ) 2788 , b ) 3500 , c ) 7282 , d ) 2782 , e ) 2729","""4 - - - 2800 5 - - - ? = > 3500 answer : b"""
Break down and solve the equation step by step.,"the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ? a ) a ) 78 , b ) b ) 82 , c ) c ) 96 , d ) d ) 91 , e ) e ) 85","""correct avg marks = 100 + ( 10 - 50 ) / 10 avg = 100 - 4 = 96 answer is c"""
Explain the solution process for the given equation.,"a person' s salary is getting reduced by 20 % . what percentage should be added to get back his original salary ? a ) 25 % , b ) 50 % , c ) 75 % , d ) 85 % , e ) 95 %","salary he get after reduced 20 % = 100 - 20 % = 80 % so , percentage should be added to get back his salary = ( 20 / 80 ) * 100 = 25 % answer : a"
"Work through the equation methodically, ensuring clarity at each step.","a small company reduced its faculty by approximately 13 percent to 195 employees . what was the original number of employees ? a ) 182 , b ) 208 , c ) 220 , d ) 224 , e ) 302","""if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of employees is 224 correct answer - d"""
Break down and solve the equation step by step.,"if square - root of 15 is 3.87 . then find the value of square - root of ( 5 / 3 ) a ) 1.29 , b ) 1.39 , c ) 1.49 , d ) 1.59 , e ) 1.69",= > root 5 / root 3 = ( root 5 / root 3 ) * ( root 3 / root 3 ) = root 15 / root 9 = 3.87 / 3 = 1.29 answer : a
"Solve the problem systematically, showing each step clearly.","maxwell leaves his home and walks toward brad' s house at the same time that brad leaves his home and runs toward maxwell' s house . if the distance between their homes is 40 kilometers , maxwell' s walking speed is 3 km / h , and brad' s running speed is 5 km / h . what is the distance traveled by maxwell when they meet in the middle ? a ) 16 , b ) 17 , c ) 18 , d ) 15 , e ) 14","""consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time' t' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 3 xt = 40 - 5 xt ( i . e distance = speed x time ) = > 8 t = 40 hence t = 5 oa = 3 x 5 = 15 km answer : d"""
"Solve the problem systematically, showing each step clearly.","when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land twice on heads and once on tails ? a ) 1 / 16 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 8","""must be once on twice and once on tails 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 answer : e"""
Provide a detailed solution to the given mathematical problem.,"ratio of two numbers x and y is 5 : 7 . if x is increased by 20 % and y is increased by 2 then the new ratio becomes 2 : 3 . what is the ratio 3 y : ( x + 6 ) a ) 7 : 8 , b ) 8 : 7 , c ) 6 : 7 , d ) 7 : 6 , e ) 2 : 7","""let : x = 5 n y = 7 n 6 n / ( 7 n + 2 ) = 2 / 3 18 n = 2 * ( 7 n + 2 ) n = 1 so , x = 5 ; y = 7 y / ( x + 3 ) = 7 / 8 answer = a"""
Explain the solution process for the given equation.,"a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many q apples did each person get before 45 people joined the feast ? a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .","""before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons q = 1430 , the answer should be a factor of 1430 . only c is . and that' s your answer . c"""
"Solve the problem systematically, showing each step clearly.","xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 6 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ? a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64","""p ( xavier will solve ) = 1 / 6 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 6 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 32 . ans . a ."""
Explain the solution process for the given equation.,"every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` dog'' ? a ) 72 , b ) 75 , c ) 78 , d ) 81 , e ) 84","""` ` dog'' = ( 4 + 15 + 7 ) * 3 = 78 . the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"the security gate at a storage facility requires a 4 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be odd , how many lock codes are possible ? a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440","x - x - x - x - x - - > there are 4 odd digits from 1 to 7 , inclusive thus options for the first and the last x' s are : 4 - x - x - 3 . other x' s can take following values : 4 - 5 - 4 - 3 - - > 4 * 5 * 4 * 3 = 240 . answer : b ."
"Work through the equation methodically, ensuring clarity at each step.","a certain university will select 2 of 5 candidates eligible to fill a position in the mathematics department and 3 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ? a ) 42 , b ) 70 , c ) 540 , d ) 565 , e ) 560","""5 c 2 * 8 c 3 = 10 * 56 = 560 the answer is ( e )"""
Explain the solution process for the given equation.,"how many prime numbers between 1 and 100 are factors of 10010 ? a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1","""factor of 10010 = 2 * 5 * 7 * 11 * 13 - - - 5 prime numbers a"""
Provide a detailed solution to the given mathematical problem.,"at a party , 13 guests brought wine and 14 guests brought beer . if exactly 11 guests brought only one of the two types of drinks , how many guests brought both types of drinks ? a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 14",say x guests brought both drinks . ( 13 - x ) + ( 14 - x ) = 11 - - > x = 8 . answer : d .
"Solve the problem systematically, showing each step clearly.","the sum of the numbers is 177 . if the ratio between the first and the second be 5 : 3 and that between the second and third be 4 : 9 , then find the second number ? a ) 12 , b ) 20 , c ) 45 , d ) 60 , e ) 52","""given ratios 5 : 3 4 : 9 20 : 12 : 27 the second number = 177 / ( 20 + 12 + 27 ) * 15 = 45 answer is c"""
Explain the solution process for the given equation.,"what is the dividend . divisor 18 , the quotient is 9 and the remainder is 4 a ) a ) 166 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158","""d = d * q + r d = 18 * 9 + 4 d = 166 answer : a"""
Provide a detailed solution to the given mathematical problem.,"benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 4 dollars . how many apples does she buy to share them equally between her eighteen kids ? a ) 8 , b ) 9 , c ) 5 , d ) 7 , e ) 10",cost of each apple = 4 dollars apples that benny can buy with the amount she has = 360 / 4 = 90 . apples that each kid gets evenly = 90 / 18 = 5 apples . so the answer is c = 5
"Work through the equation methodically, ensuring clarity at each step.","a man can row upstream at 7 kmph and downstream at 33 kmph , and then find the speed of the man in still water ? a ) 11 , b ) 77 , c ) 30 , d ) 20 , e ) 34","""us = 7 ds = 33 m = ( 33 + 7 ) / 2 = 20 answer : d"""
Explain the solution process for the given equation.,"( 8956231 x 465 ) = ? a ) 4584638125 , b ) 4164647415 , c ) 4584638135 , d ) 4584638140 , e ) 4584638145",8956231 x 465 = 4164647415 ans b
Explain the solution process for the given equation.,"on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent e of thatbeforejuly 1 last year ? a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %","""the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before e = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"""
Break down and solve the equation step by step.,"the average age of 25 students of a class is 25 years . out of these , the average age of 10 students is 22 years and that of the other 14 students is 28 years . the age of the 25 th student is ? a ) 10 , b ) 15 , c ) 13 , d ) 11 , e ) 9","""age of the 25 th student = 25 * 25 - ( 10 * 22 + 14 * 28 ) = 625 - 612 = 13 years answer is c"""
Explain the solution process for the given equation.,"if k ^ 3 is divisible by 336 , what is the least possible value of integer k ? a ) 56 , b ) 70 , c ) 84 , d ) 96 , e ) 120","""k ^ 3 = 336 * x = 2 ^ 4 * 3 * 7 * x the factors of k must at minimum include 2 ^ 2 * 3 * 7 = 84 . the answer is c ."""
"Solve the problem systematically, showing each step clearly.","if the speed of a man is 45 km per hour , then what is the distance traveled by him in 30 seconds ? a ) 275 m , b ) 360 m , c ) 375 m , d ) 420 m , e ) 480 m","""the distance traveled in 30 sec = 45 * ( 5 / 18 ) * 30 = 375 m answer : c"""
Break down and solve the equation step by step.,"3 / 4 of 1 / 2 of 2 / 5 of 5060 = ? a ) 392 , b ) 759 , c ) 753 , d ) 493 , e ) 540","""b 759 ? = 5060 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 759"""
Explain the solution process for the given equation.,"on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 46 centimeters assuming that 1 - inch is 2.54 centimeters ? a ) 174.2 , b ) 212 , c ) 288.1 , d ) 290 , e ) 282.4","""1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 46 cm . : 46 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 46 / ( 3.81 ) = 290 answer will be d ."""
Break down and solve the equation step by step.,"two goods trains each 250 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ? a ) 24 , b ) 45 , c ) 48 , d ) 51 , e ) 44","""relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 250 + 250 = 500 m . required time = 500 * 6 / 125 = 24 sec . answer : option a"""
Explain the solution process for the given equation.,"the monthly incomes of a and b are in the ratio 5 : 2 . b' s monthly income is 12 % more than c' s monthly income . if c' s monthly income is rs . 17000 , then find the annual income of a ? a ) rs . 571200 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these","""b' s monthly income = 17000 * 112 / 100 = rs . 19040 b' s monthly income = 2 parts - - - - > rs . 19040 a' s monthly income = 5 parts = 5 / 2 * 19040 = rs . 47600 a' s annual income = rs . 47600 * 12 = rs . 571200 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","the sum of the squares of two numbers is 3341 and the diference of their squares is 891 . the numbers are : a ) 35 and 46 , b ) 35 and 49 , c ) 35 and 42 , d ) 35 and 41 , e ) 35 and 48","explanation : let the numbers be x and y . then , adding ( i ) and ( ii ) , we get : subtracting ( ii ) from ( i ) , we get : so , the numbers are 35 and 46 answer : a"
Explain the solution process for the given equation.,"a certain no . when divided by 35 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9","""explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) b"""
"Work through the equation methodically, ensuring clarity at each step.","a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ? a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %","""first $ 20 million : royalties / sales ratio = 3 / 20 = 36 / 240 next $ 108 million : royalties / sales ratio = 9 / 108 = 1 / 12 = 20 / 240 answer : c"""
Explain the solution process for the given equation.,"a sum of money lent at compound interest for 2 years at 20 % per annum would fetch rs . 482 more , if the interest was payable half yearly than if it was payable annually . the sum is a ) 200000 , b ) 20000 , c ) 200029 , d ) 288778 , e ) 277789",explanation : let sum = rs . x c . i . when compounded half yearly = c . i . when compounded annually = = > x = 20000 answer : b ) 20000
Break down and solve the equation step by step.,"in the first 25 overs of a cricket game , the run rate was only 5.4 . what should be the run rate in the remaining 25 overs to reach the target of 400 runs ? a ) 16.5 , b ) 13.2 , c ) 10.6 , d ) 11.2 , e ) 7.25",required run rate = 400 - ( 5.4 x 25 ) / 25 = 265 / 25 = 10.6 option c
Break down and solve the equation step by step.,"a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by c are ? a ) 59 , b ) 58 , c ) 60 , d ) 61 , e ) 12","""a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 15 / 25 * 100 = 60 answer : c"""
Break down and solve the equation step by step.,"a van takes 5 hours to cover a distance of 450 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ? a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72","""( 3 / 2 ) * 5 = 7.5 hours 450 / 7.5 = 60 kph the answer is b ."""
Break down and solve the equation step by step.,"find out the c . i on rs . 4000 at 4 % p . a . compound half - yearly for 1 1 / 2 years a ) 244.83 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01","""a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","a boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes . how long will it take to go 5 km in stationary water ? a ) 2 hr 30 min , b ) 2 hr , c ) 4 hr , d ) 1 hr 15 min , e ) none of these","""explanation : speed upstream = 2 / 2 = 1 km / hr speed downstream = 1 / ( ( 20 / 60 ) ) = 3 km / hr speed in still water = 1 / 2 ( 3 + 1 ) = 2 km / hr time taken to travel 5 km in still water = 5 / 2 = 2 ( 1 / 2 ) hours = 2 hour 30 minutes . answer : option a"""
"Solve the problem systematically, showing each step clearly.","the ratio of the volumes of a cube to that of the sphere which will fit inside the cube is ? ['a ) 6.862 kg','b ) 6.838 kg','c ) 6.632 kg','d ) 6.832 kg','e ) 6.834 kg']",52 * 40 * 29 = 60320 48 * 36 * 27 = 46650 - - - - - - - - - - - - 13664 13664 * 1 / 2 = 6832 = > 6.832 kg answer : d
Provide a detailed solution to the given mathematical problem.,"on a certain road 12 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ? a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %","""answer is c . this question is in the og and thus well explained by ets . those who exceed : x so x = 12 % + 0,2 x id est x = 15 %"""
Break down and solve the equation step by step.,"in what time will a train 100 meters long cross an electric pole , if its speed is 126 km / hr a ) 8.5 seconds , b ) 2.86 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds","""first convert speed into m / sec speed = 126 * ( 5 / 18 ) = 35 m / sec time = distance / speed = 100 / 35 = 2.86 seconds answer : b"""
Break down and solve the equation step by step.,"the area of a square is equal to 2 times the area of a rectangle of dimensions 8 cm * 64 cm . what is the perimeter of the square ? a ) 482 , b ) 268 , c ) 800 , d ) 128 , e ) 632","""area of the square = s * s = 2 ( 8 * 64 ) = > s = 4 * 8 = 32 cm perimeter of the square = 4 * 32 = 128 cm . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 63.0 . what is the quiz score of the student who dropped the class ? a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70","total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 63 = 945 so , the score of the person who left is 55 ( 1000 - 945 ) answer will be ( d )"
"Work through the equation methodically, ensuring clarity at each step.","in filling a lot with sand , that is 40 m * 20 m * 2 m the volumes of the sand filled will be ? ['a ) 1200 cu . m','b ) 2200 cu . m','c ) 4800 cu . m','d ) 1600 cu . m','e ) 4000 cu . m']",40 * 20 * 2 = 1600 answer : d
"Work through the equation methodically, ensuring clarity at each step.","jennifer had $ 90 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ? a ) $ 12 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 0","""1 / 5 x $ 90 = $ 15 for sandwich 1 / 6 x $ 90 = $ 45 for museum 1 / 2 x $ 90 = $ 78 for book $ 15 + $ 45 + $ 18 = $ 78 spent $ 90 - $ 78 = $ 12 left over correct answer a"""
Provide a detailed solution to the given mathematical problem.,"two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined","""mixture 1 and 2 having individual profit % of 10 and 20 respectively . individual profits of vodka a for mixture 1 = 1 / 3 * 10 = 3.33 individual profits of vodka b for mixture 1 = 2 / 3 * 10 = 6.77 individual profits for a and b are increased 4 / 3 and 5 / 3 times . means profits of mixtures 1 and 2 will increase too . increased profits of vodka a for mixture 1 = 4 / 3 * 3.33 = 4.44 increased profits of vodka b for mixture 2 = 5 / 3 * 6.77 = 10.55 total increased profits for mixture 1 = 14.99 similarly total increased profits for mixture 2 = 24.42 using allegation formula va : vb = 1 : 1 = [ 24.42 - ( profit of mixture ) ] / [ ( profit of mixture ) - 14.99 ] hence profit of mixture = 19.705 approx = 20 % answer : b"""
"Solve the problem systematically, showing each step clearly.","if two integers x , y ( x > y ) are selected from - 10 to 10 ( inclusive ) , how many possible cases are there ? a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 240","""if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 21 c 2 = 21 * 20 / 2 = 210 . therefore , the answer is d"""
Explain the solution process for the given equation.,"how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 15 % solution ? a ) a ) 5.8 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9",amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 15 / 100 200 + 20 x = 300 + 3 x 17 x = 100 x = 5.8 answer is a
"Solve the problem systematically, showing each step clearly.","salesperson a' s compensation for any week is $ 360 plus 8 percent of the portion of a' s total sales above $ 1,000 for that week . salesperson b' s compensation for any week is 8 percent of a' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ? a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 7,750 , e ) $ 4,000","""sometime , setting up an equation is an easy way to go with : 350 + 0.04 ( x - 1000 ) = 0.08 x x = 7,750 ans : d"""
"Work through the equation methodically, ensuring clarity at each step.","two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 18 kmph and 72 kmph . in how much time will the trains cross each other ? a ) 8 , b ) 16 , c ) 11 , d ) 12 , e ) 21","""relative speed = ( 18 + 72 ) * 5 / 18 = 25 mps . the time required = d / s = ( 100 + 100 + 200 ) / 25 = 400 / 25 = 16 sec . answer : b"""
Explain the solution process for the given equation.,"how many of the positive factors of 24 are not factors of 30 a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5","""factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 30 - 1 , 2 , 3 , 5 , 6 , 10 , 15 and 30 . comparing both , we have four factors of 24 which are not factors of 30 - 4,8 , 12,24 answer ( c )"""
"Work through the equation methodically, ensuring clarity at each step.","a store owner estimates that the average price of type a products will increase by 30 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount paid for type a products was $ 3200 and the total price paid for type b products was $ 5800 . according to the store owner' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ? a ) $ 14,755 , b ) $ 15,325 , c ) $ 11,129 , d ) $ 16,225 , e ) $ 17,155","""cost of type a products next year = 1.3 * 3200 = 4160 cost of type b products next year = 1.2 * 5800 = 6960 total 4169 + 6960 = 11129 answer : c"""
Break down and solve the equation step by step.,"the ratio of the incomes of uma and bala is 4 : 3 and the ratio of their expenditure is 3 : 2 . if at the end of the year , each saves $ 5000 then the income of uma is ? a ) $ 24000 , b ) $ 23000 , c ) $ 22000 , d ) $ 21000 , e ) $ 20000","""let the income of uma and bala be $ 4 x and $ 3 x let their expenditures be $ 3 y and $ 2 y 4 x - 3 y = 5000 - - - - - - - 1 ) 3 x - 2 y = 5000 - - - - - - - 2 ) from 1 ) and 2 ) x = 5000 uma' s income = 4 x = 4 * 5000 = $ 20000 answer is e"""
"Work through the equation methodically, ensuring clarity at each step.","if 3 spiders make 3 webs in 3 days , then 1 spider will make 1 web in how many days ? a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3","""let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 3 webs 3 : 1 1 x 3 x x = 3 x 1 x 3 = > x = 3 answer is e"""
"Work through the equation methodically, ensuring clarity at each step.","if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 8 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ? a ) 6 , b ) 14 , c ) 22 , d ) 30 , e ) 174","""the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 2 + 12 = 14 . answer : b ."""
"Solve the problem systematically, showing each step clearly.","if 3 men or 4 women can reap a field in 10 days how long will 5 men and 6 women take to reap it ? a ) 19 / 60 , b ) 9 / 60 , c ) 2 / 3 , d ) 5 / 18 , e ) 6 / 24",explanation : 3 men reap 1 / 10 field in 1 day 1 man reap 1 / ( 3 x 10 ) 4 women reap 1 / 10 field in 1 day 1 woman reap 1 / ( 10 x 4 ) 5 men and 6 women reap ( 5 / ( 3 x 10 ) + 6 / ( 4 x 10 ) ) = 19 / 60 in 1 day 5 men and 6 women will reap the field in 19 / 60 days answer : option a
Break down and solve the equation step by step.,"find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 8 as quotient and the 15 as remainder a ) 1235 , b ) 1557.9 , c ) 1378 , d ) 1635 , e ) 1489","""let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 8 x + 15 7 x = 1350 x = 192.9 large number = 192.9 + 1365 = 1557.9 b"""
"Work through the equation methodically, ensuring clarity at each step.","a trader sold an item at a loss of 35 % . if he had increased the price by $ 80 he would have made a gain of 5 % . what is the cost price of the item ? a ) $ 245 , b ) $ 150 , c ) $ 260 , d ) $ 220 , e ) $ 250","""let c . p . be $ x then 105 % of x - 65 % of x = 100 40 % of x = 100 40 / 100 * x = 100 40 x = 10 000 x = 250 answer is e"""
Break down and solve the equation step by step.,"a car takes 6 hours to cover a distance of 432 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph","""time = 6 distence = 432 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 432 / 9 = 48 kmph a"""
Explain the solution process for the given equation.,"( 6 ! - 4 ! ) / 5 ! = ? a ) 29 / 5 , b ) 28 / 3 , c ) 27 / 6 , d ) 25 / 4 , e ) 29 / 6",( 6 ! - 4 ! ) / 5 ! ( 4 ! * 5 * 6 - 4 ! ) / 5 ! 4 ! ( 5 * 6 - 1 ) / 4 ! * 5 29 / 5 answer a
"Work through the equation methodically, ensuring clarity at each step.","if the compound interest on a certain sum of money for 4 years at 10 % per annum be rs . 993 , what would be the simple interest ? a ) rs . 880 , b ) rs . 890 , c ) rs . 1200 , d ) rs . 900 , e ) none","""let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 4 yrs = ( 3000 x 10 x 4 ) / 100 = 1200 / - answer : c ."""
Provide a detailed solution to the given mathematical problem.,"if a = ( 10 ^ 10 ) - 47 , what is the sum of all the digit of a ? a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 80","start small and check for any pattern : 10 ^ 2 - 47 = 53 - > number of digits = power of 10 ; number of 9 s = ( power of 10 ) - 2 ; 53 is the last 2 digits 10 ^ 3 - 47 = 953 - > number of digits = power of 10 ; number of 9 s = ( power of 10 ) - 2 ; 53 is the last 2 digits . . . extrapolate 10 ^ 10 - 47 - > number of digits = 10 ; number of 9 s = 8 ; 53 will be the last 2 digits sum , a = 9 * 8 + 5 + 3 = 80 . answer ( e ) ."
Explain the solution process for the given equation.,"the salaries of a , b , and c are in the ratio of 1 : 2 : 3 . the salary of b and c together is rs . 6000 . by what percent is the salary of c more than that of a ? a ) 209 % , b ) 200 % , c ) 290 % , d ) 600 % , e ) 100 %","explanation : let the salaries of a , b , c be x , 2 x and 3 x respectively . then , 2 x + 3 x = 6000 = > x = 1200 . a' s salary = rs . 1200 , b' s salary = rs . 2400 , and cs salary rs . 3600 . excess of c' s salary over a' s = [ ( 2400 / 1200 ) x 100 ] = 200 % . answer : b ) 200 %"
Provide a detailed solution to the given mathematical problem.,"a and b finish the job in 15 days . while a , b and c can finish it in 12 days . c alone will finish the job in a ) 40 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days","""explanation : 12 = ( 15 * x ) / ( 15 + x ) 180 + 12 x = 15 x 3 x = 180 x = 60 answer : option c"""
Break down and solve the equation step by step.,"if 12 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ? a ) 127 , b ) 237 , c ) 300 , d ) 450 , e ) 281","""explanation : let the required no of hectares be x . then men - - - hectares - - - days 12 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 12 * 30 / 24 * 80 x = 300 answer : c"""
Break down and solve the equation step by step.,"the perimeter of a triangle is 36 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ? a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 45","""area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : e"""
Explain the solution process for the given equation.,"find the area of a parallelogram with base 32 cm and height 18 cm ? a ) 576 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 286 cm 2","""area of a parallelogram = base * height = 32 * 18 = 576 cm 2 answer : a"""
Explain the solution process for the given equation.,"there are 41 students in a class , number of girls is one more than number of guys . we need to form a team of 4 students . all 4 in the team can not be from same gender . number of girls and guys in the team should not be equal . how many ways can such a team be made ? a ) 50540 ways , b ) 60540 ways , c ) 50840 ways , d ) 40540 ways , e ) 51540 ways","boys = 20 and girls = 21 now the combinations are { girl , girl , girl , boy } or { boy , boy , boy , girl } so 21 c 3 * 20 c 1 + 20 c 3 * 21 c 1 = 50540 ways answer : a"
Explain the solution process for the given equation.,"the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 800 meters per second , what was the speed , in meters per second , when the stopwatch was started ? a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32","let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 800 x = ( 2 ^ 5 * 25 ) / 2 ^ 9 = 25 / 16 the answer is d ."
Explain the solution process for the given equation.,"how many three digit numbers q are divisible by 78 or 91 ? a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22","""the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples q - - 11 + 9 - 1 = 19 . hence answer is 19 . b"""
Break down and solve the equation step by step.,"the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 65 , then how long is the base of isosceles triangle ? ['a ) 10','b ) 15','c ) 20','d ) 25','e ) 30']",the base of the isosceles triangle is 65 - 20 - 20 = 25 units the answer is d .
"Work through the equation methodically, ensuring clarity at each step.","if k is the greatest positive integer such that 4 ^ k is a divisor of 32 ! then k = a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10","""32 / 4 = 8 32 / 16 = 2 8 + 2 = 10 = k answer : e"""
"Solve the problem systematically, showing each step clearly.","there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total e of the book ? a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018","""first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) 6 : 4 : 3 : 13 - - - - > this means , the total number e must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."""
"Work through the equation methodically, ensuring clarity at each step.","the size of a television screen is given as the length of the screen' s diagonal . if the screens were flat , then the area of a square 22 - inch screen would be how many square inches greater than the area of a square 20 - inch screen ? a ) 2 , b ) 4 , c ) 16 , d ) 42 , e ) 40","""pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 22 ^ 2 / 2 - 20 ^ 2 / 2 = 84 / 2 = 42 ans d ."""
"Solve the problem systematically, showing each step clearly.","a man buys 56 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ? a ) 7.6 % , b ) 7.7 % , c ) 20.52 % , d ) 23.62 % , e ) 27.82 %","""explanation : let marked price be re . 1 each c . p . of 56 pens = rs . 46 s . p . of 56 pens = 99 % of rs . 56 = rs . 55.44 profit % = ( profit / c . p . ) x 100 profit % = ( 9.44 ) x 100 = 20.52 % answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","the tax on a commodity is diminished by 10 % and its consumption increased by 15 % . the effect on revenue is ? a ) 2 % decrease , b ) 3.5 % increase , c ) 9 % decrease , d ) 3 % decrease , e ) 2 % increase","""100 * 100 = 10000 90 * 115 = 10350 - - - - - - - - - - - 10000 - - - - - - - - - - - 350 100 - - - - - - - - - - - ? = > 3.5 % decrease answer : b"""
Explain the solution process for the given equation.,"the walker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the walker continues to walk at her constant rate , how many minutes must the cyclist wait until the walker catches up ? a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24",after passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 3 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 4 / 3 miles to meet the waiting cyclist . the hiker will need 1 / 3 hours or 20 mins to cover the remaining 4 / 3 miles . so the answer is c .
Provide a detailed solution to the given mathematical problem.,"the average of first 6 prime numbers is ? a ) 10.11 , b ) 11.11 , c ) 12.11 , d ) 6.83 , e ) 14.11","""sum of 6 prime no . = 41 average = 41 / 6 = 6.83 answer : d"""
"Solve the problem systematically, showing each step clearly.","what is the greater of the two numbers whose product is 1280 , given that the sum of the two numbers exceeds their difference by 32 ? a ) a ) 90 , b ) b ) 100 , c ) c ) 110 , d ) d ) 70 , e ) 80","""let the greater and the smaller number be g and s respectively . g * s = 1288 g + s exceeds g - s by 32 i . e . , g + s - ( g - s ) = 32 i . e . , 2 s = 32 = > s = 16 . g = 1280 / s = 80 . answer : e"""
Provide a detailed solution to the given mathematical problem.,"how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 9 inches than that of a rectangular sheet of paper measuring 4.5 inches by 11 inches ? a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %","""let' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 9 is twice 4.5 then the area will be double which means 100 % greater . the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"at what price must an book costing $ 47.50 be marked in order that after deducting 8 % from the list price . it may be sold at a profit of 25 % on the cost price ? a ) 72.5 , b ) 64.5 , c ) 62.5 , d ) 82.5 , e ) 60.5",c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 92 / 100 ) = 59.375 mp = 64.5 b
Break down and solve the equation step by step.,"two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ? a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9","""mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 2 and 4 parts , respectively . this will give us in the final mixture ( 5 + 2 ) : ( 3 + 4 ) , which means 7 : 7 , or 1 : 1 . answer a ."""
"Work through the equation methodically, ensuring clarity at each step.","david obtained 76 , 65 , 82 , 67 and 85 marks ( out in 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ? a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) 79","""add all those marks and divide it by 5 becz they gave us 5 subjects for finding average marks we need to divide them add them 76 + 65 + 82 + 67 + 85 / 5 = 375 / 5 = 75 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration c of the acid in the mixture ? a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5","""do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration c would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"""
"Work through the equation methodically, ensuring clarity at each step.","a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is : a ) rs . 650 , b ) rs . 690 , c ) rs . 698 , d ) rs . 700 , e ) rs . 740","""s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 815 - 117 ) = rs . 698 . answer : option c"""
Break down and solve the equation step by step.,"set a contains all the even numbers between 4 and 50 inclusive . set b contains all the even numbers between 104 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ? a ) 2400 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325","""set a contains 4 , 6 . . . 50 set b contains 104 , 106 . . . 150 number of terms in each set = 24 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 24 = 2400 answer a"""
Provide a detailed solution to the given mathematical problem.,"a 18 % stock yielding 12 % is quoted at : a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 120 , e ) s . 150","""income of rs 12 on investment of rs 100 income of rs 18 on investment of ? = ( 18 * 100 ) / 12 = 150 answer : e"""
Break down and solve the equation step by step.,"a tank is 25 m long , 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 75 paise per sq . m , is : a ) rs . 456 , b ) rs . 458 , c ) rs . 558 , d ) rs . 568 , e ) none of these",explanation : area to be plastered = [ 2 ( l + b ) x h ] + ( l x b ) = { [ 2 ( 25 + 12 ) x 6 ] + ( 25 x 12 ) } m 2 = ( 444 + 300 ) m 2 = 744 m 2 . cost of plastering = rs . 744 x 75 / 100 = rs . 558 answer : c
"Work through the equation methodically, ensuring clarity at each step.","the ratio of the arithmetic mean of two numbers to one of the numbers is 5 : 8 . what is the ratio of the smaller number to the larger number ? a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 5 , d ) 1 : 4 , e ) 1 : 3","""for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 5 : 8 , thus the smaller number must have a ratio of 2 . the ratio of the smaller number to the larger number is 2 : 8 = 1 : 4 . the answer is d ."""
Break down and solve the equation step by step.,"when average age of 22 members are 0 , how many members greater than 0 ? a ) 17 , b ) 21 , c ) 22 , d ) 24 , e ) 25",average of 22 numbers = 0 . sum of 22 numbers ( 0 x 22 ) = 0 . it is quite possible that 21 of these numbers may be positive and if their sum is a then 22 nd number is ( - a ) answer is 21 ( b )
Provide a detailed solution to the given mathematical problem.,"the sides of a cube measures 8 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number . a ) 3 , b ) 8 , c ) 7 , d ) 6 , e ) 5","first calculate the surface area of the cube . the cube is made of 6 squares with the sides measuring 8 cm each . the surface area of 1 side of the cube is 64 cm . multiply the surface area of the 1 side by 6 will give you the cube' s total surface area . the cubes total surface area is 384 cm . now we know that the surface area of the ball is 384 cm . to find out the surface area of a sphere you need to square the radius , then multiply by pi , and multiply by the number 4 . going backwards to find the radius - you will need to dived the surface area by 96 . then divide by pi . then determine the square root of the answer . the radius is 5.527 . rounding to the nearest whole number the radius is 6 . the correct answer is ( d ) ."
Provide a detailed solution to the given mathematical problem.,"convert 100 inches into centimeter ? a ) 112 cm , b ) 120 cm , c ) 150 cm , d ) 210 cm , e ) 254 cm","""1 inch = 2.54 cm 100 inches = 100 * 2.54 = 254 cm answer is e"""
Provide a detailed solution to the given mathematical problem.,"if the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ? a ) 50 , b ) 53 , c ) 49 , d ) 48 , e ) 44","""sum of 5 integer ( a , b , c , d , e ) = 5 * 45 = 225 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 225 i . e . 5 a = 215 i . e . a = 43 i . e . largest e = 43 + 10 = 53 answer : option b"""
Break down and solve the equation step by step.,"jim drove 768 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ? a ) 432 miles , b ) 651 miles , c ) 387 miles , d ) 954 miles , e ) 556 miles","""the number of miles to drive to finish his journey is given by 1200 - 768 = 432 miles correct answer a"""
Explain the solution process for the given equation.,"a and b invests rs . 4000 and rs . 6000 in a business . after 4 months , a withdraws three - fourth of his capital and 4 months later , b withdraws half of his capital . in what ratio should they share the profits at the end of the year ? a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 3 : 7 , e ) 5 : 7","""a : b ( 4000 * 4 ) + ( 1000 * 8 ) : ( 6000 * 8 ) + ( 3000 * 4 ) 24000 : 60000 2 : 5 answer : a"""
Break down and solve the equation step by step.,"7 years ago , paula was 3 times as old as karl . in 2 years , paula will be twice as old as karl . what is the sum of their ages now ? a ) 26 , b ) 32 , c ) 38 , d ) 44 , e ) 50","""p - 7 = 3 ( k - 7 ) and so p = 3 k - 14 p + 2 = 2 ( k + 2 ) ( 3 k - 14 ) + 2 = 2 k + 4 k = 16 p = 34 p + k = 50 the answer is e ."""
Break down and solve the equation step by step.,"of the 80 people in a room , 1 / 4 are women . if 3 / 4 of the people are married , what is the maximum number of women in the room who could be unmarried ? a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30","""women = 1 / 4 * 80 = 20 married = 3 / 4 * 80 = 60 unmarried = 20 max ( un - married women ) = 20 answer a"""
Break down and solve the equation step by step.,"what is the lowest positive integer that is divisible by 8 through 11 , inclusive ? a ) 999 , b ) 7811 , c ) 6555 , d ) 9200 , e ) 7920","""the integer should be divisible by : 8 , 9 , 10 and 11 . the least common multiple of these integers is lcm = 8 * 9 * 10 * 11 = 7920 answer : e"""
Explain the solution process for the given equation.,"the annual interest rate earned by an investment increased by 6 percent from last year to this year . if the annual interest rate earned by the investment this year was 15.90 percent , what was the annual interest rate last year ? a ) 20 % , b ) 18 % , c ) 16 % , d ) 25 % , e ) 15 %","""let i = interest rate i ( this year ) = i ( last year ) + 0.06 i ( last year ) = 1.06 i ( last year ) 15.90 = 1.06 x i ( last year ) i ( last year ) = 15.90 / 1.06 = 1590 / 106 = 15 % answer : e"""
Explain the solution process for the given equation.,"a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 210 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ? a ) 89 , b ) 20 , c ) 36 , d ) 41 , e ) 34","""speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 210 = 410 m . time taken = 410 / 10 = 41 sec . answer : option d"""
Provide a detailed solution to the given mathematical problem.,"for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ? a ) 12 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %","in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 75 + 70 = 145 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 145 / 500 ) x 100 % , or 29 % . answer : c ."
Break down and solve the equation step by step.,"one - third less than 20 % of 180 is equal to : a ) 24 , b ) 30 , c ) 35 , d ) 40 , e ) 45","""lots of ways to tackle this . 20 % of 180 = 36 1 / 3 of 36 = 12 so , 1 / 3 , less than 36 is equal to 36 - 12 = 24 answer : a"""
Break down and solve the equation step by step.,"what is the average of the first 10 multiples of 11 ? a ) 55.5 , b ) 61.5 , c ) 53.5 , d ) 78.5 , e ) 60.5","""( 11 + 22 + . . . + 110 ) / 10 = 11 ( 1 + 2 + . . . + 10 ) / 10 = 11 ( 10 ) ( 11 ) / ( 10 * 2 ) = 121 / 2 = 60.5 option e"""
"Work through the equation methodically, ensuring clarity at each step.","two pipes a and b can separately fill a cistern in 24 minutes and 48 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 12 minutes . in how much time , the third pipe alone can empty the cistern ? a ) 90 min , b ) 48 min , c ) 54 min , d ) 120 min , e ) 130 min","""1 / 12 - ( 1 / 24 + 1 / 48 ) = - 1 / 48 third pipe can empty in 48 minutes answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","if ( 10 ^ 4 * 3.456789 ) ^ 14 is written as a single term , how many digits would be to the right of the decimal place ? a ) 9 , b ) 14 , c ) 21 , d ) 28 , e ) 42",3.456789 ^ 14 has 6 * 14 = 84 decimal places . 10 ^ 56 moves the decimal place to the right 56 places . ( 10 ^ 4 * 3.456789 ) ^ 14 has 84 - 56 = 28 digits after the decimal point . the answer is d .
"Solve the problem systematically, showing each step clearly.","of 58 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? a ) 51 , b ) 55 , c ) 59 , d ) 71 , e ) 92",total = 58 thrower = 37 rest = 58 - 37 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 37 + 14 = 51 so a . 51 is the right answer
"Work through the equation methodically, ensuring clarity at each step.","john was 35 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty' s age is now 7 / 8 of john' s . how old is betty ? a ) 24 , b ) 35 , c ) 28 , d ) 30 , e ) 32","""assume betty' s age on marriage = x years . john' s age on marriage = 35 john' s age after 5 years = 40 years . betty' s age after 5 years = x + 5 given : x + 5 = 7 / 8 ( 40 ) = 35 therefore betty' s current age = 35 option b"""
Explain the solution process for the given equation.,"a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 100000 . if the profit at the end of a year is rs . 108000 , then the share of b is ? a ) 40000 , b ) 50000 , c ) 70000 , d ) 60000 , e ) 80000","""ratio of investments of a and b is ( 70000 * 12 ) : ( 100000 * 6 ) = 7 : 20 total profit = rs . 108000 share of b = 20 / 27 ( 108000 ) = rs . 80000 answer : e"""
Break down and solve the equation step by step.,"14 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? a ) 144 , b ) 131 , c ) 115 , d ) 189 , e ) 45","""there are 14 business exec and in each handshake 2 business execs are involved . hence 14 c 2 = 91 also , each of 14 exec will shake hand with every 7 other chairmen for total of 98 handshake . total = 91 + 98 = 189 ans : d"""
Break down and solve the equation step by step.,"a man rows his boat 75 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ? a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9","""speed downstream = d / t = 75 / ( 2 1 / 2 ) = 30 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 30 - 18 ) / 2 = 6 kmph answer : a"""
Provide a detailed solution to the given mathematical problem.,"a garden center sells a certain grass seed in 5 - pound bags at $ 13.82 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ? a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.75 , d ) $ 102.07 , e ) $ 105.3","""there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c"""
Provide a detailed solution to the given mathematical problem.,"what is the remainder when 9 ^ 1 + 9 ^ 2 + 9 ^ 3 + . . . + 9 ^ 9 is divided by 9 ? a ) 2 , b ) 3 , c ) 0 , d ) 5 , e ) none of the above","""notice that in the brackets we have the sum of 9 odd multiples of 9 , which yields remainder of 0 upon division by 9 . answer : c"""
Explain the solution process for the given equation.,"a couple spent $ 132 in total while dining out and paid this amount using a credit card . the $ 132 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ? a ) $ 100 , b ) $ 104 , c ) $ 108 , d ) $ 112 , e ) $ 116","""let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 132 x = 100 the correct answer is a ."""
Provide a detailed solution to the given mathematical problem.,"10 camels cost as much as 24 horses , 26 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ? a ) rs . 6184.5 , b ) rs . 4184.5 , c ) rs . 5700 , d ) rs . 4284.5 , e ) rs . 5184.5","""cost of the camel = p 10 camels = 24 horses 26 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 26 * 6 * 10 ) ] p = rs . ( 65280000 / 15600 ) = > p = rs . 4184.5 answer : b"""
Explain the solution process for the given equation.,"a cricket player whose bowling average was 20.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ? a ) 64 , b ) 72 , c ) 101 , d ) 111 , e ) 128","""average = total runs / total wickets total runs after last match = 20.5 w + 52 total wickets after last match = w + 5 ( 20.5 w + 52 ) / ( w + 5 ) = 20.5 - 0.5 = 20 w = 96 so total wickets aftr last match = w + 5 = 101 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 6 hours , then the distance covered at 40 kmph is a ) 220 km , b ) 120 km , c ) 100 km , d ) 140 km , e ) none of these","""let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 6 or , x / 40 + ( 250 - x ) / 60 = 6 or , ( 3 x + 500 - 2 x ) / / 120 = 6 or 500 + x = 720 x = 220 answer : a"""
Provide a detailed solution to the given mathematical problem.,"if 7 ^ k + 7 ^ k = ( 7 ^ 9 ) ^ ( 7 ^ 9 ) - 7 ^ k , then k = ? a ) 11 / 3 , b ) 11 / 2 , c ) 242 , d ) 3 ^ 10 , e ) 7 ^ 11 - 1","""7 ^ k + 7 ^ k = ( 7 ^ 9 ) ^ 7 ^ 9 - 7 ^ k 7 * ( 7 ^ k ) = 7 ^ ( 49 * 7 ^ 9 ) = 7 ^ ( 7 ^ 2 * 7 ^ 9 ) = 7 ^ ( 7 ^ 11 ) 7 ^ k + 1 = 7 ^ ( 7 ^ 11 ) so k + 1 = 7 ^ 11 so k = 7 ^ 11 - 1 answer is e"""
Break down and solve the equation step by step.,"village x has a population of 74000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ? a ) 15 , b ) 16 , c ) 11 , d ) 18 , e ) 13","""let the population of two villages be equal after p years then , 74000 - 1200 p = 42000 + 800 p 2000 p = 32000 p = 16 answer is b ."""
Provide a detailed solution to the given mathematical problem.,"the sum of number of boys and girls in a school is 900 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ? a ) 50 , b ) 40 , c ) 60 , d ) 90 , e ) 70",we have x + x % of 900 = 900 x + x / 100 * 900 = 900 10 * x = 900 x = 90 answer is d
"Work through the equation methodically, ensuring clarity at each step.","the sale price sarees listed for rs . 560 after successive discount is 20 % and 30 % is ? a ) 321 , b ) 314 , c ) 316 , d ) 265 , e ) 162","""explanation : 560 * ( 80 / 100 ) * ( 70 / 100 ) = 314 answer : b"""
Break down and solve the equation step by step.,"a , b , c hired a car for rs . 720 and used it for 9 , 10 and 13 hours respectively . hire charges paid by b are : a ) rs 220 , b ) rs . 225 , c ) rs . 230 , d ) rs . 235 , e ) rs . 255","""a : b : c = 9 : 10 : 13 . hire charges paid by b = rs . 720 * 10 / 32 = rs . 225 . answer : b"""
Break down and solve the equation step by step.,"18 men shake hands with each other . maximum no of handshakes without cyclic handshakes . a ) 190 , b ) 153 , c ) 210 , d ) 220 , e ) 230","""1 st person will shake hand with 17 people 2 nd person will shake hand with 16 people 3 rd person will shake hand with 15 people . . . . . . total no . of handshakes = 17 + . . . + 3 + 2 + 1 = 17 * ( 17 + 1 ) / 2 = 153 or , if there are n persons then no . of shakehands = nc 2 = 18 c 2 = 153 answer : b"""
Provide a detailed solution to the given mathematical problem.,"the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 20 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ? a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 6 %","""let rate in r = 100 x then p = 75 x g = 100 y p = 80 y thus 75 x = 80 y or x = 1.06 y ans r = 106 y so increase = 6 % answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 50 minutes . the total distance is ? a ) 1 km , b ) 2 km , c ) 3.19 km , d ) 4 km , e ) 5 km","""c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 50 / 60 47 x / 60 = 50 / 60 = > x = 1.06 . total distance = 3 * 1.06 = 3.19 km ."""
"Work through the equation methodically, ensuring clarity at each step.","the data a and b are equal to the data subtracted c ; the data b is 3 times the data a ; if the data a is equal to 12 what is the sum of the data a , b and c ? a ) 86 , b ) 92 , c ) 84 , d ) 102 , e ) 96",the equations raised . a + b = c b = 3 a a = 12 then b = 36 and c = 48 a + b + c = 96 answer : e
Explain the solution process for the given equation.,"a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 14.70 less , he would have gained 30 % . find the cost of the article . a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70","""let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 14.70 when c . p = ( 100 * 14.70 ) / 21 = 70 answer : e"""
"Solve the problem systematically, showing each step clearly.","pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 5 : 00 am and pipe b at 6 : 00 am , at what time will the pool be full ? a ) 13 : 00 , b ) 14 : 00 , c ) 15 : 00 , d ) 17 : 00 , e ) 16 : 00","""pipe a fills the pool in 4 hrs . 1 hour' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour' s work : 1 / 6 together if they work , 1 hour' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 5 : 00 a . m and pipe b at 6 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 6 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 5 : 00 a . m , pool is full at 15 : 00 hrs answer : c"""
Break down and solve the equation step by step.,"an ant walks an average of 600 meters in 10 minutes . a beetle walks 25 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ? a ) 2.215 . , b ) 2.5 . , c ) 2.6 , d ) 2.7 , e ) 3.5 .","""the ant walks an average of 600 meters in 10 minutes 600 meters in 5 / 30 hours the beetle walks 25 % less distance = 600 - 150 = 450 meters in 10 minutes 0.450 km in 5 / 30 = 5 / 30 hours speed = 0.450 * 30 / 5 = 2.7 km / h i guess option d should be 2.7"""
Break down and solve the equation step by step.,"of the 3 - digit integers greater than 700 , how many have distinct digits ? a ) 216 , b ) 82 , c ) 80 , d ) 45 , e ) 36",three digit number can have only following 3 patterns : a . all digits are distinct ; b . two digits are alike and third is different ; c . all three digits are alike . we need to calculate b . b = total - a - c total numbers from 700 to 999 = 299 ( 3 - digit numbers greater than 700 ) ; a . all digits are distinct = 3 * 9 * 8 = 216 answer : a
"Solve the problem systematically, showing each step clearly.","a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 300 shares of the company' s stock ? a ) $ 92 , b ) $ 96 , c ) $ 156 , d ) $ 120 , e ) $ 240","""eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 300 - - > $ 156 answer is c"""
Break down and solve the equation step by step.,"a semicircle has a radius of 20 . what is the approximate perimeter of the semicircle ? a ) 50 , b ) 25 , c ) 86 , d ) 75 , e ) 102","""circumference of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 20 + 2 * 20 = 102.8 approximately 102 answer e"""
Provide a detailed solution to the given mathematical problem.,"find the value of 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] a ) 800 , b ) 500 , c ) 900 , d ) 1600 , e ) 2400","""answer 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3 x 4 x 4 x 50 = 2400 correct option : e"""
Break down and solve the equation step by step.,"the speed of a car is 120 km in the first hour and 70 km in the second hour . what is the average speed of the car ? a ) 72 kmph , b ) 75 kmph , c ) 95 kmph , d ) 80 kmph , e ) 82 kmph","""s = ( 120 + 70 ) / 2 = 95 kmph answer : c"""
Provide a detailed solution to the given mathematical problem.,"a man buys a cycle for rs . 1800 and sells it at a loss of 25 % . what is the selling price of the cycle ? a ) s . 1090 , b ) s . 1160 , c ) s . 1190 , d ) s . 1350 , e ) s . 1256","""s . p . = 75 % of rs . 1800 = rs . 75 / 100 x 1800 = rs . 1350 answer : d"""
"Solve the problem systematically, showing each step clearly.","in a bag , there are 5 green , 6 black and 7 red pens . one pen is picked up randomly . what is the probability that it is neither red nor green ? a ) 5 / 18 , b ) 7 / 18 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 5","explanation : neither red nor green means the pen drawn is black . total number of outcomes = ( 5 + 6 + 7 ) = 18 . number of favourable outcomes = 6 = number of black pens . hence , probability of the event = 6 / 18 = 1 / 3 . answer : c"
Explain the solution process for the given equation.,"a person buys an article at $ 500 . at what price should he sell the article so as to make a profit of 20 % ? a ) 560 , b ) 449 , c ) 600 , d ) 740 , e ) 460","""c 600 cost price = $ 500 profit = 20 % of 500 = $ 100 selling price = cost price + profit = 500 + 100 = 600"""
Break down and solve the equation step by step.,"the average score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 42 , then find the average for the last 4 matches . a ) 33.5 , b ) 33.5 , c ) 34.25 , d ) 35 , e ) none of these",solution required average = ( 38.9 x 10 ) - ( 42 x 6 ) / 4 = 137 / 4 = 34.25 answer c
Break down and solve the equation step by step.,"when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ? a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12","""guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c"""
"Work through the equation methodically, ensuring clarity at each step.","after decreasing 24 % in the price of an article costs rs . 760 . find the actual cost of an article ? a ) 1218 , b ) 2777 , c ) 1000 , d ) 2688 , e ) 1991","""cp * ( 76 / 100 ) = 760 cp = 10 * 100 = > cp = 1000 answer : c"""
Break down and solve the equation step by step.,"due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? a ) a ) 5.61 , b ) b ) 8 , c ) c ) 10 , d ) d ) 17.19 , e ) e ) 24","""old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 20 = 9 * 3 / 1 = 27 time difference = 17.19 ans : d"""
Provide a detailed solution to the given mathematical problem.,"a train 125 m long passes a man , running at 20 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ? a ) 36 , b ) 50 , c ) 28 , d ) 26 , e ) 65","""speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 20 ) km / hr . x - 20 = 45 = = > x = 65 km / hr answer : e"""
Explain the solution process for the given equation.,"5220 / ? * 15 = 2175 a ) 34 , b ) 36 , c ) 33 , d ) 42 , e ) 24","""b ( 5220 / ? ) * 15 = 2175 ? = ( 5220 * 15 ) / 2175 = > ? = 36"""
Provide a detailed solution to the given mathematical problem.,"each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 45 hours if harry and james were paid the same amount last week , how many hours did harry work last week ? a ) 35 , b ) 36 , c ) 37 , d ) 43 , e ) 39","""james worked for 41 hours hence he earned 40 * x + 5 * 2 x = 50 x dollars ; we know that harry also earned the same 50 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 20 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 20 x / 1.5 x = 13 additional hours , so harry worked for total of 30 + 13 = 43 hours . answer : d ."""
Break down and solve the equation step by step.,"a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252","""first , total ways to select for all boys and girls , i . e 12 ! / ( 6 ! * 6 ! ) = 12 * 11 * 10 * 9 * 8 * 7 / 6 * 5 * 4 * 3 * 2 = 924 then there are one two way girls can have all same colors , either white or black . the number of ways in which 6 girls can select 6 white balls = 6 c 6 = 1 the number of ways in which 6 girls can select 6 black balls = 6 c 6 = 1 therefore , total favorable outcomes / total outcomes = 2 / 924 = 1 / 462 d"""
Explain the solution process for the given equation.,"what number should replace the question mark ? 2 , 16 , 4 , 14 , 6 , 12 , - - - ? a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16","answer : a 2 , 16 , 4 , 14 , 6 , 12 , 8 ? there are two alternate sequences : + 2 and - 2 ."
Explain the solution process for the given equation.,"the cross - section of a cannel is a trapezium in shape . if the cannel is 16 m wide at the top and 4 m wide at the bottom and the area of cross - section is 700 sq m , the depth of cannel is ? a ) 76 , b ) 28 , c ) 27 , d ) 80 , e ) 70","""1 / 2 * d ( 16 + 4 ) = 700 d = 70 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 170 . if the ratio of his marks in english and maths is 1 : 4 , find his marks in science ? a ) 17 , b ) 77 , c ) 66 , d ) 55 , e ) 31",s : e = 1 : 3 e : m = 1 : 4 - - - - - - - - - - - - s : e : m = 1 : 4 : 12 1 / 17 * 170 = 17 answer : a
"Solve the problem systematically, showing each step clearly.","a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 30 sec . what is the length of the goods train ? a ) 299 , b ) 277 , c ) 350 , d ) 270 , e ) 281","""speed = 72 * 5 / 18 = 20 m / sec . time = 30 sec . let the length of the train be x meters . then , ( x + 250 ) / 30 = 20 x = 350 m . answer : c"""
Explain the solution process for the given equation.,"a teacher gave the same test to 3 history classes : a , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 90 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ? a ) 74 , b ) 75 , c ) 76 , d ) 77 , e ) 79","ratio is 4 : 6 : 5 , numbers are 4 x , 6 x , 5 x total scores of each class is ( 65 * 4 x + 6 x * 90 + 77 * 5 x ) = 260 x + 540 x + 385 x = 1185 x total number of students = 15 x average = 1185 x / 15 x = 79 e is the answer"
Provide a detailed solution to the given mathematical problem.,"a pipe takes a hours to fill the tank . but because of a leakage it took 2 times of its original time . find the time taken by the leakage to empty the tank a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 120 min","""pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 120 x = 120 min answer : e"""
"Solve the problem systematically, showing each step clearly.","a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 4.5 km long ? a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 9","""d = 25 * 60 + 4500 = 6000 m t = 6000 / 60 * 18 / 5 = 360 sec = 6 mins answer : d"""
Explain the solution process for the given equation.,"the price of a certain painting increased by 20 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ? a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 140 %","""assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.15 = 120 * 0.85 = 102 hence required answer = ( 102 / 100 ) * 100 % = 102 % answer is a ."""
Explain the solution process for the given equation.,"a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability t that a + b is prime ? a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9","""total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes t = 15 / 36 . answer : c ."""
Explain the solution process for the given equation.,"what is the rate percent when the simple interest on rs . 1200 amount to rs . 400 in 4 years ? a ) 8.33 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 1 %","""interest for 4 yrs = 400 interest for 1 yr = 100 interest rate = 100 / 1200 x 100 = 8.33 % answer : a"""
Break down and solve the equation step by step.,"find the area of a parallelogram with base 34 cm and height 18 cm ? a ) 198 cm 2 , b ) 384 cm 2 , c ) 510 cm 2 , d ) 612 cm 2 , e ) 680 cm 2","""area of a parallelogram = base * height = 34 * 18 = 612 cm 2 answer : d"""
Provide a detailed solution to the given mathematical problem.,"a 70 cm long wire is to be cut into two pieces so that one piece will be 2 / 3 th of the other , how many centimeters will the shorter piece be ? a ) 35 , b ) 20 , c ) 28 , d ) 36 , e ) 30","""1 : 2 / 3 = 3 : 2 2 / 5 * 70 = 28 answer : c"""
Provide a detailed solution to the given mathematical problem.,"an employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ? a ) 9 , b ) 13 , c ) 16 , d ) 20 , e ) 25",let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.25 x now we need to find number of hours worked so that x * y = 1.25 x * z i . e z = 4 / 5 y % decrease = ( y - 4 / 5 y ) / y * 100 = 100 / 5 = 20 % . thus my answer is d
Provide a detailed solution to the given mathematical problem.,"madhav ranks seventeenth in a class of thirtyone . what is his rank from the last ? a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17",( rank from top ) + ( rank from bottom ) - 1 = total students 17 + x - 1 = 31 x = 15 answer : c
Explain the solution process for the given equation.,"operation # is defined as adding a randomly selected two digit multiple of 4 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ? a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %","""any multiple of 4 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."""
Break down and solve the equation step by step.,"a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 70 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally . a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 224","""white : yellow = x : ( x + 70 ) = 8 : 13 - - > 13 x = 8 x + 560 - - > x = 112 . the total # of balls originally x + x = 112 + 112 = 224 . answer : e ."""
"Work through the equation methodically, ensuring clarity at each step.","how many zeros are there in 50 ! a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14","""to find the number of trailing zeroes in 50 ! factorial we must find the number of integral values in : 50 / 5 + 50 / 5 ^ 2 + 50 / 5 ^ 3 + . . . . . . . . . = 10 + 2 + 0 + 0 . . . . = 12 answer : c"""
Provide a detailed solution to the given mathematical problem.,"the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.50 , in which year will commodity x cost 90 cents more than the commodity y ? a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014","""the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 30 + 90 = $ 1.20 cents on commodity y , which will take 12 years . the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"the sum of four consecutive even numbers is 140 . what would be the largest number ? a ) 33 , b ) 38 , c ) 70 , d ) 123 , e ) 12","""let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x + 1 ) = 38 . answer : b"""
"Solve the problem systematically, showing each step clearly.","in a certain company , a third of the workers do not have a retirement plan . 60 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ? a ) 80 , b ) 95 , c ) 180 , d ) 120 , e ) 210","""set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,4 * 1 / 3 * x 120 = 12 / 30 x x = 300 300 - 120 = 180 answer c"""
Provide a detailed solution to the given mathematical problem.,"there are 870 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 145","""let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 870 . hence , we have m + f = 870 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 870 / 3 = 290 solving the three equations yields the solution f = 290 , m = 580 , and d = 290 . the number of female democratic participants equals half the female participants equals 290 / 2 = 145 . answer : e"""
Break down and solve the equation step by step.,"fred and sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 2 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ? a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 45",relative distance = 35 miles relative speed = 2 + 5 = 7 miles per hour time taken = 35 / 7 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c
Explain the solution process for the given equation.,"a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 20 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ? a ) 40 , b ) 135 , c ) 50 , d ) 55 , e ) 60",a - b = 120 miles b - c = 60 miles avg speed = 20 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 20 = 180 / 4 t t = 135 b - c = 135 mph answer b
Provide a detailed solution to the given mathematical problem.,"a man rows his boat 84 km downstream and 48 km upstream , taking 2 hours each time . find the speed of the stream ? a ) 6 kmph , b ) 5 kmph , c ) 9 kmph , d ) 8 kmph , e ) 1 kmph","""speed downstream = d / t = 84 / ( 2 ) = 42 kmph speed upstream = d / t = 48 / ( 2 ) = 24 kmph the speed of the stream = ( 42 - 24 ) / 2 = 9 kmph answer : c"""
Explain the solution process for the given equation.,"solve for x and check : 15 x = 165 a ) 98 , b ) 165 , c ) 180 , d ) 253 , e ) none of these","solution : dividing each side by 15 , we obtain ( 15 x / 15 ) = ( 165 / 15 ) therefore : x = 11 check : 15 x = 165 ( 15 * 11 ) = 165 165 = 165 answer : b"
"Work through the equation methodically, ensuring clarity at each step.","find the area of a parallelogram with base 48 cm and height 36 cm ? a ) 1730 cm 2 , b ) 1728 cm 2 , c ) 1870 cm 2 , d ) 1890 cm 2 , e ) 668 cm 2","""area of a parallelogram = base * height = 48 * 36 = 1728 cm 2 answer : b"""
Explain the solution process for the given equation.,"a manufacturing company has 15 % cobalt , 25 % led and 60 % of copper . if 5 kg of led is used in a mixture how much copper we need to use a ) 12 kg , b ) 13 kg , c ) 22 kg , d ) 14 kg , e ) 15 kg",25 % = 5 kg 100 % = 20 kg 60 % of 20 kg = 12 kg 12 kg answer : a
"Solve the problem systematically, showing each step clearly.","find the value for x from below equation : x / 2 = - 2 ? a ) - 6 , b ) 1 , c ) - 2 , d ) - 3 , e ) - 4","""1 . multiply both sides by 2 : x * 2 / 2 = - 2 / 2 simplify both sides : x = - 4 e"""
Break down and solve the equation step by step.,"if the product of 12 integers is negative , at most how many of the integers can be negative ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 11","""the product of 12 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 11 correct option : e"""
Provide a detailed solution to the given mathematical problem.,"in the set of positive integers from 1 to 80 , what is the sum of all the odd multiples of 5 ? a ) 180 , b ) 245 , c ) 320 , d ) 260 , e ) 270","""reduce to 1 - 80 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 are valid multiples . add them - - > 320 c"""
Provide a detailed solution to the given mathematical problem.,"the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 124 different signs . if the company used 122 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 124 signs ? a ) 246 , b ) 248 , c ) 492 , d ) 15,128 , e ) 30,256","""ok let' s take a crack at this one . so basically we have 144 ^ 2 - 142 ^ 2 so then ( 144 + 142 ) ( 144 - 142 ) ( 246 ) ( 2 ) = 492 answer : c"""
Break down and solve the equation step by step.,"if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 58 , then * is equal to : a ) - 29 , b ) - 19 , c ) 19 , d ) 29 , e ) 39","""45 - [ 28 - { 37 - ( 15 - * ) } ] = 58 = > 45 - [ 28 - { 37 - 15 + * } ] = 58 45 - [ 28 - 37 + 15 - * ] = 58 = > 45 [ 43 - 37 - * ] = 58 45 - [ 6 - * ] = 58 = > 45 - 6 + * = 58 39 + * = 58 = > * = 58 - 39 = 19 answer : c"""
Provide a detailed solution to the given mathematical problem.,"if xy denotes x is raised to the power y , find the last two digits of 19413844 + 19714181 a ) 154 , b ) 677 , c ) 784 , d ) 148 , e ) 132","""1941 ^ 3844 unit digit = 1 ^ 4 = 1 10 th digit = 4 * 4 = 16 = 2 means last two digit = 61 and 1971 ^ 4181 unit digit = 1 10 th digit = 7 * 1 = 7 mean last two digit = 71 hence , 71 + 61 = 132"""
Provide a detailed solution to the given mathematical problem.,"a certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water . if between 8 and 15 cubic centimeters of the cube' s volume is above the surface of the water , then the length of a side of the cube is approximately a ) 3 , b ) 4 , c ) 7 , d ) 8 , e ) 9","""if sides are 7 , vol = 7 ^ 3 = 343 80 % = 274.4 , 85 % = 291.55 so vol above water , between 68.6 and 51.45 - - > too big if side are 4 , vol = 64 80 % = 51.2 , 85 % = 54.4 vol above water between 12.8 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 80 % = 100 , . 85 % = 106.25 vol above water between 18.75 - 25 ( sides are 4 cubic centimeters ) b"""
Explain the solution process for the given equation.,"a sum of 12,500 amounts to 15,500 in 4 years at the rate of simple interest . what is the rate of interest ? a ) 2 % , b ) 1 % , c ) 6 % , d ) 5 % , e ) 8 %",c 6 % s . i . = ( 15500 - 12500 ) = 3000 . rate = ( 100 x 3000 ) / ( 12500 x 4 ) % = 6 %
Provide a detailed solution to the given mathematical problem.,"in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van' s tank is 65 liters and a truck' s tank is 120 % bigger and they are all empty - ? a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 312.12 $","""mini van cost = 65 * 0.6 + 2.05 truck capacity = 65 ( 1 + 120 / 100 ) = 143 lts . cost of truck = 143 + 0.6 + 2.05 total cost = 3 * 41.05 ( car ) + 2 * 87.85 ( truck ) = 298.85 answer : d"""
Provide a detailed solution to the given mathematical problem.,"the sector of a circle has radius of 42 cm and central angle 135 o . find its perimeter ? a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 183 cm","""perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 42 ) + 2 ( 42 ) = 99 + 84 = 183 cm answer : e"""
Explain the solution process for the given equation.,"an escalator moves towards the top level at the rate of 8 ft . sec and its length is 160 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length . a ) 14 sec , b ) 10 sec , c ) 16 sec , d ) 8 sec , e ) 9 sec","""time taken to cover the entire length = tot . dist / resultant speed = 160 / ( 8 + 2 ) = 16 sec answer : c"""
Provide a detailed solution to the given mathematical problem.,"in a class of 78 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ? a ) 26 , b ) 27 , c ) 24 , d ) 18 , e ) 11","""explanation : you could solve this by drawing a venn diagram . a simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking french to find the number taking only french . likewise find those taking only german . then we have : total = only french + only german + both + neither 78 = ( 41 - 9 ) + ( 22 - 9 ) + 9 + neither . not enrolled students = 24 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","if each side of a square is increased by 50 % , the ratio of the area of the resulting square to the area of the given square is : ['a ) 5 : 4','b ) 9 : 4','c ) 4 : 5','d ) 4 : 9','e ) 1 : 2']","let , each side = a . then , original area = a 2 . new side = 150 a / 100 = 3 a / 2 . new area = 9 a 2 / 4 . required ratio = 9 a 2 / 4 : a 2 = 9 : 4 answer : b"
"Solve the problem systematically, showing each step clearly.","a fill pipe can fill 1 / 2 of cistern in 30 minutes . in how many minutes , it can fill 1 / 2 of the cistern ? a ) 15 min , b ) 20 min , c ) 25 min , d ) 30 min , e ) 35 min","""required time = 30 * 2 * 1 / 2 = 30 minutes answer is d"""
"Solve the problem systematically, showing each step clearly.","the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 46,875 , how much profit did the business make ? a ) $ 55,000 , b ) $ 75,000 , c ) $ 95,000 , d ) $ 115,000 , e ) $ 125,000","""let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 46875 p = $ 75,000 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","in the coordinate plane , one of the vertices of a square is the point ( - 3 , - 4 ) . if the diagonals of that square intersect at point ( 5 , 3 ) , what is the area of that square ? a ) 100 , b ) 169 , c ) 225 , d ) 324 , e ) 256","""one point ( - 3 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 3 - 5 = - 8 is the midpoint of the square - - > whole side 16 , 16 * 16 = 256 e"""
"Work through the equation methodically, ensuring clarity at each step.","a man rows his boat 90 km downstream and 40 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ? a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 15","""speed downstream = d / t = 90 / ( 2 1 / 2 ) = 36 kmph speed upstream = d / t = 40 / ( 2 1 / 2 ) = 16 kmph the speed of the stream = ( 36 - 16 ) / 2 = 15 kmph answer : e"""
"Solve the problem systematically, showing each step clearly.","for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 3,675 , what is the least possible value of k ? a ) 12 , b ) 14 , c ) 15 , d ) 21 , e ) 25","""we basically need 5,5 , 3,7 and 7 in the number . 14 ! , has 3 , 5 , 7 , 10 , 14 now 10 = 2 x 5 14 = 2 x 7 cross check : k ! = 3675 * m ( m is a positive integer ) k ! = 3 * 5 * 5 * 7 * 7 14 ! has all the numbers above . . therefore b . . ! answer : b"""
Explain the solution process for the given equation.,"mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 10 ft how many poles do he need ? a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 65","""if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 10 feet hence no of poles = 600 / 10 = 60 answer : d"""
Explain the solution process for the given equation.,"how many of the positive factors of 25 , 15 and how many common factors are there in numbers ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""factors of 25 - 1 , 5 , and 25 factors of 15 - 1 , 3 , 5 and 15 comparing both , we have three common factors of 45,16 - 2 answer b"""
"Solve the problem systematically, showing each step clearly.","two trains each 260 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ? a ) 15 sec , b ) 19 sec , c ) 12.48 sec , d ) 10 sec , e ) 11 sec","""explanation : d = 260 m + 260 m = 520 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 520 * 3 / 125 = 12.48 sec answer : option c"""
"Work through the equation methodically, ensuring clarity at each step.","a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 105 ounces of grape juice , how many ounces is the drink total ? a ) 220 , b ) 250 , c ) 280 , d ) 300 , e ) 340","""let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 105 x = 300 therefore there are a total of 300 ounces in the drink . the answer is d ."""
Explain the solution process for the given equation.,"mary' s income is 40 percent more than tim' s income , and tim' s income is 40 percent less than juan' s income . what percent of juan' s income is mary' s income ? a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 84 %","""juan' s income = 100 ( assume ) ; tim' s income = 60 ( 40 percent less than juan' s income ) ; mary' s income = 84 ( 40 percent more than tim' s income ) . thus , mary' s income ( 84 ) is 84 % of juan' s income ( 100 ) . answer : e ."""
Break down and solve the equation step by step.,"on dividing number by 56 , we get 29 as remainder . on dividing the same number by 8 , what will be the remainder ? a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8","let x be the number and y be the quotient . then , x = 357 * y + 39 = ( 17 * 21 * y ) + ( 17 * 2 ) + 5 = 17 * ( 21 y + 2 ) + 5 . required remainder = 5 . answer : b"
"Work through the equation methodically, ensuring clarity at each step.","if the sides of a triangle are 28 cm , 24 cm and 15 cm , what is its area ? a ) 180 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 886 cm 2","""the triangle with sides 28 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction w of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ? a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14","""if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus w = 11 / 14 of the remaining votes must be against . answer : a ."""
"Solve the problem systematically, showing each step clearly.","the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 3200 meters per second , what was the speed , in meters per second , when the stopwatch was started ? a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32","""let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 3200 x = ( 2 ^ 7 * 25 ) / 2 ^ 9 = 25 / 4 the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"in a certain company , the ratio of male to female employees is 7 : 8 . if 3 more men were hired , this ratio would increase to 8 : 9 . how many male employees are there in the company ? a ) 6 , b ) 21 , c ) 27 , d ) 189 , e ) 192","another approach is to use two variables . let m = present number of males let f = present number of females the ratio of male to female employees is 7 : 8 so , m / f = 7 / 8 cross multiply to get 7 f = 8 m if 3 more men were hired , this ratio would increase to 8 : 9 so , ( m + 3 ) / f = 8 / 9 cross multiply to get 9 ( m + 3 ) = 8 f expand : 9 m + 27 = 8 f we now have a system of two equations and two variables : 7 f = 8 m 9 m + 27 = 8 f solve to get : m = 189 and f = 216 answer : d"
Provide a detailed solution to the given mathematical problem.,"find the compound interest on $ 26,000 at 20 % per annum for 9 months , compounded quarterly a ) 2532.93 , b ) 2552.26 , c ) 2524.23 , d ) 4098.25 , e ) 2512.23","""principal = $ 26000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 26000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 30098.25 ci . = $ ( 30098.25 - 26000 ) = $ 4098.25 answer d ."""
Break down and solve the equation step by step.,"what is the least common multiple of 1227 and 40 a ) 8521 , b ) 1080 , c ) 368 , d ) 8979 , e ) 6584",factors of 12 = 2 * 2 * 3 factors of 27 = 3 * 3 * 3 factors of 40 = 2 * 2 * 2 * 5 thus the l . c . m is 2 ^ 3 * 3 ^ 3 * 5 = 1080 the answer is b
Provide a detailed solution to the given mathematical problem.,"a car is running at a speed of 96 kmph . what distance will it cover in 14 sec ? a ) 378 m , b ) 350 m , c ) 380 m , d ) 200 m , e ) 250 m","""speed = 96 kmph = 96 * 5 / 18 = 27 m / s distance covered in 14 sec = 27 * 14 = 378 m answer is a"""
Provide a detailed solution to the given mathematical problem.,"a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 10,500 sedans in anytown , how many motorcycles are there ? a ) 1260 , b ) 3000 , c ) 3600 , d ) 4200 , e ) 5200","""let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 10500 = > 7 x = 10500 = > x = 1500 total number of motorcycles = 2 x = 2 * 1500 = 3000 answer b"""
"Solve the problem systematically, showing each step clearly.","fonzie , aunt bee and lapis paid $ 7000 , $ 8000 and $ 9000 respectively to buy a map to capt . plaidstache' s treasure . when they found it , the treasure turned out to be worth a cool $ 900000 . how much of it should lapis get ? a ) $ 300000 , b ) $ 320000 , c ) $ 335000 , d ) $ 336500 , e ) $ 337500","a = 7000 b = 8000 c = 9000 a share 7 parts , b share 8 parts & c share 9 parts total 24 parts - - - - - > 900000 - - - - > 1 part - - - - - - - > 37500 c share = 9 parts - - - - - > 337500 e"
"Solve the problem systematically, showing each step clearly.","a number divided by 44 leaves remainder 17 what is the remainder when same number divided by 8 a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11","""add 44 + 17 = 61 now 61 divided by 8 so we get 5 as reaminder answer : a"""
"Solve the problem systematically, showing each step clearly.","in a class of 69 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ? a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54","""formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 69 54 + not = 69 not = 69 - 54 = 15 so answer is b"""
"Work through the equation methodically, ensuring clarity at each step.","a man' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 168 , how many hours overtime did he work ? a ) 8 , b ) 21 , c ) 14 , d ) 12 , e ) 15","""answer is : b at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 168 - $ 120 = $ 48 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 48 / $ 6 = 8"""
Explain the solution process for the given equation.,"an assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ? a ) 38 , b ) 40 , c ) 42 , d ) 45 , e ) 50",the time to produce the first 60 cogs is 60 / 36 = 5 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 8 / 3 ) hours = 45 cogs per hour . the answer is d .
"Work through the equation methodically, ensuring clarity at each step.","a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 12000 . a' s share is ? a ) 2500 , b ) 3500 , c ) 4500 , d ) 2800 , e ) 4000","""x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 12000 = 4000 answer : e"""
Explain the solution process for the given equation.,"what is the unit digit in ( 4137 ) 754 ? a ) 6 , b ) 5 , c ) 9 , d ) 13 , e ) 15","""explanation : unit digit in ( 4137 ) 754 = unit digit in { [ ( 4137 ) 4 ] 188 x ( 4137 ) 2 } = unit digit in { 292915317923361 x 17114769 } = ( 1 x 9 ) = 9 c"""
Provide a detailed solution to the given mathematical problem.,"the average of 55 results is 28 and the average of other 28 results is 55 . what is the average of all the results ? a ) 37 , b ) 25 , c ) 48 , d ) 50 , e ) none","""answer sum of 83 result = sum of 55 result + sum of 28 result . = 30 x 20 + 20 x 30 = 3080 correct option : a"""
Break down and solve the equation step by step.,"one day a car rental agency rented 3 / 4 of its cars , including 3 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ? a ) 29 / 30 , b ) 24 / 25 , c ) 19 / 20 , d ) 14 / 15 , e ) 9 / 10","""the cars with cd players which were not rented is ( 2 / 5 ) ( 3 / 5 ) = 6 / 25 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 6 / 25 ) / ( 1 / 4 ) = 24 / 25 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","how much interest will $ 10,000 earn in 9 months at an annual rate of 3 % ? a ) $ 250 , b ) $ 350 , c ) $ 450 , d ) $ 550 , e ) $ 225","""soln : - 9 months = 3 / 4 of year ; 3 % = 3 / 100 = 3 / 100 ; $ 10,000 ( principal ) * 3 / 100 ( interest rate ) * 3 / 4 ( time ) = $ 225 . answer : e"""
Provide a detailed solution to the given mathematical problem.,"in a group of cows and hens , the number of legs are 30 more than twice the number of heads . the number of cows is a ) 15 , b ) 7 , c ) 10 , d ) 12 , e ) 14","""explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 30 4 x + 2 y = 2 x + 2 y + 30 2 x = 30 x = 15 answer : a"""
"Solve the problem systematically, showing each step clearly.","when n is divided by 24 , the remainder is 4 . what is the remainder when 3 n is divided by 8 ? a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7","""let n = 4 ( leaves a remainder of 4 when divided by 24 ) 3 n = 3 ( 4 ) = 12 , which leaves a remainder of 4 when divided by 8 . answer b"""
Provide a detailed solution to the given mathematical problem.,"from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 6 kilometers per hour , while ferry q takes a route that is two times longer . if ferry p is slower than ferry q by 3 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""the distance traveled by ferry p is 18 km . then the distance traveled by ferry q is 36 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 36 / 9 = 4 hours , which is 1 hour more than ferry p . the answer is a ."""
Break down and solve the equation step by step.,"a pineapple costs rs 9 each and a watermelon costs rs . 6 each . if i spend rs 51 on total what is the number of pineapple i purchased ? a ) 6 , b ) 7 , c ) 5 , d ) 3 , e ) 2","""5 * 9 + 6 = 51 5 pineapples answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","a man can buy a new house in 4 years with all of his earnings . but he spend the same amount in household expenses in 8 years and for savings in 12 years . how many time needed for buying the house ? a ) 12 , b ) 20 , c ) 30 , d ) 15 , e ) 24",his savings in 1 year = 1 / 4 - ( 1 / 8 + 1 / 12 ) = 1 / 24 he can buy a new house in 24 years answer : e
Provide a detailed solution to the given mathematical problem.,"linda spent 5 / 6 of her savings on furniture and the rest on a tv . if the tv cost her $ 500 , what were her original savings ? a ) $ 9000 , b ) $ 3000 , c ) $ 6000 , d ) $ 7000 , e ) $ 8000","""if linda spent 5 / 6 of her savings on furniture , the rest 6 / 6 - 5 / 6 = 1 / 6 on a tv but the tv cost her $ 500 . so 1 / 6 of her savings is $ 500 . so her original savings are 6 times $ 500 = $ 3000 correct answer b"""
Explain the solution process for the given equation.,"how many odd numbers between 10 and 2000 are the squares of integers ? a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20","""the numbers are the squares of 5 , 7 , 9 , . . . , 43 which includes 20 numbers . the answer is e ."""
Explain the solution process for the given equation.,"one day , raviraj left home and cycled 20 km southwards , turned right and cycled 10 km and turned right and cycled 20 km and turned left and cycled 20 km . how many kilometres will he have to cycle to reach his home straight ? a ) 50 , b ) 30 , c ) 40 , d ) 60 , e ) 80","raviraj starts from home at a , moves 20 km in south upto b . then he turns right and moves 10 km upto c , then he turns right and moves 20 km upto d , then he turns lefts and moves 20 km upto e . so from image it is clear that , if he moves straight then he will have to move ad + de , ad = bc = 10 km so , he will have to move 10 + 20 = 30 km answer b"
Provide a detailed solution to the given mathematical problem.,"the positive numbers w , x , y , and z are such that x is 10 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ? a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %","""my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 16 - answer b"""
"Work through the equation methodically, ensuring clarity at each step.","speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7200 km and comes back to the starting point . the total time taken by him is : a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours","""explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7200 / 18 + 7200 / 14 = 400 + 514.2 = 914.2 hours answer : option a"""
Provide a detailed solution to the given mathematical problem.,"while working alone at their respective constant rates , server p uploads 480 files in 4 hours and server y uploads 480 files in 8 hours . if all files uploaded by these servers are the same size , how long would it take the two servers , working at the same time and at their respective constant rates , to process a total of 480 files ? a ) 2 hr , b ) 2 hr 20 min , c ) 2 hr 40 min , d ) 5 hr 40 min , e ) 6 hr",server p processes 480 / 4 files per hour = 120 per hour server y processes 180 / 8 files per hour = 60 per hour total files processed per hour when p and y work together = 120 + 60 per hour = 180 files per hour 480 / 180 = 2 2 / 3 hours = c
"Solve the problem systematically, showing each step clearly.","in the third grade of windblown school there are 90 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ? a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .","""total = 90 failed in math = 90 / 3 = 30 failed in literature = 90 / 6 = 15 the least failed in both can be 0 while max can be 15 answer a"""
Break down and solve the equation step by step.,". a car covers a distance of 742 km in 7 hours . find its speed ? a ) 104 , b ) 55 , c ) 148 , d ) 150 , e ) 159","""742 / 5 = 148 kmph answer : c"""
Provide a detailed solution to the given mathematical problem.,"25 people went to a hotel for combine dinner party 15 of them spent rs . 5 each on their dinner and rest spent 4 more than the average expenditure of all the 25 . what was the total money spent by them . a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 158.25 , e ) none of these","""solution : let average expenditure of 25 people be x . then , 25 x = 15 * 5 + 10 * ( x + 4 ) ; or , 25 x = 15 * 5 + 10 x + 20 ; or , x = 6.33 ; so , total money spent = 6.33 * 25 = rs . 158.25 . answer : option d"""
Explain the solution process for the given equation.,"in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 200 m . then , a wins by : a ) 60 m , b ) 100 m , c ) 43 m , d ) 20 m , e ) 23 m","""to reach the winning post a will have to cover a distance of ( 500 - 200 ) m , i . e . , 300 m . while a covers 3 m , b covers 4 m . while a covers 300 m , b covers 4 x 300 / 3 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 100 m behind . a wins by 100 m . answer : b"""
"Solve the problem systematically, showing each step clearly.","what is the probability that the sum of two dice will yield a 7 , and then when both are thrown again , their sum will again yield a 7 ? assume that each die has 6 sides with faces numbered 1 to 6 . a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3","""in order to get the sum of the two dices to be 7 , there are six combinations that satisfy this requirement . 1 + 6 = 7 2 + 5 = 7 3 + 4 = 7 4 + 3 = 7 5 + 2 = 7 6 + 1 = 7 each combination has 1 / 36 of probability of occurrence , or in total 6 / 36 for the six combinations , which is 1 / 6 . in order to get the probability of this occurring twice in a row we multiply 1 / 6 * 1 / 6 and we get 1 / 36 . the answer is b ."""
"Solve the problem systematically, showing each step clearly.","the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and dinley have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ? a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54","""if steve and dinley submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that' s the combinedno discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."""
"Work through the equation methodically, ensuring clarity at each step.","a train 420 m long is running at a speed of 48 km / hr . in what time will it pass a bridge 60 m long ? a ) 40 sec , b ) 36 sec , c ) 60 sec , d ) 48 sec , e ) 18 sec","""total length = 420 + 60 = 480 speed = 48 km / h = ( 48 * 5 ) / 18 = 40 / 3 m / s time = ( 480 * 3 ) / 40 = 36 sec . answer : b"""
"Solve the problem systematically, showing each step clearly.","what is the sum of 60 consecutive integers from - 30 inclusive , in a increasing order ? a ) - 29 , b ) 29 , c ) - 30 , d ) 30 , e ) 60",from - 39 to - 1 - - > 30 nos . zero - - > 1 number from + 1 to + 29 - - > 29 nos . when we add up nos . from - 30 to + 29 sum will be - 30 for total 60 numbers . c is the answer .
Explain the solution process for the given equation.,"two pipes a and b can fill a tank in 20 and 30 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ? a ) 12 min , b ) 15 min , c ) 25 min , d ) 50 min , e ) 55 min","""part filled by a in 1 min = 1 / 20 part filled by b in 1 min = 1 / 30 part filled by ( a + b ) in 1 min = ( 1 / 20 + 1 / 30 ) = 1 / 12 so both pipes can fill the tank in 12 minutes . answer : a"""
Explain the solution process for the given equation.,"a spider web consists of 3 concurrent lines forming radial support for 20 concentric regular hexagon . the hexagon vertices are 5 mm from their immidiate neighbour . if the innermost hexagon has a side length 3 mm how many meters is the length of the entire web including the 3 diagonals ? ['a ) 7.354 m','b ) 8.354 m','c ) 6.354 m','d ) 9.354 m','e ) 5.354 m']",for perimeter of all hexagon = 6 * ( 3 + 8 + 13 + . . . . . . . . . . . 20 th term . ) sum will be 6060 mm and for length of one diagonal find 20 th term = 98 so total length = 6060 + 294 = 6354 mm = 6.354 m answer : c
"Work through the equation methodically, ensuring clarity at each step.","36 . a 240 m long train crosses a platform of equal length in 27 s . what is the speed of the train in km / h ? a ) 48 , b ) 60 , c ) 56 , d ) 64 , e ) 68","by the formula , speed = distance / time = ( 240 + 240 ) / 27 x ( 18 / 5 ) = 480 / 27 x 18 / 5 = 64 km / h answer : d"
"Solve the problem systematically, showing each step clearly.","if the average ( arithmetic mean ) of 5 b , 6 b + 47 b , 8 b - 4 and 2 b is 140 , what is the value of b ? a ) 20 , b ) 22 , c ) 25 , d ) 30 , e ) 48","am of 5 b , 6 b + 47 b , 8 b - 4 and 2 b = 5 b + 6 b + 4 + 7 b + 8 b - 4 + 2 b = 28 b / 5 given that 28 b / 5 = 140 b = 25 answer is c"
"Solve the problem systematically, showing each step clearly.","two coins are tossed . find the probability of at most 2 tails ? a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 , e ) 3 / 4","""n ( s ) = 2 ^ 2 = 4 . . . . ( 2 coins are tossed ) let e is the event of getting at most 2 tails n ( e ) = hh , tt , ht , th = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 4 = 1 ans - d"""
Explain the solution process for the given equation.,"the difference between compound interest and simple interest on a sum for 3 years at 10 % p . a . is rs . 124 find the sum . a ) rs . 5000 , b ) rs . 4000 , c ) rs . 6000 , d ) rs . 8000 , e ) rs . 7000","""for 3 years , we know c . i - s . i = p ( r / 100 ) ^ 3 + 3 ( r / 100 ) ^ 2 so , putting all values we have , 124 = p ( ( 10 / 100 ) ^ 3 + 3 ( 10 / 100 ) ^ 2 ) = 4000 answer : b"""
Explain the solution process for the given equation.,"in what time will a train 95 m long cross an electric pole , it its speed be 214 km / hr ? a ) 1.6 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec","""speed = 214 * 5 / 18 = 59 m / sec time taken = 95 / 59 = 1.6 sec . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","a football team lost 5 yards and then gained 7 . what is the team' s progress ? a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8","for lost , use negative . for gain , use positive . progress = - 5 + 7 = 2 yards a"
"Work through the equation methodically, ensuring clarity at each step.","by selling an article for $ 180 , a person gains $ 30 . what is the gain % ? a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %","""s . p . = $ 180 gain = $ 30 c . p . = 180 - 30 = 150 gain % = 30 / 150 * 100 = 20 % answer is d"""
"Work through the equation methodically, ensuring clarity at each step.","at milk factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ? a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8","at milk factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a ."
Explain the solution process for the given equation.,"a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is : a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 6 : 5","""explanation : dog : hare = ( 2 * 3 ) leaps of hare : 3 leaps of hare = 6 : 5 . answer : e ) 6 : 5"""
"Work through the equation methodically, ensuring clarity at each step.","the jogging track in a sports complex is 660 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ? a ) 5.29 min , b ) 5.28 min , c ) 5.08 min , d ) 4.8 min , e ) 5.988 min","""clearly , the two will meet when they are 660 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 660 m apart , they take ( 100 / 825 * 660 / 1000 ) hrs = ( 660 / 8250 * 60 ) min = 4.8 min . answer : d"""
Explain the solution process for the given equation.,"when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 76.4 , what is the value of y ? a ) 20 , b ) 22 , c ) 23 , d ) 24 , e ) 25","""when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 76.4 - - > x = 76 y + 0.4 y ( so q above equals to 76 ) ; 0.4 y = 8 - - > y = 20 . answer : a ."""
"Work through the equation methodically, ensuring clarity at each step.","a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 8 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ? a ) $ 54.00 , b ) $ 89.60 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80","""correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.08 ( $ 1120 ) = $ 89.60 . the correct answer is b ."""
Provide a detailed solution to the given mathematical problem.,"excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ? a ) 17 , b ) 83 , c ) 12 , d ) 83 , e ) 28","""explanation : t = 13 / 45 * 60 = 17 answer : option a"""
Provide a detailed solution to the given mathematical problem.,"a profit of rs . 800 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ? a ) s . 260 , b ) s . 160 , c ) s . 360 , d ) s . 50 , e ) s . 90","""a profit of rs . 800 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 480 and 320 . difference in profit share = 480 - 320 = 160 answer : b"""
"Solve the problem systematically, showing each step clearly.","how many 4 digit numbers divisible by 4 can be made with digits 1 , 2 , 3 , 4 , 5 if the repetition of digits is not allowed ? a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50","a number is divisible by 4 if the last 2 numbers are divisible by 4 ( divisible by 2 twice ) ending can be 12 24 32 42 52 case : ending with 12 , 24,32 , 42,54 first digit - 3 choices second digit - 2 choices third digit - 1 choice fourth digit - 1 choice 6 possible choices for each ending ( e . g . 3412,3512 , 3212 , 4512 , 5312 , 5412 ) total number of 4 digit numbers divisible by 4 = 6 * 5 = 30 answer : c"
"Work through the equation methodically, ensuring clarity at each step.","the average weight of 10 students decreases by 6 kg when one of them weighing 120 kg is replaced by a new student . the weight of the student is a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these","""explanation : let the weight of student be x kg . given , difference in average weight = 6 kg = > ( 120 - x ) / 10 = 6 = > x = 60 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 15 % of the car' s price up to a certain price level . if the car' s price is higher than the first tier' s level , the tax on the portion of the price that exceeds this value is 10 % . if ron imported a $ 15,000 imported car and ended up paying $ 1800 in taxes , what is the first tier' s price level ? a ) $ 7000 , b ) $ 6500 , c ) $ 6050 , d ) $ 6000 , e ) $ 6100","""let t be the tier price , p be total price = 15000 per the given conditions : 0.15 t + 0.10 ( p - t ) = 1800 0.15 t + 0.10 * 15000 - 0.10 t = 1800 0.05 t + 1500 = 1800 0.05 t = 1800 - 1500 = 300 t = 300 / 0.05 = 6000 answer d"""
Break down and solve the equation step by step.,"in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is : a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) none of these","""explanation : let b' s present age = x years . then , a' s present age = ( x + 9 ) years . ( x + 9 ) + 10 = 2 ( x - 10 ) = > x + 19 = 2 x - 20 = > x = 39 . answer : c"""
"Solve the problem systematically, showing each step clearly.","if x + y = 2 x + 2 z , x - 2 y = 2 z and x + y + z = 21 , what is the value of y / z ? a ) - 4 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 2.5 .",x + y = 2 x + 2 z y = x + 2 z - - - - - - - - - - 1 x - 2 y = 2 z x - 2 z = 2 y - - - - - - - - - 2 subtracting equation 1 from equation 2 - 4 z = y y / z = - 4 a is the answer
Explain the solution process for the given equation.,"following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ? a ) 11 . , b ) 12 , c ) 13 , d ) 14 , e ) 14.5","""let the candy and soda before the increase be c and s respectively so increased price of can = c ( 1 + 25 / 100 ) = 10 - - - - - - - - - - - > c = 8 increase price of soda : s ( 1 + 1 / 2 ) = 6 - - - - - - - - - - - > s = 4 hence total = 8 + 4 = 12 . . hence answer : b"""
Provide a detailed solution to the given mathematical problem.,"a and b started a business investing rs . 90,000 and rs 30,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ? a ) 9 : 2 , b ) 3 : 1 , c ) 18 : 20 , d ) 18 : 4 , e ) 17 : 4","""a : b = 90000 : 30000 = 9 : 3 = 3 : 1 answer : b"""
Break down and solve the equation step by step.,"set a contains all the even numbers between 22 and 70 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ? a ) 600 , b ) 800 , c ) 1000 , d ) 1200 , e ) 1400","""each term in set b is 40 more than the corresponding term in set a . the difference of the sums = 25 * 40 = 1000 . the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"find the area of trapezium whose parallel sides are 10 cm and 18 cm long , and the distance between them is 15 cm . a ) 287 cm 2 , b ) 785 cm 2 , c ) 285 cm 2 , d ) 785 cm 2 , e ) 210 cm 2","""explanation : area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 10 + 18 ) * ( 15 ) = 210 cm 2 answer : option e"""
"Work through the equation methodically, ensuring clarity at each step.","how much time does a train 125 metres long running at 60 km / hr take to pass a pole ? a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s","""explanation : 60 km / hr = 60 * 5 / 18 = 16.67 m / s speed = distance / time ; v = d / t 16.67 = 125 / t t = 7.5 s answer : c"""
Provide a detailed solution to the given mathematical problem.,"find the 25 % of rs . 300 . a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 75","""explanation : 25 % of 300 = > 25 / 100 * 300 = rs . 75 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","the distance from steve' s house to work is 28 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve' s speed on the way back from work ? a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .","""time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 28 km = > speed = 14 kmph c"""
Provide a detailed solution to the given mathematical problem.,"there are 9 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ? a ) 97 , b ) 99 , c ) 101 , d ) 103 , e ) 105",the total number of ways to form a team of 4 is 9 c 4 = 126 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 7 c 2 = 21 . the number of ways to form an acceptable team is 126 - 21 = 105 . the answer is e .
Explain the solution process for the given equation.,"the compound ratio of 5 : 6 , 3 : 2 and 4 : 5 ? a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 2 , d ) 1 : 1 , e ) 1 : 7","""5 / 6 * 3 / 2 * 4 / 5 = 1 / 1 1 : 1 answer : d"""
Break down and solve the equation step by step.,"the digit in units place of the product 81 x 82 x . . . . . x 89 is a ) 0 , b ) 2 , c ) 6 , d ) 8 , e ) 9",sol . required digit = unit digit in ( 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 ) = 0 . answer a
Explain the solution process for the given equation.,"a grocer has a sale of rs . 5266 , rs . 5744 , rs . 5864 , rs . 6122 and rs . 6588 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5750 ? a ) 4016 , b ) 4076 , c ) 4816 , d ) 4916 , e ) 5916","""total sale for 5 months = rs . ( 5266 + 5744 + 5864 + 6122 + 6588 ) = rs . 29584 . required sale = rs . [ ( 5750 x 6 ) - 34500 ] = rs . ( 34500 - 29584 ) = rs . 4916 . answer : d"""
Break down and solve the equation step by step.,"the sum of 3 consecutive numbers is definitely a ) positive . , b ) divisible by 2 . , c ) divisible by 4 . , d ) divisible by 3 . , e ) divisible by 5 .","""if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : d"""
Provide a detailed solution to the given mathematical problem.,"a bowl was filled with 10 ounces of water , and 0.014 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ? a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 7 % , e ) 40 %","""total amount of water evaporated each day during a 50 - day period = . 014 * 50 = . 014 * 100 / 2 = 1.4 / 2 = . 7 percent of the original amount of water evaporated during this period = ( . 7 / 10 ) * 100 % = 7 % answer d"""
"Work through the equation methodically, ensuring clarity at each step.","a and b can do a work in 12 days and 36 days respectively . if they work on alternate days beginning with b , in how many days will the work be completed ? a ) 11 , b ) 17 , c ) 10 , d ) 17 , e ) 18","the work done in the first two days = 1 / 12 + 1 / 36 = 1 / 9 so , 9 such two days are required to finish the work . i . e . , 18 days are required to finish the work . answer : e"
"Solve the problem systematically, showing each step clearly.","in the biology lab of ` ` jefferson'' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10,800 petri dishes . how many germs live happily in a single dish ? a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000",5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c
Explain the solution process for the given equation.,"how many quarters are equal to 3 dollars ? a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 7","""3 * 4 = 12 quarters answer : c"""
"Solve the problem systematically, showing each step clearly.","in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 200 bricks in the wall , how many bricks does the bottom row contain ? a ) 42 , b ) 35 , c ) 40 , d ) 33 , e ) 38","""the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 200 5 x - 10 = 200 5 x = 190 x = 38 answer : e"""
Break down and solve the equation step by step.,"two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 5 : 1 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel . a ) 12 : 5 , b ) 11 : 5 , c ) 13 : 5 , d ) 14 : 5 , e ) 9 : 5","""vessel a = 300 gallons - - > milk = 250 , water = 50 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 550 , water 250 the ratio = 550 / 250 - - > 11 : 5 answer : b"""
Explain the solution process for the given equation.,"at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 5 on candy , how much did john spend at the supermarket ? a ) $ 75 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180","""let' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 5 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 5 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 150 = 30 t 28 t + 150 = 30 t 150 = 2 t t = 75 john spent $ 7 at the supermarket . answer : a"""
Explain the solution process for the given equation.,"population of a city in 20004 was 1500000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007 a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 3251625 / 2","""required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 3251625 / 2 e"""
Explain the solution process for the given equation.,"what is the tens digit of 7 ^ 1001 ? a ) 0 , b ) 0 , c ) 2 , d ) 3 , e ) 4","""7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten' s digit ) 0 , 4 , 4 , 0 . 1001 = 4 * 250 + 1 the ten' s digit will be 1 . answer b"""
Explain the solution process for the given equation.,"the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 40 less . what was the total cost cost of the vacation ? a ) $ 200 , b ) $ 300 , c ) $ 480 , d ) $ 500 , e ) $ 600","""c for cost . p price per person . c = 3 * p c = 4 * p - 160 substituting the value of p from the first equation onto the second we get p = 160 . plugging in the value of p in the first equation , we get c = 480 . which leads us to answer choice c"""
"Solve the problem systematically, showing each step clearly.","when 6 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ? a ) 32 , b ) 180 , c ) 60 , d ) 27 , e ) 11","""explanation : let the number be 26 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 6 = a / 30 = > a = 180 answer : b"""
Explain the solution process for the given equation.,"a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck' s tank is completely filled . if the truck' s tank has a radius of 7 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ? a ) 0.07 , b ) 0.049 , c ) 0.7 , d ) 0.49 , e ) 4.9","""the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 49 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 490 / 10,000 = 49 / 1000 = 0.049 ft the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.81 . what is the median gasoline price ? a ) $ 1 , b ) $ 1.81 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15","""ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.81 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.81 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b"""
Provide a detailed solution to the given mathematical problem.,"kim finds a 3 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ? a ) 2 / 5 , b ) 3 / 5 , c ) 8 / 15 , d ) 1 / 2 , e ) 7 / 5","3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is b"
"Solve the problem systematically, showing each step clearly.","the contents of two vessels containing copper and tin in the ratio 2 : 3 and 5 : 7 are mixed in the ratio 3 : 5 . the resulting mixture will have copper and tin in the ratio ? a ) 210 : 283 , b ) 312 : 433 , c ) 178 : 213 , d ) 197 : 283 , e ) 145 : 256",the ratio of copper and tin the new vessel = ( 2 / 5 * 3 / 8 + 5 / 12 * 5 / 8 ) : ( 3 / 5 * 3 / 8 + 7 / 12 * 5 / 8 ) = 197 / 480 : 283 / 480 = 197 : 283 answer is d
"Work through the equation methodically, ensuring clarity at each step.","by selling 16 pencils for a rupee a man loses 28 % . how many for a rupee should he sell in order to gain 28 % ? a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 4","""72 % - - - 16 128 % - - - ? 72 / 128 * 16 = 9 answer : b"""
Provide a detailed solution to the given mathematical problem.,"a vendor sells 20 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 20 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ? a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72","let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.8 ) x = 0.4 x . the remaining pears are ( 0.5 ) ( 0.8 ) x = 0.4 x . on day two , the vendor throws away ( 0.8 ) ( 0.4 ) x = 0.32 x . the vendor throws away a total of 0.4 x + 0.32 x = 0.72 x . the vendor throws away 72 percent of the pears . the answer is e ."
"Solve the problem systematically, showing each step clearly.","a total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates . find the respective number of boys and girls ? a ) 32 , b ) 60 , c ) 27 , d ) 29 , e ) 21","let the number of boys be x . number of girls is 120 - x . total number of chocolates received by boys and girls = 2 x + 3 ( 120 - x ) = 300 = > 360 - x = 300 = > x = 60 . so , the number of boys or girls is 60 . answer : b"
Provide a detailed solution to the given mathematical problem.,"company p had 15 percent more employees in december than it had in january . if company p had 500 employees in december , how many employees did it have in january ? a ) 391 , b ) 435 , c ) 410 , d ) 423 , e ) 445","""d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 500 j = 500 / 1.15 j = 50,000 / 115 = 435 thus b is the correct answer ."""
"Work through the equation methodically, ensuring clarity at each step.","a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many w apples did each person get before 45 people joined the feast ? a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .","""before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons w = 1430 , the answer should be a factor of 1430 . only c is . and that' s your answer . c"""
Provide a detailed solution to the given mathematical problem.,"for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 1 and 100 ? a ) 1250 , b ) 1530 , c ) 2120 , d ) 2540 , e ) 2550","""average of the set : ( largest + smallest ) / 2 = ( 100 + 2 ) / 2 = 51 ; # of terms : ( largest - smallest ) / 2 + 1 = ( 100 - 2 ) / 2 + 1 = 50 the sum = 51 * 50 = 2550 answer : e"""
Provide a detailed solution to the given mathematical problem.,"when a number is divided by 6 & then multiply by 12 the answer is 15 what is the no . ? a ) 4.5 , b ) 5 , c ) 5.6 , d ) 7.5 , e ) 6.5","""if $ x $ is the number , x / 6 * 12 = 15 = > 2 x = 15 = > x = 7.5 d"""
"Work through the equation methodically, ensuring clarity at each step.","what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 500 inclusive ? a ) 190 , b ) 255 , c ) 200 , d ) 205 , e ) 210","this question can be solved with the average formula and' bunching .' we' re asked for the average of all of the multiples of 10 from 10 to 500 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 50 ( 10 ) = 500 so we know that there are 50 total numbers . we can now figure out the sum of those numbers with' bunching' : 10 + 500 = 510 20 + 490 = 510 30 + 480 = 510 etc . since there are 50 total terms , this pattern will create 25' pairs' of 510 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 25 ) ( 510 ) / ( 50 ) = 255 final answer : b"
Explain the solution process for the given equation.,"find the area of a cuboid of length 4 cm , breadth 6 cm . and height 5 cm . ['a ) 120 cm cube','b ) 110 cm cube','c ) 220 cm cube','d ) 430 cm cube','e ) 480 cm cube']",area of a cuboid = lxbxh = 4 cm x 6 cm x 5 cm = 120 cm cube answer : a
Break down and solve the equation step by step.,"a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 800 square feet , what is the total length of the fence , in feet ? a ) 40 , b ) 80 , c ) 100 , d ) 120 , e ) 200","""two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 800 ie x ^ 2 = 400 ie x = 20 l = 40 w = 20 total length of fence = 2 * 20 + 40 = 80 my answer is b"""
Explain the solution process for the given equation.,"pipe a fills a tank in 56 minutes . pipe b can fill the same tank 7 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ? a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8",a' s rate is 1 / 56 and b' s rate is 1 / 8 . the combined rate is 1 / 56 + 1 / 8 = 1 / 7 the pipes will fill the tank in 7 minutes . the answer is d .
"Solve the problem systematically, showing each step clearly.","an engineer undertakes a project to build a road 10 km long in 30 days and employs 30 men for the purpose . after 10 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time . a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70","""30 workers working already let x be the total men required to finish the task in next 20 days 2 km done hence remaining is 8 km also , work has to be completed in next 20 days ( 30 - 10 = 20 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 10 ) / ( 2 * 20 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : a"""
Provide a detailed solution to the given mathematical problem.,"for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 20 , then v = a ) 36 , b ) 39 , c ) 42 , d ) 45 , e ) 48","""( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 20 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 45 the answer is d ."""
Explain the solution process for the given equation.,"in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability t this college graduate has a graduate degree ? a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43","""in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability t of cgd / ( cg ) - > 3 / 19 answer d"""
Provide a detailed solution to the given mathematical problem.,"the average of first five multiples of 7 is ? a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 21","""average = 7 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 105 / 5 = 21 . answer : e"""
Provide a detailed solution to the given mathematical problem.,"the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ? a ) 2 : 7 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 9 , e ) 2 : 2","""let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : option b explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"""
Explain the solution process for the given equation.,"beginning in town a , biker bob rides his bike 12 miles west , 6 miles north , 4 miles east , and then 12 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . ) a ) 18.97 miles , b ) 20 miles , c ) 22 miles , d ) 23 miles , e ) 25 miles","""using pythagoras we have one side i , e total distance traveled in north direction = 12 + 6 = 18 m other being the base ie distance traveled west - distance traveled eat = 12 - 6 = 6 m now this third side or the distance between town a and town b = 18 ^ 2 + 6 ^ 2 = sq root 360 = 18.97 mile answer : a"""
Explain the solution process for the given equation.,"excluding the stoppages , the speed of a bus is 64 km / hr and including the stoppages the speed o the bus is 48 km / hr . for how many minutes does the bus stop per hour ? a ) 22 , b ) 15 , c ) 77 , d ) 28 , e ) 91",answer : b ) 15 minutes
"Work through the equation methodically, ensuring clarity at each step.","a can do a job in 30 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ? a ) 14 days , b ) 26 days , c ) 30 days , d ) 31 days , e ) 39 days","""c 1 / 30 + 1 / 30 = 1 / 15 15 * 2 = 30 days"""
"Solve the problem systematically, showing each step clearly.","two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability w that jane will be on the same committee as albert ? a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %","""total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability w = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"""
"Solve the problem systematically, showing each step clearly.","the average of 5 numbers is 7.4 . if one of the numbers is multiplied by a factor of 3 , the average of the numbers increases to 9.2 . what number is multiplied by 3 ? a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.5 , e ) 6.0","""the average of 5 numbers is 7.4 the sum of 5 numbers will be 7.4 x 5 = 37 the average of 5 number after one of the number is multiplied by 3 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 37 = 9 let the number multiplied by 3 be n then , 3 n = n + 9 or 2 n = 9 or n = 4.5 answer : - d"""
Explain the solution process for the given equation.,"in a race where 18 cars are running , the chance that car x will win is 1 / 8 , that y will win is 1 / 12 and that z will win is 1 / 6 . assuming that a dead heat is impossible , find the chance that one of them will win . a ) 1 / 140 , b ) 1 / 180 , c ) 3 / 12 , d ) 3 / 8 , e ) 57 / 120","""required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 8 + 1 / 12 + 1 / 6 = 3 / 8 answer : d"""
"Solve the problem systematically, showing each step clearly.","at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 4 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ? a ) $ 1220 , b ) $ 1160 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880","""i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 4 ) = $ 160 total revenue : 1000 + 160 = $ 1160 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","the cost price of 30 articles is the same as the selling price of x articles . if the profit is 25 % , what is x ? a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26",let the cost price = y the cost price of 30 articles = 30 y the selling price of x articles = 1.25 y * x 1.25 y * x = 30 y x = 30 / 1.25 = 24 the answer is d .
Explain the solution process for the given equation.,"the total number of digits used in numbering the pages of a book having 266 pages is a ) 732 , b ) 990 , c ) 109 , d ) 130 , e ) 690","""total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 167 ) = ( 9 + 180 + 501 ) = 690 . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","the average of 13 numbers is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ? a ) 43 , b ) 30 , c ) 35 , d ) 45 , e ) 50","""sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . answer a"""
Provide a detailed solution to the given mathematical problem.,"a student gets 50 % in one subject , 70 % in the other . to get an overall of 70 % how much should get in third subject . a ) 90 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %","""let the 3 rd subject % = x 50 + 70 + x = 3 * 70 120 + x = 210 x = 210 - 120 = 90 answer : a"""
Explain the solution process for the given equation.,"weights of two friends ram and shyam are in the ratio 4 : 5 . if ram' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ? a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none","""solution : given ratio of ram and shayam' s weight = 4 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 4 / 5 or , x = 19 % . answer : option a"""
Provide a detailed solution to the given mathematical problem.,"in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 10 liters of milk , the can would be full and the ratio of milk and water would become 5 : 2 . find the capacity of the can ? a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32",let c be the capacity of the can . ( 4 / 7 ) * ( c - 10 ) + 10 = ( 5 / 7 ) * c 4 c - 40 + 70 = 5 c c = 30 the answer is d .
"Solve the problem systematically, showing each step clearly.","789.009 - ? + 56.84 = 215.943 a ) 899.015 , b ) 752.804 , c ) 714.642 , d ) 629.906 , e ) none of these","""explanation : 629.906 answer : option d"""
"Work through the equation methodically, ensuring clarity at each step.","the edges of three metal cubes are 1 cm , 3 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ? a ) 3.9 , b ) 4.2 , c ) 4.5 , d ) 4.8 , e ) 5.1",the total volume is 1 ^ 3 + 3 ^ 3 + 4 ^ 3 = 92 the edge of the new cube is the cube root of 92 which is about 4.5 cm . the answer is c .
"Work through the equation methodically, ensuring clarity at each step.","if ( n + 2 ) ! / n ! = 110 , n = ? a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12","""( n + 2 ) ! / n ! = 110 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 110 from here , we might just test the answer choices . since ( 11 ) ( 10 ) = 110 , we can see that n = 9 b"""
"Work through the equation methodically, ensuring clarity at each step.","what is 15 percent of 64 ? a ) 7.2 , b ) 8.4 , c ) 9.6 , d ) 10.4 , e ) 11.8","""( 15 / 100 ) * 64 = 9.6 the answer is c ."""
Explain the solution process for the given equation.,"tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ? a ) 3 / 10 , b ) 1 / 2 , c ) 2 / 5 , d ) 3 / 7 , e ) 1 / 6","""here , s = { 1 , 2,3 , . . . . . . , 19,20 } e = event getting a multiple of 3 = { 3,6 , 9,12 , 15,18 } probability = 6 / 20 = 3 / 10 correct option is a"""
Provide a detailed solution to the given mathematical problem.,"evaluate 45 / . 05 a ) 700 , b ) 900 , c ) 705 , d ) none of these , e ) 506","""explanation : 45 / . 05 = 4500 / 5 = 900 option b"""
Explain the solution process for the given equation.,"the lowest number which should be added to 8247 so that the sum is exactly divisible by 5 , 6 , 7 , 8 and 9 is : a ) 1833 , b ) 1853 , c ) 1733 , d ) 1233 , e ) 1832","""l . c . m . of 5 , 6 , 7 , 8 and 9 = 2520 . on dividing 8247 by 2520 , the remainder is 687 . number to be added = ( 2520 - 687 ) = 1833 . answer : option' a'"""
"Solve the problem systematically, showing each step clearly.","the ratio between the number of sheep and the number of horses at the stewart farm is 4 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ? a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 60","""actual number of horses = 12,880 / 230 ( hold it since it is a harder calculation ) ratio multiplier = 1288 / ( 23 * 7 ) actual number of sheep = 1288 / ( 23 * 7 ) * 4 . first divide 1288 by 7 to get : 184 * 4 / 23 use the last digit to figure out that 23 will go 8 times into 184 . confirm . 8 * 4 = 32 answer ( c )"""
Break down and solve the equation step by step.,"in a 150 member association consisting of men and women , exactly 10 % of men and exactly 20 % women are homeowners . what is the least number of members who are homeowners ? a ) 22 , b ) 21 , c ) 20 , d ) 19 , e ) 18","solution simple out of 150 10 % are male i . e 15 and 20 % are female i . e 30 , so total homeowner is 45 . now min number homeowner is 15 and max is 30 so question ask us to find least and 18 has least value among all option . so ans is 18 . ans : e"
"Solve the problem systematically, showing each step clearly.","the price of a t . v . set worth rs . 60000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ? a ) 22678 , b ) 59000 , c ) 26788 , d ) 19000 , e ) 26711","""money paid in cash = rs . 1000 balance payment = ( 60000 - 1000 ) = rs . 59000 answer : b"""
"Solve the problem systematically, showing each step clearly.","veena ranks 65 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ? a ) 96 , b ) 108 , c ) 110 , d ) 90 , e ) 93","""total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 65 + 1 = 96 answer : a"""
Provide a detailed solution to the given mathematical problem.,"a rectangular field has a length 10 meters more than it is width . if the area of the field is 231 , what is the length ( in meters ) of the rectangular field ? a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29","""area = l * w = ( l ) * ( l - 10 ) = 231 trial and error : 20 * 10 = 200 ( too low ) 21 * 11 = 231 the length is 21 meters . the answer is a ."""
"Work through the equation methodically, ensuring clarity at each step.","harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 3 of her books to their new home . what fraction of millicent' s old library capacity is the new home' s library capacity ? a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6","""because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h' = 1 / 3 h = 10 books m' = 1 / 3 m = 20 books total = 30 books m' = 30 = 1 / 2 * 60 ratio : 1 / 2 ans : a"""
"Solve the problem systematically, showing each step clearly.","of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 110 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ? a ) 280 , b ) 400 , c ) 540 , d ) 550 , e ) 840","""of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 110 geese survived the first year : 1 / 5 * ( total ) = 110 - - > ( total ) = 550 . answer : d ."""
Explain the solution process for the given equation.,"one paper sheet can be used to create 8 paper boats or 6 paper planes . if total exact 80 paper toys are to be made , minimum how many sheets need to be used to make paper boats ? a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1","let us say x sheets are used to create paper boats and y sheets are used to create paper planes . since total 80 paper toys are to be created , 8 x + 6 y = 80 . = > 8 x = 80 - 6 y = > x = 10 - ( 6 / 8 ) y = > x = 10 - ( 3 / 4 ) y to minimize x , we need to maximize y . and y needs to be multiple of 4 . y = 4 , x = 10 - ( 3 / 4 ) 4 = 7 y = 8 , x = 10 - ( 3 / 4 ) 8 = 4 y = 12 , x = 10 - ( 3 / 4 ) 12 = 1 beyond this , x will become negative for greater values of y . so , minimum 1 sheet is required to be used for creating paper boats . answer : e"
Provide a detailed solution to the given mathematical problem.,"a school has 7 maths 6 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8","total subjects = 7 + 6 + 5 = 18 max subjects by 1 teacher = 3 so , min of teachers required = 18 / 3 = 6 answer : c"
Break down and solve the equation step by step.,"a , b , and c were to be paid in proportion to the part of work they did while working on the same piece of work . a and b individually can finish the piece of work in 12 days and 15 days respectively . they worked together for 5 days and then c completed the remaining work all alone . if $ 810 was the net sum to be paid for the entire work , what was the average daily wage of b ? a ) $ 144 , b ) $ 90 , c ) $ 60 , d ) $ 54 , e ) $ 48",the correct answer is d .
"Work through the equation methodically, ensuring clarity at each step.","5358 x 55 = ? a ) 272258 , b ) 272358 , c ) 294690 , d ) 274258 , e ) 274358","""5358 x 51 = 5358 x ( 50 + 5 ) = 5358 x 50 + 5358 x 5 = 267900 + 26790 = 294690 . c )"""
Explain the solution process for the given equation.,"in the biotechnology class of 2000 , there were x graduates . 32 of the graduates found a job , 45 continued on to their second degree and 13 did both . if only 9 people did n' t do both , what is x equal to ? a ) 69 . , b ) 71 , c ) 73 , d ) 75 , e ) 76",graduates got job = 32 graduates continued to second degree = 45 graduates got job and continued to second degree = 13 graduates did n' t get job and did n' t continue to second degree = 9 job no job total second degree 13 32 45 no second degree 19 9 28 total 32 41 x therefore x = 73 answer c
"Work through the equation methodically, ensuring clarity at each step.","( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = a ) 99 , b ) 9.9 , c ) 990 , d ) 0.99 , e ) 0.099","""( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 450 / 5 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : c"""
Explain the solution process for the given equation.,"what should be the least number to be added to the 1202 number to make it divisible by 4 ? a ) 12 , b ) 17 , c ) 18 , d ) 77 , e ) 2",answer : 2 option : e
Explain the solution process for the given equation.,"a person distributed 15 % of his income to his 3 children each . he deposited 30 % of his income to his wife' s account . he donated 10 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ? a ) a ) 266666.7 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000",3 children got = 3 * 15 % = 45 % wife got = 30 % orphan house = 10 % total = 45 + 30 + 10 = 85 % remaining = 100 - 85 = 15 % 15 % = 40000 100 % = 40000 * 100 / 15 = $ 266666.7 answer is a
Break down and solve the equation step by step.,"a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 199 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ? a ) 10,000 , b ) 11,025 , c ) 14,400 , d ) 12,696 , e ) can not be determined","""let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 199 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 199 ( x + y ) ( x - y ) = 199 199 is a prime number and thus it will be ( 100 + 99 ) * ( 100 - 99 ) . thus x = 100 and y = 99 x ^ 2 = 100 ^ 2 = 10,000 the answer is a ."""
"Work through the equation methodically, ensuring clarity at each step.","people were sitting in a circle . 7 th one is direct opposite to 18 th one . . then how many were there in that group ? ['a ) 21','b ) 22','c ) 23','d ) 24','e ) 20']",7 th one is exactly opposite represents half of circle . with 7 and 18 total members are 12 for remaing half = 12 * 2 - 2 ( 7 th and 18 th ( already taken ) ) = 22 answer : b
Explain the solution process for the given equation.,"if henry were to add 5 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ? a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96",7 / 8 x - 3 / 4 x = 5 galls 1 / 8 * x = 5 gallons x = 40 gallons answer : b
"Solve the problem systematically, showing each step clearly.","in the fifth grade at parkway elementary school there are 420 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? a ) 69 . , b ) 73 . , c ) 81 , d ) 65 , e ) 108","""total students = 420 boys = 320 , girls = 100 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 100 - 35 = 65 . correct option : d"""
Explain the solution process for the given equation.,"a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.8 per box per month for the record storage , what is the total amount that the company pays each month for record storage ? a ) a . 480 , b ) b . 300 , c ) c . 600 , d ) d . 410 , e ) e . 240","""volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.8 = 480 answer : a"""
Provide a detailed solution to the given mathematical problem.,"a rectangular room 14 m long , 12 m broad is surrounded by a varandah , 3 m wide . find the area of the varandah ? ['a ) 170','b ) 180','c ) 190','d ) 210','e ) 150']",area of varandah = ( l + b + 2 p ) 2 p = ( 14 + 12 + 6 ) 6 = 180 m ( power ) 2 answer is b .
Explain the solution process for the given equation.,"if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 350 , what is the least possible value of n ? a ) 5 , b ) 7 , c ) 12 , d ) 13 , e ) 14","""350 = 2 * 5 * 5 * 7 so the least value forncan be 7 . b"""
Break down and solve the equation step by step.,"the moon revolves around the earth at a speed of approximately 1.04 kilometers per second . this approximate speed is how many kilometers per hour ? a ) 60 , b ) 61.2 , c ) 3,744 , d ) 3,600 , e ) 3,672","""moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.04 * 3600 = 3744 kilometers per hour . option c is correct"""
"Solve the problem systematically, showing each step clearly.","the cost per pound of milk powder and coffee were the same in june . in july , the price of coffee shot up by 300 % and that of milk powder dropped by 80 % . if in july , a mixture containing equal quantities of milk powder and coffee costs $ 6.30 for 3 lbs , how much did a pound of milk powder cost in july ? a ) $ 4 , b ) $ 0.2 , c ) $ 1 , d ) $ 3 , e ) $ 1.65",lets assume price of coffee in june = 100 x price of milk powder in june = 100 x price of coffee in july = 400 x ( because of 300 % increase in price ) price of milk powder in july = 20 x ( because of 80 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of milk powder in july will be = 600 x + 30 x = 630 x as per question 630 x = 6.30 $ x = 0.01 s so the price of milk powder in july = 20 x = 20 x 0.01 = 0.2 $ / pound answer b
Break down and solve the equation step by step.,"a present value of a machine is $ 400 . its value depletiation rate is 25 % per annum then find the machine value after 2 years ? a ) $ 125 , b ) $ 100 , c ) $ 200 , d ) $ 215 , e ) $ 225","""p = $ 400 r = 25 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 400 * 3 / 4 * 3 / 4 = $ 225 approximately answer is e"""
Explain the solution process for the given equation.,"10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 4 children take to complete the work ? a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10","""1 women' s 1 day work = 1 / 70 1 child' s 1 day work = 1 / 140 ( 5 women + 4 children )' s 1 day work = ( 5 / 10 + 4 / 140 ) = 1 / 10 5 women and 4 children will complete the work in 10 days . e"""
"Solve the problem systematically, showing each step clearly.","a person is traveling at 65 km / hr and reached his destiny in 3 hr then find the distance ? a ) 205 km , b ) 195 km , c ) 295 km , d ) 115 km , e ) 215 km","""t = 3 hrs d = t * s = 65 * 3 = 195 km answer is b"""
Provide a detailed solution to the given mathematical problem.,"find the compound ratio of ( 2 : 5 ) , ( 6 : 11 ) and ( 11 : 2 ) is a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 6 : 5 , e ) 2 : 3","""required ratio = 2 / 5 * 6 / 11 * 11 / 2 = 2 / 1 = 6 : 5 answer is d"""
Explain the solution process for the given equation.,"how many of the positive factors of 56 , 96 and how many common factors are there in numbers ? a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 1","""factors of 56 - 1 , 2 , 4 , 7 , 8 , 14 , 28 , 56 factors of 96 - 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 32 , 48 , 96 comparing both , we have three common factors of 56 and 96 - 1 , 2,4 answer ( c )"""
"Solve the problem systematically, showing each step clearly.","at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 80 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ? a ) 20 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 44 %","""another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 80 = 25 + b + 25 b / 100 b = 44 answer ( e )"""
Explain the solution process for the given equation.,"if x is 20 percent greater than 40 , then x = a ) 48 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108","""x is 20 % greater than 40 means x is 1.2 times 40 ( in other words 40 + 20 / 100 * 40 = 1.2 * 40 ) therefore , x = 1.2 * 40 = 48 answer : a"""
Provide a detailed solution to the given mathematical problem.,"8.008 / 2.002 a ) 0.004 , b ) 0.04 , c ) 4 , d ) 40 , e ) 400","""answer is 4 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 2002 = 4 answer c"""
Provide a detailed solution to the given mathematical problem.,"how much water should be added to 10 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ? a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters","""let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 10 + x ) ) ) 2 = 5 % * ( 10 + x ) - - - - - - - - > x = 30 answer : c"""
Explain the solution process for the given equation.,"at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 1 / 2 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ? a ) 4 / 7 , b ) 5 / 7 , c ) 8 / 11 , d ) 7 / 12 , e ) 11 / 15","""let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( x / 2 ) ( 3 y / 4 ) = 3 xy / 8 the total number of boxes is xy + 3 xy / 8 = 11 xy / 8 the fraction loaded by the day crew is xy / ( 11 xy / 8 ) = 8 / 11 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"the distance from steve' s house to work is 20 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve' s speed on the way back from work ? a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .","""time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 20 km = > speed = 10 kmph b"""
Break down and solve the equation step by step.,"p , q and r together earn rs . 1980 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ? a ) s . 30 , b ) s . 70 , c ) s . 90 , d ) s . 100 , e ) s . 120","""explanation : amount earned by p , q and r in 1 day = 1980 / 9 = 220 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 220 = 30 = > amount earned by r in 1 day = 30 answer : option a"""
Provide a detailed solution to the given mathematical problem.,"how many two digit prime numbers are there in which both digits are prime numbers ? ( for example , 23 is one of these numbers but 31 is not , since 1 is not a prime number . ) a ) 3 , b ) 4 , c ) 5 , d ) 8 , e ) 15","the second digit can only be 3 or 7 , so the choice quickly narrows down to 23 , 27 , 33 , 37 , 53 , 57 , 73 , and 77 . of these , 27 , 33 , and 57 are divisible by 3 , and 77 by 7 , leaving 23 , 37 , 53 , and 73 . it is easy to see that none of these is divisible by 2 , 3 , 5 , or 7 , and there is no need to look at greater prime divisors since root 77 < 11 . correct answer b"
"Solve the problem systematically, showing each step clearly.","in a group of cows and hens , the number of legs are 14 more than twice the number of heads . the number of cows is a ) 22 , b ) 7 , c ) 8 , d ) 6 , e ) 51","""let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 14 4 x + 2 y = 2 x + 2 y + 14 2 x = 14 x = 7 . answer : b"""
"Solve the problem systematically, showing each step clearly.","the ratio of two no . addition and subtraction be 4 : 3 . the what is the ratio of numbers ? a ) 3 : 2 , b ) 4 : 3 , c ) 5 : 1 , d ) 6 : 5 , e ) 7 : 1",( x + y ) / ( x - y ) = 4 / 3 dividing numerator and denominator by y ( x / y ) + 1 / ( x / y ) - 1 = 4 / 3 let x / y be z z + 1 / z - 1 = 4 / 3 3 z + 3 = 4 z - 4 z = 7 x / y = 7 answer e
Explain the solution process for the given equation.,"how many integers k greater than 100 and less than 1100 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ? a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90","""not sure if this is the shortest . . but this is how i did this there are 9 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . . . . 7 . 708 | 807 8 . 809 | 908 9 . 910 | 1001 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 9 sets with 10 such number in each set will give 9 x 10 = 90 integers . e"""
Break down and solve the equation step by step.,"what is the area of a square with perimeter 12 p ? ['a ) 16 p ^ 2','b ) 4 p','c ) 9 p ^ 2','d ) p / 16','e ) p ^ 2 / 16']",each side is 3 p a = ( 3 p ) ^ 2 = 9 p ^ 2 answer c
"Work through the equation methodically, ensuring clarity at each step.","if the product of the integers w , x , y and z is 68 , and if 0 < w < x < y < z , what is the value of w + z ? a ) 10 , b ) 5 , c ) 16 , d ) 18 , e ) 21","24 = 1 * 2 * 3 * 4 so w = 1 , x = 2 , y = 3 , z = 4 w + z = 1 + 4 = 5 answer - b"
"Solve the problem systematically, showing each step clearly.","if 20 typists can type 40 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ? a ) 63 , b ) 72 , c ) 144 , d ) 180 , e ) 400","""20 typists can type 40 letters , so 30 typists can type = 40 * 30 / 20 40 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 40 * 30 * 60 / 20 * 20 = 180 d is the answer"""
Provide a detailed solution to the given mathematical problem.,"a student scored an average of 70 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ? a ) 130 , b ) 120 , c ) 110 , d ) 180 , e ) 150","""given m + p + c = 70 * 3 = 210 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 210 = 110 answer : c"""
"Solve the problem systematically, showing each step clearly.","a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 12 brown mice in the experiment , how many mice in total are in the experiment ? a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 36","""let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 12 = > m = 36 answer e"""
Break down and solve the equation step by step.,"anna left for city a from city b at 5.20 a . m . she traveled at the speed of 80 km / hr for 2 hrs 15 min . after that the speed was reduced to 60 km / hr . if the distance between two cities is 350 kms , at what time did anna reach city a ? a ) 10.21 , b ) 10.27 , c ) 10.25 , d ) 10.23 , e ) 60.25","distance covered in 2 hrs 15 min i . e . , 2 1 / 4 hrs = 80 * 9 / 4 = 180 hrs . time taken to cover remaining distance = ( 350 - 180 ) / 60 = 17 / 6 hrs = 2 5 / 6 = 2 hrs 50 min total time taken = ( 2 hrs 15 min + 2 hrs 50 min ) = 5 hrs 5 min . so , anna reached city a at 10.25 a . m . answer : e"
Explain the solution process for the given equation.,"if the speed of a man is 66 km per hour , then what is the distance traveled by him in 30 seconds ? a ) 550 m , b ) 500 m , c ) 375 m , d ) 420 m , e ) 440 m","""the distance traveled in 30 sec = 66 * ( 5 / 18 ) * 30 = 550 m answer : a"""
Break down and solve the equation step by step.,"at what rate percent per annum will the simple interest on a sum of money be 2 / 5 of the amount in 10 years ? a ) 4 % , b ) 74 % , c ) 64 % , d ) 74 % , e ) 94 %","let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 2 x ) / ( x * 5 * 10 ) = 4 % answer : a"
Break down and solve the equation step by step.,"of the 120 passengers on flight 750 , 55 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ? a ) 44 , b ) 48 , c ) 50 , d ) 52 , e ) 58",number of passengers on flight = 120 number of female passengers = . 5 * 120 = 66 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 66 - 8 = 58 answer e
Provide a detailed solution to the given mathematical problem.,"n and m are each 3 - digit integers . each of the numbers 1 , 2 , 3 , 4,5 and 6 is a digit of either n or m . what is the smallest possible positive difference between n and m ? a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131","""you have 6 digits : 1,2 , 3 , 4 , 5 , 6 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let' s not use 1 and 6 in the hundreds places and reserve them for the tens places now what are the options ? try and make a pair with ( 2 * * and 3 * * ) . make the 2 * * number as large as possible and make the 3 * * number as small as possible . 265 and 314 ( difference is 49 ) or try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . we get 463 and 512 ( difference is 49 ) b"""
"Work through the equation methodically, ensuring clarity at each step.","when positive integer n is divided by 5 , the remainder is 2 . when n is divided by 11 , the remainder is 8 . what is the smallest positive integer k such that k + n is a multiple of 55 ? a ) 2 , b ) 3 , c ) 6 , d ) 7 , e ) 10","""n = 5 p + 2 = 11 q + 8 n + 3 = 5 p + 5 = 11 q + 11 n + 3 is a multiple of 5 and 11 , so it is a multiple of 55 . the answer is b ."""
Break down and solve the equation step by step.,"the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? a ) 2277 , b ) 2977 , c ) 2677 , d ) 4530 , e ) 1971","""area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 5 = rs . 4530 answer : d"""
Break down and solve the equation step by step.,"pipe a can fill a tank in 10 hrs and pipe b can fill it in 8 hrs . if both the pipes are opened in the empty tank . there is an outlet pipe in 3 / 4 th of the tank . in how many hours will it be fill 3 / 4 th of that tank ? a ) 3 hr , b ) 3.10 hr , c ) 3.15 hr , d ) 3.20 hr , e ) 3.30 hr","part filled a in 1 hr = ( 1 / 10 ) part filled b in 1 hr = ( 1 / 8 ) part filled by ( a + b ) together in 1 hr = ( 1 / 10 ) + ( 1 / 8 ) = 18 / 80 so , the tank will be full in 80 / 18 hrs . time taken to fill exact 3 / 4 th of the tank = ( 80 / 18 ) * ( 3 / 4 ) = 3.20 hrs answer : d"
"Work through the equation methodically, ensuring clarity at each step.","how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 72 kmph ? a ) 22 sec , b ) 77 sec , c ) 25 sec , d ) 18 sec , e ) 12.5 sec","""d = 100 + 150 = 250 s = 72 * 5 / 18 = 20 mps t = 250 / 20 = 12.5 sec answer : e"""
Break down and solve the equation step by step.,"if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 15 km more . the actual distance traveled by him is ? a ) 30 , b ) 50 , c ) 15 , d ) 12 , e ) 20","""let the actual distance traveled be x km . then , x / 10 = ( x + 15 ) / 15 x - 30 = > x = 30 km . answer : a"""
"Solve the problem systematically, showing each step clearly.","pradeep has to obtain 35 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are a ) 300 , b ) 600 , c ) 800 , d ) 1000 , e ) 900","explanation : let their maximum marks be x . then , 35 % of x = 185 + 25 = > 35 / 100 x = 210 x = ( 210100 / 35 ) x = 600 . answer : b"
Explain the solution process for the given equation.,"marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 12000 and the marginal cost is $ 200 , and the total cost is $ 16000 , what is the value of n ? a ) 20 , b ) 50 , c ) 60 , d ) 80 , e ) 100","total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 12,000 + n * $ 200 - - > n = 20 . answer : a ."
Explain the solution process for the given equation.,"if x , y , and z are positive integers and x = 4 y = 7 z , then the least possible value of x - y - z is a ) 33 , b ) 17 , c ) 49 , d ) 16 , e ) 23","x - y - z = x - x / 4 - x / 7 = ( 28 - 7 - 4 ) x / 28 = 17 x / 28 17 is not divisible by 28 ( it' s a prime # ) , so for least value , x = 28 answer - b"
"Solve the problem systematically, showing each step clearly.","the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 70 kmph its consumption is 1 litre per hour . if each litre costs $ 70 and other expenses per hous is $ 70 , then what would be the minimum expenditure required to cover a distance of 700 km ? a ) 1000 , b ) 1500 , c ) 1240 , d ) 1630 , e ) 1400","""70 kmph consumption is 1 lt / hr so 700 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 70 so 10 lt costs $ 700 extra expenses for 1 hr - $ 70 10 hrs - $ 700 total expense - $ 700 + $ 700 = $ 1400 answer : e"""
Provide a detailed solution to the given mathematical problem.,"a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 17 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ? a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 27 / 100 , e ) 9 / 100","c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 17 - 2 cmb = 100 b - cb - mb - 2 cmb = 27 hence the probability = 27 / 100 d"
"Solve the problem systematically, showing each step clearly.","mixture a is 10 percent alcohol , and mixture b is 40 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 20 percent alcohol , approximately how many gallons of mixture a are in the mixture ? a ) 1.6 , b ) 1.7 , c ) 1.8 , d ) 1.9 , e ) 2.0","""( 40 - 20 ) / ( 20 - 15 ) = qa / qb 20 / 10 = qa / qb 2 / 1 = qa / qb qa = ( 2 / 5 ) * 4 = 8 / 5 = 1.6 approx answer : a"""
"Solve the problem systematically, showing each step clearly.","when x is multiplied by 3 , the result is 16 more than the result of subtracting x from 36 . what is the value of x ? a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22","""the equation that can be formed is : 3 x - 16 = 36 - x or , 4 x = 52 or , x = 13 . answer : d"""
Break down and solve the equation step by step.,"an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 2 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ? a ) 7 : 5 , b ) 12 : 11 , c ) 17 : 15 , d ) 22 : 17 , e ) 27 : 25","""let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 2 y and y . 2 ( 3 x + 2 x ) = 2 ( 2 y + y ) 5 x = 3 y ( 5 / 3 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 2 y * y = 6 x ^ 2 : 2 y ^ 2 = 6 x ^ 2 : 2 * ( 25 / 9 ) * x ^ 2 = 54 : 50 = 27 : 25 the answer is e ."""
Break down and solve the equation step by step.,"( 3136 + 6160 ) / 28 a ) 380 , b ) 350 , c ) 332 , d ) 310 , e ) none of these","""explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9296 ) / 28 = 332 option c"""
"Work through the equation methodically, ensuring clarity at each step.","what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19 ? a ) 10 : 7 , b ) 9 : 8 , c ) 2 : 1 , d ) 13 : 11 , e ) 14 : 8","correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 6 : 3 = 2 : 1"
"Work through the equation methodically, ensuring clarity at each step.","the distance from city a to city b is 120 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ? a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 54",the time it takes bob to drive to city b is 120 / 40 = 3 hours . alice needs to take less than 2.5 hours for the trip . alice needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour . the answer is b .
"Work through the equation methodically, ensuring clarity at each step.","in a recent election , geoff received 0.5 percent of the 5,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 2,571 more votes to win the election , what is the value of x ? a ) 50 , b ) 54 , c ) 52 , d ) 60 , e ) 63","""word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 25 votes he needs 2571 more votes so : 25 + 2571 = 2596 now what' s the problem wants ? ? a x % . . . . . . . . 2596 is what % of total votes 5000 . . . . . . . . translating : 2596 = x / 100 * 5000 - - - x = 52 % . . . . . . . . . . c"""
Explain the solution process for the given equation.,"a train 550 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ? a ) 30 , b ) 60 , c ) 25 , d ) 40 , e ) 10",speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 550 * 3 / 55 ] sec = 30 sec answer : a
"Work through the equation methodically, ensuring clarity at each step.","two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.65 km respectively . the time taken by the slower train to cross the faster train in seconds is ? a ) 42 , b ) 77 , c ) 48 , d ) 99 , e ) 11",relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.65 = 1.75 km = 1750 m . required time = 1750 * 3 / 125 = 42 sec . answer : a
Explain the solution process for the given equation.,"two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 54 seconds . what is the length of each train ( in meters ) ? a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85","""the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 54 seconds , the relative difference in distance traveled is 54 * 25 / 9 = 150 meters this distance is twice the length of each train . the length of each train is 150 / 2 = 75 meters the answer is d ."""
"Solve the problem systematically, showing each step clearly.","6 lights begin to flash together at 12 : 00 noon and flash respectively at intervals of 3 , 4 , 5 , 6 , 7 , and 8 seconds . not including the flash at 12 : 00 noon , how many more times will all 6 lights flash together before 1 : 00 pm ( i . e . one hour later ) ? a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12",the least common multiple is 2 * 2 * 2 * 3 * 5 * 7 = 840 . 3600 seconds / 840 = 4 + remainder . the answer is a .
Break down and solve the equation step by step.,"john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ? a ) 45 , b ) 65 , c ) 98 , d ) 107 , e ) 198","""rakesh : rahul : ranjan : rohit = 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 1 x 60 ) = 60 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 60 x + 20 x + 15 x + 12 x ) = 107 x . for minimum number of pencils x = 1 . the person should have at least 107 pencils . d )"""
"Solve the problem systematically, showing each step clearly.","a can do a piece of work in 4 hours ; b and c together can do it in 2 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ? a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 4","""a' s 1 hour' s work = 1 / 4 ; ( b + c )' s 1 hour' s work = 1 / 2 ; ( a + c )' s 1 hour' s work = 1 / 2 . ( a + b + c )' s 1 hour' s work = ( 1 / 4 + 1 / 2 ) = 3 / 4 . b' s 1 hour' s work = ( 3 / 4 - 1 / 2 ) = 1 / 4 . therefore a alone will take 4 hours to do the work . e"""
"Work through the equation methodically, ensuring clarity at each step.","cereal a is 9 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ? a ) 2 : 9 , b ) 2 : 5 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3","""( 9 / 100 ) a + ( 2 / 100 ) b = ( 4 / 100 ) ( a + b ) 5 a = 2 b = > a / b = 2 / 5 answer is b ."""
"Solve the problem systematically, showing each step clearly.","when positive integer x is divided by positive integer y , the remainder is 5.76 . if x / y = 96.12 , what is the value of y ? a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12","""when positive integer x is divided by positive integer y , the remainder is 5.76 - - > x = qy + 5.76 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 5.76 - - > y = 48 . answer : c ."""
Provide a detailed solution to the given mathematical problem.,"a positive number x is multiplied by 4 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ? a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2",sq rt ( 4 x / 3 ) = x = > 4 x / 3 = x ^ 2 = > x = 4 / 3 ans - c
Break down and solve the equation step by step.,"at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 40 liters of fuchsia to change it to mauve paint ? a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 26.6","""in 40 liters , red = 5 / 8 * 40 = 25 and blue = 15 so , 25 / ( 15 + x ) = 3 / 5 or , x = 26.6 ( answer e )"""
Break down and solve the equation step by step.,"if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 81 , how much does one shirt cost ? a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 21 , e ) $ 16.80","""3 j + 2 s = 69 2 j + 3 s = 81 - - - - - - - - - - - - - - - - 5 j + 5 s = 150 - - - - ( divide by 5 ) - - - > j + s = 30 3 j + 2 s = j + 2 ( j + s ) = j + 60 = 69 - - - > j = 9 3 * 9 + 2 s = 69 27 + 2 s = 69 2 s = 42 s = 21 answer : d"""
"Solve the problem systematically, showing each step clearly.","light glows for every 18 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am a ) 281 , b ) 277 , c ) 283 , d ) 384 , e ) 385","""the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 18 = 276 . so total 277 times light ll glow answer : b"""
Provide a detailed solution to the given mathematical problem.,"working at constant rate , pump x pumped out half of the water in a flooded basement in 6 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ? a ) a . 10 , b ) b . 12 , c ) c . 14 , d ) d . 28 , e ) e . 24","""rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 28 hours d"""
"Solve the problem systematically, showing each step clearly.","let exp ( m , n ) = m to the power n . if exp ( 10 , m ) = n exp ( 22 ) where m and n are integers then n = ___ ? a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28",10 ^ m = n * ( 2 ^ 2 ) ( 2 * 5 ) ^ m = n * ( 2 ^ 2 ) ( 2 ^ m ) * ( 5 ^ m ) = n * ( 2 ^ 2 ) now equate both side we get m = 2 and ( 5 ^ m ) = n ( 5 ^ 2 ) = n = > n = 25 answer : b
"Solve the problem systematically, showing each step clearly.","an assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ? a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72","""the time to produce the first 60 cogs is 60 / 90 = 2 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 5 / 3 ) hours = 72 cogs per hour . the answer is e ."""
Provide a detailed solution to the given mathematical problem.,"a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 7 cm x 6 cm . the maximum number ofboxes that can be carried in the wooden box , is a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 2000000 , e ) none of these",explanation : number = ( 800 * 700 * 600 ) / 8 * 7 * 6 = 2000000 answer : d
Break down and solve the equation step by step.,"a certain pair of used shoes can be repaired for $ 13.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ? a ) 17.69 , b ) 14.85 , c ) 21.3 , d ) 16.5 , e ) 18.51","""1 ) cost of repairing = 13.5 ( for one year ) , therefore for 2 years it would be $ 27 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 32 - 27 ) / ( 27 ) * 100 = 18.51 % . ans is e"""
Break down and solve the equation step by step.,"the least number , which when divided by 12 , 31 , 20 and 54 leaves in each case a remainder of 8 is : a ) 448 , b ) 488 , c ) 16748 , d ) 548 , e ) 560","""required number = ( l . c . m . of 12 , 31 , 20 , 54 ) + 8 = 16740 + 8 = 16748 . answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","if - 3 x + 2 y = 28 and 3 x + 6 y = 84 , what is the product of x and y ? a ) 264 . , b ) 428 , c ) 0 , d ) 462 , e ) 642","""given - 3 x + 2 y = 28 - - - eq 1 3 x + 6 y = 84 - - eq 2 sum both eqns we get 8 y = 112 = > y = 14 sum 2 y in eq 1 = > - 3 x - 28 = 28 . = > x = 0 now xy = 0 * 14 = 0 . option c is correct answer ."""
Provide a detailed solution to the given mathematical problem.,"how many integers between 100 and 160 , inclusive , can not be evenly divided by 3 nor 5 ? a ) 32 , b ) 27 , c ) 25 , d ) 35 , e ) 29","""the total numbers between 100 and 160 , inclusive , is 61 . 3 * 34 = 102 and 3 * 53 = 159 so the number of multiples of 3 is 20 . 5 * 20 = 100 and 5 * 32 = 160 so the number of multiples of 5 is 13 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 10 = 150 so the number of multiples of 15 is 4 . thus the total number is 61 - 20 - 13 + 4 = 32 . the answer is a ."""
Provide a detailed solution to the given mathematical problem.,"john had a stock of 1000 books in his bookshop . he sold 20 on monday , 120 on tuesday , 200 on wednesday , 250 on thursday and 300 on friday . what percentage of the books were not sold ? a ) 68 % , b ) 74 % , c ) 76 % , d ) 62 % , e ) 89 %","""let n be the total number of books sold . hence n = 20 + 120 + 200 + 250 + 300 = 890 let m be the books not sold m = 1000 - n = 1200 - 890 = 798 percentage books not sold / total number of books = 890 / 1000 = 0.89 = 89 % correct answer e"""
"Solve the problem systematically, showing each step clearly.","a bag consists of 60 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? a ) 11 / 12 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16","bag consists of 60 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 60 - 5 - 9 = 46 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 60 + 46 / 60 = 55 / 60 = 11 / 12 hence , answer will be a ."
Explain the solution process for the given equation.,"a store reduced the price of all items in the store by 8 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ? a ) 80.0 , b ) 80.9 , c ) 81.0 , d ) 81.1 , e ) 82.8",consider price of the all items as $ 100 after a initial reduction of 8 % price becomes = 0.92 * 100 = $ 92 after the final reduction of 10 % price becomes = 0.9 * 92 = $ 82.8 price of all items on second day is 82.8 % of price on first day correct answer option e
"Solve the problem systematically, showing each step clearly.","the average weight of 8 person' s increases by 5 kg when a new person comes in place of one of them weighing 35 kg . what might be the weight of the new person ? a ) 80 kg , b ) 85 kg , c ) 75 kg , d ) 100 kg , e ) 110 kg","""total weight increased = ( 8 x 5 ) kg = 40 kg . weight of new person = ( 35 + 40 ) kg = 75 kg . answer : c"""
Break down and solve the equation step by step.,"find the value of 72519 x 9999 = m ? a ) 455465473 , b ) 654676854 , c ) 667676753 , d ) 725117481 , e ) 764534522","""72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"""
Provide a detailed solution to the given mathematical problem.,"a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 13000 , then the share of b is ? a ) 6000 , b ) 12000 , c ) 18000 , d ) 24009 , e ) 24002","""ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 13000 share of b = 6 / 13 ( 13000 ) = rs . 6000 answer : a"""
Explain the solution process for the given equation.,"in a bag , there are 2400 ball , and their colors are red , green blue . . the ratio of the balls are 15 : 13 : 17 . then how many red color balls are available in the bag ? a ) 900 , b ) 1600 , c ) 750 , d ) 890 , e ) 1010",red : green : blue = 15 + 13 + 17 = 45 ; ratio of the red balls = 15 / 40 simplify = 3 / 8 * 2400 = 900 . answer = a
Explain the solution process for the given equation.,"steve traveled the first 2 hours of his journey at 30 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ? a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph","""distance traveled in 2 hours = 2 * 30 = 60 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 60 = 300 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 300 / 5 = 60 mph answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","12 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ? a ) 190 , b ) 132 , c ) 210 , d ) 220 , e ) 225","""though 2 * ( 12 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 11 , so he' ll play 22 matches . similarly , second guy has to play with the rest of 10 as his 2 games with the first guy are already played . so he plays 20 matches . this continues like this and the total matches are 22 + 20 + 18 . . . + 2 22 + 20 + . . . + 2 = 2 ( 11 + 10 + . . . + 1 ) = 2 ( ( 11 * 12 ) / 2 ) = 11 * 12 = 132 . answer : b"""
Break down and solve the equation step by step.,"two trains each 170 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 55 km / h while the other travels at 50 km / h . how long will it take for them to pass each other completely . a ) 15 sec , b ) 11.6 sec , c ) 31.6 sec , d ) 12.6 sec , e ) 23 sec",explanation : d = 170 m + 170 m = 340 m rs = 55 + 50 = 105 * 5 / 18 = 146 / 5 t = 340 * 5 / 146 = 11.6 sec answer : option b
Provide a detailed solution to the given mathematical problem.,"7 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ? a ) 40 , b ) 48 , c ) 45 , d ) 42 , e ) 22","""though 2 * ( 7 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 6 , so he' ll play 12 matches . similarly , second guy has to play with the rest of 5 as his 2 games with the first guy are already played . so he plays 10 matches . this continues like this and the total matches are 12 + 10 + 8 . . . + 2 12 + 10 + . . . + 2 = 2 ( 6 + 5 + . . . + 1 ) = 2 ( ( 6 * 7 ) / 2 ) = 6 * 7 = 42 . answer : d"""
Provide a detailed solution to the given mathematical problem.,"find a sum for 1 st 5 prime no .' s ? a ) 23 , b ) 28 , c ) 30 , d ) 32 , e ) 34","""required sum = ( 2 + 3 + 5 + 7 + 11 ) = 28 note : 1 is not a prime number option b"""
Explain the solution process for the given equation.,"a clock shows the time as 12 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ? a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 30 minutes , e ) 40 minutes","""there are 6 hours in between 12 a . m . to 6 p . m . 6 * 5 = 30 minutes . answer : d"""
Explain the solution process for the given equation.,"convert 200 inches into centimeter ? a ) 512 cm , b ) 520 cm , c ) 508 cm , d ) 510 cm , e ) 554 cm","""1 inch = 2.54 cm 200 inches = 200 * 2.54 = 508 cm answer is c"""
"Work through the equation methodically, ensuring clarity at each step.","in one hour , a boat goes 15 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is : a ) 2 , b ) 4 , c ) 10 , d ) 12 , e ) 15","""sol . speed in still water = 1 / 2 ( 15 + 5 ) kmph = 10 kmph . answer c"""
"Solve the problem systematically, showing each step clearly.","a dog takes 4 leaps for every 5 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is : a ) 12 : 5 , b ) 4 : 3 , c ) 9 : 5 , d ) 9 : 1 , e ) 9 : 2","""explanation : dog : hare = ( 4 * 3 ) leaps of hare : 5 leaps of hare = 12 : 5 . answer : a ) 12 : 5"""
Break down and solve the equation step by step.,"if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 39 , find the value of ab . a ) 15 , b ) 8 , c ) 4 , d ) 10 , e ) 3","""2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 39 - 9 = 30 ab = 15 . answer is a ."""
Explain the solution process for the given equation.,"a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 2.9 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ? a ) 1.6 , b ) 1.9 , c ) 2.2 , d ) 2.5 , e ) 2.8","""72 km / hr = 1.2 km / min the total distance is 3 km . 3 / 1.2 = 2.5 minutes the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 60 = x ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",a ) 1
"Work through the equation methodically, ensuring clarity at each step.","compare the rates of two trains , one travelling at 45 km / hr and other is at 10 m / s ? a ) 5 : 4 , b ) 3 : 2 , c ) 1 : 5 , d ) 2 : 7 , e ) 3 : 5","""speed of the 1 st train = 45 km / hr speed of the 2 nd train = 10 m / s = 10 * 18 / 5 = 36 km / hr ratio of the speeds of the train = 45 : 36 = 5 : 4 answer is a"""
"Solve the problem systematically, showing each step clearly.","what is the remainder when 7 ^ 74 - 5 ^ 74 is divided by 2 ? a ) 5 , b ) 1 , c ) 2 , d ) 3 , e ) none of these","""easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 24 * 2 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : e"""
Explain the solution process for the given equation.,"the average of first 18 natural numbers is ? a ) 5.6 , b ) 9.5 , c ) 9.1 , d ) 9.8 , e ) 5.2","""sum of 18 natural no . = 342 / 2 = 171 average = 171 / 18 = 9.5 answer : b"""
"Solve the problem systematically, showing each step clearly.","a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 6 days before the completion of the work . in how many days was the work completed ? a ) 12 days , b ) 16 days , c ) 18 days , d ) 11.5 days , e ) 38 days","""one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 6 days = 6 * ( 1 / 24 + 1 / 30 ) = 9 / 20 remaining work = 11 / 20 the number of days required for this initial work = 5.5 days . the total number of days required = 6 + 5.5 = 11.5 days . answer : d"""
Break down and solve the equation step by step.,"find the ratio in which rice at rs . 7.00 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg a ) 6 : 7 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8","""by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 70 = 6 : 7 answer : a"""
Break down and solve the equation step by step.,"a walks at 30 kmph and 30 hours after his start , b cycles after him at 45 kmph . how far from the start does b catch up with a ? a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2700 km , e ) 3600 km","""suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 45 = 30 x = 2700 km answer is d"""
Explain the solution process for the given equation.,"an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 1 / 4 % , then the amount invested at 11 % was ? a ) 12500 , b ) 37500 , c ) 29977 , d ) 26777 , e ) 19871","""let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 37 / 4 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 37000 / 4 = 925000 x = 87500 sum invested at 9 % = rs . 87500 sum invested at 11 % = rs . ( 100000 - 87500 ) = rs . 12500 . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","how many of the positive factors of 24 are not factors of 26 a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 6","""factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 26 - 1 , 2 , 13 , 26 comparing both , we have 6 factors of 24 which are not factors of 26 - 3 , 4 , 6 , 8 , 12,24 answer : e"""
Provide a detailed solution to the given mathematical problem.,"8 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ? a ) 2 , b ) 6 , c ) 4 , d ) 7 , e ) 5","""required number of machines = 8 * 10 / 40 = 2 answer is a"""
Provide a detailed solution to the given mathematical problem.,"bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 20 white marbles . how many red marbles could be in bag a ? a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8","""6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 20 = 6 k + 4 k k = 2 total red' s in bag a will be 2 k = 4 c"""
Break down and solve the equation step by step.,"there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 11,000 after 3 years at the same rate ? a ) 3641 , b ) 2572 , c ) 4542 , d ) 2343 , e ) 3972","""let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 11000 . t = 3 years and r = 10 % p . a . c . i . = rs . 11000 x 1 + 10 3 - 1 100 = rs . 11000 x 331 1000 = 3641 . a"""
"Work through the equation methodically, ensuring clarity at each step.","the cross - section of a cannel is a trapezium in shape . if the cannel is 6 m wide at the top and 4 m wide at the bottom and the area of cross - section is 10290 sq m , the depth of cannel is ? a ) 258 , b ) 260 , c ) 262 , d ) 264 , e ) 266",1 / 2 * d ( 6 + 4 ) = 10290 d = 258 answer : a
Provide a detailed solution to the given mathematical problem.,"how long does a train 100 m long traveling at 54 kmph takes to cross a station of 250 m in length ? a ) 22 sec , b ) 20 sec , c ) 15 sec , d ) 23 sec , e ) 16 sec","""d = 100 + 245 = 345 m s = 54 * 5 / 18 = 15 t = 345 * 1 / 15 = 23 sec answer : d"""
"Solve the problem systematically, showing each step clearly.","in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ? a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 480 $","""total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 55 ) = 21 + 429 = > 450 hence answer will be ( d ) 450"""
Provide a detailed solution to the given mathematical problem.,"how many integers between 1 and 1,400 are divisible by 25 , and 35 ? a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8","""lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e"""
Explain the solution process for the given equation.,"the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 70 sq . cm . find the length of the rectangle . a ) 12 cm , b ) 14 cm , c ) 16 cm , d ) 18 cm , e ) 20 cm","""explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 70 = > 5 x - 25 = 70 = > x = 18 . length of the rectangle = 18 cm . answer : option d"""
"Work through the equation methodically, ensuring clarity at each step.","donovan took a math test and got 35 correct and 13 incorrect answers . what was the percentage of correct answers ? ( round to the nearest hundredth ) a ) 57.78 % , b ) 67.78 % , c ) 72.92 % , d ) 47.78 % , e ) 97.78 %",35 correct our of 48 total ( 35 + 13 ) 35 / 48 correct answer c
Provide a detailed solution to the given mathematical problem.,"if 5 men undertook a piece of construction work and finished half the job in 15 days . if two men drop out , then the job will be completed in a ) 5 days , b ) 15 days , c ) 10 days , d ) 25 days , e ) 20 days","that is , half the work done = 5 * 15 * 1 / 2 then , 5 * 15 * 1 / 2 = 3 * ? * 1 / 2 i . e . 5 * 15 = 3 * ? = 5 * 15 / 3 = 25 day d"
"Work through the equation methodically, ensuring clarity at each step.","bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 15 left in his pocket . what was the value of n ? a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68","started to test answer c if he had 52 , then he spent 13 at hardware store now he was left with 39 $ he spent 9 dollars on cleaning , thus he remained with 30 $ he then spent 1 / 2 of 30 , or 15 , and was left with 15 . hence , the only option that can be right is c ."
"Work through the equation methodically, ensuring clarity at each step.","the average of 11 results is 60 . if the average of first 6 results is 58 and that of the last 6 is 63 , find the sixth result ? a ) 50 , b ) 52 , c ) 65 , d ) 42 , e ) 66",sixth result = 58 * 6 + 63 * 6 - 60 * 11 = 66 answer is e
Provide a detailed solution to the given mathematical problem.,"how many integers are divisible by 9 between 10 ! and 10 ! + 100 inclusive ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10","""e - 7 10 ! is divisible by 9 there are 11 numbers between 10 ! and 10 ! + 100 that are divisible by 9 . hence 10"""
"Work through the equation methodically, ensuring clarity at each step.","a batsman in his 17 th innings makes a score of 85 and their by increasing his average by 3 . what is his average after the 17 th innings ? a ) 28 , b ) 27 , c ) 12 , d ) 37 , e ) 01","""explanation : 16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a bowl of fruit contains 14 apples and 25 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ? a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 19","""number of apples = 14 number of oranges = 25 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 25 - x ) = 39 - x 14 / ( 39 - x ) = 7 / 10 = > 20 = 39 - x = > x = 19 answer e"""
Break down and solve the equation step by step.,"a batch of cookies was divided amomg 3 tins : 3 / 4 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 3 / 5 , e ) 9 / 7","""this will help reduce the number of variables you have to deal with : g + b = 3 / 4 r = 1 / 3 b = 1 / 4 we can solve for g which is 1 / 2 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 1 / 2 + 1 / 3 ) = 1 / 2 x = 3 / 5 answer : d"""
Break down and solve the equation step by step.,"the length of the bridge , which a train 160 metres long and travelling at 45 km / hr can cross in 30 seconds , is : a ) 200 m , b ) 215 m , c ) 245 m , d ) 250 m , e ) 270 m","""let the length of the bridge : l the equation now is l + 160 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 215 m answer : b"""
Explain the solution process for the given equation.,"sum of two numbers prime to each other is 16 and their l . c . m . is 63 . what are the numbers ? a ) 9 and 10 , b ) 8 and 9 , c ) 11 and 5 , d ) 7 and 8 , e ) 7 and 9","as two numbers are prime , only options satisfy all but option c will not make the product of numbers i . e 63 answer : e"
Break down and solve the equation step by step.,"a and b complete a work in 9 days . a alone can do it in 18 days . if both together can do the work in how many days ? a ) 6 days , b ) 8 days , c ) 5 days , d ) 7 days , e ) 15 days","""1 / 9 + 1 / 18 = 1 / 6 6 / 1 = 6 days answer : a"""
"Solve the problem systematically, showing each step clearly.","an association of mathematics teachers has 1,500 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 40 percent of the votes cast ? a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 14 %","""total umber of members = 1500 number of members that cast votes = 525 since , winning candidate received 40 percent of the votes cast number of votes for winning candidate = ( 40 / 100 ) * 525 = 210 percent of total membership that voted for winning candidate = ( 210 / 1500 ) * 100 = 14 % answer e"""
Explain the solution process for the given equation.,"in a graduate physics course , 70 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is married ? a ) 2 / 7 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7","""let assume there are 100 students of which 70 are male and 30 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 70 = 20 males are married if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married . total females = 30 married females = 10 then single females = 30 - 10 = 20 we need to find the fraction of female students who are single i . e single female students / total female student = 10 / 30 = 1 / 3 [ b ]"""
Provide a detailed solution to the given mathematical problem.,"a rectangle having length 140 cm and width 40 cm . if the length of the rectangle is increased by thirty percent then how much percent the breadth should be decreased so as to maintain the same area . a ) 17.64 % , b ) 33.33 % , c ) 40 % , d ) 75 % , e ) none of these",explanation : solution : ( 30 / ( 140 + 30 ) * 100 ) % = 17.64 % answer : a
Explain the solution process for the given equation.,"the sector of a circle has radius of 21 cm and central angle 135 o . find its perimeter ? a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm","""perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 49.5 + 42 = 91.5 cm answer : a"""
Provide a detailed solution to the given mathematical problem.,"every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 4 / 5 of the juniors is equal to 1 / 2 of the seniors , what fraction of the students in the room are juniors ? a ) 13 / 20 , b ) 11 / 3 , c ) 5 / 13 , d ) 12 / 17 , e ) 17 / 20","""let total number of juniors = j total number of seniors = s ( 4 / 5 ) j = ( 1 / 2 ) s = > s = 8 / 5 j total number of students = j + s = ( 13 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 13 / 5 ) j ] = 5 / 13 answer c"""
"Solve the problem systematically, showing each step clearly.","after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5265 . what was the number of original inhabitants ? a ) 7500 , b ) 7800 , c ) 8100 , d ) 8400 , e ) 8700","""let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5265 ( 27 / 40 ) * x = 5265 x = 5265 * 40 / 27 = 7800 the answer is b ."""
Explain the solution process for the given equation.,"when jessica withdrew $ 400 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 4 of the remaining balance , what will be the final balance in her bank account ? a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 750",as per the question 400 = 2 a / 5 thus - a which is the total amount = 1000 the amount thus left = 600 she then deposited 1 / 4 of 600 = 150 total amount in her account = 750 answer e
Break down and solve the equation step by step.,"a sum of money lent out at s . i . amounts to a total of $ 520 after 2 years and to $ 820 after a further period of 5 years . what was the initial sum of money that was invested ? a ) $ 340 , b ) $ 360 , c ) $ 380 , d ) $ 400 , e ) $ 420","""s . i for 5 years = $ 820 - $ 520 = $ 300 the s . i . is $ 60 / year s . i . for 2 years = $ 120 principal = $ 520 - $ 120 = $ 400 the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"a rectangular tiled patio is composed of 48 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 48 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ? a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28","""suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 48 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 48 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 48 ( 2 r - 4 ) * r = 48 2 r ^ 2 - 4 r - 48 = 0 r can not be negative so r = 6 and c = 8 so , answer will be b"""
Explain the solution process for the given equation.,"10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3168 , how much was it in the beginning ? a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600","""x * ( 90 / 100 ) * ( 80 / 100 ) = 3168 x = 4400 answer : c"""
Break down and solve the equation step by step.,"what annual payment will discharge a debt of rs . 1090 due in 2 years at the rate of 5 % compound interest ? a ) 993.2 , b ) 586.21 , c ) 534.33 , d ) 543.33 , e ) 646.33","explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1090 820 x + 1090 * 441 x = 586.21 so , value of each installment = rs . 586.21 answer : option b"
"Work through the equation methodically, ensuring clarity at each step.","a bowl was filled with 10 ounces of water , and 0.006 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ? a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 3 % , e ) 40 %","""total amount of water evaporated each day during a 50 - day period = . 006 * 50 = . 006 * 100 / 2 = . 6 / 2 = . 3 percent of the original amount of water evaporated during this period = ( . 3 / 10 ) * 100 % = 3 % answer d"""
Explain the solution process for the given equation.,"alfred buys an old scooter for $ 4400 and spends $ 800 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ? a ) 5.45 % , b ) 6.23 % , c ) 7 % , d ) 8.12 % , e ) 11.5 %","""c . p . = 4400 + 800 = $ 5200 s . p . = $ 5800 gain = 5800 - 5200 = $ 600 gain % = 600 / 5200 * 100 = 11.5 % answer is e"""
"Solve the problem systematically, showing each step clearly.","how many numbers from 9 to 79 are exactly divisible by 11 ? a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12","""9 / 11 = 0 and 79 / 11 = 7 = = > 7 - 0 = 7 numbers answer : b"""
Break down and solve the equation step by step.,"5358 x 53 = ? a ) 272258 , b ) 272358 , c ) 283974 , d ) 274258 , e ) 274358","""5358 x 51 = 5358 x ( 50 + 3 ) = 5358 x 50 + 5358 x 3 = 267900 + 16074 = 283974 . c )"""
Provide a detailed solution to the given mathematical problem.,"john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ? a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .","""the total distance d traveled by john is given by d = 45 * 2 + 3 * 55 = 255 miles . answer c"""
Provide a detailed solution to the given mathematical problem.,"if 2 ^ 5 , 3 ^ 3 , and 10 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ? a ) 26 , b ) 39 , c ) 120 , d ) 65 , e ) 156","""here 156 has three two' s two three' s and one 10 rest of them must be in w so w = 10 * 3 * 4 = 120 smash c"""
"Solve the problem systematically, showing each step clearly.","the banker' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6.6 . the true discount is a ) rs . 72 , b ) rs . 36 , c ) rs . 55 , d ) rs . 50 , e ) none",solution t . d = [ b . g x 100 / r x t ] = rs . ( 6.6 x 100 / 12 x 1 ) = rs . 55 . answer c
"Work through the equation methodically, ensuring clarity at each step.","a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a a ) rs . 300 , b ) rs . 56 , c ) rs . 100 , d ) rs . 240 , e ) rs . 90","""explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = rs . 240 answer : d"""
Break down and solve the equation step by step.,"one fourth of a solution that was 22 % sugar by weight was replaced by a second solution resulting in a solution that was 35 percent sugar by weight . the second solution was what percent sugar by weight ? a ) 74 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %","""say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.22 + 1 / 4 * x = 1 * 0.35 - - > x = 0.74 . alternately you can consider total solution to be 100 liters and in this case you' ll have : 75 * 0.22 + 25 * x = 100 * 0.35 - - > x = 0.74 . answer : a ."""
"Work through the equation methodically, ensuring clarity at each step.","how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 7 ? a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9","""the numbers should be of the form 7 c + 3 . the minimum is 3 when c = 0 . the maximum is 45 when c = 6 . there are 7 such numbers . the answer is c ."""
Explain the solution process for the given equation.,"the compound interest earned by sunil on a certain amount at the end of two years at the rate of 5 % p . a . was rs . 492 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned . a ) rs . 4935 , b ) rs . 4925 , c ) rs . 5390 , d ) rs . 5290 , e ) rs . 5292","""let the sum be rs . p p { [ 1 + 5 / 100 ] 2 - 1 } = 492 p ( 5 / 100 ) ( 2 + 5 / 100 ) = 492 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 492 / ( 0.05 ) ( 2.05 ) = 4800 . amount = 4800 + 492 = rs . 5292 answer : e"""
Provide a detailed solution to the given mathematical problem.,"john' s bank' s saving amount is decreased 50 % due to loan payment and current balance is rs . 50000 . find the actual balance before deduction ? a ) 100000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 10000","""50 % decreased 50 % balance = 50000 100 % = 50000 / 50 * 100 = 100000 answer : a"""
Break down and solve the equation step by step.,"a bicycle wheel has a diameter of 0.81 m . how many complete revolutions does it make in 1 km ? a ) 246 , b ) 448 , c ) 393 , d ) 710 , e ) 223","""1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.81 m ) = 393.2 . hence 393 complete revolutions . answer c"""
Explain the solution process for the given equation.,"the number n is 5 , h 64 , where h represents the 100' s digit . if n is divisible by 4 , what is the value of h ? a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) all the above value","if the number is divisible by 4 , the last two digits must be divisible by 4 . all the values yields such a number . answer : e"
Break down and solve the equation step by step.,"a train running at 1 / 5 of its own speed reached a place in 20 hours . how much time could be saved if the train would have run at its own speed ? a ) 8 hrs , b ) 10 hrs , c ) 12 hrs , d ) 16 hrs , e ) 6 hrs","""time taken if run its own speed = 1 / 5 * 20 = 4 hrs time saved = 20 - 4 = 16 hrs answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 12 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ? a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 14 %","""total time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 12 = 14 gallons - - - > 2 / 14 = 14 % of the fuel used . e is the correct answer ."""
Explain the solution process for the given equation.,"tom left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ? a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600","in order not to lose money because of the change tom' s total commission must beat least $ 75000 - $ 45000 = $ 30000 , so total sales must beat least $ 30000 / 0.15 = $ 200000 . which means that he must makeat least $ 200000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d ."
Break down and solve the equation step by step.,"a certain maroon paint contains 50 percent blue pigment and 50 percent red pigment by weight . a certain green paint contains 30 percent blue pigment and 70 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ? a ) 3 , b ) 3.5 , c ) 2.5 , d ) 4 , e ) 4.5","10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 5 = 2.5 grams of red pigment"
"Solve the problem systematically, showing each step clearly.","when the price of an article was reduced by 40 % its sale increased by 80 % . what was the net effect on the sale ? a ) 8 % increase , b ) 4 % decrease , c ) 6 % increase , d ) 66 % increase , e ) 66 % decrease","""if n items are sold for $ p each , revenue is $ np . if we reduce the price by 40 % , the new price is 0.6 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.6 p ) ( 1.8 n ) = 1.08 np , which is 1.08 times the old revenue , so is 8 % greater . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ? a ) 17 years , b ) 19 years , c ) 29 years , d ) 8 years , e ) 12 years","""let c' s age be x years . then , b' s age = 2 x years . a' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b' s age = 2 x = 8 years . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","how many even number in the range between 10 to 120 inclusive are not divisible by 3 a ) 15 , b ) 30 , c ) 31 , d ) 37 , e ) 46","""we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 120 using ap formula , we can say 120 = 10 + ( n - 1 ) * 2 or n = 56 . for 6 , 12,18 , . . . 120 using ap formula , we can say 120 = 12 + ( n - 1 ) * 6 or n = 19 . hence , only divisible by 2 but not 3 = 56 - 19 = 37 . hence , answer d"""
Break down and solve the equation step by step.,"every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 83200 ? a ) 81000 , b ) 81028 , c ) 105300 , d ) 29889 , e ) 22312",83200 * 9 / 8 * 9 / 8 = 105300 . answer : c
"Solve the problem systematically, showing each step clearly.","a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ] a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7","""let there be g geese , of which 0.3 g are male and 0.7 g are female lets say m geese migrated , 0.2 m are male and 0.8 m are female migration rate male = 0.2 m / 0.3 g = ( 2 / 3 ) * ( m / g ) migration rate female = 0.8 m / 0.7 g = ( 8 / 7 ) * ( m / g ) ratio of migration rates = ( 2 / 3 ) / ( 8 / 7 ) = 7 / 12 answer is ( b )"""
Break down and solve the equation step by step.,"the class mean score on a test was 60 , and the standard deviation was 5 . if jack' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ? a ) 30 , b ) 31 , c ) 45 , d ) 40 , e ) 89","""1 sd from the mean is adding and subtrating the amount if standard deviation from the mean one time . 2 sd from the mean is adding and subtracting twice . 1 sd from the mean ranges from 65 to 55 , where 65 is within sd above the mean and 55 within 1 sd below the mean 2 sd = 5 twice = 10 from the the mean , which is 70 to 40 , where 70 is within 2 sd above the mean and 40 is within 2 sd below the mean . answer = d"""
Break down and solve the equation step by step.,"it takes 3 workers a total of 9 hours to build a giant machine with each worker working at the same rate . if 3 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 2 : 00 pm , at what time will the machine be complete ? a ) 5 : 15 , b ) 5 : 26 , c ) 5 : 37 , d ) 5 : 48 , e ) 5 : 59","""3 workers build 1 / 9 of a machine in one hour . 1 worker builds 1 / 27 of a machine in one hour . in the first 3 hours , 3 workers build 3 * ( 1 / 27 ) * 3 = 9 / 27 of a machine from 2 : 00 to 3 : 00 , 4 workers build another 4 / 27 . the total is 13 / 27 . from 3 : 00 to 4 : 00 , 5 workers build another 5 / 27 . the total is 18 / 27 . from 4 : 00 to 5 : 00 , 6 workers build another 6 / 27 . the total is 24 / 27 . to build another 3 / 27 , 7 workers need ( 3 / 7 ) * 60 minutes which is about 26 minutes . the machine is complete at about 5 : 26 . the answer is b ."""
"Solve the problem systematically, showing each step clearly.","what will be the cost of building a fence around a square plot with area equal to 81 sq ft , if the price per foot of building the fence is rs . 58 ? a ) 3944 , b ) 2287 , c ) 2977 , d ) 2088 , e ) 1298","""let the side of the square plot be a ft . a 2 = 81 = > a = 9 length of the fence = perimeter of the plot = 4 a = 36 ft . cost of building the fence = 36 * 58 = rs . 2088 . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","two tracks are parallel . the first track has 6 checkpoints and the second one has 10 checkpoints . in how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle ? ['a ) 120','b ) 150','c ) 200','d ) 270','e ) 420']","to make a triangle , you need 2 checkpoints from one track and 1 from the other . you can not have all 3 from the same track since then the points will be in a line ( assuming straight line of track ) you select 2 checkpoints from the first track and one from the second or two from the second track and one from the first . 6 c 2 * 10 c 1 + 10 c 2 * 6 c 1 = 150 + 270 = 420 answer ( e )"
Provide a detailed solution to the given mathematical problem.,"how many bricks each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall 8 m x 6 m x 22.5 m a ) 5600 , b ) 600 , c ) 6400 , d ) 7200 , e ) none of these","""explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 25 x 11.25 x 6 ) = 6400 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","the average of 6 no .' s is 6.40 . the average of 2 of them is 6.2 , while the average of the other 2 is 6.1 . what is the average of the remaining 2 no' s ? a ) 2.3 , b ) 2.6 , c ) 6.9 , d ) 4.5 , e ) 4.6","""sum of the remaining two numbers = ( 6.4 * 6 ) - [ ( 6.2 * 2 ) + ( 6.1 * 2 ) ] = 38.40 - ( 12.4 + 12.2 ) = 38.40 - 24.6 = 13.80 required average = ( 13.8 / 2 ) = 6.9 answer : c"""
Explain the solution process for the given equation.,"an aeroplane covers a certain distance of 530 kmph in 5 hours . to cover the same distance in 3 2 / 3 hours , it must travel at a speed of a ) 440 , b ) 540 , c ) 640 , d ) 722 , e ) 250","""speed of aeroplane = 530 kmph distance travelled in 5 hours = 530 * 5 = 2650 km speed of aeroplane to acver 2650 km in 11 / 3 = 2650 * 3 / 11 = 722 km answer d"""
Provide a detailed solution to the given mathematical problem.,"a certain junior class has 1,000 students and a certain senior class has 400 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ? a ) 3 / 20,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15","""total number of ways of choosing one student from each group is = 400 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 60 / ( 400 * 1000 ) = 3 / 20,000 a"""
Provide a detailed solution to the given mathematical problem.,"find the sum of the number of combinations possible by using 12 , 34 such that no number is repeated ( ex : - 12234322 are invalid 12344321 are valid ) more than once . a ) 66660 , b ) 66760 , c ) 66860 , d ) 66960 , e ) 67660","total no . formed = 4 ! = 4 * 3 * 2 * 1 = 24 each digit will be used at each positions , 6 times sum of digits at unit place = 6 * 1 + 6 * 2 + 6 * 3 + 6 * 4 = 6 * ( 1 + 2 + 3 + 4 ) = 60 this sum will be same for hundred , tens & unit places sum of all 4 digit numbers formed using digits 12 , 34 = 1000 * 60 + 100 * 60 + 10 * 60 + 60 = 60 * ( 1000 + 100 + 10 + 1 ) = 60 * 1111 = 66660 answer : a"
"Solve the problem systematically, showing each step clearly.","a and b are mixed together in the ratio 9 : 11 . what is the weight of mixture , if 26.1 kg of a has been consumed in it ? a ) 56 , b ) 45 , c ) 58.2 , d ) 58 , e ) 46","explanation : for 9 kg a , mixture = ( 9 + 11 ) kg . for 26.1 kg a , mixture = ( ( 20 / 9 ) x 26.1 ) kg = 58 kg . answer : d"
"Solve the problem systematically, showing each step clearly.","an urn contains 5 red , 6 blue and 8 green balls . 3 balls are randomly selected from the urn , find the probability that the drawn ball are 2 blue and 1 red ? a ) 25 / 323 , b ) 21 / 969 , c ) 28 / 989 , d ) 74 / 879 , e ) 23 / 589","""sample space = no . of ways 3 balls were drawn from urn = 19 c 3 = 969 no . ways 2 blue balls and 1 red were drawn from bag = 6 c 2 * 5 c 1 = 75 probability = 75 / 969 = 25 / 323 ans - a"""
Provide a detailed solution to the given mathematical problem.,"mary' s income is 60 % more than tim' s income and tim' s income is 30 % less than juan' s income . what % of juan' s income is mary' s income . a ) 112 % , b ) b . 100 % , c ) 96 % , d ) 80 % , e ) 64 %","""even i got 96 % j = 100 t = 100 * 0.7 = 70 m = 70 * 1.6 = 112 if mary' s income is x percent of j m = j * x / 100 x = m * 100 / j = 112 * 100 / 100 = 112 ans : a"""
Explain the solution process for the given equation.,"3 candidates in an election and received 1000 , 2000 and 4000 votes respectively . what % of the total votes did the winning candidate got in that election ? a ) 45 % , b ) 50 % , c ) 57.14 % , d ) 60 % , e ) 65.12 %","""total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 so , required percentage = 4000 / 7000 * 100 = 57.14 % c"""
Explain the solution process for the given equation.,"a can do a work in 40 days , b in 60 days . a alone start the work after 10 days he left work . in how many days b can finish the work ? a ) 20 days , b ) 15 days , c ) 30 days , d ) 45 days , e ) 50 days",10 days work of a = 10 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 b can finish 3 / 4 work = 60 * 3 / 4 = 45 days answer is d
"Work through the equation methodically, ensuring clarity at each step.","a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 16 km ? a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 7","""m = 4 s = 2 us = 4 - 2 = 2 d = 16 t = 16 / 2 = 8 answer : c"""
Explain the solution process for the given equation.,"two cyclist start from the same places in opposite directions . one is going towards north at 5 kmph and the other is going towards south 5 kmph . what time will they take to be 50 km apart ? a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs","""to be ( 5 + 5 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 10 * 50 = 5 hrs answer is d"""
Explain the solution process for the given equation.,"in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 12 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ? a ) 40 , b ) 44 , c ) 66 , d ) 52 , e ) none of these","""let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 12 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 12 = 4 / 9 ( t - 12 ) 10 t = 1188 - 528 = > t = 66 . answer : c"""
Break down and solve the equation step by step.,"100 is increased by 50 % . find the final number . a ) 100 , b ) 110 , c ) 150 , d ) 155 , e ) 160","""final number = initial number + 50 % ( original number ) = 100 + 50 % ( 100 ) = 100 + 50 = 150 . answer c"""
"Work through the equation methodically, ensuring clarity at each step.","how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 11 inches than that of a rectangular sheet of paper measuring 5.5 inches by 11 inches ? a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %","""let' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 11 is twice 5.5 then the area will be double which means 100 % greater . the answer is c ."""
"Solve the problem systematically, showing each step clearly.","if two positive numbers are in the ratio 1 / 7 : 1 / 5 , then by what percent is the second number more than the first ? a ) 70 % , b ) 90 % , c ) 60 % , d ) 40 % , e ) 65 %","""given ratio = 1 / 7 : 1 / 5 = 5 : 7 let first number be 5 x and the second number be 7 x . the second number is more than first number by 2 x . required percentage = 2 x / 5 x * 100 = 40 % . answer : d"""
"Solve the problem systematically, showing each step clearly.","a driver just filled the car' s gas tank with 36 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ? a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3","""let x be the number of liters of ethanol added to the gas tank . 0.05 ( 36 ) + x = 0.1 ( 36 + x ) 0.9 x = 3.6 - 1.8 = 1.8 x = 2 liters the answer is c ."""
Explain the solution process for the given equation.,"the cross - section of a cannel is a trapezium in shape . if the cannel is 12 m wide at the top and 5 m wide at the bottom and the area of cross - section is 344 sq m , the depth of cannel is ? a ) 39 , b ) 28 , c ) 27 , d ) 40 , e ) 71","""1 / 2 * d ( 12 + 5 ) = 344 d = 40 answer : d"""
"Solve the problem systematically, showing each step clearly.","in the x - y plane , there are 4 points ( 00 ) , ( 04 ) , ( 54 ) , and ( 50 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ? a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 7 , e ) 5 / 8","the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b ."
"Solve the problem systematically, showing each step clearly.","how long does a train 110 m long running at the speed of 54 km / hr takes to cross a bridge 132 m length ? a ) 12.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 16.13 sec , e ) 14.9 sec","""speed = 54 * 5 / 18 = 15 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 15 = 16.13 sec . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a dog travelled for 2 hours . he covered the first half of the distance at 10 kmph and remaining half of the distance at 5 kmph . find the distance travelled by the dog ? a ) 20 km , b ) 16 km , c ) 6 km , d ) 3 km , e ) 61 km",let the distance travelled be x km . total time = ( x / 2 ) / 10 + ( x / 2 ) / 5 = 2 = > x / 20 + x / 10 = 2 = > ( 1 x + 2 x ) / 20 = 2 = > x = 20 km answer : a
Break down and solve the equation step by step.,"the perimeter of a semi circle is 113 cm then the radius is ? a ) 17 , b ) 28 , c ) 19 , d ) 11 , e ) 22","""36 / 7 r = 113 = > r = 22 answer : e"""
Break down and solve the equation step by step.,"what is the value of 10 ^ 7 - 6 ^ 5 ? a ) 99 , 91,223 , b ) 99 , 92,224 , c ) 99 , 94,265 , d ) 99 , 95,300 , e ) 99 , 96,307","""as 10 ^ n will always have last digit as 0 and 6 ^ n will always as last digit 6 . . hence difference of such sum should always be ending with 4 and there is only on option . . answer b"""
"Solve the problem systematically, showing each step clearly.","a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase w in sales ? a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %","""last year' s sales = $ 320 million ; this year' s sales = $ 385 million ; increase w = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."""
"Solve the problem systematically, showing each step clearly.","3 consecutive odd integers are in increasing order such that the sum of the last two integers is 17 more than the first integer . find the 3 integers ? a ) 11 , 1315 , b ) 7 , 2 , 10 , c ) 7 , 9 , 10 , d ) 7 , 9 , 11 , e ) 7 , 9 , 29","explanation : let the three consecutive odd integers be x , x + 2 and x + 4 respectively . x + 4 + x + 2 = x + 17 = > x = 11 hence three consecutive odd integers are 11 , 13 and 15 answer : a"
Provide a detailed solution to the given mathematical problem.,"a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 4.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ? a ) 16.5 % , b ) 20 % , c ) 33 % , d ) 55 % , e ) 65 %","""the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.045 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 45 f - - > s = 2 f - - > f / s = 1 / 2 - - > f / ( s + f ) = 1 / ( 1 + 2 ) = 1 / 3 = 0.33 . answer : c ."""
"Solve the problem systematically, showing each step clearly.","the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 20 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ? a ) 32.5 , b ) 35 , c ) 48 , d ) 65 , e ) 66.67","""1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 20 % , therefore bringing down the price to $ 60 . 4 ) now 60 has to be added byx % in order to equal the original price . 60 + ( x % ) 60 = 100 . solving this eq for x , we get x = 66.67 ans is e ."""
Provide a detailed solution to the given mathematical problem.,"the average of 5 quantities is 10 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ? a ) 19 , b ) 14 , c ) 8 , d ) 9.5 , e ) none of these",answer : a ( 5 x 10 - 3 x 4 ) / 2 = 19
Provide a detailed solution to the given mathematical problem.,"the least common multiple of positive integer d and 3 - digit integer n is 690 . if n is not divisible by 3 and d is not divisible by 2 , what is the value of n ? a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690","the lcm of n and d is 690 = 2 * 3 * 5 * 23 . d is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to d . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b ."
Explain the solution process for the given equation.,"two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.50 km and 1.25 km respectively . the time taken by the slower train to cross the faster train in seconds is ? a ) 12 , b ) 77 , c ) 66 , d ) 99 , e ) 11","""relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.50 + 1.25 = 2.75 km = 2750 m . required time = 2750 * 3 / 125 = 66 sec . answer : c"""
Explain the solution process for the given equation.,"of the 170 people at a party , 70 were women , and 30 women tried the appetizer . if 60 people did not try the appetizer , what is the total number of men who tried the appetizer ? a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80",total people at party = 170 women = 70 so men 170 - 70 = 100 no . of pple who tried appetizer = 170 - 60 ( given info ) = 110 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 110 - 30 = 80 correct option e
Provide a detailed solution to the given mathematical problem.,"a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 110 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ? a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 220","""it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 110 total = 110 + 110 = 220 answer ( e )"""
"Work through the equation methodically, ensuring clarity at each step.","find a sum for first 6 prime number' ss ? a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 41",required sum = ( 2 + 3 + 5 + 7 + 11 + 13 ) = 41 note : 1 is not a prime number option e
Provide a detailed solution to the given mathematical problem.,"the ratio of buses to cars on river road is 1 to 13 . if there are 60 fewer buses than cars on river road , how many cars are on river road ? a ) 65 , b ) 60 , c ) 55 , d ) 40 , e ) 45","""b / c = 1 / 13 c - b = 60 . . . . . . . . . > b = c - 60 ( c - 60 ) / c = 1 / 13 testing answers . clearly eliminate bcde put c = 65 . . . . . . . . . > ( 65 - 60 ) / 65 = 5 / 65 = 1 / 13 answer : a"""
Explain the solution process for the given equation.,"you and your friend spent a total of $ 15 for lunch . your friend spent $ 1 more than you . how much did your friend spend on their lunch ? a ) $ 9 , b ) $ 8 , c ) $ 4 , d ) $ 6 , e ) $ 5","""my lunch = l , my friends lunch = l + 1 ( l ) + ( l + 1 ) = 15 l + l + 1 - 1 = 15 - 1 2 l = 14 l = 7 my friends lunch l + 1 = 7 + 1 = $ 8 , the answer is b"""
Explain the solution process for the given equation.,"an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 24 gallons of ethanol , how many gallons of fuel a were added ? a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 200","""say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 24 gallons then 0.12 a + 0.16 ( 200 - a ) = 24 - - > a = 200 . answer : e ."""
"Work through the equation methodically, ensuring clarity at each step.","the workforce of company x is 60 % female . the company hired 28 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ? a ) 160 , b ) 220 , c ) 336 , d ) 360 , e ) 420","""let' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 28 ) = females after adding men as quantity of women does n' t change we can make an equation : 0.6 x = 0.55 ( x + 28 ) 0.05 x = 15.4 x = 308 - this is quantity of employees before adding 28 men so after adding it will be 336 answer is c"""
Explain the solution process for the given equation.,"find the smallest number of 6 digits which is exactly divisible by 111 ? a ) 12000 , b ) 15550 , c ) 100011 , d ) 158993 , e ) 100010","""smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 answer b"""
Explain the solution process for the given equation.,"the compound interest on $ 2000 at 10 % per annum is $ 662 . the period ( in years ) is ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6",a = p ( 1 + r / 100 ) ^ t 2662 = 2000 ( 1 + 10 / 100 ) ^ t ( 11 / 10 ) ^ t = 2662 / 2000 ( 11 / 10 ) ^ t = ( 11 / 10 ) ^ 3 t = 3 years answer is b
Break down and solve the equation step by step.,"a carpenter worked alone for 1 day on a job that would take him 7 more days to finish . he and another carpenter completed the job in 4 more days . how many days would it have taken the second carpenter to do the complete job working alone ? a ) 16 , b ) 7 , c ) 9 , d ) 14 , e ) 24","""a carpenter worked only 1 day on something that takes him 7 more days . means ; carpenter finishes his work in 8 days . let his buddy finish the same task in x days . respective rates per day : 1 / 8 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 8 per day . second one worked for 4 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 8 + 4 * 1 / x = 1 5 x + 32 = 8 x 2 x = 32 x = 16 days . ans : a"""
"Work through the equation methodically, ensuring clarity at each step.","there are 408 boys and 264 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed . a ) 28 , b ) 32 , c ) 35 , d ) 30 , e ) 45","""explanation : hcf ( 408 , 264 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 264 / 24 = 17 + 11 = 28 answer : a"""
Provide a detailed solution to the given mathematical problem.,"carrie likes to buy t - shirts at the local clothing store . they cost $ 9.65 each . one day , she bought 12 t - shirts . how much money did she spend ? a ) $ 115.8 , b ) $ 248.75 , c ) $ 200 , d ) $ 171.6 , e ) $ 190",$ 9.65 * 12 = $ 115.8 . answer is a .
Provide a detailed solution to the given mathematical problem.,"rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 200 pages , of which 80 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ? a ) $ 1360 , b ) $ 1620 , c ) $ 1650 , d ) $ 680 , e ) $ 770","""for 200 - 80 - 20 = 100 pages only cost is 5 $ per page for the first time page is typed - 100 * 5 = 500 $ ; for 80 pages the cost is : first time 5 $ + 3 $ of the first revision - 80 * ( 5 + 3 ) = 640 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 500 + 640 + 220 = 1360 $ . answer : a ."""
"Solve the problem systematically, showing each step clearly.","an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 10 - meter platform and caught it after it had traveled 29.65 meters . how many times did the ball bounce ? a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9","""ans : 6 division of total diatance travelled will be 10 + 10 + 5 + 2.5 + 1.25 + 0.6 + 0.3 ans b"""
"Solve the problem systematically, showing each step clearly.","a 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 second . what is the length of the other train ? a ) 150 m , b ) 230 m , c ) 290 m , d ) 310 m , e ) 420 m",relative speed = 120 + 80 = 200 * 5 / 18 = 500 / 9 m / s let the length of the other train be x meters x + 270 / 9 = 500 / 9 x = 230 m answer is b
Explain the solution process for the given equation.,"a train of length 240 m crosses a bridge of length 150 m in 20 seconds . what is the speed of train ? a ) 33 , b ) 27 , c ) 25 , d ) 70.2 , e ) 72","""sol : ( length of train + length of bridge ) = speed of train x time ( 240 + 150 ) = 20 x speed speed = 390 / 20 = 19.5 m / s = 70.2 km / h answer = d"""
Explain the solution process for the given equation.,"if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 3 x ^ 2 + 6 x , then f ( - 1 ) = a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2",f ( - 1 ) = 3 ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 3 ( - 1 ) ^ 2 + 6 ( - 1 ) = 3 + 4 - 3 - 6 = - 2 the answer is a .
"Work through the equation methodically, ensuring clarity at each step.","claire has a total of 80 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ? a ) 39 , b ) 50 , c ) 54 , d ) 57 , e ) 36","""g + h = 80 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 80 - h or 3 ( 80 - h ) + 4 h = 300 h = 300 - 240 = 60 then g = 96 - 60 = 36 e"""
Provide a detailed solution to the given mathematical problem.,"the ratio of boarders to day scholars at a school is 7 to 16 . however , after a few new students join the initial 560 boarders , the ratio changed to 1 to 2 , respectively . if no boarders became day scholars and vice versa , and no students left the school , how many boarders joined the school ? a ) 48 , b ) 64 , c ) 70 , d ) 80 , e ) 84","let day scholars be ds and boarders be b given b / ds = 7 / 16 - - - > eq 1 initially b = 560 and x be new boarders joined then from eq 1 , we get ds = 16 / 7 * 560 = 1280 now , new ration is 560 + x / ds = 1 / 2 560 + x / 1280 = 1 / 2 = > 1120 + 2 x = 1280 = > 2 x = 160 = > x = 80 ans option d"
Provide a detailed solution to the given mathematical problem.,"what is the probability for a family with 5 children to have two boys and 3 girls ( assuming the probability of having a boy or a girl is equal ) ? a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16",one possible case is : girl - girl - girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 3 = 10 such cases so we should multiply by 10 . p ( two boys and three girls ) = 10 / 32 = 5 / 16 the answer is e .
"Work through the equation methodically, ensuring clarity at each step.","a train is 460 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ? a ) 76 seconds , b ) 18 seconds , c ) 40 seconds , d ) 48 seconds , e ) 45 seconds","""speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 460 + 140 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","a man swims downstream 76 km and upstream 48 km taking 4 hours each time ; what is the speed of the current ? a ) 3 kmph , b ) 1.5 kmph , c ) 3.5 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph","""explanation : 76 - - - 4 ds = 19 ? - - - - 1 48 - - - - 4 us = 12 ? - - - - 1 s = ? s = ( 19 - 12 ) / 2 = 3.5 answer : option c"""
Provide a detailed solution to the given mathematical problem.,"the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 70 cents more than the commodity y ? a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014","""the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 70 = 90 cents on commodity y , which will take 9 years . the answer is a ."""
"Work through the equation methodically, ensuring clarity at each step.","at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 7 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ? a ) $ 1220 , b ) $ 1280 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880","""i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 7 ) = $ 280 total revenue : 1000 + 280 = $ 1280 the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"if rs . 578 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ? a ) s . 300 , b ) s . 408 , c ) s . 389 , d ) s . 368 , e ) s . 323","""( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 578 * 2 / 17 = rs . 68 b' s share = 578 * 3 / 17 = rs . 102 c' s share = 578 * 12 / 17 = rs . 408 . answer : b"""
Break down and solve the equation step by step.,"a bag marked at $ 150 is sold for $ 120 . the rate of discount is ? a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 45 %","""rate of discount = 30 / 150 * 100 = 20 % answer is c"""
"Solve the problem systematically, showing each step clearly.","a can give b 80 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ? a ) 130.12 , b ) 130.43 , c ) 130.22 , d ) 111.0 , e ) 111.12","a runs 1000 m while b runs 920 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 920 = 869.56 m b can give c = 1000 - 869.56 = 130.43 m . answer : b"
Break down and solve the equation step by step.,"a volume of 10940 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ? a ) 2812 , b ) 8231 , c ) 2734 , d ) 2735 , e ) 4254","""a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10940 l can be kept in ( 10940 / 4 ) hemispheres ans . 2735 answer : d"""
Break down and solve the equation step by step.,"a man can row upstream at 25 kmph and downstream at 35 kmph , and then find the speed of the man in still water ? a ) 22 , b ) 77 , c ) 30 , d ) 99 , e ) 12","""us = 25 ds = 35 m = ( 35 + 25 ) / 2 = 30 answer : c"""
Break down and solve the equation step by step.,"a part of certain sum of money is invested at 9 % per annum and the rest at 21 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ? a ) 4 : 2 , b ) 4 : 8 , c ) 7 : 3 , d ) 4 : 0 , e ) 4 : 9","""21 : 9 = 7 : 3 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 22 percent are juniors and 74 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ? a ) 42 , b ) 48 , c ) 56 , d ) 208 , e ) 256","""sophomores = 26 % juniors = 22 % seniors = 160 / 800 = 20 % total : 68 % 1 - 68 % = 32 % ( freshmen ) 0,32 * 800 - 0,26 * 800 = 256 - 208 = 48 . answer choice b"""
"Solve the problem systematically, showing each step clearly.","a began business with rs . 27000 and was joined afterwards by b with rs . 36000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ? a ) 1.5 , b ) 6.5 , c ) 7.5 , d ) 8 , e ) 2","""27 * 12 : 36 * x = 2 : 1 x = 4.5 12 - 4.5 = 7.5 answer : c"""
"Solve the problem systematically, showing each step clearly.","tough and tricky questions : arithmetic . ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 = a ) 4 , b ) 18 , c ) 29 , d ) 8 , e ) 116",ans is 8 my approach was : ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 = 56 ( 56 + 56 ) / 28 * 28 = 56 * 112 / 28 * 28 = 2 * 4 = 8 d
"Solve the problem systematically, showing each step clearly.","in a recent election , james received 0.5 percent of the 2000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ? a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001",james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d
"Work through the equation methodically, ensuring clarity at each step.","cubes with each side one inch long are glued together to form a larger cube . the larger cube' s face is painted with red color and the entire assembly is taken apart . 22 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ? a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 103","""use the options . the options which after getting added to 27 shows a cube of a number could be right . here 64 + 22 = 86 72 + 22 = 94 86 + 22 = 108 98 + 22 = 120 103 + 22 = 125 - - - ( 5 * 5 * 5 ) so we have 103 as the answer ! e"""
Provide a detailed solution to the given mathematical problem.,"1000 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ? a ) 12.8 , b ) 12.6 , c ) 12.5 , d ) 12.2 , e ) 16.6","""1000 * 20 = 1200 * x x = 16.6 . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","yesterday i noticed that in my clock , there is time when the hour needle and the minute needle are exactly between 1 and 2 . also both the needles lie on top of each other . what time i and talking about ? a ) 10 : 00 , b ) 11 : 00 , c ) 09 : 00 , d ) 12 : 00 , e ) 07 : 00",d 12 : 00 both minute and hour clock lie exactly between the number one and two in the number .
"Solve the problem systematically, showing each step clearly.","a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 320,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ? a ) $ 1,333 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796","""making the numbers a little easy looking : monthly payment = 320,000 * ( 80 / 100 * 4 / 100 + 20 / 100 * 9 / 100 ) / 12 = 3200 / 12 * ( 3.2 + 1.8 ) = 16000 / 12 = 1333 answer : a"""
"Solve the problem systematically, showing each step clearly.","every day daniel drives 100 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ? a ) 10 % , b ) 28 % , c ) 33 % , d ) 42 % , e ) 52 %","""let' s test x = 4 . . . . on sunday , daniel drove 100 miles at 4 miles / hour . d = ( r ) ( t ) 100 = ( 4 ) ( t ) 100 / 4 = 25 = t it takes 25 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 68 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 68 = ( 2 ) ( t ) 68 / 2 = 34 = t it takes 34 hours for the second part total time to drive home on monday = 4 + 34 = 38 hours we' re asked by what percent 38 hours is greater than 25 hours . 38 / 25 = 1.52 , so it is 52 % greater . e"""
Explain the solution process for the given equation.,"two thirds of the roads from a to b are at least 5 miles long , and 3 / 4 of the roads from b to c are at least 5 miles long . if you randomly pick a road from a to b and then randomly pick a road from b to c , what is the probability that at least one of the roads you pick is at least 5 miles long ? a ) 1 / 6 , b ) 1 / 4 , c ) 2 / 3 , d ) 3 / 4 , e ) 11 / 12",so please : find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long : p = 1 - 1 / 3 * 1 / 4 = 11 / 12 . answer : e .
"Work through the equation methodically, ensuring clarity at each step.","two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ? a ) 65 sec , b ) 36 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec","""relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.4 = 1.5 km = 1500 m . required time = 1500 * 3 / 125 = 36 sec . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 2 can be used only once ? a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320","""4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 4 = 20 . thus there are 320 - 20 = 300 such numbers . answer : d ."""
Provide a detailed solution to the given mathematical problem.,"find the least number must be added to 228712 so that remaining no . is divisible by 9 ? a ) 5 , b ) 3 , c ) 1 , d ) 6 , e ) 2","on dividing 228712 by 9 we get the remainder 4 , so 5 should be subtracted a"
Provide a detailed solution to the given mathematical problem.,"the ratio between the number of sheep and the number of horses at the stewar farm is 2 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ? a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 58","""et no of sheep and horses are 2 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 2 * 8 ) = 16 answer : b"""
Explain the solution process for the given equation.,"what is log 3 ( 4 ) log 4 ( 5 ) . . . log 80 ( 81 ) ? a ) 1 , b ) 4 , c ) 81 , d ) log 80 243 , e ) e 81","recall the change of base formula logb ( a ) = ln ( a ) ln ( b ) : ( alternatively , we can substitute logc for ln on the right , as long as the base is the same on the top and on the bottom . ) using this , we can rewrite the entire expression using natural logarithms , as ln ( 4 ) ln ( 3 ) ln ( 5 ) ln ( 4 ) ln ( 81 ) ln ( 80 ) = ln ( 81 ) ln ( 3 ) = log 3 ( 81 ) = log 3 ( 34 ) = 4 : correct answer b"
"Work through the equation methodically, ensuring clarity at each step.","a cube is divided into 125 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ? a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60","""each side of the cube has 5 x 5 = 25 cubelets . only the interior cubelets are painted one colour . on each side , 3 x 3 = 9 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 9 = 54 the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","two trains of length 90 m and 100 m are 200 m apart . they start moving towards each other on parallel tracks , at speeds 71 kmph and 89 kmph . after how much time will the trains meet ? a ) 47 / 10 , b ) 46 / 10 , c ) 45 / 10 , d ) 42 / 10 , e ) 43 / 10","""they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 71 + 89 ) * 5 / 18 = 44.4 mps . the time required = d / s = 200 / 44.4 = 45 / 10 sec . answer : c"""
"Solve the problem systematically, showing each step clearly.","if | 4 x + 14 | = 46 , what is the sum of all the possible values of x ? a ) 2 , b ) - 7 , c ) 4 , d ) - 5 , e ) 6","""there will be two cases 4 x + 14 = 46 or 4 x + 14 = - 46 = > x = 8 or x = - 15 sum of both the values will be - 15 + 8 = - 7 answer is b"""
"Solve the problem systematically, showing each step clearly.","14 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ? a ) 27.5 days , b ) 15.5 days , c ) 17.5 days , d ) 16.5 days , e ) 18.5 days","""14 * 25 = 20 * x = > x = 17.5 days answer : c"""
Break down and solve the equation step by step.,"in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 35 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ? a ) 70 , b ) 245 , c ) 150 , d ) 35 , e ) 250","""since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 35 , so 0.14 * { total } = 35 - - > { total } = 250 . answer : e ."""
"Solve the problem systematically, showing each step clearly.","at the end of the first quarter , the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 75 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ? a ) 20 % , b ) 25 % , c ) 30 % , d ) 34.6 % , e ) 40 %","""another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 75 = 30 + b + 30 b / 100 b = 34.6 answer ( d )"""
Break down and solve the equation step by step.,"which is less than 3 ? a ) 3 , b ) 0.3 , c ) 33 , d ) 3 / 1 , e ) 13","""0.3 less than 3 . answer : b"""
Break down and solve the equation step by step.,"a sum fetched a total simple interest of rs . 1000 at the rate of 10 p . c . p . a . in 4 years . what is the sum ? a ) 2500 , b ) 2800 , c ) 3500 , d ) 1900 , e ) 1500",sol . principal = rs . [ 100 * 1000 / 10 * 4 ] = rs . [ 100000 / 40 ] = rs . 2500 . answer a
Break down and solve the equation step by step.,"some of 15 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 30 % . what fraction of the original paint was replaced ? a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 3 / 2 , e ) 3 / 5","""let total paint = 1 let amount replaced = x 15 ( 1 - x ) + 25 x = 30 x = 3 / 2 answer : d"""
Provide a detailed solution to the given mathematical problem.,"there are 12 pieces of radioactive metal a that look identical . 11 of the pieces give the same radiation count when measured , the 12 th piece is a counterfeit and gives a different radiation level , which may be more or less than the other 11 . we are given a radiation scale , which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different , which set has the higher level of radiation . what is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6","first of all if you are down to just 3 pieces and you know that if the offending piece is less or more active , then it takes exactly 1 measurement to find out the offending piece . so you know you have to reduce the problem to three . now when you are down to either a or b after measurement 1 , you need the next measurement to ( a ) reduce the problem set to 3 and ( b ) to know whether anser is more or less . now you can not compare a group of 4 to 4 , as in the best case it will only reduce the problem to 4 elements which is not good enough . if you have to choose a set of 3 to compare , you can not pick any 3 on the same side from the same set ( a or b ) because if you do this , a quick check will show you that in every choice there is a case where you can only get down to 4 elements . eg . if you weighed { 1 , 23 } v / s { 5 , 910 } and they were equal you' re problem would only reduce to { 46 , 78 } the easiest way to solve this then is to compare 3 to 3 , and make sure each side has elements from both ab such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only . which is why the sets { 1 , 59 } and { 2 , 67 } or { a , b , c } { a , b , b } . the extra element from c is just taken to make the problem symmetric so to say , we have 8 elements and we make it 9 , to compose 3 sets of 3 each . = b"
"Solve the problem systematically, showing each step clearly.","a and b invests rs . 6000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ? a ) 32 : 99 , b ) 8 : 21 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21","""a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 48000 : 126000 8 : 21 answer : b"""
Explain the solution process for the given equation.,"60 percent of movie theatres in town x have 2 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ? a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44","""lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 40 ( 44 - 12 ) must be those with four screens or more d is the answer"""
Break down and solve the equation step by step.,"angelina walked 600 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina' s speed , in meters per second , from the grocery to the gym ? a ) 2 , b ) 3 , c ) 4 , d ) 9 , e ) 12","""let the speed be x . . . so time taken from home to grocery = 600 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 600 / x - 240 / x = 40 . . 360 / x = 40 . . x = 9 m / secs . . so grocery to gym = 2 * 9 = 18 m / s . . . d"""
Break down and solve the equation step by step.,"a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b' s share in total profit of rs . 24,000 earned at the end of 2 years from the startingof the business ? a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,500 , e ) s . 7,200","""a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b' s share = rs . 24000 x 3 / 10 = rs . 7,200 . e"""
Provide a detailed solution to the given mathematical problem.,"the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 21 ? a ) 33 , b ) 35 , c ) 37 , d ) 39 , e ) 41","""$ 21 = 3 * $ 6 + $ 3 the number of doughnuts is 3 * 12 + 3 = 39 the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"the cost price of a radio is rs . 2300 and it was sold for rs . 1800 , find the loss % ? a ) 18 , b ) 99 , c ) 27 , d ) 26 , e ) 21","""2300 - - - - 500 100 - - - - ? = > 21 % answer : e"""
Provide a detailed solution to the given mathematical problem.,"in a class , 30 students pass in english and 20 students in maths , while some students among these pass in both . how many students do only english as compared to those doing only maths ? a ) 10 , b ) 15 , c ) 4 , d ) 12 , e ) indeterminate","""for doing union or intersection we would need three values . in this question the missing information in this question is total no . of students in the class . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","two men start together to walk a certain distance , one at 4 kmph and another at 3 kmph . the former arrives half an hour before the latter . find the distance . a ) 6 km , b ) 7 km , c ) 8 km , d ) 9 km , e ) none of these","let the distance be x km . then , x / 3 - x / 4 = 1 / 2 ( 4 x - 3 x ) / 12 = 1 / 2 x = 6 km answer : a"
Explain the solution process for the given equation.,"in a sample of college students , 20 percent are third year students and 80 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ? a ) 1 / 4 , b ) 2 / 3 , c ) 4 / 7 , d ) 1 / 2 , e ) 3 / 7","""= 20 / 80 . = 1 / 4 my answer is a too"""
"Solve the problem systematically, showing each step clearly.","the average runs scored by a batsman in 35 matches is 36 . in the next 14 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ? a ) 31 , b ) 35 , c ) 29 , d ) 25 , e ) 30",total score of the batsman in 35 matches = 1260 . total score of the batsman in the next 14 matches = 210 . total score of the batsman in the 30 matches = 1470 . average score of the batsman = 1470 / 49 = 30 . answer : e
Explain the solution process for the given equation.,"a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 60 square feet of the wall , and no tiles overlap , what is the area of the entire wall ? ['a ) 160','b ) 240','c ) 330','d ) 440','e ) 560']",the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 60 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 60 = 270 . total area = 60 + 270 = 330 . answer : c .
"Solve the problem systematically, showing each step clearly.","michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 6.4 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ? a ) 117 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %","since michelle earns 6.4 % interest compounded semiannually , then she earns 3.2 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 3.2 % * 5 = 16 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 16 % , only answer choice a fits . answer : a"
Break down and solve the equation step by step.,"if the remainder is 15 when the integer n is divided by 28 , what is the remainder when 2 n is divided by 14 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","""n = 28 k + 15 2 n = 2 ( 28 k + 15 ) = 4 k * 14 + 30 = 4 k * 14 + 2 * 14 + 2 = 14 j + 2 the answer is c ."""
Explain the solution process for the given equation.,"how many positive integers less than 60 have a reminder 01 when divided by 3 ? a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 20","""1 also gives the remainder of 1 when divided by 3 . so , there are total of 20 numbers . answer : e ."""
"Solve the problem systematically, showing each step clearly.","if a and b are positive numbers , and a ^ 3 + b ^ 3 = 140 , then the greatest possible value of a is between : a ) 0 and 2 , b ) 2 and 3 , c ) 3 and 4 , d ) 4 and 5 , e ) 5 and 8","if a = 5.1 and b is a bit less than 2 , then a ^ 3 + b ^ 3 can equal 140 . if a > 8 , then a ^ 3 + b ^ 3 > 140 . the answer is e ."
Provide a detailed solution to the given mathematical problem.,"claire has a total of 90 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ? a ) 39 , b ) 50 , c ) 66 , d ) 57 , e ) 60",g + h = 90 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 90 - h or 3 ( 90 - h ) + 4 h = 300 h = 300 - 270 = 30 then g = 96 - 30 = 66 c
"Solve the problem systematically, showing each step clearly.","how many integers are divisible by 2 between 10 ! and 10 ! + 20 inclusive ? a ) 6 , b ) 7 , c ) 21 , d ) 9 , e ) 10","""c = 21 10 ! is divisible by 2 there are 20 numbers between 10 ! and 10 ! + 20 that are divisible by 1 . hence 21"""
Explain the solution process for the given equation.,"a mixture contains alcohol and water in the ratio 4 : 3 . if 9 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 22 litres , e ) 18 litres","""let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 9 ) = 4 / 5 20 x = 4 ( 3 x + 9 ) 8 x = 36 x = 4.5 quantity of alcohol = ( 4 x 4.5 ) litres = 18 litres . answer is e"""
Break down and solve the equation step by step.,"a box measuring 49 inches long by 42 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ? a ) 78 , b ) 82 , c ) 84 , d ) 86 , e ) 88","""least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 42 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 42 / 7 * 14 / 7 = 84 ans c ."""
Explain the solution process for the given equation.,"ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1600 then loss of pyarelal ? a ) 600 , b ) 700 , c ) 840 , d ) 940 , e ) 1440","""let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1600 , loss of pyarelal = 1600 * 9 x / 10 x = 1440 answer : e"""
"Solve the problem systematically, showing each step clearly.","a snail , climbing a 36 feet high wall , climbs up 8 feet on the first day but slides down 4 feet on the second . it climbs 8 feet on the third day and slides down again 4 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ? a ) 12 , b ) 14 , c ) 15 , d ) 20 , e ) 21","""total transaction in two days = 8 - 4 = 4 feet in 15 days it will climb 36 feet thus reaching the top therefore , total no of days required = 15 c"""
Break down and solve the equation step by step.,"if 14 men do a work in 80 days , in how many days will 20 men do it ? a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 56 days","""14 * 80 = 20 * x x = 56 days answer : e"""
Explain the solution process for the given equation.,"there are 6 boxes numbered 1 , 2 , . . . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is a ) 5 , b ) 21 , c ) 33 , d ) 60 , e ) 40","given the constraints of this question , we have to consider 6 possible outcomes . . . 1 green ball : 6 options grrrrr rgrrrr rrgrrr rrrgrr rrrrgr rrrrrg 2 green balls : 5 options ggrrrr rggrrr rrggrr rrrggr rrrrgg 3 green balls : 4 options gggrrr rgggrr rrgggr rrrggg 4 green balls : 3 options ggggrr rggggr rrgggg 5 green balls : 2 options gggggr rggggg 6 green balls : 1 option gggggg 6 + 5 + 4 + 3 + 2 + 1 = 21 options . b"
"Work through the equation methodically, ensuring clarity at each step.","in a forest 190 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ? a ) 150 , b ) 750 , c ) 1,250 , d ) 1,900 , e ) 2,500","""the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 190 tagged deers comprise 10 % of total # of deers - - > total # of deers = 190 * 10 = 1,900 . answer : d ."""
"Work through the equation methodically, ensuring clarity at each step.","if 5 x * x + 14 * x + k = 0 having two reciprocal roots find the value of k . a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",product of reciprocal roots = 1 product of roots of quadratic eqn ax ^ 2 + bx + c = 0 is c / a . hence k / 5 = 1 k = 5 answer : e
"Work through the equation methodically, ensuring clarity at each step.","two trains 121 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? a ) 7.19 , b ) 7.18 , c ) 7.16 , d ) 7.15 , e ) 7.12","""t = ( 121 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.15 answer : d"""
Explain the solution process for the given equation.,"hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is : ['a ) 720','b ) 900','c ) 1200','d ) 1800','e ) 2100']",2 ( 15 + 12 ) x h = 2 ( 15 x 12 ) h = 180 / 27 m = 20 / 3 m . volume = 15 x 12 x 20 / 3 m 3 answer : option c
Break down and solve the equation step by step.,"if a tire rotates at 400 revolutions per minute when the car is traveling 144 km / h , what is the circumference of the tire ? a ) 2 meters , b ) 6 meters , c ) 5 meters , d ) 3 meters , e ) 7 meters","""400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 144,000 m : c is the circumference c = 6 meters correct answer b"""
Explain the solution process for the given equation.,"during 2003 , a company produced an average of 2,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 150 % over its 2003 average ? a ) 287,000 , b ) 290,000 , c ) 284,000 , d ) 285,000 , e ) 286,000","company produced 12 * 2000 = 24,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 24,000 . the gives the average of ( x + 24,000 ) / 4 . this average needs to be 300 % higher than that in 2003 . in math terms , 36,000 + 150 % ( 36,000 ) = 80,000 . so : ( x + 36,000 ) / 4 = 80,000 x + 36,000 = 320,000 x = 284,000 the answer is c ."
Provide a detailed solution to the given mathematical problem.,"the water level in a rectangular swimming pool measuring 40 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons ) a ) 100 , b ) 250 , c ) 750 , d ) 3750 , e ) 5625","""6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 40 * 25 * 1 / 2 = 500 feet ^ 3 of water must be removed , which equals to 500 * 7.5 = 3750 gallons . answer : d ."""
"Work through the equation methodically, ensuring clarity at each step.","the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 10 minutes , then the area of the park ( in sq . m ) is a ) 153200 , b ) 240000 , c ) 153600 , d ) 154000 , e ) 154200","""perimeter = distance covered in 10 min . = 12000 x 10 m = 2000 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 2000 or x = 200 . length = 600 m and breadth = 400 m . area = ( 600 x 400 ) m 2 = 240000 m 2 . b"""
Explain the solution process for the given equation.,"4 , 25,49 , 121,169 , 289,361 , a ) 149 , b ) 169 , c ) 189 , d ) 529 , e ) 219","""23 ^ 2 = 529 because follow sequence of square of the prime numbers answer : d"""
Provide a detailed solution to the given mathematical problem.,"a large box contains 16 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ? a ) 250 , b ) 350 , c ) 450 , d ) 400 , e ) 650","""the number of chocolate bars is equal to 16 * 25 = 400 correct answer d"""
"Solve the problem systematically, showing each step clearly.","two goods trains each 680 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ? a ) 228 , b ) 65.28 , c ) 48.32 , d ) 27 , e ) 21.1","""relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 680 + 680 = 1360 m . required time = 1360 * 6 / 125 = 65.28 sec . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 35 , what is the greatest possible value of b x a ? a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 35","""i also was confused when i was looking forabove number : d as far as i understood , 35 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let' s try 35 x 1 ( a = 3 , b = 5 respectively we have = 15 ) . but we do n' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 35 x 3 = 105 ( a = 0 b = 5 respectively . hey ! that' s 0 now . 35 x 5 = 175 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) . this is the greatest possible value of b x a . imo e ."""
"Solve the problem systematically, showing each step clearly.","at the faculty of aerospace engineering , 312 students study random - processing methods , 222 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ? a ) 404 , b ) 452 , c ) 444 , d ) 468 , e ) 422","""312 + 222 - 112 ( since 112 is counted twice ) = 422 e is the answer"""
Break down and solve the equation step by step.,"a is 2 times as fast as b . a alone can do the work in 20 days . if a and b working together in how many days will the work be completed ? a ) 23 , b ) 13 , c ) 21 , d ) 24 , e ) 25","""a can finish 1 work in 20 days b can finish 1 / 2 work in 20 days - since a is 2 faster than b this means b can finish 1 work in 20 * 2 days = 40 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 40 / ( 20 + 40 ) = 13 days so answer is b"""
Provide a detailed solution to the given mathematical problem.,"a particular library has 150 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 122 books in the special collection at that time , how many books of the special collection were loaned out during that month ? a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120","""the total number of books is 150 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 122 books , thus the number of un - returned books is 150 - 122 = 28 books . 0.35 x = 28 x = 80 the answer is c ."""
"Solve the problem systematically, showing each step clearly.","the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than a a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15","""explanation : given that a + b = 15 + b + c = > a ? c = 15 + b ? b = 15 = > c is younger than a by 15 years answer : option e"""
Provide a detailed solution to the given mathematical problem.,"sam invested rs . 5000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ? a ) 500.2 , b ) 320.0 , c ) 220.5 , d ) 100.1 , e ) 230.2","""p = rs . 5000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 5000 * ( 1 + 5 / 100 ) 2 ] = ( 5000 * 21 / 20 * 21 / 20 ) = rs . 220.50 answer : c"""
Break down and solve the equation step by step.,"the speed of a car is 120 km in the first hour and 60 km in the second hour . what is the average speed of the car ? a ) 89 kmph , b ) 92 kmph , c ) 90 kmph , d ) 65 kmph , e ) 77 kmph","""s = ( 120 + 60 ) / 2 = 90 kmph c"""
Explain the solution process for the given equation.,"what is the least common multiple of 6 , 18 , and 24 ? a ) 72 , b ) 120 , c ) 240 , d ) 360 , e ) 720","""let us first write the numbers in the form of prime factors : 6 = 2 * 3 18 = 2 * 3 ^ 2 24 = 2 ^ 3 * 3 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 72 option a"""
Explain the solution process for the given equation.,"two stations a and b are 110 km apart on a straight line . one train starts from a at 4 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ? a ) 15 a . m , b ) 10 a . m , c ) 7 a . m , d ) 02 a . m , e ) 05 a . m","""suppose they meet x hours after 4 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 7 a . m . answer : c"""
Break down and solve the equation step by step.,"the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 1600 meters per second , what was the speed , in meters per second , when the stopwatch was started ? a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32","""let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 1600 x = ( 2 ^ 6 * 25 ) / 2 ^ 9 = 25 / 8 the answer is c ."""
Explain the solution process for the given equation.,"in may mrs lee' s earnings were 60 percent of the lee family' s total income . in june mrs lee earned 10 percent more than in may . if the rest of the family' s income was the same both months , then , in june , mrs lee' s earnings were approximately what percent of the lee family' s total income ? a ) 62 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %","""let in may lee family' s total income = 100 in may mrs lee' s income = 60 in may rest of the family' s income = 40 in june mrs lees income = 60 * 110 / 100 = 66 in june total income = 66 + 40 = 106 % of mrs lee' s income = 66 / 106 = 62.26 ( a )"""
"Work through the equation methodically, ensuring clarity at each step.","- 84 x 19 + 100 = ? a ) 2436 , b ) 2801 , c ) - 1496 , d ) - 2071 , e ) none of them","""given exp . = - 84 x ( 20 - 1 ) + 100 = - ( 84 x 20 ) + 84 + 100 = - 1680 + 184 = - 1496 answer is c"""
Break down and solve the equation step by step.,"what percent of 9.6 kg is 28 gms ? a ) 25 , b ) 66 , c ) 288 , d ) 29 , e ) 17","""explanation : required percentage = ( 28 / 9600 * 100 ) % = 29 / 100 % = 0.29 % answer : d ) . 29 %"""
"Work through the equation methodically, ensuring clarity at each step.","what least value should be replaced by * in 223431 * so the number become divisible by 5 a ) 0 , b ) 4 , c ) 5 , d ) 6 , e ) 7","explanation : trick : number is divisible by 5 , if last digit is 0 or 5 so that least number is 0 . answer : option a"
Break down and solve the equation step by step.,"product of two co - prime numbers is 117 . their l . c . m should be a ) 222 , b ) 117 , c ) 278 , d ) 767 , e ) 298","h . c . f of co - prime numbers is 1 . so , l . c . m = \ inline \ fn _ jvn \ frac { 117 } { 1 } = 117 answer : b"
"Solve the problem systematically, showing each step clearly.","how many prime numbers are between 25 / 8 and 213 / 6 ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10","""25 / 8 = 4 - 213 / 6 = 36 - prime numbers between 4 and 36 are 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , and 31 - sign signifies that the number is marginally less . answer d"""
Explain the solution process for the given equation.,"the length of rectangle is thrice its breadth and its perimeter is 56 m , find the area of the rectangle ? a ) 432 , b ) 212 , c ) 252 , d ) 992 , e ) 147","""2 ( 3 x + x ) = 56 l = 21 b = 7 lb = 21 * 7 = 147 answer : e"""
Provide a detailed solution to the given mathematical problem.,"in a graduating class of 242 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ? a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 123","""greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 242 = 21 greatest - smallest is 144 - 21 = 123 so answer must be e . 123"""
"Solve the problem systematically, showing each step clearly.","the average of squares of first 11 consecutive even numbers is : a ) 164 , b ) 174 , c ) 184 , d ) 194 , e ) 204",2 ( n + 1 ) ( 2 n + 1 ) / 3 ( 2 * 12 * 23 ) / 3 = 2 * 4 * 23 = 184 answer : c
Provide a detailed solution to the given mathematical problem.,"lionel left his house and walked towards walt' s house , 48 miles away . two hours later , walt left his house and ran towards lionel' s house . if lionel' s speed was 3 miles per hour and walt' s 3 miles per hour , how many miles had lionel walked when he met walt ? a ) 12 , b ) 16 , c ) 20 , d ) 27 , e ) 28","""in the first 2 hours lionel at the rate of 3 miles per hour covered distance = rate * time = 3 * 2 = 6 miles . so , the distance between him and walt was 48 - 6 = 42 miles when walt left his house . now , their combined rate to cover this distance was 3 + 3 = 6 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 42 / 6 = 7 hours . total time that lionel was walking is 2 + 7 = 9 hours , which means that he covered in that time interval distance = rate * time = 3 * 9 = 27 miles . answer : d ."""
Break down and solve the equation step by step.,"find the lcm of 23 , 46,827 a ) 227 , b ) 83 , c ) 23 , d ) 827 , e ) none of these","explanation : whenever we have to solve this sort of question , remember the formula . lcm = \ \ begin { aligned } \ \ frac { hcf of denominators } { lcm of numerators } \ \ end { aligned } so answers will be option 2 , please also give attention to the difference in formula of hcf and lcm answer : option b"
"Work through the equation methodically, ensuring clarity at each step.","if 102 x = 25 , then 10 - x equals : a ) a ) 3 , b ) b ) 2 , c ) c ) 6 , d ) d ) 9 , e ) e ) 1 / 5","""102 x = 25 ( 10 x ) 2 = 52 10 x = 5 1 / 10 x = 1 / 5 10 - x = 1 / 5 answer : e"""
Provide a detailed solution to the given mathematical problem.,"a fill pipe can fill 1 / 2 of cistern in 10 minutes . in how many minutes , it can fill 1 / 2 of the cistern ? a ) 1 min , b ) 4 min , c ) 6 min , d ) 10 min , e ) 25 min","""required time = 10 * 2 * 1 / 2 = 10 minutes answer is d"""
Explain the solution process for the given equation.,"two cars start from the opposite places of a main road , 150 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ? a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21",answer : a ) 65 km
Explain the solution process for the given equation.,"if a man buys 1 liter of milk for 12 rs . and mixes it with 20 % water and sells it for 15 rs then what is the % age of gain . . . a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70",quantity after adding 20 % water = 1.2 liter sp of 1.2 lit . @ 15 rs . / liter = 15 * 1.2 = 18 rs cp = 12 rs / lit . % profit = 100 * ( 18 - 12 ) / 12 = 50 answer : c
"Work through the equation methodically, ensuring clarity at each step.","if the sides of a triangle are 36 cm , 34 cm and 20 cm , what is its area ? a ) 320 cm 2 , b ) 360 cm 2 , c ) 340 cm 2 , d ) 310 cm 2 , e ) 300 cm 2","""the triangle with sides 36 cm , 34 cm and 20 cm is right angled , where the hypotenuse is 36 cm . area of the triangle = 1 / 2 * 34 * 20 = 340 cm 2 answer : c"""
Explain the solution process for the given equation.,"( x + 6 ) is a factor in x ^ 2 - mx - 42 . what is the value of m ? a ) 2 , b ) 2.2 , c ) 1 , d ) 4 , e ) 5","i solved the second degree equation and found it like this : x ^ 2 - mx - 42 = 0 ( x - 7 ) ( x + 6 ) = 0 x = 7 or x = - 6 substituting both values for x in the equation we find : x ^ 2 - mx - 42 = > ( - 6 ) ^ 2 - m ( - 6 ) = 42 = > 36 + 6 m = 42 = > 6 m = 42 - 36 = 6 = > m = 1 and with 7 , using a similar process we end up with : ( 7 ) ^ 2 - m ( 7 ) = 42 - 7 m = 42 - 49 = - 7 m = - 1 ao , ans c"
Break down and solve the equation step by step.,"how many liters of water must be added to 14 liters of milk and water containing 10 % water to make it 30 % water ? a ) 1 liter , b ) 2 liters , c ) 3 liters , d ) 4 liters , e ) 5 liters","by rule of alligation : 30 % - 10 % = 20 % 100 % - 30 % = 70 % quantity of pure water : quantity of the mixture = 2 : 7 there are 14 liters of mixture , so we need to add 4 liters of pure water . the answer is d ."
"Work through the equation methodically, ensuring clarity at each step.","if an integer w is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that w ( w + 1 ) ( w + 2 ) will be divisible by 8 ? a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4","for w total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d"
Explain the solution process for the given equation.,"if 8 men do a work in 80 days , in how many days will 20 men do it ? a ) 18 days , b ) 32 days , c ) 42 days , d ) 48 days , e ) 44 days","""8 * 80 = 20 * x x = 32 days answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? a ) 7 sec , b ) 6 sec , c ) 4 sec , d ) 2 sec , e ) 9 sec","""speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 110 * 3 / 55 = 6 sec . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","if n is a positive integer and n ^ 2 is divisible by 150 , then what is the largest positive integer that must divide n ? a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50","""150 = 2 * 3 * 5 ^ 2 if 150 divides n ^ 2 , then n must be divisible by 2 * 3 * 5 = 30 the answer is c ."""
Break down and solve the equation step by step.,"at a certain organisation , the number of male members went up by 14 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ? a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 7","""men increase by 14 % = = > 1.14 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.14 m + 0.94 f = 1.012 * ( m + f ) 1.14 m + 0.94 f = 1.012 m + 1.012 f 1.14 m - 1.012 m = 1.012 f - 0.94 f 0.128 m = 0.072 f m / f = ( 0.072 ) / ( 0.128 ) = 72 / 128 = 4 / 7 answer = ( e )"""
"Work through the equation methodically, ensuring clarity at each step.","what annual installment will discharge a debt of rs . 4600 due in 4 years at 10 % simple interest ? a ) 1000 , b ) 1030 , c ) 1100 , d ) none of these , e ) 1101","""let the 1 st installment = 100 / - it is 3 yrs before due iind is 2 yr before due iii 3 rd is 1 yr before due ivth is 0 yrs before due on 1 st installment interest will be paid for 3 yrs 2 nd installment interest will be paid for 2 yrs 3 rd installment interest will be paid for 1 yr 4 th installment interest will be paid for 0 yr interest = p [ ( 100 ( 3 + 2 + 1 + 0 ) x 10 ) / 100 ] = 60 / - total loan discharged = 4 * 100 + 60 / - = 460 / - now installment of 100 / - loan discharged = 460 / - loan discharged 4600 / - ? installment = 1000 / - answer : a ."""
"Solve the problem systematically, showing each step clearly.","a man buys an article for $ 10 . and sells it for $ 15 . find the gain percent ? a ) 25 % , b ) 50 % , c ) 20 % , d ) 15 % , e ) 30 %",c . p . = $ 10 s . p . = $ 15 gain = $ 5 gain % = 5 / 10 * 100 = 50 % answer is b
Break down and solve the equation step by step.,"two cubes of their volumes in the ratio 27 : 125 . the ratio of their surface area is : a ) 1.5 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 5","""the ratio of their surface area is 27 : 125 3 : 5 answer is c ."""
Provide a detailed solution to the given mathematical problem.,"of the 120 passengers on flight 750 , 40 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ? a ) 40 , b ) 48 , c ) 50 , d ) 52 , e ) 56","""number of passengers on flight = 120 number of female passengers = . 4 * 120 = 48 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 48 - 8 = 40 answer a"""
Break down and solve the equation step by step.,"a worker' s daily wage is increased by 40 % and the new wage is $ 35 per day . what was the worker' s daily wage before the increase ? a ) $ 20 , b ) $ 21 , c ) $ 24 , d ) $ 25 , e ) $ 28","""let x be the daily wage before the increase . 1.4 x = $ 35 x = $ 25 the answer is d ."""
Explain the solution process for the given equation.,". on dividing a number by 357 , we get 36 as remainder . on dividing the same number 17 , what will be the remainder ? a ) 0 , b ) 3 , c ) 5 , d ) 8 , e ) 2","let x be the number and y be the quotient . then , x = 357 x y + 36 = ( 17 x 21 x y ) + ( 17 x 2 ) + 2 = 17 x ( 21 y + 2 ) + 2 ) required remainder = 2 . answer : option e"
Provide a detailed solution to the given mathematical problem.,"a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . how far is the place ? a ) 2.29 , b ) 2.88 , c ) 2.2 , d ) 2.12 , e ) 2.14","""m = 6 s = 1.2 ds = 6 + 1.2 = 7.2 us = 6 - 1.2 = 4.8 x / 7.2 + x / 4.8 = 1 x = 2.88 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","let a be the event that a randomly selected two digit number is divisible by 2 and let b be the event that a randomly selected two digit number is divisible by 10 . what is p ( a and b ) ? a ) 1 / 20 , b ) 1 / 15 , c ) 1 / 12 , d ) 1 / 8 , e ) 1 / 2","""p ( a and b ) = 1 / 2 * 1 / 10 = 1 / 20 the answer is a ."""
"Work through the equation methodically, ensuring clarity at each step.","length of a rectangular plot is 10 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ? a ) 55 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m","""let breadth = x metres . then , length = ( x + 10 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 10 ) + x ] = 200 2 x + 10 = 100 2 x = 90 x = 45 . hence , length = x + 10 = 55 m a"""
Break down and solve the equation step by step.,"96 % of 5 / 8 = a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0","""should be simple . 0.96 * 5 / 8 = 4.8 / 8 = 0.6 correct option : c"""
Provide a detailed solution to the given mathematical problem.,"if two painters can complete two rooms in two hours , how many rooms painted if 10 painters work for 6 hours ? a ) 35 , b ) 25 , c ) 20 , d ) 30 , e ) 15","""explanation : two painters can complete two rooms in two hours . so 30 rooms can be painted in 6 hrs by 10 painters answer : d ) 10 painters"""
Break down and solve the equation step by step.,"if a certain toy store' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 6 of its revenue in november , then the store' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ? a ) 3 / 2 , b ) 5 / 4 , c ) 10 / 3 , d ) 20 / 7 , e ) 25 / 9",n = 3 d / 5 j = n / 6 = d / 10 the average of november and january is ( n + j ) / 2 = 7 d / 10 / 2 = 7 d / 20 d is 20 / 7 times the average of november and january . the answer is d .
"Solve the problem systematically, showing each step clearly.","a 280 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ? a ) 220 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m","""relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 280 ) / 9 = 500 / 9 x + 280 = 500 x = 220 . a"""
Explain the solution process for the given equation.,"three fifth of the square of a certain number is 126.15 . what is the number ? ['a ) 210.25','b ) 75.69','c ) 14.5','d ) 145','e ) 150']","let the number be x given , 3 / 5 x ^ 2 = 126.5 x ^ 2 = 126.15 * 5 / 3 x ^ 2 = 42.05 * 5 = 210.25 x = 14.5 answer c ."
Provide a detailed solution to the given mathematical problem.,"two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 4 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10","let x be the total time it takes for the cistern to fill . 4 / 12 + x / 15 = 1 x / 15 = 2 / 3 x = 10 after the first pipe is turned off , it takes 6 more minutes to fill the cistern . the answer is a ."
Provide a detailed solution to the given mathematical problem.,"in a class of 79 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ? a ) 6 , b ) 15 , c ) 25 , d ) 33 , e ) 54","""formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 79 54 + not = 79 not = 79 - 54 = 25 so answer is c"""
Explain the solution process for the given equation.,"a , b and c rents a pasture for rs . 1130 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ? a ) 270 , b ) 199 , c ) 351 , d ) 156 , e ) 122","""12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 1130 = 351 answer : c"""
Explain the solution process for the given equation.,"5 percent of a certain grass seed is timothy . if the amount of the mixture needed to plant one acre contains 2 pounds of timothy , how many acres can be planted with 600 pounds of the seed mixture ? a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 120","if the mixture contains 2 pounds of timothy , the mixture must be 40 pounds . thus we need 40 pounds of mixture per acre . 600 / 40 = 15 acres the answer is b ."
Break down and solve the equation step by step.,"what is 10 - 8 + 6 - 4 + . . . + ( - 12 ) ? a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16","""the expression considers all even numbers between 10 and - 12 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , and - 12 now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 = 42 - 30 = 12 hence the correct answer choice is c ."""
Explain the solution process for the given equation.,"the cross - section of a stream is a trapezium in shape . if the stream is 10 m wide at the top and the area of cross - section is 640 sq m , the depth of stream is 80 m and width at the bottom is ? a ) 2 m , b ) 6 m , c ) 4 m , d ) 8 m , e ) 9 m",1 / 2 * 80 ( 10 + b ) = 640 b = 6 m answer : b
Break down and solve the equation step by step.,"12 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ? a ) 80 , b ) 160 , c ) 720 , d ) 1600 , e ) 1848",no . of ways of picking 2 biology books ( from 12 books ) = 12 c 2 = ( 12 * 11 ) / 2 = 66 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 66 * 28 = 1848 ( option e )
Explain the solution process for the given equation.,"27 is a perfect cube . when x is added to the prime factor of 27 , the result is also a perfect cube . what is x ? a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 11","""27 is 3 * 3 * 3 a 3 + 1 = 4 , 4 = 2 * 2 b 3 + 3 = 6 , 6 = 2 * 3 c 3 + 5 = 8 , 8 = 2 * 2 * 2 d 3 + 7 = 10 , 10 = 2 * 5 e 3 + 11 = 14 , 14 = 2 * 7 c is the only addition that gives a perfect cube ."""
Explain the solution process for the given equation.,"a 6 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point ? ['a ) 2 / 3','b ) 3 / 4','c ) 4 / 5','d ) 5 / 6','e ) 6 / 7']",the longer wire will form a square with an area more than 1 if the wire is cut at a point within two meters of either end . the probability of this is 4 / 6 = 2 / 3 . the answer is a .
Provide a detailed solution to the given mathematical problem.,"the average length of the sides of triangle abc is 12 . what is the perimeter of triangle abc ? ['a ) 4','b ) 6','c ) 12','d ) 24','e ) 36']",( average ) = ( perimeter ) / 3 ; 12 = ( perimeter ) / 3 ; ( perimeter ) = 36 . answer : e .
Explain the solution process for the given equation.,"if shares of two persons in profits are rs . 400 and rs . 1200 then ratio of their capitals is a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2",profit = time * capital so 400 : 1200 = 1 : 3 answer : d
Break down and solve the equation step by step.,"an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 26 metre of cloth ? a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 115 seconds , e ) 203 seconds","""explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 26 : x = > x = { \ color { blue } \ frac { 26 \ times 1 } { 0.128 } } = > x = 203.13 so time will be approx 203 seconds answer : e"""
"Solve the problem systematically, showing each step clearly.","john and jacob set out together on bicycle traveling at 12 and 9 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 12 miles per hour ? ( consider john' s deceleration / acceleration before / after the flat to be negligible ) a ) 3 , b ) 2 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 4 1 / 2","""john' s speed - 12 miles / hr jacob' s speed - 9 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 12 x 2 / 3 = 8 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 9 x 5 / 3 = 15 miles . now , when john starts riding back , the distance between them is 7 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 12 - 9 = 3 miles / hr . thus , to cover 7 miles at 3 miles / hr , john will take 7 / 3 = 2 1 / 3 hours answer b"""
Break down and solve the equation step by step.,"solution a is 20 % sugar and solution b is 80 % sugar . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % sugar solution ? a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 7","forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 20 ) = 1 / 1 so the volume of the two solutions will be equal . answer has to be 4 : 4 = c"
"Solve the problem systematically, showing each step clearly.","a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 48 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ? a ) a 8 , b ) b 22 , c ) c 27 , d ) d 40 , e ) e 51","""l = 48 / 12 = 4 ft w = 72 / 12 = 6 ft area of paper = 24 area of cube = 4 * side ^ 2 side of cube = 2 v of cube = 8"""
Break down and solve the equation step by step.,"the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 55 % profit ? a ) $ 480 , b ) $ 450 , c ) $ 992 , d ) $ 870 , e ) $ 660","""c let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 155 % of $ 640 = 150 / 100 * 640 = $ 992 ."""
"Work through the equation methodically, ensuring clarity at each step.","a mixture contains alcohol and water in the ratio 4 : 3 . if 6 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 12 litres , e ) 8 litres","""let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 6 ) = 4 / 5 20 x = 4 ( 3 x + 6 ) 8 x = 24 x = 3 quantity of alcohol = ( 4 x 3 ) litres = 12 litres . answer is d"""
"Work through the equation methodically, ensuring clarity at each step.","the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 16000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is a ) 20 , b ) 21 , c ) 35 , d ) 23 , e ) 24","""solution let the toatl number of workers be x . then 8000 x = ( 16000 x 7 ) + 6000 ( x - 7 ) x = 35 . answer c"""
"Work through the equation methodically, ensuring clarity at each step.","a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 4 . the ratio of economy cars to sport utility vehicles is 3 : 2 . what is the ratio of luxury cars to sport utility vehicles ? a ) 9 : 8 , b ) 8 : 9 , c ) 6 : 5 , d ) 2 : 3 , e ) 1 : 2","""the ratio of economy to luxury cars is 5 : 4 - - > e : l = 5 : 4 = 15 : 12 . the ratio of economy cars to sport utility vehicles is 3 : 2 - - > e : s = 3 : 2 = 15 : 10 . thus , l : s = 12 : 10 = 6 : 5 . answer : c ."""
Provide a detailed solution to the given mathematical problem.,"two brothers ram and ravi appeared for an exam . the probability of selection of ram is 3 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected . a ) 3 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5","""let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 3 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 3 / 7 x 1 / 5 = 3 / 35 answer : a"""
"Solve the problem systematically, showing each step clearly.","a hall 36 m long and 15 m broad is to be paved with stones , each measuring 6 dm by 5 dm . the number of stones required is : a ) 180 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1.8","""area of the hall = 3600 * 1500 area of each stone = ( 60 * 50 ) therefore , number of stones = ( 3600 * 1500 / 60 * 50 ) = 1800 answer : b"""
Explain the solution process for the given equation.,"find number which is 60 % less than 80 . a ) 18 , b ) 32 , c ) 28 , d ) 26 , e ) 98","""explanation : 60 % less is 40 % of the given number therefore , 40 % of 80 is 32 . answer : b"""
Explain the solution process for the given equation.,"what should be the least number to be added to the 2496 number to make it divisible by 5 ? a ) 12 , b ) 17 , c ) 18 , d ) 4 , e ) 26","""answer : 4 option : d"""
Provide a detailed solution to the given mathematical problem.,"how long does a lorry 200 m long traveling at 80 kmph takes to cross a bridge of 200 m in length ? a ) 15 , b ) 17 , c ) 15 , d ) 16 , e ) 18",d = 200 + 200 = 400 m s = 80 * 5 / 18 = 200 / 9 t = 400 * 9 / 200 = 18 sec answer : e
"Solve the problem systematically, showing each step clearly.","a certain number when divided by 39 leaves a remainder 15 , what is the remainder when the same number is divided by 13 ? a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 2","""explanation : 39 + 15 = 54 / 13 = 2 ( remainder ) answer : e"""
Explain the solution process for the given equation.,"a toy factory stores its toys in either a big box or a small box . the big box can store 35 toys while the small box can store 14 toys . if the factory is to store 86 newly manufactured toys , what is the least number of toys that will be left unboxed ? a ) 2 , b ) 1 , c ) 3 , d ) 5 , e ) 4",total toys to be stored 86 the big box can store 35 small box can store 14 storing 85 toys in big box 85 / 35 = 2 r 16 store remainder in small box 16 / 14 = 1 r 2 least number of toys that will be left unboxed = 2 answer : a
Provide a detailed solution to the given mathematical problem.,"a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 380 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ? a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 240","""orchestra seats - a balcony seats - b a + b = 380 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 380 = 3320 - 3040 = 280 i . e . a = 70 and b = 380 - 70 = 310 more seats in balcony than orchestra = b - a = 310 - 70 = 240 answer : option e"""
"Work through the equation methodically, ensuring clarity at each step.","a man rows his boat 95 km downstream and 60 km upstream , taking 2 hours each time . find the speed of the stream ? a ) 76 kmph , b ) 6 kmph , c ) 9 kmph , d ) 8 kmph , e ) 4 kmph","""speed downstream = d / t = 95 / ( 2 ) = 48 kmph speed upstream = d / t = 60 / ( 2 ) = 30 kmph the speed of the stream = ( 48 - 30 ) / 2 = 9 kmph answer : c"""
Explain the solution process for the given equation.,"a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 10 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ] a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 27 , e ) 8 / 7","""let' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 10 % are male i . e 10 / 100 * 20 = 2 geese ( males ) and now we know out of the total 20 geese , 2 are male , then 18 have to be female . now the ratio part , male geese ratios = 2 / 30 = 1 / 15 . - a female geese ratios = 18 / 70 = 9 / 35 - b cross multiply equations a and b and you get = 7 / 27 . ans d"""
Break down and solve the equation step by step.,"1297 x 1297 = ? a ) a ) 1682209 , b ) b ) 1951601 , c ) c ) 1951602 , d ) d ) 1951603 , e ) e ) 1951604","""1297 x 1297 = ( 1297 ) 2 = ( 1300 - 3 ) 2 = ( 1300 ) 2 + ( 3 ) 2 - ( 2 x 1300 x 3 ) = 1690000 + 9 - 7800 = 1690009 - 7800 = 1682209 . answer : a"""
"Solve the problem systematically, showing each step clearly.","for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 ? a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .","""[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 = 6 * 0 + 2 * 7.2 + 8 - 6.2 = 0 + 14.4 + 1.8 16.2 answer d"""
Provide a detailed solution to the given mathematical problem.,"what is the remainder when 9 ^ 1 + 9 ^ 2 + 9 ^ 3 + . . . + 9 ^ 9 is divided by 3 ? a ) 0 , b ) 3 , c ) 2 , d ) 5 , e ) none of the above","""notice that in the brackets we have the sum of 8 odd multiples of 3 , which yields remainder of 0 upon division by 3 . answer : a"""
Explain the solution process for the given equation.,"in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 50 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ? a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25","percent of students who are 25 years old or older is 0.5 * 48 + 0.2 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 3 = 66 . answer : b ."
"Solve the problem systematically, showing each step clearly.","at a special sale , 6 tickets can be purchased for the price of 3 tickets . if 6 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 6 tickets ? a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 50 % , e ) 66.6 %","let the price of a ticket be rs . 100 , so 3 tickets cost 300 & 6 tickets cost 600 6 tickets purchased at price of 3 tickets ie . , for 300 , so amount saved s rs . 300 , % of 6 tickets = ( 300 / 600 ) * 100 = 50 % answer : d"
Explain the solution process for the given equation.,"if 9 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ? a ) 127 , b ) 237 , c ) 387 , d ) 400 , e ) 481","""explanation : let the required no of hectares be x . then men - - - hectares - - - days 9 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 9 * 30 / 24 * 80 x = 400 answer : d"""
Explain the solution process for the given equation.,"from a total of 3 boys and 4 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ? a ) 18 , b ) 24 , c ) 60 , d ) 120 , e ) 240","""answer = c = 18 no of 4 person committees that can be formed = 3 c 2 * 4 c 2 = 18 answer a"""
"Solve the problem systematically, showing each step clearly.","the price of a t . v . set worth rs . 10000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ? a ) 9000 , b ) 26699 , c ) 96000 , d ) 19000 , e ) 26711","""money paid in cash = rs . 1000 balance payment = ( 10000 - 1000 ) = rs . 9000 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","a and b go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 60 kmph . after how much time will they meet for the first time at the starting point ? a ) 120 sec , b ) 176 sec , c ) 178 sec , d ) 187 sec , e ) 180 sec","""time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 36 * 5 / 18 ) , 600 / ( 60 * 5 / 18 ) } = 180 sec . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 21 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ? a ) 347.8 , b ) 987.8 , c ) 877.8 , d ) 898.8 , e ) 667.4","""let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 21 = 2 r a = 12 / 5 r and r = 63 a = 151.2 required total cost = 4 * 151.2 + 3 * 63 + 5 * 21 = 604.8 + 189 + 105 = $ 898.80 d"""
Explain the solution process for the given equation.,"if a square mirror has a 20 - inch diagonal , what is the approximate perimeter q of the mirror , in inches ? a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120","""if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter q must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b"""
"Solve the problem systematically, showing each step clearly.","a farmer spent $ 34 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ? a ) $ 37.40 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60","""a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 34 = $ 13.6 on chicken feed , thus he spent the remaining 34 - 13.6 = $ 20.4 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 13.6 - - > x = $ 17 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 17 + 20.4 = $ 37.4 . answer : a ."""
Explain the solution process for the given equation.,"- 84 x 29 + 365 = ? a ) 2071 , b ) 2436 , c ) 2801 , d ) - 2801 , e ) - 2071","""e given exp . = - 84 x ( 30 - 1 ) + 365 = - ( 84 x 30 ) + 84 + 365 = - 2520 + 449 = - 2071"""
Explain the solution process for the given equation.,"a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 222 for it , the cost price of the cricket bat for a is : a ) 150 , b ) 148 , c ) 130 , d ) 160 , e ) 210","""125 % of 120 % of a = 222 125 / 100 * 120 / 100 * a = 222 a = 222 * 2 / 3 = 148 . answer b"""
"Work through the equation methodically, ensuring clarity at each step.","a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 20 % ? a ) 600 , b ) 2877 , c ) 208 , d ) 1882 , e ) 191",explanation : cost price = rs . 500 profit = 20 % of 500 = rs . 100 selling price = cost price + profit = 500 + 100 = 600 answer : a
"Work through the equation methodically, ensuring clarity at each step.","linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ? a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1800 , e ) $ 1900","""if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 300 . so 1 / 4 of her savings is $ 300 . so her original savings are 4 times $ 300 = $ 1200 correct answer a"""
Provide a detailed solution to the given mathematical problem.,"in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 20 % of the people have the job of their choice , what percent of the people have a university diploma ? a ) 30 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %","""setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 20 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 20 % of people have their job of choice , then 80 % of people do not have their job of choice . 25 % of 80 % = 20 % . we can also see that 10 % of the people have their job of choice and a diploma ( 20 % - 10 % = 10 % ) . 10 % + 20 % = 30 % . therefore 30 % of the people in country z have a diploma . ans a"""
"Solve the problem systematically, showing each step clearly.","the average age of applicants for a new job is 32 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ? a ) 8 , b ) 77 , c ) 7 , d ) 18 , e ) 34","""minimum age = average - 1 standard deviation = 32 - 8 = 24 maximum age = average + 1 standard deviation = 32 + 8 = 40 maximum number of different ages of the applicants = 30 - 24 + 1 = 7 answer c"""
"Work through the equation methodically, ensuring clarity at each step.","on day one , a store sold 96 pens . on each of the next d days , the company sold 44 pens . if the average daily sales of pens over this time period ( including day one ) is 48 pens , what is the value of d ? a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13",96 + 44 d = 48 ( d + 1 ) . 4 d = 48 . d = 12 . the answer is d .
"Work through the equation methodically, ensuring clarity at each step.","a goes to place x and b goes to place y . after a travelled 180 km more than b they together meet at a point between xy . they together had their lunch for half an hour . after that a took 2 hrs to reach x and b took 4.5 hrs to reach y . find distance between x and y ? a ) 900 km , b ) 540 km , c ) 720 km , d ) 820 km , e ) 920 km",let speed of a be - - - - - - - sa let speed of b be - - - - - - - - sb let the distance covered by b while going to position xy be - - - - - - - - - - - x so distance covered by a in same time while going to xy is - - - - - - - - - - 180 + x ( it' s given in the question ) so total distance b / w x and y is = x + ( x + 180 ) while going to position xy : - time taken by a = time taken by b ( x + 180 ) / sa = x / sb sa / sb = ( x + 180 ) / x - - - - - - - - - - - - - - - - - - - - - 1 after lunch : - a . c . t ( according to question ) sa = x / 2 sb = ( x + 180 ) / 4.5 dividing sa / sb = ( x * 4.5 ) / ( ( x + 180 ) * 2 ) - - - - - - - - - - - - - - - - - - - - 2 equating equations 1 and 2 9 / 4 = ( x + 180 ) ^ 2 / x ^ 2 now taking square root on both sides we get 3 / 2 = ( x + 180 ) / x x = 360 therefore distance between x and y = x + ( x + 180 ) = 900 km answer : a
Break down and solve the equation step by step.,"one pipe can fill a tank in 15 hour . but because of hole in a tank , this tank fill in 20 hour . so in how much time this hole will empty the full tank ? a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70",in 1 hour hole empty = [ 1 / 15 - 1 / 20 ] = 1 / 60 so total time taken to empty the full tank through hole = 60 hour . answer d
Explain the solution process for the given equation.,"a man whose speed is 7.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ? a ) 10 , b ) 8 , c ) 9 , d ) 7.2 , e ) 6","""m = 7.5 s = 1.5 ds = 9 us = 6 as = ( 2 * 9 * 6 ) / 15 = 7.2 answer : d"""
Provide a detailed solution to the given mathematical problem.,"the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1512 respectively . what is the rate of interest ? a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %","""1512 - 1400 = 112 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 112 ) / ( 1400 ) = 8 % the answer is d ."""
"Solve the problem systematically, showing each step clearly.","when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction f of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ? a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14","""if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus f = 11 / 14 of the remaining votes must be against . answer : a ."""
Break down and solve the equation step by step.,"three coins are tossed . find the probability of at most 2 tails ? a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 7 / 8 , e ) 3 / 8","""n ( s ) = 2 ^ 3 = 8 let e is the event of getting at most 2 tails n ( e ) = hhh , tth , htt , tht , hht , hth , thh = 7 p ( e ) = n ( e ) / n ( s ) = 7 / 8 ans - d"""
"Work through the equation methodically, ensuring clarity at each step.","a person' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old is the mother at present ? a ) 32 yrs , b ) 36 yrs , c ) 40 yrs , d ) 48 yrs , e ) none","""explanation : let the mother' s present age be x years . then , the person' s present age = ( 2 / 5 ) * x years . ( ( 2 / 5 ) * x ) + 8 = ( 1 / 2 ) ( x + 8 ) 2 ( 2 x + 40 ) = 5 ( x + 8 ) x = 40 . answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","find the greatest number which leaves the same remainder when it divides 25 , 62 and 105 . a ) 1 , b ) 8 , c ) 12 , d ) 16 , e ) none of these","""105 - 62 = 43 62 - 25 = 37 105 - 25 = 80 the h . c . f of 37 , 43 and 80 is 1 . answer : a"""
"Solve the problem systematically, showing each step clearly.","a sum of money at simple interest amounts to rs . 855 in 3 years and to rs . 854 in 4 years . the sum is : a ) s . 650 , b ) s . 690 , c ) s . 738 , d ) s . 700 , e ) s . 718","""s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 855 - 117 ) = rs . 738 . answer : option c"""
Explain the solution process for the given equation.,"a man can swim in still water at 6 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ? a ) 3 , b ) 7.5 , c ) 2.25 , d ) 2 , e ) 4","""m = 6 s = x ds = 6 + x us = 6 - x 6 + x = ( 6 - x ) 2 6 + x = 12 - 2 x 3 x = 6 x = 2 answer : d"""
Break down and solve the equation step by step.,"a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 4 years ago ? a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16","""let' s say age of richard is ` ` r'' age of david is ` ` d'' age of scott is ` ` s'' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 4 years ago ? i . e . d - 4 = 14 - 4 = 10 years answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is : a ) 23 , b ) 19 , c ) 42 , d ) 20 , e ) 21","""let the total number of workers be x . then , 8000 x = ( 18000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 84000 = x = 42 . answer : c"""
"Solve the problem systematically, showing each step clearly.","divide $ 1162 among a , b , c in the ratio 35 : 28 : 20 . a ) 490 , 490,490 , b ) 360 , 392,460 , c ) 490 , 392,280 , d ) 260 , 160,60 , e ) 492 , 390,280","""sum of ratio terms = ( 35 + 28 + 20 ) = 83 . a' s share = $ ( 1162 x ( 35 / 83 ) ) = $ 490 ; b' s share = $ ( 1162 x ( 28 / 83 ) ) = $ . 392 ; c' s share = $ ( 1162 x ( 20 / 83 ) ) = $ 280 . answer c 490 , 392,280"""
"Solve the problem systematically, showing each step clearly.","marts income is 60 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %","""tim = 100 mary' s income is 60 percent more than tims income ; mary' s income = t + 0.6 t = 1.6 t = 1.6 * 100 = 160 tims income is 40 percent less than juans income . 100 is 40 % less than juan' s income 100 = j - 0.4 j 100 = 0.6 j j = 100 / 0.6 = 1000 / 6 what percentage of juans income is marts income ( 160 / ( 1000 / 6 ) ) * 100 = ( 160 * 6 * 100 ) / 1000 = 96 % answer : c"""
Break down and solve the equation step by step.,"a man took loan from a bank at the rate of 12 % p . a . s . i . after 20 years he had to pay rs . 2100 interest only for the period . the principal amount borrowed by him was ? a ) 600 , b ) 715 , c ) 600 , d ) 875 , e ) 900","""principal = ( 100 * 2100 ) / ( 12 * 20 ) = rs . 875 answer : d"""
Explain the solution process for the given equation.,"if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 116 kilograms . what is the student' s present weight in kilograms ? a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80","""let x be the weight of the sister . then the student' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 116 3 x = 111 x = 37 kg then the student' s weight is 79 kg . the answer is d ."""
Explain the solution process for the given equation.,"an aeroplane covers a certain distance at a speed of 240 kmph in 6 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of : a ) 520 , b ) 620 , c ) 820 , d ) 740 , e ) 864","""distance = ( 240 x 6 ) = 1440 km . speed = distance / time speed = 1440 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 1440 x 3 / 5 ) km / hr = 864 km / hr answer e ) 864 km / hr"""
"Work through the equation methodically, ensuring clarity at each step.","4 + 4 a ) 8 , b ) 2 , c ) 1 , d ) 5 , e ) 2",c
Explain the solution process for the given equation.,"what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 448 * 348 ) ^ 2 a ) 86 , b ) 76 , c ) 56 , d ) 36 , e ) 16","""( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 448 * 348 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 8,8 ; 5 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 48 * 48 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 56 * 48 ) ) ^ 2 = ( 44 * 88 ) ^ 2 = 72 ^ 2 = 84 hence answer is a"""
"Work through the equation methodically, ensuring clarity at each step.","three numbers are in the ratio 4 : 5 : 6 and their average is 20 . the largest number is : a ) 24 , b ) 32 , c ) 36 , d ) 42 , e ) 45","""explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 20 15 x = 60 x = 4 largest number = 6 x = 24 . answer a"""
"Solve the problem systematically, showing each step clearly.","the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 2 months , find for how much time did q invest the money ? a ) 8 , b ) 10 , c ) 18 , d ) 4 , e ) 12","""7 * 5 : 2 * x = 7 : 10 x = 4 answer : 4 answer is d"""
"Solve the problem systematically, showing each step clearly.","of the votes cast on a certain proposal , 58 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . ) a ) 230 , b ) 245 , c ) 260 , d ) 275 , e ) 290","""let x be the total number of votes cast . 0.6 x = 0.4 x + 58 0.2 x = 58 x = 290 the answer is e ."""
"Solve the problem systematically, showing each step clearly.","a watch was sold at a loss of 36 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ? a ) 350 , b ) 288 , c ) 799 , d ) 778 , e ) 901","""64 % 104 % - - - - - - - - 40 % - - - - 140 100 % - - - - ? = > rs . 350 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","90 percent of your marbles are a solid color . 5 percent of your marbles are solid yellow . what percentage of your marbles are a solid color other than yellow ? a ) 5 , b ) 15 , c ) 85 , d ) 90 , e ) 95","90 percent are solid colors including solid yellow . 5 percent are solid yellow . 90 % - 5 % = 85 % , so 85 percent are a solid color other than yellow = > ( c )"
Explain the solution process for the given equation.,"the average weight of a , b and c is 44 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is : a ) 17 kg , b ) 28 kg , c ) 26 kg , d ) 31 kg , e ) 35 kg","""let d sum of a , b , c is 3 * 44 = 132 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 43 = 86 hence 80 + 86 - 132 = 28 ans = 28 answer : b"""
Break down and solve the equation step by step.,"a 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ? a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3","""you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 3 kg when 30 kg alloy is immersed . this is a loss of ( 3 / 30 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver' s loss - avg loss ) / ( avg loss - tin' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"""
Break down and solve the equation step by step.,"two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 11 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ? a ) 477 , b ) 384 , c ) 279 , d ) 276 , e ) 291","""1 h - - - - - 5 ? - - - - - - 60 12 h rs = 11 + 21 = 32 t = 12 d = 32 * 12 = 384 . answer : b"""
"Solve the problem systematically, showing each step clearly.","excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 35 km / hr . for how many minutes does the bus stop per hour ? a ) 22 , b ) 88 , c ) 24 , d ) 20 , e ) 99","""in 1 hr , the bus covers 60 km without stoppages and 35 km with stoppages . stoppage time = time take to travel ( 60 - 35 ) km i . e 25 km at 60 km / hr . stoppage time = 25 / 60 hrs = 24 min . answer : c"""
Break down and solve the equation step by step.,"what is the remainder when 3 ^ 29 is divided by 5 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","""the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 29 has the form 4 k + 1 , so the units digit of 3 ^ 29 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."""
"Solve the problem systematically, showing each step clearly.","one pump drains one - half of a pond in 2.5 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ? a ) 1 hour , b ) 1.2 hour , c ) 3 hours , d ) 1.25 hours , e ) 6 hours","""the tricky part here , i believed is one half hour = 1 / 2 . then everything would be easy . we have the 1 st pump working rate / hour = 1 / 2 : 5 / 2 = 1 / 5 working rate of 2 pumps : 1 / 2 : 1 / 2 = 1 . working rate of 2 nd pump : 1 - 1 / 5 = 4 / 5 - - > time taken for the 2 nd pump to finish : 1 : 4 / 5 = 5 / 4 = 1.25 hours . d"""
"Work through the equation methodically, ensuring clarity at each step.","the sum of the first 40 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? a ) 6,500 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600","""101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 40 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 40 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 40 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 4000 + 2500 = 6500 a is the answer ."""
"Solve the problem systematically, showing each step clearly.","if the sum of a number and its square is 132 , then what is the number ? a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14","""explanation : let the number be x . then , x 2 + x = 132 = > x 2 + x - 132 = 0 = > ( x + 12 ) ( x - 11 ) = 0 = > x = 11 answer : option b"""
Provide a detailed solution to the given mathematical problem.,"a 6 - liter solution is 25 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ? a ) 2.1 , b ) 2.4 , c ) 2.7 , d ) 3.0 , e ) 3.3","""let x be the amount of pure alcohol required . 0.25 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.5 x = 3 liters the answer is d ."""
"Solve the problem systematically, showing each step clearly.","the least number , which when divided by 12 , 15 , 20 and 63 leaves in each case a remainder of 8 is : a ) 448 , b ) 488 , c ) 542 , d ) 1268 , e ) 560","""required number = ( l . c . m . of 12 , 15 , 20 , 63 ) + 8 = 1260 + 8 = 1268 . answer : d"""
Explain the solution process for the given equation.,"a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 12 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ? a ) 210 , b ) 150 , c ) 280 , d ) 300 , e ) 420","""however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 5 * 12 * 7 placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60 we get = 5 x 6 x 5 = 150 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( b )"""
Break down and solve the equation step by step.,"the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718","""area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e"""
Provide a detailed solution to the given mathematical problem.,"total dinning bill for 10 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 24.26",211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 10 = 24.26 answer : e
Explain the solution process for the given equation.,"a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ? a ) 39 , b ) 35 , c ) 42 , d ) 40.5 , e ) 41","""explanation : let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 87 = total runs scored in 17 innings = > 16 ( x - 3 ) + 87 = 17 x = > 16 x - 48 + 87 = 17 x = > x = 39 answer : option a"""
"Work through the equation methodically, ensuring clarity at each step.","the average age of 16 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 12 th student is a ) 11 , b ) 66 , c ) 18 , d ) 16 , e ) 42","""explanation : age of the 16 th student = [ 16 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 256 - 214 ) = 42 years . answer : e"""
Break down and solve the equation step by step.,"the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.7 kg . the weight of the new student is ? a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 14.9 kg , e ) none","""answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.7 - 19 x 15 ) kg = 9 kg . correct option : e"""
Explain the solution process for the given equation.,"p and q together can do a work in 6 days . if p alone can do it in 15 days . in how many days can q alone do it ? a ) 5 , b ) 4 , c ) 10 , d ) 11 , e ) 12",1 / 6 - 1 / 15 = = > 1 / 10 = = > 10 answer c
"Work through the equation methodically, ensuring clarity at each step.","a goods train runs at the speed of 72 kmph and crosses a 260 m long platform in 26 seconds . what is the length of the goods train ? a ) 260 m , b ) 270 m , c ) 643 m , d ) 832 m , e ) 270 m","""speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 260 / 26 = 20 x + 260 = 520 x = 260 . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","express a speed of 54 kmph in meters per second ? a ) 10 mps , b ) 76 mps , c ) 15 mps , d ) 97 mps , e ) 16 mps","""54 * 5 / 18 = 15 mps answer : c"""
Break down and solve the equation step by step.,"if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 25 ( q + 1 ) , what is the least possible value of p + q ? a ) 36 , b ) 42 , c ) 40 , d ) 46 , e ) none","""17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 25 , so the least value of p is 24 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 24 + 16 = 40 . answer : c ."""
Break down and solve the equation step by step.,"on my sister' s birthday , she was 147 cm in height , having grown 5 % since the year before . how tall was she the previous year ? a ) 145 cm , b ) 140 cm , c ) 142 cm , d ) 138 cm , e ) 135 cm","""let the previous year' s height be x . 1.05 x = 147 x = 140 the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 12 km / hr respectively . they will meet for the first time in ? a ) 32 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min","""clearly , the two will meet when they are 1000 m apart to be 20 + 12 = 32 km apart , they take 1 hour to be 1000 m apart , they take 32 * 1000 / 1000 = 32 min . answer is a"""
"Solve the problem systematically, showing each step clearly.","for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 5 + 3 and * 5 + 5 , inclusive ? a ) none , b ) one , c ) two , d ) three , e ) four","generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 5 would be divisible by all numbers from 1 to 5 . = > * 5 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 5 is divisible by 3 ) in fact adding anyprimenumber between 1 to 5 to * 5 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 5 + 3 and * 5 + 11 then the answer would be 1 . for * 5 + 3 and * 5 + 13 , it is 2 and so on . . . a"
"Work through the equation methodically, ensuring clarity at each step.","the compound ratio of 1 : 3 , 3 : 2 and 4 : 5 ? a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 2 : 5 , e ) 1 : 4","""1 / 3 * 3 / 2 * 4 / 5 = 2 / 5 = 2 : 5 answer : d"""
"Solve the problem systematically, showing each step clearly.","a train 100 m long crosses a platform 100 m long in 12 sec ; find the speed of the train ? a ) 60 kmph , b ) 65 kmph , c ) 54 kmph , d ) 16 kmph , e ) 18 kmph","""d = 100 + 100 = 200 t = 12 s = 200 / 12 * 18 / 5 = 60 kmph answer : a"""
"Solve the problem systematically, showing each step clearly.","a jogger running at 9 km / hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ? a ) 67 sec , b ) 89 sec , c ) 38 sec , d ) 87 sec , e ) 45 sec","""speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 260 + 120 = 380 m . time taken = 380 / 10 = 38 sec . answer : c"""
Provide a detailed solution to the given mathematical problem.,"find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 12 cm . a ) 335 cm 2 , b ) 228 cm 2 , c ) 285 cm 2 , d ) 825 cm 2 , e ) 725 cm 2","""area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 12 ) = 228 cm 2 answer : b"""
Break down and solve the equation step by step.,"if 2 + 7 = 57 ; 3 + 6 = 63 ; 5 + 9 = 206 then 4 + 8 = ? a ) 125 , b ) 126 , c ) 127 , d ) 128 , e ) 129",2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 4 ^ 3 + 8 ^ 2 = 128 answer : d
"Work through the equation methodically, ensuring clarity at each step.","q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 60 , what is the greatest possible value of q minus r ? a ) 52 , b ) 54 , c ) 55 , d ) 56 , e ) 58","""a two - digit integer ` ` ab'' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 60 . the greatest multiple of 9 which is less than 60 is 54 . the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","( 0.12 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.12 ) ( power 2 ) + 0.012 + ( 0.1 ) ( power 2 ) is : a ) 0.68 , b ) 0.086 , c ) 0.86 , d ) 0.068 , e ) none of them","""given expression = ( 0.12 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.12 ) ( power 2 ) + ( 0.12 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.12 - 0.1 ) = 0.02 answer is e ."""
Explain the solution process for the given equation.,"the price of a tv was increased by 30 percent . the new price was then increased by 40 percent . a single increase of what percent is equivalent to these two successive increases ? a ) 82 % , b ) 75 % , c ) 65 % , d ) 50 % , e ) 45 %","""consider base price - $ 100 30 % increase = 1.30 * 100 = $ 130 another 40 % increase on new price = 1.4 * 130 = $ 182 so final price of radio - $ 182 therefore a 82 % increase correct option - a"""
Provide a detailed solution to the given mathematical problem.,"a jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? a ) 3.6 sec , b ) 18 sec , c ) 36 sec , d ) 72 sec , e ) none","category formulae examples directions : problems based on trains . 11 . a train 280 m long , running with a speed of 63 km / hr will pass a tree in a . 15 sec . b . 16 sec . c . 18 sec . d . 20 sec . solution speed = ( 63 x 5 / 18 ) m / sec = 35 / 2 msec time taken = ( 280 x 2 / 35 ) m / sec = 16 sec . 12 . a train running at the speed of 60 km / hr crosses a pole in 9 seconds . what is ihe length of the train ? a . 120 metres b . 180 metres c . 324 metres d . none of these solution 13 . a jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? a . 3.6 sec b . 18 sec c . 36 sec d . 72 sec solution speed of train relative to jogger = ( 45 - 9 ) km / hr = 36 km / hr = ( 36 x 5 / 18 ) m / sec = 10 m / sec distance covered = ( 240 + 120 ) m = 360 m time taken = ( 360 / 10 ) sec = 36 sec . answer c"
Break down and solve the equation step by step.,"a can give b 60 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ? a ) 63.83 , b ) 111.67 , c ) 111.64 , d ) 111.11 , e ) 101.12","""a runs 1000 m while b runs 940 m and c runs 880 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 880 ) / 940 = 936.17 m . b can give c = 1000 - 936.17 = 63.83 m . answer : a"""
Break down and solve the equation step by step.,"rs . 1170 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ? a ) rs . 720 , b ) rs . 920 , c ) rs . 537 , d ) rs . 540 , e ) rs . 637",a + b + c = 1170 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1170 = rs . 540 answer : d
"Work through the equation methodically, ensuring clarity at each step.","a rectangular block has the dimensions 5 x 6 x 7 cm it is dropped into a cylindrical vessel of radius 6 cm and height 10 cm . if the level of the fluid in the cylinder rises by 4 cm , what portion of the block is immersed in the fluid ? ['a ) 22 / 7 x 24 / 35','b ) 22 / 7 x 36 x 4','c ) 22 / 7 x 36 / 5','d ) 22 / 7 x 37 / 21','e ) 22 / 7 x 32 / 21']","explanation : since level of water increased in cylinder by height 4 . this is because of the rectangular block . therefore , area of rectangular block immersed in water is = 22 / 7 x ( 6 ) ^ 2 x 4 thats why portion of block immersed in water is = ( 22 / 7 x 36 x 4 ) / total vol . of rectangle = ( 22 / 7 x 36 x 4 ) / ( 7 x 5 x 6 ) = 22 / 7 x 24 / 35 . answer is a"
"Solve the problem systematically, showing each step clearly.","what is the remainder of e = 3 ^ 19 when divided by 10 ? a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9","i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , e = when divided by 10 , the remainder must be 7 . d"
Provide a detailed solution to the given mathematical problem.,"10 percent of ram' s monthly salary is equal to 8 percent of shyam' s monthly salary . shyam' s monthly salary is twice abhinav' s monthly salary . if abhinav' s annual salary is rs . 1.92 lakhs , find ram' s monthly salary ? a ) rs . 18000 , b ) rs . 20000 , c ) rs . 25600 , d ) rs . 32000 , e ) none of these",let the monthly salaries of ram and shyam be rs . r and rs . s respectively . 10 / 100 r = 8 / 100 s r = 4 / 5 s monthly salary of abhinav = ( 1.92 lakhs ) / 12 = rs . 0.16 lakhs s = 2 ( 0.16 lakhs ) = 0.32 lakhs r = 4 / 5 ( 0.32 lakhs ) = rs . 25600 answer : c
"Work through the equation methodically, ensuring clarity at each step.","15 men take 20 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ? a ) 27.57 , b ) 28.57 , c ) 29.57 , d ) 30.57 , e ) 32",3 w = 2 m 15 m - - - - - - 20 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 15 * 20 * 8 = 14 * x * 6 x = 28.57 answer : b
"Work through the equation methodically, ensuring clarity at each step.","a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is d' s share ? a ) $ 1000 , b ) $ 1200 , c ) $ 1500 , d ) $ 1800 , e ) $ 2000","let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 d' s share = 3 x = 3 * $ 500 = $ 1500 the answer is c ."
Provide a detailed solution to the given mathematical problem.,"if 9 ^ y = 3 ^ 12 , what is y ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6","""3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e"""
Explain the solution process for the given equation.,"the sum of ages of 5 children born 4 years different each is 70 yrs . what is the age of the elder child ? a ) 8 , b ) 9 , c ) 22 , d ) 17 , e ) 18","""let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) and ( x + 16 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) + ( x + 16 ) = 70 5 x = 30 x = 6 x + 16 = 6 + 16 = 22 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 5,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ? a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 11.11 %","the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 5,500 = 4,500 gallons and sodium chloride is 500 gallons ( 5 % of initial solution of 10,000 gallons ) then sodium chloride is 500 / 4,500 * 100 = ~ 11.11 % of the remaining solution of 4,500 gallons . answer : e ."
"Work through the equation methodically, ensuring clarity at each step.","on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.90 per glass on the first day , what was the price per glass on the second day ? a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.6","""on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.9 = 3 * x - - > x = $ 0.6 . answer : e ."""
Explain the solution process for the given equation.,"farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 5000 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is : a ) 15 % , b ) 16 % , c ) 0.125 % , d ) 0.2083 % , e ) none","""this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 5000 ) x 100 = 9.6 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 9.6 % x ( 100 / 60 ) = 16 % the correct answer is ( b ) ."""
"Solve the problem systematically, showing each step clearly.","when a number is divided by 6 & then multiply by 12 the answer is 10 what is the no . ? a ) 4.5 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 6.5","""if $ x $ is the number , x / 6 * 12 = 10 = > 2 x = 10 = > x = 5 b"""
"Work through the equation methodically, ensuring clarity at each step.","ram and shakil run a race of 2000 meters . first , ram gives shakil a start of 200 meters and beats him by one minute . if , ram gives shakil a start of 6 minutes ram is beaten by 1000 meters . find the time in minutes in which ram and shakil can run the races separately . a ) 7,10 , b ) 8,10 , c ) 9,10 , d ) 10,10 , e ) 10,12","let x and y are the speeds of ram and shakil . . then by problem we got following equation 2000 / x = ( 1800 / y ) - 1 1000 / x = ( 2000 / y ) - 6 solve equation 1 and 2 , we get x = 250 and y = 200 therefore , time taken by ram and shakilk to complete a race of 2000 m is 8 min and 10 min answer : b"
Break down and solve the equation step by step.,"( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) = a ) 8.4 , b ) 840 , c ) 84.0 , d ) 0.84 , e ) 0.084",( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) = 0.0048 * 350 / 5 ( 0.1 ) ( 0.004 ) = 0.048 * 70 / 1 ( 0.004 ) = 48 * 70 / 4 = 12 * 70 = 840 answer : b
Explain the solution process for the given equation.,"a bag contains 6 black and 6 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? a ) 3 / 4 , b ) 1 / 2 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3","""let number of balls = ( 6 + 6 ) = 12 . number of white balls = 6 . p ( drawing a white ball ) = 6 / 12 = 1 / 2 . option b ."""
"Solve the problem systematically, showing each step clearly.","in a recent head - to - head run - off election , 12,000 absentee ballets were cast . 1 / 2 of the absentee ballets were thrown out and 1 / 2 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ? a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000","""1 / 2 * 1 / 2 ( total absentee votes ) = 1 / 4 ( total votes ) = 1 / 4 * 12000 = 3000 answer is b"""
Explain the solution process for the given equation.,"last year the range of the annual yield on equal amount of investments in 100 mutual funds was $ 10000 . if the annual yield this year for each of the 100 mutual funds has improved by 15 percent this year than it was last year , what is the range of the annual yield on mutual funds this year ? a ) $ 12700 , b ) $ 13000 , c ) $ 23000 , d ) $ 11500 , e ) $ 33000","let the lowest yield be x . therefore , highest yield is x + 10000 . now yield of each mutual fund investment is improved by 10 % . therefore the yields will remain arranged in the same order as before . or lowest yield = 1.15 x and highest = 1.15 * ( x + 10000 ) or range = highest - lowest = 1.15 * ( x + 10000 ) - 1.15 x = 11500 , hence , d"
Explain the solution process for the given equation.,"if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 57 , then * is equal to : a ) - 29 , b ) - 19 , c ) 18 , d ) 29 , e ) 39","""45 - [ 28 - { 37 - ( 15 - * ) } ] = 57 = > 45 - [ 28 - { 37 - 15 + * } ] = 57 45 - [ 28 - 37 + 15 - * ] = 57 = > 45 [ 43 - 37 - * ] = 57 45 - [ 6 - * ] = 57 = > 45 - 6 + * = 57 39 + * = 57 = > * = 57 - 39 = 18 answer : c"""
Provide a detailed solution to the given mathematical problem.,"how many positive integers less than 17 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ? a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 10","""the number = 2 a + 3 b < 17 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 , 12 , 15 - > the number = 5 , 8 , 11 , 14 - - > 4 numbers when a = 2 , b = 1,2 , 3,4 - > . . . . - - > 4 numbers when a = 3 , b = 1 , 2,3 - - > . . . . - - > 3 numbers total number is already 11 . look at the answer there is no number greater than 11 - - > we dont need to try any more answer must be d"""
Break down and solve the equation step by step.,"two pipes a and b can fill a cistern in 12 and 20 minutes respectively , and a third pipe c can empty it in 30 minutes . how long will it take to fill the cistern if all the three are opened at the same time ? a ) 15 min , b ) 13 min , c ) 12 min , d ) 10 min , e ) 17 min","""1 / 12 + 1 / 20 - 1 / 30 = 1 / 10 10 / 1 = 10 answer : d"""
"Solve the problem systematically, showing each step clearly.","jaya ranks 5 th in a class of 53 . what is her rank from the bottom in the class ? a ) 49 th , b ) 48 th , c ) 47 th , d ) 50 th , e ) none of these",there are 4 students above her . when takan from bottom there are 4 students below her rank . so her rank wud be 53 - 4 i . e . 49 th . answer : a
"Solve the problem systematically, showing each step clearly.","of the two - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a ) 24 , b ) 9 , c ) 72 , d ) 144 , e ) 216","of the two - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for x - 9 ways ; # of permutations of 3 digits in xx - 2 ! / 2 ! total : 9 * 2 ! / 2 ! = 9 . answer : b ."
Provide a detailed solution to the given mathematical problem.,"a train travels 225 km in 3.5 hours and 370 km in 5 hours . find the average speed of train . a ) 80 kmph , b ) 60 kmph , c ) 70 kmph , d ) 90 kmph , e ) none of these","""as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 225 + 370 = 595 km thus , total speed = 8.5 hrs or , average speed = 595 / 8.5 or , 70 kmph . answer : c"""
Provide a detailed solution to the given mathematical problem.,"in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 24 . what is the total number of students in the school ? a ) 50 , b ) 80 , c ) 120 , d ) 150 , e ) 100","""explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 24 + 2 / 3 of 24 80 / 100 x = 40 x = 50 . answer : option a"""
"Work through the equation methodically, ensuring clarity at each step.","i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 90 mph . what was my average speed for the trip ? a ) 198 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph",( 110 mph + 90 mph ) / 2 = 100 mph correct answer is : d
Explain the solution process for the given equation.,"carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 6 inches tall . carmen places her sculpture on a base that is 12 inches tall . how tall are the sculpture andbase together ? a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.83 feet","""we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 12 = 44 46 / 12 = 3.83 feet answer : e"""
"Solve the problem systematically, showing each step clearly.","kanul spent $ 5000 in buying raw materials , $ 200 in buying machinery and 30 % of the total amount he had as cash with him . what was the total amount ? a ) $ 7456.00 , b ) $ 7500.55 , c ) $ 7428.57 , d ) $ 7852.56 , e ) $ 7864.00","""let the total amount be x then , ( 100 - 20 ) % of x = 5000 + 200 70 % of x = 5200 70 x / 100 = 5200 x = $ 52000 / 7 x = $ 7428.57 answer is c"""
Explain the solution process for the given equation.,"in a college , 50 % of total 400 arts students are locals . 25 % of students from 100 science students are locals and 85 % of total 120 commerce students are locals . what is the total percentage of locals from arts , science and commerce . a ) 322 , b ) 340 , c ) 333 , d ) 327 , e ) 500",locals from arts = 50 % of 400 = 200 locals from science = 25 % of 100 = 25 locals from commerce = 85 % of 120 = 102 total locals = 200 + 25 + 102 = 327 d
Provide a detailed solution to the given mathematical problem.,"a man can row his boat with the stream at 24 km / h and against the stream in 10 km / h . the man' s rate is ? a ) 1 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph","""explanation : ds = 24 us = 10 s = ? s = ( 24 - 10 ) / 2 = 7 kmph answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","find the ones digit of 73 ^ 353 a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9","""the units digit of 73 ^ 353 will be the same as the units digit of 3 ^ 353 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 353 = 352 + 1 = ( multiple of 4 ) + 1 , then the units digit of 3 ^ 353 will be the first number in the pattern thus 3 . answer : a ."""
Provide a detailed solution to the given mathematical problem.,"a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 5 per sq m ? a ) 675 , rs . 3375 , b ) 575 , rs . 1350 , c ) 1350 , rs . 675 , d ) 1450 , rs . 775 , e ) 1550 , rs . 875","""area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 5 = rs . 3375 answer : a"""
Explain the solution process for the given equation.,"what distance will be covered by a city bus moving at 72 kmph in 30 seconds ? a ) 200 m , b ) 300 m , c ) 600 m , d ) 500 m , e ) 400 m",72 kmph = 72 * 5 / 18 = 20 mps dist = speed * time = 20 * 30 = 600 m . answer c
Explain the solution process for the given equation.,"on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction t of the total distance did he cover while the sun was shining on him ? a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7","if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is t = 2 / 14 = 1 / 7 . answer : e"
Break down and solve the equation step by step.,"two numbers are respectively 71 % and 80 % more than a third number . the percentage that is first of the second is ? a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %","""i ii iii 171 180 100 180 - - - - - - - - - - 171 100 - - - - - - - - - - - ? = > 5 % answer : b"""
Break down and solve the equation step by step.,"what sum of money will produce rs . 70 as simple interest in 3 years at 3 1 / 2 percent ? a ) 263 , b ) 500 , c ) 367 , d ) 368 , e ) 666.7","""70 = ( p * 3 * 7 / 2 ) / 100 p = 666.7 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","which is the least number that must be subtracted from 1100 so that the remainder when divided by 7 , 12 , 16 is 4 ? a ) 58 , b ) 68 , c ) 78 , d ) 88 , e ) 90","""first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1100 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 88 d"""
Explain the solution process for the given equation.,"find the compound interest on $ 30000 in 2 years at 4 % per annum , the interest being compounded half - yearly ? a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 2472.96 , e ) $ 1020.45","""principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 30000 * ( 1 + 2 / 100 ) ^ 4 = 30000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 32472.96 c . i . = 32472.96 - 10000 = $ 2472.96 answer is d"""
"Solve the problem systematically, showing each step clearly.","if 5 spiders make 5 webs in 5 days , then 1 spider will make 1 web in how many days ? a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3","""let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 5 webs 5 : 1 1 x 5 x x = 5 x 1 x 5 = > x = 5 answer is c"""
Explain the solution process for the given equation.,"what will be the cost of building a fence around a square plot with area equal to 144 sq ft , if the price per foot of building the fence is rs . 58 ? a ) 2784 , b ) 2287 , c ) 2977 , d ) 2668 , e ) 1298","""let the side of the square plot be a ft . a 2 = 144 = > a = 12 length of the fence = perimeter of the plot = 4 a = 48 ft . cost of building the fence = 48 * 58 = rs . 2784 . answer : a"""
Explain the solution process for the given equation.,"the product of two numbers is 4107 . if the h . c . f of these numbers is 37 , then the greater number is ? a ) 377 , b ) 126 , c ) 111 , d ) 727 , e ) 121","""let the numbers be 37 a and 37 b . then , 37 a * 37 b = 4107 = > ab = 3 now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 * 1 , 37 * 3 ) i . e . , ( 1 , 111 ) . greater number = 111 . answer : c"""
"Solve the problem systematically, showing each step clearly.","what least number should be subtracted from 1,439 so that the remainder when divided by 5 , 11 , and 13 will leave in each case the same remainder 3 ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6","""the lcm of 5 , 11 , and 13 is 715 . the next multiple is 2 * 715 = 1,430 . 1,430 + { remainder } = 1,430 + 3 = 1,433 , which is 6 less than 1,439 . answer : e ."""
"Solve the problem systematically, showing each step clearly.","the number which exceeds 16 % of it by 42 is : a ) 50 , b ) 52 , c ) 58 , d ) 60 , e ) 62","""solution solution let the number be x . x - 16 % of x = 42 x - 16 / 100 x = 42 x - 4 / 25 x = 42 21 / 25 x = 42 x = ( 42 x 25 / 21 ) = 50 answer a"""
Break down and solve the equation step by step.,"a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 752 in total compensation , how many total hours did he work that week ? a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52","""for 40 hrs = 40 * 16 = 640 excess = 752 - 640 = 112 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 112 / 28 = 28 / 7 = 4 total hrs = 40 + 4 = 44 answer c 44"""
"Work through the equation methodically, ensuring clarity at each step.","if 40 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ? a ) 540 , b ) 528 , c ) 530 , d ) 520 , e ) 510","""we know 37.5 % people study biology , therefore the no of people not studying = 100 - 40 = 60 % > therefore the people not studying biology out of a total 880 people are = 60 % of 880 > ( 60 / 100 ) * 880 = 528 people b"""
"Solve the problem systematically, showing each step clearly.","find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm ? a ) 288 , b ) 276 , c ) 285 , d ) 299 , e ) 261","""area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : c"""
Break down and solve the equation step by step.,"donald duck can can swim his pool downstream ( with the pool current helping time ) in exact 40 seconds and upstream ( against the pool current ) in a pool in exact 60 seconds . the length of pool is 2 kilometers . how long donald duck can cover distance of one side at a still pool ( with no current ) . a ) 40 minutes , b ) 45 minutes , c ) 38 minutes , d ) 48 minutes , e ) 30 minutes","d 48 minutes . donald duck' s speed = x km / seconds pool current speed = y km / seconds 2 / ( x + y ) = 40 2 / ( x - y ) = 60 solving the simultaneous equations gives x = 1 / 24 therefore , to cover 2 km will take 2 / x = 48 seconds"
Break down and solve the equation step by step.,"a milk man has 30 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : a ) 20 % , b ) 25 % , c ) 33.33 % , d ) 35 % , e ) none of these","explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 30 liters of milk . therefore , profit percentage = 35 % . answer : d"
Break down and solve the equation step by step.,"if ( m - 8 ) is a factor of m ^ 2 - qm - 24 , then q = a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16","""( m - 8 ) ( m - a ) = m ^ 2 - qm - 24 a = - 3 q = 8 + a = 5 = b"""
Provide a detailed solution to the given mathematical problem.,"a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 39000 , then the share of b is ? a ) a ) 34500 , b ) b ) 24000 , c ) c ) 24098 , d ) d ) 19007 , e ) e ) 18000","""ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 39000 share of b = 6 / 13 ( 39000 ) = rs . 18000 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is one - half of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ? a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100","""total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = x / 2 x + x / 2 + 600 = 1800 3 x / 2 = 1200 x = 800 km the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","if the digits 33 in the decimal 0.00033 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00033 ) ? a ) 0.33 , b ) 33 , c ) 0.033 , d ) 0.0033 , e ) 3.3 e - 05",99 * 0.33 = 32.67 approx . 33 answer : b
"Solve the problem systematically, showing each step clearly.","the present ages of 3 persons are in proportions 4 : 7 : 9 . 7 years ago , the sum of their ages was 79 . find their present ages . a ) 20 , 28 , b ) 28 , 36 , c ) 35 , 45 , d ) 35 , 55 , e ) of these","let their present ages be 4 x , 7 x and 9 x years respectively . then , ( 4 x - 7 ) + ( 7 x - 7 ) + ( 9 x - 7 ) = 79 20 x = 100 = > x = 5 their present ages are 20 , 35 and 45 years respectively . answer : c"
"Work through the equation methodically, ensuring clarity at each step.","the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam ? a ) 22 , b ) 26 , c ) 25 , d ) 28 , e ) 12","""let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c"""
Provide a detailed solution to the given mathematical problem.,"the h . c . f . of two numbers is 10 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is : a ) 150 , b ) 300 , c ) 299 , d ) 322 , e ) 345","""the numbers are ( 10 x 11 ) and ( 10 x 15 ) . larger number = ( 10 x 15 ) = 150 . answer : a"""
Break down and solve the equation step by step.,"if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 11 ) , what is the value of x ? a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17","""( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 11 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 11 hence x = 13 . answer is c"""
Provide a detailed solution to the given mathematical problem.,"two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 4 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ? a ) 3.5 , b ) 4 , c ) 4.5 , d ) 5 , e ) 5.5","""let x be the total time it takes for the cistern to fill . 4 / 10 + x / 15 = 1 x / 15 = 3 / 5 x = 9 after the first pipe is turned off , it takes 5 more minutes to fill the cistern . the answer is d ."""
Explain the solution process for the given equation.,"a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 76 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ? a ) 2 , b ) 1 , c ) 4 , d ) 6 , e ) 8","""we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 76 / 25 = 3 . . . . so the max is 3 76 / 20 = 3 . . . so the max is 3 76 - 75 = 1 answer : b"""
Break down and solve the equation step by step.,"in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is ? a ) 1 hr , b ) 2 hr , c ) 6 hr , d ) 8 hr , e ) 7 hr","let the duration of the flight be x hours . then , 600 / x - 600 / ( x + 1 / 2 ) = 200 x ( 2 x + 1 ) = 3 2 x 2 + x - 3 = 0 ( 2 x + 3 ) ( x - 1 ) = 0 x = 1 hr . answer : a"
Break down and solve the equation step by step.,"every day daniel drives 64 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ? a ) 15 % , b ) 25 % , c ) 35 % , d ) 45 % , e ) 55 %","""let' s test x = 4 . . . . on sunday , daniel drove 64 miles at 4 miles / hour . d = ( r ) ( t ) 64 = ( 4 ) ( t ) 64 / 4 = 16 = t it takes 16 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 32 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 32 = ( 2 ) ( t ) 32 / 2 = 16 = t it takes 16 hours for the second part total time to drive home on monday = 4 + 16 = 20 hours we' re asked by what percent 20 hours is greater than 16 hours . 20 / 16 = 1.25 , so it is 25 % greater . b"""
"Solve the problem systematically, showing each step clearly.","by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 40 % ? a ) s . 429 , b ) s . 480 , c ) s . 429 , d ) s . 128 , e ) s . 384","""sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 40 % = 40 % of 640 = rs . 256 sp = cp - loss = 640 - 256 = rs . 384 answer : e"""
Explain the solution process for the given equation.,"a is twice as good a workman as b and they took 7 days together to do the work b alone can do it in ? a ) 25 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 13 days","""wc = 2 : 1 2 x + x = 1 / 7 x = 1 / 21 = > 21 days answer : c"""
Provide a detailed solution to the given mathematical problem.,"how many diagonals does a 63 - sided convex polygon have ? a ) 1890 , b ) 1953 , c ) 3780 , d ) 3843 , e ) 3906","""a 63 - sided convex polygon has 63 vertices . if we examine a single vertex , we can see that we can connect it with 60 other vertices to create a diagonal . note : there are 60 options because we ca n' t connect the vertex to itself , and we ca n' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 63 vertices can be connected with 60 vertices to create a diagonal then . . . . . . the total number of diagonals = ( 63 ) ( 60 ) = 3780 however , before we select answer choice c , we must recognize that we have counted every diagonal twice . for example , we might connect vertex a with vertex f and count that as 1 diagonal , and at the same time we connect vertex f with vertex a and count that as 1 diagonal . of course these diagonals are the same . to account for counting each diagonal twice , we must divide 3780 by 2 to get : 1890 answer : a"""
Provide a detailed solution to the given mathematical problem.,"john was thrice as old as tom 6 years ago . john will be 2 times as old as tom in 4 years . how old is tom today ? a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20","j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 4 = 2 ( t + 4 ) ( 3 t - 12 ) + 4 = 2 t + 8 t = 16 the answer is c ."
Provide a detailed solution to the given mathematical problem.,"when positive integer e is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","the equation that can be formed e is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b"
"Solve the problem systematically, showing each step clearly.","how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 35 % iodine solution ? a ) 35 , b ) 49 , c ) 100 , d ) 105 , e ) 140","""solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % iodine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 35 / 100 40 x + 700 = 35 x + 1225 5 x = 525 x = 105 lts correct option : d"""
Break down and solve the equation step by step.,"p , q and r have rs . 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ? a ) rs . 3000 , b ) rs . 1600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these","""let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 . answer : b"""
Explain the solution process for the given equation.,"a tank is filled in sixteen hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ? a ) 56 hours , b ) 28 hours , c ) 55 hours , d ) 66 hours , e ) 47 hours",1 / a + 1 / b + 1 / c = 1 / 16 ( given ) also given that a = 2 b and b = 2 c = > 1 / 2 b + 1 / b + 2 / b = 1 / 16 = > ( 1 + 2 + 4 ) / 2 b = 1 / 16 = > 2 b / 7 = 16 = > b = 56 hours . answer : a
Break down and solve the equation step by step.,"a cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is : a ) 49 m 2 , b ) 50 m 2 , c ) 52 m 2 , d ) 62 m 2 , e ) 55 m 2","""area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 8 x 1.25 + 4 x 1.25 ) + 8 x 4 ] m 2 = 62 m 2 . answer : d"""
Provide a detailed solution to the given mathematical problem.,"one night 18 percent of the female officers on a police force were on duty . if 144 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ? a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700","""let x be the number of female police officers on the police force . the number of female police officers on duty was 72 . 0.18 x = 72 x = 400 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 60 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ? a ) 1800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600","""volume of pool = 60 * 150 * 10 cu . ft , 80 % full = 60 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 60 * 150 * 10 * 0.8 / 60 min = 1200 min c"""
"Work through the equation methodically, ensuring clarity at each step.","a can do a piece of work in 8 days . he works at it for 4 days and then b finishes it in 6 days . in how many days can a and b together finish the work ? a ) 4.1 days , b ) 4.8 days , c ) 3.8 days , d ) 2.8 days , e ) 4.5 days",4 / 8 + 6 / x = 1 = > x = 12 1 / 8 + 1 / 12 = 5 / 24 = > 4.8 days answer : b
Explain the solution process for the given equation.,"if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 650 , what is the least possible value of n ? a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14","""650 = 2 * 5 * 5 * 13 so the least value forncan be 13 . d"""
Break down and solve the equation step by step.,"the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the numbers is 720 , then the other is : a ) 8 , b ) 10 , c ) 12 , d ) 4 , e ) 6","""other number = ( 12 x 600 ) / 720 = 10 . answer : c"""
Break down and solve the equation step by step.,"p alone can complete a job in 12 days . the work done by q alone in one day is equal to one - half of the work done by p alone in one day . in how many days can the work be completed if p and q work together ? a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9","""p' s rate is 1 / 12 q' s rate is 1 / 24 the combined rate is 1 / 12 + 1 / 24 = 1 / 8 if they work together , the job will take 8 days . the answer is d ."""
Explain the solution process for the given equation.,"on the number line , if x is halfway between - 6 and 4 , and if y is halfway between - 2 and 6 , what number is halfway between x and y ? a ) - 2.5 , b ) - 1.5 , c ) - 0.5 , d ) 0.5 , e ) 1.5","""x = - 1 and y = 2 . the answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","along a yard 273 metres long , 14 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees a ) 18 , b ) 19 , c ) 10 , d ) 21 , e ) 12","""explanation : 14 trees have 13 gaps between them , required distance ( 273 / 13 ) = 21 option d"""
Break down and solve the equation step by step.,"if grapes are 90 % water and raisins are 15 % water , then how many kilograms did a quantity of raisins , which currently weighs 12 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . ) a ) 96 , b ) 98 , c ) 100 , d ) 102 , e ) 104","""let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 85 % of the raisins , 0.1 x = 0.85 ( 12 kg ) . then x = 8.5 * 12 = 102 kg . the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"a tank contains 8,000 gallons of a solution that is 4 percent sodium chloride by volume . if 3,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ? a ) 3.40 % , b ) 4.40 % , c ) 5.40 % , d ) 6.40 % , e ) 7.40 %","""we start with 8,000 gallons of a solution that is 4 % sodium chloride by volume . this means that there are 0.04 x 8,000 = 320 gallons of sodium chloride . when 3,000 gallons of water evaporate we are left with 5,000 gallons of solution . from here we can determine what percent of the 5,000 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 320 / 5,000 ) x 100 = ? 0.064 x 100 = ? = 6.4 % answer is d ."""
Explain the solution process for the given equation.,"what is the probability that a number selected from number 1 to 30 is prime number , when each of the given numbers is equally likely to be selected ? a ) 10 / 30 , b ) 20 / 30 , c ) 1 , d ) 5 / 30 , e ) 15 / 30","x = { 2,3 , 5,7 , 11,13 , 17,19 , 23,29 } n ( x ) = 10 n ( s ) = 30 hence required probability = n ( x ) / n ( s ) = 10 / 30 option a is answer"
Explain the solution process for the given equation.,"a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 15 seconds . the speed of the train is ? a ) 35 , b ) 50 , c ) 88 , d ) 22 , e ) 12","""speed of the train relative to man = ( 125 / 15 ) m / sec = ( 25 / 3 ) m / sec . [ ( 25 / 3 ) * ( 18 / 5 ) ] km / hr = 30 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 30 = = > x = 35 km / hr . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","on dividing 23 by a number , the quotient is 7 and the remainder is 2 . find the divisor . a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 7","""d = ( d - r ) / q = ( 23 - 2 ) / 7 = 21 / 7 = 3 c"""
Break down and solve the equation step by step.,"there are 250 men and 150 women in a committee , if all will work they will complete 12 units per day , if all men work they will complete 15 units per day , how many units will women complete per day ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7","i think there is a mistake in this question . if all men and women together complete 12 units , how only men can do 15 units of work a day ? forgetting about the reality , women can do - 3 units a day . answer : b"
Break down and solve the equation step by step.,"a merchant sells an item at a 20 % discount , but still makes a gross profit of 50 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ? a ) 20 % , b ) 40 % , c ) 87.5 % , d ) 60 % , e ) 75 %","""original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.5 c ( 50 % profit ) x = 1.5 / . 8 * c x = 15 / 8 c original selling price is 1.875 c which is 87.5 % profit answer c"""
"Work through the equation methodically, ensuring clarity at each step.","in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 2200 , how many purple chips were selected ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""2200 = 1 * 5 ^ 2 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."""
Provide a detailed solution to the given mathematical problem.,"two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.15 km respectively . the time taken by the slower train to cross the faster train in seconds is ? a ) 65 sec , b ) 54 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec","""relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.15 = 2.25 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a candidate got 35 % of the votes polled and he lost to his rival by 2340 votes . how many votes were cast ? a ) 7500 , b ) 3388 , c ) 2665 , d ) 7800 , e ) 2661","""35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2340 100 % - - - - - - - - - ? = > 7800 answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","the number 149 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? a ) 19 , b ) 16 , c ) 15 , d ) 14 , e ) 13","""2 ^ 2 + 8 ^ 2 + 9 ^ 2 = 149 - - > 2 + 9 + 8 = 19 . a"""
Explain the solution process for the given equation.,"a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 20 % ? a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 48","""production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 2.40 = 45 thus , solution a is correct ."""
"Work through the equation methodically, ensuring clarity at each step.","in a mixed college 160 students are there in one class . out of this 160 students 3 / 8 students are girls . how many boys are there ? a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 100 , e ) e ) 140","""total number of students : 160 total girls : 160 * 3 / 8 = 60 total boys : 160 - 60 = 100 answer is d"""
Provide a detailed solution to the given mathematical problem.,"calculate the number of bricks , each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10 % of its volume is occupied by mortar ? a ) 3388 , b ) 27678 , c ) 6000 , d ) 2977 , e ) 27681",10 * 4 / 100 * 5 * 90 / 100 = 25 / 100 * 15 / 100 * 8 / 100 * x 10 * 20 * 90 = 15 * 2 * x = > x = 6000 answer : c
"Work through the equation methodically, ensuring clarity at each step.","calculate how many days it will take for 8 boys to paint a 50 m long wall if 6 boys can paint a 60 m long wall in 5 days , a ) 4.13 days , b ) 3.13 days , c ) 513 days , d ) 9.13 days , e ) 2 days",the length of wall painted by one boy in one day = 60 / 6 * 1 / 5 = 2 m no . of days required to paint 50 m cloth by 8 boys = 50 / 8 * 1 / 2 = 3.13 days . b
Explain the solution process for the given equation.,"bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 70 more . what was his original selling price ? a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840","""let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 70 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 70 = > 0.07 x = 70 = > x = $ 1000 original purchase price = $ 1000 hence , original selling price ( at 10 % of profit ) = 1.1 ( 1000 ) = $ 1100 option d"""
Explain the solution process for the given equation.,"a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 52 , then how old is b ? a ) 17 years , b ) 20 years , c ) 29 years , d ) 10 years , e ) 12 years","""let c' s age be x years . then , b' s age = 2 x years . a' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 52 5 x = 50 = > x = 10 hence , b' s age = 2 x = 20 years . answer : b"""
Provide a detailed solution to the given mathematical problem.,"if ( 10 ^ 4 * 3.456789 ) ^ 9 is written as a single term , how many digits would be to the right of the decimal place ? a ) 6 , b ) 12 , c ) 18 , d ) 32 , e ) 48","""3.456789 ^ 9 has 6 * 9 = 54 decimal places . 10 ^ 36 moves the decimal place to the right 36 places . ( 10 ^ 4 * 3.456789 ) ^ 9 has 54 - 36 = 18 digits after the decimal point . the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ? a ) a ) 40 , b ) b ) 30 , c ) c ) 20 , d ) d ) 10 , e ) e ) 5","""explanation : t = 16 / 48 * 60 = 20 answer : option c"""
Break down and solve the equation step by step.,"the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 142 . what is the number of frogs in the pond ? a ) 148 , b ) 152 , c ) 156 , d ) 145 , e ) none","""solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 142 . so , total number of ducks and frogs in the pond , = 2 * 142 = 284 . therefore , number of frogs , = ( 284 * 39 ) / 76 = 145 . answer : option d"""
"Solve the problem systematically, showing each step clearly.","a man buys an article for $ 100 . and sells it for $ 115 . find the gain percent ? a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %","""c . p . = $ 100 s . p . = $ 115 gain = $ 15 gain % = 15 / 100 * 100 = 25 % answer is b"""
Break down and solve the equation step by step.,"excluding stoppages , the average speed of a bus is 50 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ? a ) 12 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 26 min","""in 1 hr , the bus covers 50 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 50 - 40 ) km i . e 10 km at 50 km / hr . stoppage time = 10 / 50 hrs = 12 min answer : a"""
Explain the solution process for the given equation.,"there were two candidates in an election . winner candidate received 60 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ? a ) 776 , b ) 864 , c ) 299 , d ) 257 , e ) 125","""w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 288 60 % - - - - - - - - ? = > 864 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","two trains 140 m and 150 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? a ) 10.9 sec , b ) 13.8 sec , c ) 53.8 sec , d ) 10.44 sec , e ) 10.4 sec","""relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 150 = 290 m . required time = 290 * 9 / 250 = 10.44 sec . answer : d :"""
"Solve the problem systematically, showing each step clearly.","a person crosses a 1800 m long street in 12 minutes . what is his speed in km per hour ? a ) 4.1 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 9","""speed = 1800 / ( 12 x 60 ) m / sec = 2.5 m / sec . converting m / sec to km / hr = 2.5 x ( 18 / 5 ) km / hr = 9 km / hr . answer : e"""
Provide a detailed solution to the given mathematical problem.,"find the l . c . m of 2 / 15 , 3 / 10 , 6 / 5 a ) 6 / 5 , b ) 2 / 3 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5","""explanation : lcm of fractions = lcm of numerators / hcf of denominators ( lcm of 2 , 3 , 6 ) / ( hcf of 15 , 10 , 5 ) = 6 / 5 answer : option a"""
Provide a detailed solution to the given mathematical problem.,"the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 168,000 . what was the percent increase in the cost of the home ? a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %","""increase = 168000 - 120000 = 48000 % increase = 48000 * 100 / 120000 = 40 % answer : option d"""
Provide a detailed solution to the given mathematical problem.,"if x , y , and z are positive integers and 3 x = 7 y = 5 z , then the least possible value of x + y + z is a ) 15 , b ) 25 , c ) 71 , d ) 35 , e ) 45","""given 3 x = 7 y = 5 z x + y + z in terms of x = x + ( 3 x / 7 ) + ( 3 x / 5 ) = 71 x / 35 now checking with each of the answers and see which value gives a minimum integer value . a x = 35 / 71 * 15 , not an integer b , d , e can be ruled out similarly . c is minimum value as x = 71 * 35 / 71 = 35 answer is c"""
Break down and solve the equation step by step.,"what is the area of a square field whose diagonal of length 16 m ? a ) 128 , b ) 289 , c ) 200 , d ) 112 , e ) 178","""d 2 / 2 = ( 16 * 16 ) / 2 = 128 answer : a"""
Break down and solve the equation step by step.,"4 , 12 , 48 , 240 , 1440 , ( . . . ) a ) 7620 , b ) 6200 , c ) 10020 , d ) 10080 , e ) 11000","""go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7 4 x 3 = 12 ; 12 x 4 = 48 . . . . . 1440 x 7 = 10080 answer is d ."""
"Solve the problem systematically, showing each step clearly.","the least number which when divided by 4 , 6 , 7 and 8 leaves a remainder 6 , but when divided by 9 leaves no remainder , is a ) 340 , b ) 342 , c ) 523 , d ) 363 , e ) none of these","""explanation : l . c . m of 4 , 6 , 7 , 8 = 168 therefore required number is of the form 168 k + 6 . least value of k for which ( 168 k + 6 ) is divisible by 9 is k = 2 therefore required number = ( 168 x 2 + 6 ) = 342 . answer : b"""
"Solve the problem systematically, showing each step clearly.","25 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 5 : 4 ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""let x be the amount of liquid q to be added . ( 2 / 5 ) * 25 + x = ( 4 / 9 ) * ( 25 + x ) 450 + 45 x = 500 + 20 x 25 x = 50 x = 2 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","a is a working partner and b is a sleeping partner in a business . a puts in 80,000 and b 70,000 . a gets 25 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the profit if b get 14000 . a ) 42000 , b ) 46000 , c ) 54000 , d ) 40000 , e ) none of these","""let amount distributed between a and b is x ratio of capital between a and b is 8 : 7 if b get 14000 then x * 7 / 15 = 14000 x * 7 = 210000 x = 30000 let total profit = y y * 75 / 100 = 30000 y = 40000 answer d"""
Break down and solve the equation step by step.,"a merchant marks his goods up by 50 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ? a ) 20 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 19 %","""let the price be 100 . the price becomes 150 after a 50 % markup . now a discount of 20 % on 150 . profit = 120 - 100 20 % answer a"""
"Work through the equation methodically, ensuring clarity at each step.","company z has 53 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday . a ) 6 , b ) 7 , c ) 8 , d ) 11 , e ) 12","""say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 53 . now , plug options for x . d x > y as needed . answer : d ."""
Provide a detailed solution to the given mathematical problem.,"a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey' s list price is $ 80 , approximately what percent q of the list price is the lowest possible sale price ? a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50","""let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is q = 40 % of 80 hence , d is the answer"""
Provide a detailed solution to the given mathematical problem.,"a 1500 m long train crosses a tree in 120 sec , how much time will it take to pass a platform 500 m long ? a ) 288 , b ) 160 , c ) 188 , d ) 188 , e ) 12","""l = s * t s = 1500 / 120 s = 12.5 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 12.5 t = 160 sec answer : b"""
"Solve the problem systematically, showing each step clearly.","rs . 1040 is divided amongst a , b , c so that 2 times a' s share , 3 times b' s share and 4 times c' s share are all equal . find a' s share ? a ) 177 , b ) 150 , c ) 817 , d ) 480 , e ) 616",a + b + c = 1040 2 a = 3 b = 4 c = x a : b : c = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 6 / 13 * 1040 = rs . 480 answer : d
Provide a detailed solution to the given mathematical problem.,"circles x and y are concentric . if the radius of circle x is 6 times that of circle y , what is the probability that a point selected inside circle x at random will be outside circle y ? a ) 13 , b ) pi / 3 , c ) pi / 2 , d ) 35 / 36 , e ) 8 / 9","small circle radius = a , so area = pi a ^ 2 large circle radius = 6 a , so area = 9 . pi a ^ 2 area of shaded region = 36 pi a ^ 2 - pi a ^ 2 = 35 pi a ^ 2 so , probability = ( 35 pi a ^ 2 ) / ( 36 pi a ^ 2 ) = 35 / 36 = answer = d"
"Work through the equation methodically, ensuring clarity at each step.","the dimensions of an open box are 50 cm , 40 cm and 23 cm . its thickness is 2 cm . if 1 cubic cm of metal used in the box weighs 0.5 gms , find the weight of the box . ['a ) 8.04 kg','b ) 8.14 kg','c ) 8.24 kg','d ) 9.04 kg','e ) none of these']",explanation : volume of the metal used in the box = external volume - internal volume = [ ( 50 x 40 x 23 ) - ( 44 x 34 x 20 ) ] cm 3 = 16080 cm 3 weight of the metal = [ ( 16080 x 0.5 ) / 1000 ] kg = 8.04 kg . answer : a
Provide a detailed solution to the given mathematical problem.,"money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 1800 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ? a ) $ 16,200 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500","""x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1800 triples to $ 5400 , in 28 years , it will again triple to $ 5400 * 3 = $ 16,200 answer a"""
Explain the solution process for the given equation.,"if 10 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is a ) $ 11.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00","""a for me 9 people with 1 $ each - > maximum = 11"""
Provide a detailed solution to the given mathematical problem.,"what is the leastvalue of x . so that 45 x 09 is divisible by 3 ? a ) 0 , b ) 5 , c ) 2 , d ) 6 , e ) 7","""the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + 5 + x + 0 + 9 = 18 + x least value of x may be 0 therefore 18 + 0 = 18 is divisible by 3 . a"""
Provide a detailed solution to the given mathematical problem.,"debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour . this week , however , she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20 % . if debanshu averages between 12 and 16 miles per hour when biking , how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives ? a ) 135 , b ) 105 , c ) 95 , d ) 75 , e ) 45","debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour . use formula d = rt car : t 1 : 45 min r 1 : 40 mph d 1 : [ ( 40 * 45 ) / 60 ] = 30 miles bike : t 1 : ? r 2 : 12 - 16 mph d 2 : 08 * d 1 = 24 miles t 1 : [ ( 24 * 60 ) / 12 ] = 120 min ( only 12 mph speed yields an answer given in the choices ) therefore , deb has to leave 120 min - 45 min = 75 min early answer : d"
"Work through the equation methodically, ensuring clarity at each step.","if it is assumed that 65 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ? a ) 400 , b ) 420 , c ) 461.5 , d ) 500 , e ) 600","""minimum no of mail to be sent for getting 300 responses at 65 % = 300 / 0.65 = 461.5 option c"""
Break down and solve the equation step by step.,"there are 15 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? a ) 10 , b ) 30 , c ) 105 , d ) 60 , e ) 90",15 players are there . two players play one game with one another . so 15 c 2 = 15 x 14 / 2 = 105 so option c is correct
"Solve the problem systematically, showing each step clearly.","what is the smallest positive integer x such that 507 + x is the cube of a positive integer ? a ) 15 , b ) 5 , c ) 50 , d ) 2 , e ) 4","""given 507 + x is a perfect cube so we will take 512 = 8 * 8 * 8 507 + x = 512 x = 512 - 507 = 5 correct option is b"""
Break down and solve the equation step by step.,"the area of the floor of a room is 20 m 2 that of a longer wall 15 m 2 and of the shorter wall 12 m 2 , find the edge of the new cube ? ['a ) 450 m 3','b ) 100 m 2','c ) 60 m 3','d ) 400 m 3','e ) 500 m 3']",lb = 20 ; lh = 15 ; fh = 12 ( lbh ) 2 = 20 * 15 * 12 = > lbh = 60 m 3 answer : c
Provide a detailed solution to the given mathematical problem.,"2 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other ) a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24","""first arrange 3 women . 3 women can be arranged in 3 places in 3 ! ways . now w blank w blankw we have to fill the two blanks with 2 men . we can arrange 2 persons in 2 places in 2 ! ways . 3 ! * 2 ! = 12 ways . a is the answer"""
Explain the solution process for the given equation.,"a & b started a partnership business . a' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4000 as profit , what is their total profit ? a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these","""explanation : suppose b' s investment = x . then a' s investment = 3 x suppose bs period of investment = y , then a' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4000 = > total profit = 4000 * 7 = 28000 . answer : option a"""
Break down and solve the equation step by step.,"150 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ? a ) 90 liters , b ) 20 liters , c ) 50 liters , d ) 20 liters , e ) 70 liters","""milk = 3 / 5 * 150 = 90 liters water = 50 liters 90 : ( 50 + p ) = 3 : 4 150 + 3 p = 360 = > p = 70 50 liters of water are to be added for the ratio become 3 : 4 . answer : c"""
Provide a detailed solution to the given mathematical problem.,"if 4 men and 1 boy working together , can do two times as much work per hour as a man and a boy together . find the ratio of the work done by a man and that of a boy for a given time ? a ) 3 : 2 , b ) 2 : 1 , c ) 3 : 3 , d ) 1 : 2 , e ) 6 : 1",4 m + 1 b = 2 ( 1 m + 1 b ) 4 m + 1 b = 2 m + 2 b 2 m = 1 b the required ratio of work done by a man and a boy = 1 : 2 d
"Solve the problem systematically, showing each step clearly.","the average weight of 7 person' s increases by 6.2 kg when a new person comes in place of one of them weighing 76 kg . what might be the weight of the new person ? a ) 160 kg , b ) 175 kg , c ) 180.7 kg , d ) 119.4 kg , e ) 190.8 kg","""total weight increased = ( 7 x 6.2 ) kg = 43.4 kg . weight of new person = ( 76 + 43.4 ) kg = 119.4 kg option d"""
"Solve the problem systematically, showing each step clearly.","a man goes downstream at 15 kmph , and upstream 8 kmph . the speed of the stream is a ) 0 kmph , b ) 3.5 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph","""speed of the stream = 1 / 2 ( 15 - 8 ) kmph = 3.5 kmph . correct option : b"""
"Work through the equation methodically, ensuring clarity at each step.","sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 252 per week . how much does she earn in dollars per hour ? a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7","""let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 252 per week 36 x = 252 x = 7 correct option : e"""
Break down and solve the equation step by step.,"a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was a ) 665 , b ) 127 , c ) 272 , d ) 287 , e ) 227","""let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a"""
Break down and solve the equation step by step.,"a certain farmer pays $ 60 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet ? ( 43,560 square feet = 1 acre ) a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 600 , e ) $ 150","basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 600 ( d )"
"Work through the equation methodically, ensuring clarity at each step.","the h . c . f . of two numbers is 59 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is : a ) 678 , b ) 944 , c ) 456 , d ) 323 , e ) 899",": explanation : clearly , the numbers are ( 59 x 13 ) and ( 59 x 16 ) . { \ color { blue } \ therefore } larger number = ( 59 x 16 ) = 944 . answer : b ) 944"
"Work through the equation methodically, ensuring clarity at each step.","shekar scored 76 , 65 , 82 , 67 and 55 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ? a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90","""explanation : average = ( 76 + 65 + 82 + 67 + 55 ) / 5 = 375 / 5 = 69 hence average = 69 answer : b"""
"Solve the problem systematically, showing each step clearly.","what is the square root of 9 ? a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 9","""3 x 3 = 9 answer b"""
Provide a detailed solution to the given mathematical problem.,"jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 10 percent sulfuric acid , approximately how many liters of the 2 percent solution will be required ? a ) 18 , b ) 12 , c ) 24 , d ) 36 , e ) 42","""let a = amount of 2 % acid and b = amount of 12 % acid . now , the equation translates to , 0.02 a + . 12 b = . 1 ( a + b ) but a + b = 60 therefore . 02 a + . 12 b = . 1 ( 60 ) = > 2 a + 12 b = 600 but b = 60 - a therefore 2 a + 12 ( 60 - a ) = 600 = > 10 a = 120 hence a = 12 . answer : b"""
"Solve the problem systematically, showing each step clearly.","at what rate percent on simple interest will rs . 415 amount to rs . 514 in 4 years ? a ) 4.58 % , b ) 5.96 % , c ) 6.52 % , d ) 4.98 % , e ) none of these","""explanation : difference in amount = 514 - 415 = 99 99 = ( 415 x 4 x r ) / 100 r = 5.96 % answer is b"""
"Solve the problem systematically, showing each step clearly.","in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 9 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ? a ) 80 % , b ) 72 % , c ) 120 % , d ) 124.2 % , e ) 138 %","""x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,09 = 9 / 100 x = 80 * 9 / 100 x = 7.2 7.2 / 10 = 0.72 = 72 % , answer b"""
Explain the solution process for the given equation.,"of the female students at barkely university , 3 / 5 are on the honor roll . of the male students , 2 / 5 are on the honor roll . if 5 / 9 of the students are female , what fraction of all the students are on the honor roll ? a ) 5 / 9 , b ) 3 / 15 , c ) 23 / 45 , d ) 43 / 60 , e ) 53 / 90","""let the total students be 45 given 5 / 9 of the students are females = 25 then males = 4 / 9 = 20 3 / 5 of the females are on honor roll = 15 males on the honor roll = 2 / 5 = 8 total students on honor roll = 15 + 8 = 23 fraction = 23 / 45 c"""
"Work through the equation methodically, ensuring clarity at each step.","the bankers discount of a certain sum of money is rs . 72 and the true discount on the same sum for the same time is rs . 60 . the sum due is : a ) rs . 360 , b ) rs . 432 , c ) rs . 540 , d ) rs . 1080 , e ) rs . 1280","""sum = ( b . d * t . d ) / ( b . d - t . d ) ( 72 * 60 ) / 72 - 60 ; 360 answer : a"""
"Solve the problem systematically, showing each step clearly.","on dividinng 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor . a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 17",d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 18 a
Break down and solve the equation step by step.,"the ages of two person differ by 20 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10","""let their ages be x and ( x + 20 ) years . then , 5 ( x - 5 ) = ( x + 20 - 5 ) = > 4 x = 40 = > x = 10 their present ages are 30 years and 10 year . answer : a"""
"Solve the problem systematically, showing each step clearly.","walking with 4 / 5 of my usual speed , i arrive at the bus stop 6 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ? a ) 20 min , b ) 22 min , c ) 15 min , d ) 18 min , e ) 24 min","""let t = usual time = distance / usual speed t + 6 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 24 the answer is e ."""
Break down and solve the equation step by step.,"a cube is divided into 64 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ? a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 30","""each side of the cube has 4 x 4 = 16 cubelets . only the interior cubelets are painted one colour . on each side , 2 x 2 = 4 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 4 = 24 the answer is d ."""
"Solve the problem systematically, showing each step clearly.","the length of the longest tape in cm which can be used to measure exactly , the length 6 m ; 5 m ; and 12 m is : a ) 200 , b ) 100 , c ) 50 , d ) 1200 , e ) 500","the three lengths in cm are 600,500 & 1200 . hcf of 600 , 500 & 1200 is 100 hence , the answer is 100 cm . answer : b"
"Solve the problem systematically, showing each step clearly.","express a speed of 46 kmph in meters per second ? a ) 10.78 mps , b ) 12.78 mps , c ) 97.78 mps , d ) 17.78 mps , e ) 18.78 mps","""46 * 5 / 18 = 12.78 mps answer : b"""
Break down and solve the equation step by step.,"if 12 : 18 : : x : 9 , then find the value of x a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10","explanation : treat 12 : 18 as 12 / 18 and x : 9 as x / 9 , treat : : as = so we get 12 / 18 = x / 9 = > 18 x = 108 = > x = 6 option c"
Break down and solve the equation step by step.,"length of a rectangular plot is 12 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ? ['a ) 56 m','b ) 60 m','c ) 80 m','d ) 82 m','e ) 84 m']","let breadth = x metres . then , length = ( x + 12 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 12 ) + x ] = 200 2 x + 12 = 100 2 x = 88 x = 44 hence , length = x + 12 = 56 m a"
Break down and solve the equation step by step.,"a man whose bowling average is 12.4 , takes 7 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ? a ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147",12.4 * x + 26 = ( 7 + x ) 12 solve equation x = 145 answer : c
Provide a detailed solution to the given mathematical problem.,"machine x and machine b are each used to manufacture 660 sprockets . it takes machine x 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine x . how many sprockets per hour does machine x produces ? a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110","i think the correct answer is a . machine x produces at a speed of x sp / hour and b at a speed of b sp / hour . so , 660 / x = ( 660 / b ) + 10 and x = 1,1 x - - - > 1,1 * 660 = 660 + 11 x - - - > a = 6 , so answer a is correct"
"Work through the equation methodically, ensuring clarity at each step.","a survey was sent to 95 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ? a ) 2 % , b ) 5 % , c ) 7 % , d ) 28 % , e ) 63 %","""case 1 : ( 7 / 95 ) = x / 100 x = 7 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 7 ) % = 7 % answer is c"""
Break down and solve the equation step by step.,"you have been given a physical balance and 7 weights of 43 , 45 , 30 , 33 , 28 , 37 and 55 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 145 kgs . a ) 145 , b ) 143 , c ) 147 , d ) 141 , e ) 142",55 + 43 + 45 = 143 answer : b
Break down and solve the equation step by step.,"how many even multiples of 55 are there between 549 and 1101 ? a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11","""550 = 10 * 55 1100 = 20 * 55 the even multiples are 55 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."""
Break down and solve the equation step by step.,"at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 40 % on the cost price ? a ) 62.5 , b ) 69.5 , c ) 67.5 , d ) 62.5 , e ) 70","""cp = 47.50 sp = 47.50 * ( 140 / 100 ) = 66.5 mp * ( 95 / 100 ) = 66.5 mp = 70 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 80 , and what number ? a ) 35 , b ) 30 , c ) 25 , d ) 20 , e ) 15",a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 90 = 15 e
"Solve the problem systematically, showing each step clearly.","a 40 - liter solution of alcohol and water is 5 percent alcohol . if 6.5 liters of alcohol and 3.5 liters of water are added to this solution , what percent of the solution produced is alcohol ? a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %","""the percent of alcohol in the solution is ( 0.05 ( 40 ) + 6.5 ) / 50 = 8.5 / 50 = 17 % the answer is e ."""
Explain the solution process for the given equation.,"in a fuel station the service costs $ 2.10 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van' s tank is 65 liters and a truck' s tank is 120 % bigger and they are all empty ? a ) $ 338.50 , b ) $ 341.40 , c ) $ 344.30 , d ) $ 347.20 , e ) $ 350.10",the service cost of 3 vans and 2 trucks is 5 * 2.10 $ 10.50 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 10.50 = $ 347.20 the answer is d .
Break down and solve the equation step by step.,"3 people have $ 28 , $ 72 , and $ 98 , respectively . if they pool their money then redistribute it among them , what is the maximum value for the median amount of money ? a ) $ 72 , b ) $ 85 , c ) $ 99 , d ) $ 101 , e ) $ 202","solution - total money distributed is $ 198 . in order to maximize median , one person has to accept $ 0 and remaining two people share $ 99 each . hence median is $ 99 . ans c"
"Solve the problem systematically, showing each step clearly.","sonika deposited rs . 13000 which amounted to rs . 10200 after 4 years at simple interest . had the interest been 5 % more . she would get how much ? a ) 18990 , b ) 13002 , c ) 12800 , d ) 12300 , e ) 14500","""( 13000 * 4 * 5 ) / 100 = 2600 10200 - - - - - - - - 12800 answer : c"""
Break down and solve the equation step by step.,"a part of certain sum of money is invested at 10 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ? a ) 4 : 2 , b ) 4 : 8 , c ) 4 : 3 , d ) 4 : 0 , e ) 6 : 5","""12 : 10 = 6 : 5 answer : e"""
Explain the solution process for the given equation.,"peter invests a sum of money and gets back an amount of $ 815 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ? a ) 670 , b ) 664 , c ) 698 , d ) 744 , e ) 700","""since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 815 = 39 interest earned for 3 years = 39 * 3 = 117 amount invested = 815 - 117 = 698 answer : c"""
Provide a detailed solution to the given mathematical problem.,"a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 6 days . for how many number of days should a and c should work together to complete the remaining work ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""b work 1 / 8 * 6 = 3 / 4 remaining work = 1 - 3 / 4 = 1 / 4 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocial 4 * remaining work = 4 * 1 / 4 = 1 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","a river 2 m deep and 45 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ? a ) 3000 m 3 , b ) 4580 m 3 , c ) 18500 m 3 , d ) 4900 m 3 , e ) 4700 m 3","""explanation : ( 2000 * 2 * 45 ) / 60 = 3000 m 3 answer : option a"""
Provide a detailed solution to the given mathematical problem.,"albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born . what is the difference between the ages of her parents ? a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10",mother' s age when albert' s brother was born = 46 years father' s age when albert' s brother was born = 48 + 2 = 50 years required difference = 50 - 46 = 4 years answer is b
"Work through the equation methodically, ensuring clarity at each step.","mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 130 mangoes . a ) 360 , b ) 380 , c ) 400 , d ) 406 , e ) 433","""mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 130 mangoes = 130 * 3.33 = 433 . answer e"""
"Work through the equation methodically, ensuring clarity at each step.","two trains 120 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? a ) 7.16 , b ) 7.16 , c ) 7.07 , d ) 7.15 , e ) 7.11","""t = ( 120 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.07 answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","joe drives 180 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ? a ) 42 , b ) 50 , c ) 50 , d ) 54 , e ) 56","""t 1 = 180 / 60 = 3 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 6 hours avg speed = total distance / t = 300 / 6 = 50 mph = b"""
Break down and solve the equation step by step.,"if ( 1 / 2 ) ^ 18 ( 1 / 81 ) ^ k = 1 / 18 ^ 18 , then k = a ) 9 , b ) 12 , c ) 16 , d ) 24 , e ) 36","""i' m going to focus on denominator only . . ( 2 ^ 18 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 18 hence 4 k = 36 k = 9 answer a i hope it' s quite clear"""
Break down and solve the equation step by step.,"if a' s height is 45 % less than that of b , how much percent b' s height is more than that of a ? a ) 66.66 % , b ) 81.81 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %","""excess of b' s height over a' s = [ ( 45 / ( 100 - 45 ) ] x 100 % = 81.81 % answer : b )"""
"Work through the equation methodically, ensuring clarity at each step.","geetha' s home has one tap , working alone at its maximum constant rate , can fill a certain sink in 210 seconds . a second tap , working alone at its maximum constant rate , can fill the same sink in 214 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the sink is closest to a ) 106 seconds , b ) 130 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds","tap 1 : 210 secs tap 2 : 214 secs considering the average of these 2 taps : 212 secs . so 1 tap can fill the tank in 212 secs , so 2 taps can fill the tank in 212 / 2 = 106 secs . closest answer is a ."
Explain the solution process for the given equation.,"a rectangular circuit board is designed to have width w inches , perimeter p inches , and area x square inches . which of the following equations must be true ? ['a ) w ^ 2 + pw + x = 0','b ) w ^ 2 - pw + 2 x = 0','c ) 2 w ^ 2 + pw + 2 x = 0','d ) 2 w ^ 2 - pw - 2 x = 0','e ) 2 w ^ 2 - pw + 2 x = 0']","notice that we can discard options a , and c right away . the sum of 3 positive values can not be 0 . now , assume : width = w = 1 inchand length = 1 inch ; perimeter = p = 4 inches ; area = x = 1 square inches . plug the values of w , p , and x into the answer choices : only for e 2 w ^ 2 - pw + 2 x = 2 - 4 + 2 = 0 . answer : e ."
Break down and solve the equation step by step.,". if the sides of two cubes are in the ratio 3 : 1 the ratio of their total surface area is ? ['a ) 3 : 1','b ) 8 : 1','c ) 9 : 1','d ) 12 : 1','e ) 9 : 1']",a 1 : a 2 = 3 : 1 6 a 12 : 6 a 22 = 9 : 1 answer : c
"Work through the equation methodically, ensuring clarity at each step.","a no . when divided by 242 gives a remainder 100 , what remainder will be obtainedby dividingthe same no . 18 ? a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19","""242 + 100 = 342 / 18 = 19 ( remainder ) e"""
"Solve the problem systematically, showing each step clearly.","ada and paul received their scores on 3 tests . on the first test , ada' s score was 10 points higher than paul' s score . on the second test , ada' s score was 4 points higher than paul' s score . if paul' s average ( arithmetic mean ) score on the 3 tests was 4 points higher than ada' s average score on the 3 tests , then paul' s score on the third test was how many points higher than ada' s score ? a ) 9 , b ) 14 , c ) 17 , d ) 23 , e ) 26","my take is option d ( 23 ) i followed a simple approach ( explained below ) : test 1 : ada' s score = paul' s score + 10 test 2 : ada' s score = paul' s score + 4 avg . of paul' s score = 4 points higher than avg . of ada' s score this implies that : sum of paul' s score [ 3 tests ] = 12 points higher than sum of ada' s score [ 3 tests ] ( 12 points higher since 3 points were given in terms of average of 3 scores ) so , paul needs to score 23 points higher than ada in test 3 , since paul needs to compensate for the lower score in test 1 and test 2 ( 26 = 10 + 4 + 12 ) e"
Provide a detailed solution to the given mathematical problem.,"the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - half of the males and one - fourth of the females in the class ? a ) 120 , b ) 126 , c ) 132 , d ) 138 , e ) 144","""1 / 2 * 2 / 5 + 1 / 4 * 3 / 5 = 4 / 20 + 3 / 20 = 7 / 20 the number of degrees is 7 / 20 * 360 = 126 degrees the answer is b ."""
Explain the solution process for the given equation.,"find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 . a ) 29 , b ) 27 , c ) 28 , d ) 24 , e ) 21","""( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is a ."""
Break down and solve the equation step by step.,"the monthly incomes of a and b are in the ratio 5 : 2 . b' s monthly income is 12 % more than c' s monthly income . if c' s monthly income is rs . 14000 , then find the annual income of a ? a ) rs . 420000 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 470400 , e ) none of these","""b' s monthly income = 14000 * 112 / 100 = rs . 15680 b' s monthly income = 2 parts - - - - > rs . 15680 a' s monthly income = 5 parts = 5 / 2 * 15680 = rs . 39200 a' s annual income = rs . 39200 * 12 = rs . 470400 answer : d"""
Break down and solve the equation step by step.,"one bottle is half - full of oil and another bottle with twice the capacity is one quarter full of oil . if water is added so that both the bottles are full and the contents of both are then poured into a third bottle that is empty and large enough to hold the contents of both , what fractions of the contents in the third bottle is oil ? a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 8 , d ) 2 / 3 , e ) 1 / 2","let assume that 1 st bottle capacity = 1 litre ; therefore , it contain 1 / 2 litre oil and 1 / 2 litre water . ( i . e ) water = 1 / 2 litre oil = 1 / 2 litre 2 nd bottle is twice the capacity i . e . 2 litre capacity it means , 1 / 2 litre filled with oil and 1 ( 1 / 2 ) litre filled with water . i . e . oil = 1 / 2 liter water = 1 ( 1 / 2 ) litre in total the third bottle will contain , 1 litre oil and 2 litre water . i . e . , oil = 1 litre water = 2 liter therefore , oil proportion is 1 / 3 answer : b"
"Solve the problem systematically, showing each step clearly.","in what time will a railway train 80 m long moving at the rate of 40 kmph pass a telegraph post on its way ? a ) 3 , b ) 5 , c ) 4 , d ) 6.4 , e ) 7.2","""t = 80 / 40 * 18 / 5 = 7.2 sec answer : e"""
"Solve the problem systematically, showing each step clearly.","an object thrown directly upward is at a height of h feet after t seconds , where h = - 15 ( t - 2 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ? a ) 72 , b ) 90 , c ) 124 , d ) 132 , e ) 140","""we see that h will be a maximum h = 150 when t - 2 = 0 , that is when t = 2 . at t = 4 , h = - 15 ( 4 - 2 ) ^ 2 + 150 = - 15 ( 4 ) + 150 = 90 the answer is b ."""
Explain the solution process for the given equation.,"the difference of two numbers is 1097 . on dividing the larger number by the smaller , we get 10 as quotient and the 17 as remainder . what is the smaller number ? a ) 230 , b ) 120 , c ) 95 , d ) 310 , e ) 320","""solution : let the smaller number be x . then larger number = ( x + 1097 ) x + 1097 = 10 x + 17 9 x = 1080 x = 120 answer b"""
"Work through the equation methodically, ensuring clarity at each step.","the simple form of the ratio 8 / 5 : 2 / 3 is ? a ) 12 : 5 , b ) 12 : 7 , c ) 7 : 12 , d ) 5 : 7 , e ) 4 : 7","""8 / 5 : 2 / 3 = 12 : 5 answer : a"""
Provide a detailed solution to the given mathematical problem.,"the sum of the present ages of two persons a and b is 45 . if the age of a is twice that of b , find the sum of their ages 5 years hence ? a ) 55 , b ) 60 , c ) 70 , d ) 80 , e ) 90","""a + b = 45 , a = 2 b 2 b + b = 45 = > b = 15 then a = 30 . 5 years , their ages will be 35 and 20 . sum of their ages = 35 + 20 = 55 . answer : a"""
Provide a detailed solution to the given mathematical problem.,"sandy is younger than molly by 14 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ? a ) 36 , b ) 45 , c ) 54 , d ) 63 , e ) 72","""s = m - 14 s / m = 7 / 9 9 s = 7 m 9 ( m - 14 ) = 7 m m = 63 the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 123 , what is the least possible value of n ? a ) 37 , b ) 123 , c ) 41 , d ) 52 , e ) 87","123 is 3 * 41 , so n needs to be at least 41 , so the answer is c ."
Break down and solve the equation step by step.,"little john had $ 10.50 . he spent $ 2.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ? a ) $ 1.85 , b ) $ 3.85 , c ) $ 4.85 , d ) $ 6.85 , e ) $ 5.85","""john spent and gave to his two friends a total of 2.25 + 2.20 + 2.20 = $ 6.65 money left 10.50 - 6.65 = $ 3.85 correct answer is b ) $ 3.85"""
Provide a detailed solution to the given mathematical problem.,"the sum of 4 consecutive even numbers is 36 . find the sum of the squares of these numbers ? a ) 296 , b ) 252 , c ) 344 , d ) 388 , e ) none of these","let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c"
Break down and solve the equation step by step.,"calculate the average of all the numbers between 7 and 49 which are divisible by 6 . a ) 20 , b ) 18 , c ) 19 , d ) 15 , e ) 30","""explanation : numbers divisible by 6 are 12 , 18,24 , 30,36 , 42,48 , average = ( 12 + 18 + 24 + 30 + 36 + 42 + 48 , ) / 7 = 210 / 7 = 30 answer : e"""
Explain the solution process for the given equation.,"the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ? a ) 17 , b ) 18 , c ) 19 , d ) 21 , e ) 22","""total age of the 4 sibling is 21 x 4 = 84 years . . we already have the total age of all the children is 4 y + 16 so , 4 y + 16 = 84 or , 4 y = 68 or , y = 17 so , age of the youngest child is 17 years . answer : a"""
Break down and solve the equation step by step.,"working together , printer a and printer b would finish the task in 20 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ? a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 340","""20 * a + 20 * b = x pages in 20 mins printer a will print = 20 / 60 * x pages = 1 / 3 * x pages thus in 20 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 4 more pages per min that printer a . in 20 mins printer b will print 80 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 80 = > x = 240 pages answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","one hour before john started walking from p to q , a distance of 23 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ? a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 15 miles","ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 23 - 3 = 20 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 20 miles so it will take them 20 / 5 = 4 hours to meet . in 4 hrs , ann would have covered 4 hrs * 3 miles per hour = 12 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 12 = 15 miles . answer ( e )"
"Solve the problem systematically, showing each step clearly.","the average of first 3 prime numbers greater than 20 is ? a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50",23 + 29 + 31 = 83 / 3 = 27.7 answer : d
Explain the solution process for the given equation.,"what will be the compound interest on a sum of rs . 23,000 after 3 years at the rate of 12 % p . a . ? a ) rs . 9313.34 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none","""amount = [ 23000 * ( 1 + 12 / 100 ) 3 ] = 23000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 32313.34 c . i . = ( 32313.34 - 23000 ) = rs . 9313.34 answer : a"""
Provide a detailed solution to the given mathematical problem.,"the diagonals of a rhombus are 15 cm and 21 cm . find its area ? a ) 277 , b ) 266 , c ) 150 , d ) 288 , e ) 157.5","""1 / 2 * 15 * 21 = 157.5 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 2 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ? a ) 187 km , b ) 480 km , c ) 278 km , d ) 240 km , e ) 671 km","""let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 2 2 x / 15 - x / 8 = 2 = > x = 240 km . answer : d"""
"Solve the problem systematically, showing each step clearly.","a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 30 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ? a ) 90 , b ) 45 , c ) 50 , d ) 55 , e ) 60","""a - b = 120 miles b - c = 60 miles avg speed = 30 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 30 = 180 / 4 t t = 90 b - c = 90 mph answer a"""
Break down and solve the equation step by step.,"the average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results ? a ) 24 , b ) 25 , c ) 48 , d ) 50 , e ) none","""answer sum of 50 result = sum of 30 result + sum of 20 result . = 30 x 20 + 20 x 30 = 1200 correct option : a"""
"Work through the equation methodically, ensuring clarity at each step.","in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 2000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ? a ) 20000 , b ) 25000 , c ) 24000 , d ) 23000 , e ) 22000","""winner - looser 55 % - 45 % if 2000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 2,000 people compose 10 % of all voters , which means that the total number of votes is 20,000 . answer : a ."""
Break down and solve the equation step by step.,"a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio w of revenue from car sales in 1996 to revenue from truck sales in 1996 ? a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3",a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2
"Work through the equation methodically, ensuring clarity at each step.","a certain number when divided by 39 leaves a remainder 16 , what is the remainder when the same number is divided by 13 ? a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 3","""explanation : 39 + 16 = 55 / 13 = 3 ( remainder ) answer : e"""
"Solve the problem systematically, showing each step clearly.","find the greatest number which on dividing 4351 and 5161 , leaves a reminder of 8 and 10 respectively a ) 125 , b ) 111 , c ) 129 , d ) 101 , e ) 141","""explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 4351 - 8 ) and ( 5161 - 10 ) = hcf ( 4343 , 5151 ) = 101 option d"""
"Solve the problem systematically, showing each step clearly.","bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 18 white marbles . how many red marbles could be in bag a ? a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8","""6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 18 = 6 k + 4 p = > k = 1 , p = 3 total red' s in bag a will be 2 k = 2 a"""
Explain the solution process for the given equation.,"the average ( arithmetic mean ) of 8 numbers is 8 . if 4 is added from each of 5 of the numbers , what is the new average ? a ) 4.5 , b ) 8.9 , c ) 10.5 , d ) 4.5 , e ) 5.6","sum of 8 numbers = 8 * 8 = 64 if 4 is added from each of five of the numbers , we added 4 * 5 = 20 from the total sum sum of 8 number after adding 4 from each of five of the numbers = 64 + 20 = 84 new average = 84 / 8 = 10.5 answer c"
"Solve the problem systematically, showing each step clearly.","in a certain country 1 / 3 of 4 = 8 . assuming the same proportion , what would be the value of 1 / 8 of 4 ? a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3","""e 3"""
Break down and solve the equation step by step.,"according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 25 , by how much does the temperature in degrees celsius ( c ) increase ? a ) 9 , b ) 13.88 , c ) 47 , d ) 48 3 / 5 , e ) 59","""you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 25 = 57 - - > c = 5 / 9 * 25 = 13.88 . increase = 13.88 degrees . answer : b ."""
Explain the solution process for the given equation.,"if the perimeter of a rectangular garden is 800 m , its length when its breadth is 100 m is ? a ) 286 m , b ) 899 m , c ) 300 m , d ) 166 m , e ) 187 m","""2 ( l + 100 ) = 800 = > l = 300 m answer : c"""
Explain the solution process for the given equation.,"in an office , totally there are 6400 employees and 65 % of the total employees are males . 25 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ? a ) 1040 , b ) 2080 , c ) 3120 , d ) 4160 , e ) none of these","""number of male employees = 6400 * 65 / 100 = 4160 required number of male employees who are less than 50 years old = 4160 * ( 100 - 25 ) % = 4160 * 75 / 100 = 3120 . answer : c"""
Provide a detailed solution to the given mathematical problem.,"a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 13 multiples of 14 , how many multiples of 7 are there in q ? a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27","halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 13 + 12 = 25 . the answer is c ."
"Solve the problem systematically, showing each step clearly.","for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of odd all the integers between 1 and 50 ? a ) 500 , b ) 625 , c ) 750 , d ) 550 , e ) 600","""numbers are 1 , 3,5 - - - - - - - , 47,49 average of the set : ( largest + smallest ) / 2 = ( 49 + 1 ) / 2 = 25 ; # of terms : ( largest - smallest ) / 2 + 1 = ( 49 - 1 ) / 2 + 1 = 25 the sum = 25 * 25 = 625 answer : b"""
Provide a detailed solution to the given mathematical problem.,"a pipe takes a hours to fill the tank . but because of a leakage it took 3 times of its original time . find the time taken by the leakage to empty the tank a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min","""pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 180 x = 90 min answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","an investment yields an interest payment of $ 240 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ? a ) $ 28,300 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 32,000","""let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 240 = > p = ( 240 * 4 * 10 ^ 2 ) / 3 = 80 * 4 * 10 ^ 2 = 320 * 10 ^ 2 = 32000 answer e"""
"Work through the equation methodically, ensuring clarity at each step.","among 300 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ? a ) 30 , b ) 90 , c ) 120 , d ) 172 , e ) 188","""i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 90 using your analysis : we see that the total number of students who study either maths or sociology = 132 + 168 - 90 = 210 so , in the image we know that the number of students in the zone with the black boundary = 210 let' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 300 , we can write : 210 + b + w = 300 or , b + w = 300 - 210 = 90 that is , b = 90 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 90 b"""
"Work through the equation methodically, ensuring clarity at each step.","jack and jill are marathon runners . jack can finish a marathon ( 41 km ) in 4.5 hours and jill can run a marathon in 4.1 hours . what is the ratio of their average running speed ? ( jack : jill ) a ) 41 / 45 , b ) 15 / 14 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined","""average speed of jack = distance / time = 41 / ( 9 / 2 ) = 82 / 9 average speed of jill = 41 / ( 4.1 ) = 10 ratio of average speed of jack to jill = ( 82 / 9 ) / 10 = 82 / 90 = 41 / 45 answer a"""
"Work through the equation methodically, ensuring clarity at each step.","the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 202 to 300 inclusive ? a ) 5,150 , b ) 7,550 , c ) 10,150 , d ) 12,550 , e ) 20,150","""2 + 4 + 6 + 8 + . . . + 100 = 2550 202 + 204 + . . . + 300 = 50 ( 200 ) + ( 2 + 4 + . . . + 100 ) = 10,000 + 2550 = 12,550 the answer is d ."""
"Solve the problem systematically, showing each step clearly.","find the simple interest on rs . 70,400 at 16 2 / 3 % per annum for 9 months . a ) s . 8500 , b ) s . 8000 , c ) s . 7500 , d ) s . 8800 , e ) s . 6500","""p = rs . 70400 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 70,400 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8800 answer is d ."""
"Work through the equation methodically, ensuring clarity at each step.","find the area of a parallelogram with base 14 cm and height 24 cm . a ) 336 , b ) 384 , c ) 345 , d ) 244 , e ) 242","""area of a parallelogram = base * height = 14 * 24 = 336 cm 2 answer : option a"""
Explain the solution process for the given equation.,"alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 985 . find the cost of each ice - cream cup ? a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20",explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 985 96 + 225 + 490 + 6 x = 985 6 x = 174 = > x = 29 . answer : c
"Solve the problem systematically, showing each step clearly.","the smallest number when increased by ` ` 1 ` ` is exactly divisible by 12 , 18 , 24 , 32 and 40 is : a ) 1439 , b ) 1440 , c ) 1459 , d ) 1449 , e ) 1500",lcm = 1440 1440 - 1 = 1439 answer : a
Break down and solve the equation step by step.,"how many two - digit numbers yield a remainder of 2 when divided by both 5 and 16 ? a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4","""easier to start with numbers that are of the form 16 p + 2 - - - > 18,34 , 50,66 , 82,96 . out of these , there is only one number ( 82 ) is also of the form 5 q + 2 . thus 1 is the answer . b is the correct answer ."""
Break down and solve the equation step by step.,"set v consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set v , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ? a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2","v = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 016 , - 59 } y > 21 so l = median of v = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c"
Explain the solution process for the given equation.,"set s consists of integers { 6 , 7 , 10 , 12 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 40 % . what is the value of integer n ? a ) 26 , b ) 30 , c ) 34 , d ) 38 , e ) 42","""the average of the numbers in set s is 10 . if we increase the mean by 40 % , the new mean is 14 . thus , on average , 5 numbers increase by 4 . therefore n = 14 + 20 = 34 the answer is c ."""
Explain the solution process for the given equation.,"an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2400 , what will be the difference between q and r' s share ? a ) 1266 , b ) 3000 , c ) 2866 , d ) 2999 , e ) 2678","""4 - - - 2000 5 - - - ? = > 3000 answer : b :"""
"Work through the equation methodically, ensuring clarity at each step.","how many positive integers between 20 and 2000 ( both are inclusive ) are there such that they are multiples of 10 ? a ) 201 , b ) 193 , c ) 200 , d ) 199 , e ) 195","""multiples of 10 = 20 , 30,40 - - - - - , 1990,2000 number of multiples of 10 = > 2000 - 20 / 10 + 1 = 199 answer is d"""
"Solve the problem systematically, showing each step clearly.","a man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ? a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes","let' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 18 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 18 , d = 18 b - 18 c ; every 6 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 6 , d = 6 b + 6 c ; d = 18 b - 18 c = 6 b + 6 c , - - > b = 2 c , - - > d = 18 b - 9 b = 9 b . interval = \ frac { d } { b } = \ frac { 9 b } { b } = 9 answer : d ( 9 minutes ) ."
"Solve the problem systematically, showing each step clearly.","a raz' s company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ? a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3",a raz' s company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . 1996 - x - - - - - y - - - - - - - x + y 1997 - x 1 - - - - y 1 - - x 1 + y 1 x 1 = a * x . . . . . ( p ) y 1 = 1.07 * y . . . ( q ) x 1 + y 1 / x + y = 1.01 solve using p and q and find x / y
"Work through the equation methodically, ensuring clarity at each step.","a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 220 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 270 for the purchase ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""imo it should be c that is 4 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 220 1 b + 6 c = 190 solving both we get b that is bat = 70 and c that is ball = 20 new equation 270 to be divided in equal 3 b + 3 c = 270 3 * 70 + 3 * 20 = 270 210 + 60 = 270"""
Explain the solution process for the given equation.,"a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 8 of th area of the garden . what is the radius of the circular garden ? ['a ) 1','b ) 2','c ) 4','d ) 8','e ) 16']","as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 8 ( pir ^ 2 ) pir ^ 2 = 16 pir r = 16 answer : e"
"Work through the equation methodically, ensuring clarity at each step.","a wooden box of dimensions 8 m x 10 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 5 cm x 6 cm . the maximum number ofboxes that can be carried in the wooden box , is a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 4000000 , e ) none of these",explanation : number = ( 800 * 1000 * 600 ) / 4 * 5 * 6 = 4000000 answer : d
Break down and solve the equation step by step.,"it takes 60 identical printing machines 2 hours to print 300 cards . how much more time would it take 50 of these machines to print the same total ? a ) 20 min , b ) 25 min , c ) 26 min , d ) 36 min , e ) 30 min",50 % of 60 = 30 % or 0.30 2 hr x 60 min = 120 min 120 min x 0.30 = 36 min it will take 36 min longer to print them with only 50 printers . answer is d
Provide a detailed solution to the given mathematical problem.,"a person travels equal distances with speeds of 3 km / hr , 4 km / hr , 5 km / hr . and takes a total time of 47 minutes . find the total distance ? a ) 3 , b ) 2 , c ) 5 , d ) 4 , e ) 6","""let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 4 ) + ( x / 5 ) = 47 / 60 x = 1 total distance = 3 * 1 = 3 km correct option is a"""
Provide a detailed solution to the given mathematical problem.,"the number of positive integers valued pairs ( x , y ) ssatisfying 4 x - 17 y = 1 and x < = 1000 ( x is less than or equal to 1000 ) is a ) fifty nine , b ) 57 , c ) 55 , d ) 58 , e ) 60","4 x - 17 y = 1 y = ( 4 x - 1 ) / 17 x has to be a positive integer such that 1 < = x < = 1000 ( 4 x - 1 ) is a factor of 17 so that y is also a positive integer so we need to know how many numbers in the set { 37 , 1115 , . . . . , 3999 } are divisible by 17 lets try to observe the pattern 1 . 3 mod 17 = 3 2 . 7 mod 17 = 7 3 . 11 mod 17 = 11 4 . 15 mod 17 = 15 5 . 19 mod 17 = 2 6 . 23 mod 17 = 6 7 . 27 mod 17 = 10 8 . 31 mod 17 = 14 9 . 35 mod 17 = 1 10 . 39 mod 17 = 5 11 . 43 mod 17 = 9 12 . 47 mod 17 = 13 13.51 mod 17 = 0 14 . 55 mod 17 = 4 15 . 59 mod 17 = 8 16 . 63 mod 17 = 12 17 . 67 mod 17 = 16 . . . and after this the remainders will repeat ( this is no co - incidence that the cyclicity is also 17 ) so the right choices are x = 1313 + 1713 + 17 + 17 , . . . . . the number of such numbers is 59 ( highest one being 999 ) a"
Break down and solve the equation step by step.,"mary works 9 hours per day on monday , wednesday and friday , and 5 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 407 per week . how much does she earn in dollars per hour ? a ) 12 , b ) 10 , c ) 9 , d ) 8 , e ) 11","so , she works 27 hours in 3 days so , she works 10 hours in 2 days so in a week she works 37 hours ( 27 + 10 ) and earns $ 407 so , hourly wage is 407 / 37 = > 11 hence answer will be ( e ) 11"
Break down and solve the equation step by step.,"a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.2 hrs , e ) 30 hrs","""net part filled in 1 hour = 1 / 5 - 1 / 6 = 1 / 30 therefore the cistern will be filled in 30 hours . answer : e"""
"Solve the problem systematically, showing each step clearly.","a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 8 km , if the person completes half of the distance by walking and the other half by running ? a ) 0.5 , b ) 1.5 , c ) 2.5 , d ) 3.5 , e ) 4.5","""time = 4 / 4 + 4 / 8 = 12 / 8 = 1.5 hours the answer is b ."""
Explain the solution process for the given equation.,"in a ratio which is equal to 4 : 6 , if the antecedent is 20 , then the consequent is ? a ) 72 , b ) 85 , c ) 30 , d ) 51 , e ) 45","""we have 4 / 6 = 20 / x 4 x = 20 * 6 x = 30 consequent = 30 answer is c"""
Provide a detailed solution to the given mathematical problem.,"the speed of a train is 90 kmph . what is the distance covered by it in 20 minutes ? a ) 15 , b ) 66 , c ) 77 , d ) 30 , e ) 42","""90 * 20 / 60 = 30 kmph answer : d"""
Provide a detailed solution to the given mathematical problem.,"a taxi leaves point a 5 hours after a bus left the same spot . the bus is traveling 20 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours . a ) 34 , b ) 32 , c ) 36 , d ) 38 , e ) 40","""let the speed of bus be v - 20 , speed of taxi be v the bus travelled a total of 8 hrs and taxi a total of 3 hrs . hence 8 * ( v - 20 ) = 3 v 8 v - 160 = 3 v 5 v = 160 v = 32 mph b"""
Explain the solution process for the given equation.,"john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 4 % and the mobile phone at a profit of 10 % . overall how much he make aprofit . a ) rs . 90 , b ) rs . 120 , c ) rs . 200 , d ) rs . 250 , e ) rs . 290","""let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . c"""
Explain the solution process for the given equation.,"laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 22 kmph and prasanna moves southward at a speed of 24 kmph . how far will be prasanna from laxmi after 60 minutes ? a ) 44 , b ) 50 , c ) 28 , d ) 27 , e ) 18","""explanation : we know 60 min = 1 hr total northward laxmi' s distance = 22 kmph x 1 hr = 22 km total southward prasanna' s distance = 24 kmph x 1 hr = 24 km total distance between prasanna and laxmi is = 22 + 24 = 44 km . answer : a"""
Explain the solution process for the given equation.,"there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 15,000 after 3 years at the same rate ? a ) 2372 , b ) 2572 , c ) 4542 , d ) 4965 , e ) 3972","""let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 15000 . t = 3 years and r = 10 % p . a . c . i . = rs . 15000 x 1 + 10 3 - 1 100 = rs . 15000 x 331 1000 = 4965 . d"""
"Solve the problem systematically, showing each step clearly.","75 boys can complete a work in 36 days . how many men need to complete twice the work in 20 days a ) 160 , b ) 170 , c ) 270 , d ) 190 , e ) 200",one man can complete the work in 36 * 75 = 2700 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 2700 m = 270 workers answer : c
Explain the solution process for the given equation.,"if 4 x + y = 34 , 2 x - y = 20 , for integers of x and y , y ^ 2 = ? a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 3",4 x + y = 34 2 x - y = 20 6 x = 54 x = 9 y = - 2 y ^ 2 = 4 answer is b
Provide a detailed solution to the given mathematical problem.,"patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon . if she made no stops during the run and her average speed for the entire marathon was 5 mph , for what fraction of the total time did she run at 3 mph ? a ) 1 / 5 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 3","we do n' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire marathon was 5 mph , she ran at 6 mph for a longer duration . 2 1 3 - - 5 - - - - 6 this shows that you can divide the entire journey in 3 equal parts . thus , 2 / 3 part she ran at 6 mph and 1 / 3 part she ran at 3 mph . answer : e"
Provide a detailed solution to the given mathematical problem.,"of 90 applicants for a job , 42 had at least 4 years' experience , 54 had degrees , and 8 had less than 4 years' experience and did not have a degree . how many of the applicants had at least 4 years' experience and a degree ? a ) 10 , b ) 8 , c ) 14 , d ) 16 , e ) 12","""90 - 8 = 82 82 - 42 - 54 = - 14 then 14 are in the intersection between 4 years experience and degree . answer : c"""
"Solve the problem systematically, showing each step clearly.","the tax on a commodity is diminished by 15 % and its consumption increased by 10 % . the effect on revenue is ? a ) 8.5 , b ) 6.5 , c ) 5.5 , d ) 5.6 , e ) 4.4","""100 * 100 = 10000 85 * 110 = 9350 - - - - - - - - - - - 10000 - - - - - - - - - - - 650 100 - - - - - - - - - - - ? = > 6.5 % decrease answer : b"""
Break down and solve the equation step by step.,"there are 22 students in a class . in how many different ways can a committee of 3 students be formed ? a ) 1180 , b ) 1320 , c ) 1540 , d ) 1760 , e ) 1920","""22 c 3 = 22 * 21 * 20 / 6 = 1540 the answer is c ."""
"Solve the problem systematically, showing each step clearly.","all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 158 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ? a ) 1264 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372","""a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 158 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 158 = 3 k + 158 = > 2 k = 316 = > k = 158 the initial quantity of milk in a = 8 k = 8 * 158 = 1264 liters ."""
"Work through the equation methodically, ensuring clarity at each step.","machine c takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine c to make 40 widgets ? a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12","i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of c is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and c reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of c . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer"
"Work through the equation methodically, ensuring clarity at each step.","if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 } is used exactly once , in how many ways can the digits be arranged ? a ) 720 , b ) 830 , c ) 940 , d ) 1050 , e ) 1160",6 ! = 720 the answer is a .
Break down and solve the equation step by step.,"a scale 6 ft . 8 inches long is divided into 2 equal parts . find the length of each part . a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 40 inches",explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 2 parts = 80 / 2 = 40 inches answer : e
Provide a detailed solution to the given mathematical problem.,"if x / ( 11 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ? a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99",x / ( 11 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 11 * 2 = 66 answer d
Provide a detailed solution to the given mathematical problem.,"a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ? a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 32 sec",speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 120 = 320 m . time taken = 320 / 10 = 32 sec . answer : e
"Solve the problem systematically, showing each step clearly.","on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number t of races we need to conduct to get the top 3 fastest horses ? a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11","""t = 7 is the correct answer . good solution buneul . b"""
Provide a detailed solution to the given mathematical problem.,"if the height of a cone is increased by 120 % then its volume is increased by ? a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 120","""120 % answer : e"""
Break down and solve the equation step by step.,"the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 40 , what is the possible maximum range of the temperatures ? a ) 20 , b ) 25 , c ) 40 , d ) 50 , e ) 75","""there are 5 days so the sum of temperature can be 50 * 5 = 250 lowest is 40 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 40 = 160 . on the fifth day it is 250 - 160 = 90 range is therefore 90 - 40 = 50 answer d"""
Provide a detailed solution to the given mathematical problem.,"how many seconds will a train 200 meters long running at the rate of 36 kmph take to pass a certain telegraph post ? a ) 10 sec , b ) 20 sec , c ) 25 sec , d ) 30 sec , e ) 35 sec",distance = length of train = 200 meters speed = 36 kmph = 36 * 5 / 18 = 10 m / s required time = 200 / 10 = 20 sec answer is b
Provide a detailed solution to the given mathematical problem.,"a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a ) 15.6 , b ) 18.1 , c ) 17.5 , d ) 18.7 , e ) 19.1",a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.50 + $ 15.6 = $ 18.1 . answer : b .
Break down and solve the equation step by step.,"9000 + 16 2 / 3 % of ? = 10500 a ) 2387 , b ) 2888 , c ) 9000 , d ) 2837 , e ) 2271","""explanation : 9000 + 16 2 / 3 % of ? = 10500 = > 9000 + 50 / 3 % of ? = 10500 50 / ( 3 * 100 ) of ? = 1500 = > ? = 1500 * 6 ? = 9000 answer : c"""
Explain the solution process for the given equation.,"a is twice efficient as b and together they do the same work in as much time as c and d together . if c and d can complete the work in 20 and 30 daysrespectively , working alone , then in how many days a can complete the work individually : a ) 12 days , b ) 18 days , c ) 24 days , d ) 30 days , e ) none of these","explanation : a + b = c + d | | | | ratio of efficiency 10 x + 5 x 9 x + 6 x | ________| | _________| 15 x 15 x therefore , ratio of efficiency of a : c = 10 : 9 therefore , ratio of days taken by a : c = 9 : 10 therefore , number of days taken by a = 18 days answer : b"
Explain the solution process for the given equation.,"find the missing value : 8597 - ? = 7429 - 4358 a ) 5526 , b ) 5426 , c ) 5326 , d ) 5226 , e ) none of them","""let 8597 - x = 7429 - 4358 . then , x = ( 8597 + 4358 ) - 7429 = 12955 - 7429 = 5526 . answer is a ."""
Explain the solution process for the given equation.,"pipe a and pipe b fill water into a tank of capacity 1000 litres , at a rate of 200 l / min and 50 l / min . pipe c drains at a rate of 25 l / min . pipe a is open for 1 min and closed , then pipe b is open for 2 min and closed . further the pipe c is opened and drained for another 2 min . this process is repeated until the tank is filled . how long will it take to fill the tank ? a ) 15 , b ) 17 , c ) 18 , d ) 56 , e ) 20","""tank capacity : 1000 l , 1 st - 200 l / min for 1 min , volume filled : 200 l 2 nd - 100 l / min for 2 min , volume filled : 100 l 3 rd ( water draining ) : 25 l / min * 2 : 50 l total : ( 200 + 100 ) - 50 = 250 l filled for 1 cycle number of 250 in 1000 l tank : 1000 / 250 = 4 time taken to fill : 4 * total time = 4 * 5 = 20 ( option e )"""
"Work through the equation methodically, ensuring clarity at each step.","how many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 55","""solution speed of train relative to man = ( 63 - 3 ) km / hr = 60 km / hr = ( 60 x 5 / 18 ) m / sec = 50 / 3 m / sec time taken to pass the man = ( 500 x 3 / 50 ) sec = 30 sec answer b"""
Provide a detailed solution to the given mathematical problem.,"what will be the difference between simple interest and compound interest @ 10 % per annum on a sum of rs . 1000 after 3 years ? a ) 22 , b ) 77 , c ) 26 , d ) 19 , e ) 31","""explanation : s . i . = rs . [ ( 1000 x 10 x 3 ) / 100 ] = rs . 300 c . i . = rs . [ 1000 x ( 1 + ( 10 / 100 ) ) 3 - 1000 ] = rs . 331 difference = rs . ( 331 - 300 ) = rs . 31 answer : e"""
Explain the solution process for the given equation.,"the average of 45 results is 12 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ? a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 560","""23 th result = sum of 45 results - sum of 44 results 12 * 45 - 15 * 22 + 20 * 22 = 540 - 330 + 440 = 650 answer is d"""
Explain the solution process for the given equation.,"in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 3 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ? a ) 50 , b ) 70 , c ) 100 , d ) 130 , e ) 140","""rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 3 of all one - bedroom : 1 / 3 * { all one bedroom } = 40 - - > { all one - bedroom } = 120 { all two - bedroom } = 490 - 120 = 370 . two - bedroom not rented = 370 - 240 = 130 answer : d ."""
"Work through the equation methodically, ensuring clarity at each step.","in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those 3 teams , how many ny mets fans are there in this town ? a ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135",the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b .
"Work through the equation methodically, ensuring clarity at each step.","240 is increased by 20 % . find the final number . a ) 200 , b ) 210 , c ) 180 , d ) 288 , e ) 220",explanation final number = initial number + 20 % ( original number ) = 240 + 20 % ( 240 ) = 240 + 48 = 288 . answer d
"Solve the problem systematically, showing each step clearly.","50 boys and 100 girls are examined in a test ; 50 % of the boys and 40 % of the girls pass . the percentage of the total who failed is ? a ) 42.5 % , b ) 62.1 % , c ) 56.7 % , d ) 39.9 % , e ) 51.4 %","""total number of students = 50 + 100 = 150 number of students passed = ( 50 % of 50 + 40 % of 100 ) = 25 + 40 = 65 number of failures = 85 * 100 / 150 = 56.7 % answer is c"""
Provide a detailed solution to the given mathematical problem.,"local kennel has cats and dogs in the ratio of 3 : 4 . if there are 8 fewer cats than dogs , how many dogs are in the kennel ? a ) 28 , b ) 26 , c ) 24 , d ) 32 , e ) 30","""lets work with the data given to us . we know that there ratio of cats to dogs is 3 : 4 or cats 3 dogs 4 we can write number of cats as 3 x and number of dogs as 4 x and we know that 4 x - 3 x = 8 ( therefore x = 8 ) then # of dogs = 4 x 8 = 32 answer is d"""
Explain the solution process for the given equation.,"how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 7.5 m x 6 m x 22.5 cm ? a ) 6000 , b ) 6410 , c ) 6440 , d ) 6500 , e ) 6800","""number of bricks = volume of wall / volume of bricks = 750 x 600 x 22.5 / 25 x 11.25 x 6 = = 6000 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","the price of lunch for 15 people was $ 208.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ? a ) $ 11.73 , b ) $ 12.60 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87","""take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 208 is for 115 then we have to calculate for 100 for 115 208 for 100 x so by cross multiplication we get 115 x = 100 * 208 = > x = 100 * 208 / 110 by simplifying we get x as 189 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 189 / 15 = 12.6 so our answer is b )"""
Explain the solution process for the given equation.,"at a certain zoo , the ratio of sea horse to penguins is 5 to 11 . if there are 85 more penguins than sea horses at the zoo , how many sea horses are there ? a ) 24 , b ) 36 , c ) 48 , d ) 70 , e ) 132",5 / 11 = x / x + 85 5 * 85 = 6 x x = 70 d . 70
Explain the solution process for the given equation.,"two trains 121 meters and 153 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? a ) 7.19 , b ) 6.8 , c ) 7.2 , d ) 7.15 , e ) 7.11","""t = ( 121 + 153 ) / ( 80 + 65 ) * 18 / 5 t = 6.8 answer : b"""
Explain the solution process for the given equation.,"in an election between two candidates , the first candidate got 60 % of the votes and the second candidate got 480 votes . what was the total number of votes ? a ) 900 , b ) 1200 , c ) 1500 , d ) 1800 , e ) 2100","""let v be the total number of votes . 0.4 v = 480 v = 1200 the answer is b ."""
"Work through the equation methodically, ensuring clarity at each step.","he total marks obtained by a student in physics , chemistry and mathematics is 110 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ? a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95","""let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 110 + p c + m = 110 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 110 / 2 = 55 . answer : a"""
Break down and solve the equation step by step.,"the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously ? a ) 5 kg , b ) 12,5 kg , c ) 25 kg , d ) 30 kg , e ) none","""solution : let rs . 100 be spend on rice initially for 10 kg . as the price falls by 20 % , new price for 10 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 10 = rs . 8 per kg . rice can bought now at = 100 / 8 = 12,5 kg . answer : option b"""
"Solve the problem systematically, showing each step clearly.","a box contains 12 apples , 11 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ? a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7","""p ( choosing a red apple 7 times in a row ) = 11 / 12 * 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 12 < 0.5 the answer is e ."""
Explain the solution process for the given equation.,"what is the sum of all possible solutions to | x - 6 | ^ 2 + | x - 6 | = 20 ? a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14","denote | x - 6 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 6 | , so it' s an absolute value and thus can not be negative . y = | x - 6 | = 4 - - > x = 10 or x = - 2 . the sum = 12 . answer : d ."
Provide a detailed solution to the given mathematical problem.,"every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 1600 ? a ) 3000 , b ) 4200 , c ) 2025 , d ) 1205 , e ) 3251","""1800 * 9 / 8 * 9 / 8 = 2025 answer : c"""
Explain the solution process for the given equation.,"a man can row upstream at 30 kmph and downstream at 60 kmph , and then find the speed of the man in still water ? a ) 27 , b ) 29 , c ) 30 , d ) 20 , e ) 45","""us = 30 ds = 60 m = ( 30 + 60 ) / 2 = 45 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","a container contains 40 litres of milk . from this container 4 litres of milk was taken out and replaced by water . this process was repeated further two times . how much milk is now contained by the container . a ) 26.34 litres , b ) 27.36 liters , c ) 28 litres , d ) 29.16 litres , e ) can not be determined",solution amount of milk left after 3 operations [ 40 ( 1 - 4 / 40 ) 3 ] litres = ( 40 x 9 / 10 x 9 / 10 x 9 / 10 ) = 29.16 litres answer d
Explain the solution process for the given equation.,"in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 172 votes . find the total number of valid votes ? a ) 430 , b ) 438 , c ) 436 , d ) 434 , e ) 422","""let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 172 = > 4 x / 10 = 172 = > 4 x = 1720 = > x = 430 . answer : a"""
Explain the solution process for the given equation.,"in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25,000 votes how many votes did candidate x received ? a ) 18000 , b ) 22500 , c ) 24000 , d ) 26000 , e ) 32000","z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b ."
"Solve the problem systematically, showing each step clearly.","in a college , the ratio of the number of boys to girls is 6 : 5 . if there are 200 girls , the total number of students in the college is a ) 440 , b ) 520 , c ) 620 , d ) 720 , e ) 820","""explanation : let the boy are 6 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 6 x + 5 x = 11 x = 11 ( 40 ) = 440 option a"""
Break down and solve the equation step by step.,"a train covers a distance of 15 km in 10 min . if it takes 10 sec to pass a telegraph post , then the length of the train is ? a ) 240 m , b ) 150 m , c ) 120 m , d ) 200 m , e ) 165 m","""speed = ( 15 / 10 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 20 * 10 = 200 m . answer : d"""
Provide a detailed solution to the given mathematical problem.,"a fort had provision of food for 150 men for 45 days . after 15 days , 25 men left the fort . the number of days for which the remaining food will last , is : a ) 36 , b ) 37 1 / 4 , c ) 42 , d ) 54 , e ) 48","""after 15 days : 150 men had food for 30 days . suppose 125 men had food for x days . now , less men , more days ( indirect proportion ) therefore 125 : 150 : : 30 : x < = > 125 x x = 150 x 30 = > x = 150 x 30 / 125 = > x = 36 . correct answer is a"""
"Work through the equation methodically, ensuring clarity at each step.","in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ? a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000","""total fish = x percentage of second catch = ( 2 / 50 ) * 100 = 4 % so , x * 4 % = 50 x = 1250 answer : c"""
Explain the solution process for the given equation.,"a train covers a distance of 12 km in 10 min . if it takes 4 sec to pass a telegraph post , then the length of the train is ? a ) 20 , b ) 110 , c ) 120 , d ) 80 , e ) 60","""speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 4 = 80 m . answer : option d"""
Break down and solve the equation step by step.,"find the l . c . m of 22 , 25 , 44 and 20 . a ) 1240 , b ) 1600 , c ) 1320 , d ) 1150 , e ) 1100","""explanation : 2 x 2 x 11 x 5 x 5 = 1100 answer : option e"""
Break down and solve the equation step by step.,"a 60 cm long wire is to be cut into two pieces so that one piece will be 2 / 4 th of the other , how many centimeters will the shorter piece be ? a ) a ) 73 , b ) b ) 20 , c ) c ) 83 , d ) d ) 21 , e ) e ) 52","""explanation : 1 : 2 / 4 = 4 : 2 2 / 6 * 60 = 20 answer : option b"""
"Work through the equation methodically, ensuring clarity at each step.","rs . 585 is divided amongst a , b , c so that 4 times a' s share , 6 times b' s share and 3 times c' s share are all equal . find c' s share ? a ) 260 , b ) 150 , c ) 817 , d ) 716 , e ) 616",a + b + c = 585 4 a = 6 b = 3 c = x a : b : c = 1 / 4 : 1 / 6 : 1 / 3 = 3 : 2 : 4 4 / 9 * 585 = rs . 260 answer : a
Provide a detailed solution to the given mathematical problem.,"if the average of 10 consecutive integers is 19.5 then the 10 th integer is : - a ) 15 , b ) 20 , c ) 23 , d ) 24 , e ) 25","""the average falls between the 5 th and 6 th integers , integer 5 = 19 , integer 6 = 20 . counting up to the tenth integer we get 24 . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","question : a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 180 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 195 for the purchase ? options : a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",imo it should be c that is c reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 180 1 b + 6 c = 190 solving both we get b that is bat = 40 and c that is ball = 25 new equation 195 to be divided in equal 3 b + 3 c = 195 3 * 40 + 3 * 25 = 195 120 + 75 = 195
"Solve the problem systematically, showing each step clearly.","the number of diagonals of a polygon of n sides is given by the formula z = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ? a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8","""z = n ( n - 3 ) z = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"""
"Solve the problem systematically, showing each step clearly.","if 5 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ? a ) 2 : 5 , b ) 20 : 3 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3","""let 5 % of a = 1 / 3 b then 5 a / 100 = 1 b / 3 a / 20 = b / 3 a / b = 20 / 3 a : b = 20 : 3 answer is b"""
"Work through the equation methodically, ensuring clarity at each step.","in a recent election , james received 15 percent of the 10000 votes cast . to win the election , a candidate needed to receive more than 51 percent of the vote . how many additional votes would james have needed to win the election ? a ) 1004 , b ) 1000 , c ) 3600 , d ) 1201 , e ) 3601","""james = ( 15 / 100 ) * 10000 = 1500 votes to win = ( 51 / 100 ) * total votes + 1 = ( 51 / 100 ) * 10000 + 1 = 5101 remaining voted needed to win election = 5101 - 1500 = 3601 answer : option e"""
"Solve the problem systematically, showing each step clearly.","in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 85 % of the total ? a ) 515 . , b ) 545 . , c ) 606 . , d ) 644 . , e ) 666 .","""answer is c : 606 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 85 % of total is 515 , so 100 % is approx . 606 ."""
Break down and solve the equation step by step.,"a cube of edge 5 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 10 cm * 5 cm , find the rise in water level ? a ) 2.5 cm , b ) 3.6 cm , c ) 5 cm , d ) 6.43 cm , e ) 7.56 cm","""increase in volume = volume of the cube = 5 * 5 * 5 cm ^ 3 rise in water level = volume / area = 5 * 5 * 5 / 10 * 5 = 2.5 cm answer is a"""
"Solve the problem systematically, showing each step clearly.","jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 12 percent solution will be required ? a ) 18 , b ) 20 , c ) 24 , d ) 36 , e ) 42","let a = amount of 2 % acid and b = amount of 12 % acid . now , the equation translates to , 0.02 a + . 12 b = . 05 ( a + b ) but a + b = 60 therefore . 02 a + . 12 b = . 05 ( 60 ) = > 2 a + 12 b = 300 but b = 60 - a therefore 2 a + 12 ( 60 - a ) = 300 = > 10 a = 420 hence a = 42 . , b = 60 - 42 = 18 answer : a"
Break down and solve the equation step by step.,"jayes can eat 25 marshmallows is 20 minutes . dylan can eat 25 in one hour . in how much time will the two eat 150 marshmallows ? a ) 40 minutes . , b ) 1 hour and 30 minutes . , c ) 1 hour . , d ) 1 hour and 40 minutes . , e ) 2 hours and 15 minutes .",rate = output / time jayes rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min
Explain the solution process for the given equation.,"an outlet pipe can empty 2 / 3 of a cistern in 12 minutes . in 4 minutes , what part of the cistern will be emptied ? a ) 1 / 3 , b ) 2 / 5 , c ) 2 / 7 , d ) 2 / 9 , e ) 3 / 10","""4 / 12 * 2 / 3 = 2 / 9 the answer is d ."""
Explain the solution process for the given equation.,"if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 16 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ? a ) 6 , b ) 16 , c ) 22 , d ) 30 , e ) 174","""the number of integers that belong to set x only is 16 - 6 = 10 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 10 + 12 = 22 . answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","an artist wishes to paint a circular region on a square poster that is 3.4 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ? ['a ) 1 / pi','b ) sqrt ( 2 / pi )','c ) 1','d ) 2 / sqrt ( pi )','e ) sqrt ( 5.78 / pi )']",area of the poster is 3.4 x 3.4 = 11.56 1 / 2 the area = 5.78 pi * r ^ 2 = 5.78 r ^ 2 = 5.78 / pi r = sqrt ( 5.78 / pi ) answer ( e )
Break down and solve the equation step by step.,"what is the sum of the greatest common factor and the lowest common multiple of 12 and 36 ? a ) 48 , b ) 22 , c ) 32 , d ) 36 , e ) 38","""prime factorization of 12 = 2 x 2 x 3 prime factorization of 36 = 2 x 2 x 3 x 3 gcf = 12 lcm = 36 sum = 48 . answer a ."""
Explain the solution process for the given equation.,"how many pounds of salt at 80 cents / lb must be mixed with 40 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ? a ) 5 , b ) 15 , c ) 40 , d ) 50 , e ) 25","""selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 80 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 80 - 40 ) / ( 40 - 35 ) = 8 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 5 lbs . answer ( a )"""
Break down and solve the equation step by step.,"sandy had $ 217 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ? a ) $ 270 , b ) $ 290 , c ) $ 310 , d ) $ 330 , e ) $ 350","""let the money sandy took for shopping be x . 0.7 x = 217 x = 310 the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"of 70 players on a football team , 40 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? a ) 54 , b ) 59 , c ) 60 , d ) 71 , e ) 92","""total = 70 thrower = 40 rest = 70 - 40 = 30 left handed = 30 / 3 = 10 right handed = 20 if all throwe 0 r are right handed then total right handed is 40 + 20 = 60 so c . 60 is the right answer"""
Break down and solve the equation step by step.,"on a trip covering 250 km , a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour . what is the average speed , in km per hour , for the entire trip ? a ) 15.8 , b ) 16.3 , c ) 16.7 , d ) 17.2 , e ) 17.5","""time 1 = 100 / 20 = 5 hours time 2 = 150 / 15 = 10 hours total time = 15 hours average speed = 250 / 15 = 16.7 km / hr the answer is c ."""
Provide a detailed solution to the given mathematical problem.,"12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 1 cm height . what is the diameter of each sphere ? a ) 2 cm , b ) 4 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm","""volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 1 cm ^ 3 r = 1 cm d = 2 cm the answer is a ."""
Explain the solution process for the given equation.,"if a car had traveled 10 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 30 km , at what speed did it travel ? a ) 20 kmh , b ) 25 kmh , c ) 30 kmh , d ) 35 kmh , e ) 40 kmh","""time = distance / speed difference in time = 1 / 2 hrs 30 / x - 30 / ( x + 10 ) = 1 / 2 substitute the value of x from the options . - - > x = 20 - - > 30 / 20 - 30 / 30 = 3 / 2 - 1 = 1 / 2 answer : a"""
Explain the solution process for the given equation.,"a man rows his boat 95 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ? a ) 5 kmph , b ) 7 kmph , c ) 9 kmph , d ) 8 kmph , e ) 10 kmph","""speed downstream = d / t = 95 / ( 2 1 / 2 ) = 38 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 38 - 18 ) / 2 = 10 kmph answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 210 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ? a ) 88 , b ) 45 , c ) 36 , d ) 80 , e ) 12","""speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 210 = 450 m . time taken = 450 / 10 = 45 sec . answer : b"""
Break down and solve the equation step by step.,"in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 10 , 0 ) , ( 0 , - 3.5 ) , ( - 10 , 0 ) ? a ) 56 , b ) 88 , c ) 70 , d ) 116 , e ) 120","""area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 10 + 10 = 20 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 20 * 7 = 70 c is the answer"""
Provide a detailed solution to the given mathematical problem.,"two stations a and b are 110 km apart on a straight line . one train starts from a at 6 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ? a ) 11 , b ) 10 , c ) 9 , d ) 12 , e ) 15","""suppose they meet x hours after 6 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 9 a . m . answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","if in a race of 70 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by : a ) 20 m , b ) 16 m , c ) 14 m , d ) 10 m , e ) 15 m","""explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 70 * 5 ) / 25 = 14 m hence , a beats b by 14 m . answer c"""
Explain the solution process for the given equation.,"last year elaine spent 10 % of her annual earnings on rent . this year she earned 15 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ? a ) 252.5 , b ) 364.5 , c ) 367.5 , d ) 375 , e ) 345","""for this it is easiest to use simple numbers . let' s assume that elaine' s annual earnings last year were $ 100 . she would' ve spent $ 10 of this on rent . this year she earned 15 % more , or $ 115 . she would' ve spent 30 % of this on rent , or $ 34.5 do $ 34.5 / $ 10 this will give you 345 % e is the correct answer ."""
Provide a detailed solution to the given mathematical problem.,"if two painters can complete two rooms in two hours , how many painters would it take to do 18 rooms in 6 hours ? a ) 8 , b ) 6 , c ) 5 , d ) 4 , e ) 1","""explanation : two painters can complete two rooms in two hours . so 18 rooms can be painted in 6 hrs by 6 painters answer : b ) 6 painters"""
Provide a detailed solution to the given mathematical problem.,"the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 40 kg of rice previously ? a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 50 kg , e ) none","""solution : let rs . 100 be spend on rice initially for 40 kg . as the price falls by 20 % , new price for 40 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 40 = rs . 2 per kg . rice can bought now at = 100 / 2 = 50 kg . answer : option d"""
Provide a detailed solution to the given mathematical problem.,"a man is 22 years older than his son . in three years , his age will be thrice the age of his son . the present age of this son is a ) 8 years , b ) 2 years , c ) 7 years , d ) 8 years , e ) 5 years","""let' s son age is x , then father age is x + 22 . = > 3 ( x + 3 ) = ( x + 22 + 3 ) = > 3 x + 9 = x + 25 = > 2 x = 16 years = 8 years answer : d"""
"Solve the problem systematically, showing each step clearly.","if the length of the sides of two cubes are in the ratio 7 : 1 , what is the ratio of their total surface area ? a ) 7 : 1 , b ) 14 : 1 , c ) 21 : 1 , d ) 42 : 1 , e ) 49 : 1","""let x be the length of the small cube' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 7 x ) ^ 2 = 294 x ^ 2 . the ratio of surface areas is 49 : 1 . the answer is e ."""
"Work through the equation methodically, ensuring clarity at each step.","i bought two books ; for rs . 460 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? a ) 337.33 , b ) 280.33 , c ) 299.33 , d ) 268.33 , e ) 289.33","""x * ( 85 / 100 ) = ( 460 - x ) 119 / 100 x = 280 answer : d"""
"Solve the problem systematically, showing each step clearly.","the difference between the local value and the face value of 7 in the numeral 32675149 is a ) 69990 , b ) 69993 , c ) 70000 , d ) 77000 , e ) 78000","""explanation : ( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 b )"""
Explain the solution process for the given equation.,"a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations g are possible ? a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) g = 8","""the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10 , 24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e"""
"Solve the problem systematically, showing each step clearly.","12.1212 + 17.0005 - 9.1103 = ? a ) 20.0015 , b ) 20.0105 , c ) 20.0115 , d ) 20.0114 , e ) none",solution given expression = ( 12.1212 + 17.0005 ) - 9.1103 = ( 29.1217 - 9.1103 ) = 20.0114 . answer d
"Solve the problem systematically, showing each step clearly.","find the compound interest on $ 1200 for 5 years at 20 % p . a . if ci is component yearly ? a ) $ 120 , b ) $ 150 , c ) $ 1786 , d ) $ 250 , e ) $ 300","""a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 5 = $ 2986 ci = $ 1786 answer is c"""
"Work through the equation methodically, ensuring clarity at each step.","the difference of two numbers is 1515 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ? a ) a ) 270 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310","""let the smaller number be x . then larger number = ( x + 1515 ) . x + 1515 = 6 x + 15 5 x = 1500 x = 300 smaller number = 300 . d )"""
Explain the solution process for the given equation.,"6.006 / 3.003 a ) 0.002 , b ) 0.02 , c ) 0.2 , d ) 20 , e ) 2","""answer is 2 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 6006 / 3003 = 2 answer e"""
Explain the solution process for the given equation.,"of the 3 - digit integers greater than 700 , how many have two digits t that are equal to each other and the remaining digit different from the other two ? a ) 90 , b ) 82 , c ) 80 , d ) 45 , e ) 36","three - digit integers greater than 700 : 701 to 999 , inclusive . possible values for hundreds - digit - - > 7 , 89 possible values for tens - digit and ones - digit - - > 0 , 1 , 23 , 45 , 67 , 89 when hundreds - digit and tens - digit are the same : ( 3 x 1 x 10 ) - 3 = 27 - - - > we minus three to exclude 777 , 888 and 999 when hundreds - digit and ones - digit are the same : ( 3 x 10 x 1 ) - 3 = 27 - - - > we minus three to exclude 777 , 888 and 999 when tens - digit and hundreds - digit are the same : [ ( 3 x 10 x 1 ) - 3 ] - 1 = 26 - - - > we minus three to exclude 777 , 888 and 999 ; we minus one to exclude 700 t = 27 + 27 + 26 = 80 answer : c"
Explain the solution process for the given equation.,"3 different containers contain 496 litres , 403 litres and 713 litres of mixtures of milk and water respectively . what biggest measure can measure all the different quantities exactly ? a ) 30 litres , b ) 31 litres , c ) 32 litres , d ) 33 litres , e ) 34 litres",403 ) 713 ( 1 403 - - - - - - - - - 310 ) 403 ( 1 310 - - - - - - - - - - 93 ) 310 ( 3 279 - - - - - - - - 31 ) 93 ( 3 93 - - - - - - - x so answer is 31 litres . . . . . . answer : b
"Solve the problem systematically, showing each step clearly.","tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 8 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ? a ) 7 / 15 , b ) 11 / 25 , c ) 17 / 35 , d ) 23 / 45 , e ) 27 / 55","""tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 15 / 24 ) = 8 / 15 hours peter worked for 23 / 15 hours so he painted 23 / 15 * 1 / 3 = 23 / 45 of the room . the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ? a ) 54 , b ) 51 , c ) 59 , d ) 55 , e ) 52","""for 40 hrs = 40 * 14 = 560 excess = 976 - 560 = 416 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 416 / 24.5 = 18.82 = 19 approx . total hrs = 40 + 19 = 59 answer c 59"""
Provide a detailed solution to the given mathematical problem.,"in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 1,000 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 9,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ? a ) 50 % , b ) 40 % , c ) 20 % , d ) 30 % , e ) 10 %","""ratio of 2 bedroom apartment : 1 bedroom apartment = 1000 : 9000 - - - - - > 1 : 9 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 10 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 10 ) * 100 - - - > 10 % answer : e"""
"Solve the problem systematically, showing each step clearly.","the lcm and hcf of two numbers are 1000 and 100 respectively . find the larger of the two numbers if their sum is 1100 . a ) 1000 , b ) 10 , c ) 567 , d ) 57 , e ) 678","""there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 1000 * 100 = 100000 so the answer which we are looking for has to be a factor of 100000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 100000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"""
Explain the solution process for the given equation.,"a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 231 for it , the cost price of the cricket bat for a is : a ) 150 , b ) 120 , c ) 154 , d ) 160 , e ) 210",125 % of 120 % of a = 231 125 / 100 * 120 / 100 * a = 231 a = 231 * 2 / 3 = 154 . answer c
"Work through the equation methodically, ensuring clarity at each step.","what is the remainder when 43 * 49 is divided by 8 ? a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7","""we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 43 * 49 ) / 8 } } = remainder of ( 43 / 8 ) * remainder of ( 49 / 8 ) = 3 * 1 = 3 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","virginia , adrienne , and dennis have taught history for a combined total of 93 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ? a ) 23 , b ) 32 , c ) 40 , d ) 41 , e ) 44","""let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 93 = > 3 d = 93 + 27 = 120 = > d = 40 answer c"""
Explain the solution process for the given equation.,"the profits of qrs company rose 35 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ? a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 %","assume 100 in march , then 135 in april as 35 % increase , then 108 in may as 20 % decrease from april , and then 162 in june which is 150 % of 108 . so overall increase is from 100 to 162 is 62 % answer d"
"Solve the problem systematically, showing each step clearly.","roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 7 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ? a ) 22 km , b ) 40 km , c ) 65 km , d ) 18 km , e ) 16 km","""distance = relative speed * time = ( 7 + 3 ) * 4 = 40 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b"""
Provide a detailed solution to the given mathematical problem.,"a goods train runs at a speed of 72 kmph and crosses a 240 m long platform in 26 seconds . what is the length of the goods train ? a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 280 m","""s = 240 + x / t 72 * 5 / 18 = 240 + x / 26 x = 280 answer : e"""
"Solve the problem systematically, showing each step clearly.","if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 61 , how much does one shirt cost ? a ) $ 9 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80",3 j + 2 s = 69 2 j + 3 s = 61 - - - - - - - - - - - - - - - - 5 j + 5 s = 130 - - - - ( divide by 5 ) - - - > j + s = 26 3 j + 2 s = j + 2 ( j + s ) = j + 52 = 69 - - - > j = 17 3 * 17 + 2 s = 69 51 + 2 s = 69 2 s = 18 s = 9 answer : a
"Solve the problem systematically, showing each step clearly.","when average age of 24 members are 0 , how many members greater than 0 ? a ) 17 , b ) 23 , c ) 21 , d ) 24 , e ) 25","""average of 24 numbers = 0 . sum of 24 numbers ( 0 x 24 ) = 0 . it is quite possible that 23 of these numbers may be positive and if their sum is a then 24 th number is ( - a ) answer is 23 ( b )"""
Provide a detailed solution to the given mathematical problem.,"a man buys an item at rs . 750 and sells it at the loss of 20 percent . then what is the selling price of that item a ) rs . 660 , b ) rs . 760 , c ) rs . 600 , d ) rs . 960 , e ) none of these","""explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 750 = 80 / 100 * 750 = 600 option c"""
"Solve the problem systematically, showing each step clearly.","a cargo ships engines failed 100 miles away from the port . due to the changing wind direction , it is moving 12 miles towards the port and 6 miles away from the port . if the wind pattern remains same , how many miles it will travel before reaching the port ? a ) a - 179 , b ) b - 240 , c ) c - 280 , d ) d - 100 , e ) e - 155",ships overall distance covered per cycle is + 6 miles take 100 - 6 take 94 / 6 to lowest divisible number - 90 / 6 this means that it will take 15 ` ` overall'' actions to reach the 90 th mile . - 15 * 18 miles added later set cycle start at 90 . travel 10 miles and reach the anchor point - add 10 to total 15 * 18 + 10 = 280 miles in total answer : c
"Solve the problem systematically, showing each step clearly.","if 9 a - b = 10 b + 65 = - 12 b - 2 a , what is the value of 11 a + 11 b ? a ) - 11 , b ) - 5 , c ) 0 , d ) 5 , e ) 11","""( i ) 9 a - 11 b = 65 ( ii ) 2 a + 22 b = - 65 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."""
"Work through the equation methodically, ensuring clarity at each step.","if x / y = 7 / 3 , then ( x + y ) / ( x - y ) = ? a ) 5 , b ) 5 / 2 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5","""any x and y satisfying x / y = 7 / 3 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 3 , then ( x + y ) / ( x - y ) = ( 7 + 3 ) / ( 7 - 3 ) = 5 / 2 . answer : b ."""
Break down and solve the equation step by step.,"what is the unit digit in 12 ^ 100 ? a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6",unit digit in 12 ^ 100 = unit digit in [ ( 12 ^ 4 ) ^ 25 ] but unit digit in 12 ^ 4 = 6 unit digit 12 ^ 100 = 6 answer is e
Provide a detailed solution to the given mathematical problem.,"the h . c . f and l . c . m of two numbers are 11 and 385 respectively . if one number lies between 75 and 125 , then that number is a ) 77 , b ) 88 , c ) 99 , d ) 110 , e ) 120","""explanation : product of numbers = 11 x 385 = 4235 let the numbers be 11 a and 11 b . then , 11 a x 11 b = 4235 inline fn _ jvn rightarrow ab = 35 now , co - primes with product 35 are ( 1,35 ) and ( 5,7 ) so , the numbers are ( 11 x 1 , 11 x 35 ) and ( 11 x 5 , 11 x 7 ) since one number lies 75 and 125 , the suitable pair is ( 55,77 ) hence , required number = 77 . answer : a"""
Break down and solve the equation step by step.,"christine and siri have 21 rs between them . christine has 20 rs more than siri . how much does christine have . a ) 16.5 , b ) 17.5 , c ) 18.5 , d ) 19.5 , e ) 20.5","let siri has x rs , then christine has 20 + x rs given x + ( 20 + x ) = 21 = > 2 x = 1 or x = 0.5 so christine and siri has 20.5 and 0.5 rs respectively . answer : e"
Break down and solve the equation step by step.,"a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 5 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ? a ) $ 198 , b ) $ 228 , c ) $ 220 , d ) $ 230 , e ) $ 240","""wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 5 emlpoyee paid = . 95 * 240 = 228 $ answer b"""
Provide a detailed solution to the given mathematical problem.,"on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ? a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %","""say there are 100 motorists . { # of motorists who exceed speed & receive tickets } + { # of motorists who exceed speed & do n' t receive tickets } = { total # of motorist who exceed speed } ; given : { # of motorists who exceed speed & receive tickets } = 10 ; also , if { total # of motorist who exceed speed } = x , then 0.2 x = { # of motorists who exceed speed & do n' t receive tickets } ; 10 + 0.2 x = x - - > x = 12.5 answer : b ."""
"Solve the problem systematically, showing each step clearly.","a train 200 m long passes a man , running at 6 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ? a ) 36 , b ) 50 , c ) 78 , d ) 66 , e ) 22","""speed of the train relative to man = ( 200 / 10 ) m / sec = 20 m / sec . [ 20 * ( 18 / 5 ) ] km / hr = 72 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 6 ) km / hr . x - 6 = 72 = = > x = 78 km / hr . answer : c"""
Provide a detailed solution to the given mathematical problem.,"george is 8 years more than christopher and ford is 2 years younger than christopher . the sum of their ages is 60 . find the ages of christopher . a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22","christopher age = x george age , y = x + 8 - - - - - - - - - - > ( 1 ) ford age , z = x - 2 - - - - - - - - - - - - > ( 2 ) sum of their ages , x + y + z = 60 - - - - > ( 3 ) substitute z and y values in equation ( 3 ) therefore , x + ( x + 8 ) + ( x - 2 ) = 60 = > 3 x + 8 - 2 = 60 = > 3 x = 60 - 6 = > 3 x = 54 = > x = 54 / 3 x = 18 answer : a"
"Work through the equation methodically, ensuring clarity at each step.","a rotameter is a device that measures flow of liquid and gases . when measuring liquid phase flows , 2.5 inches represent 60 liters per minute of liquid . with gas measurements the rotameter moves 50 % of the movement he moves with the liquid phase . how many liters of gas passed through the rotameter if it measured 4 inches ? a ) 176 , b ) 192 , c ) 202 , d ) 218 , e ) 284",in case of liquid - 2.5 inches represents 60 lit / min . in case of gas - 50 % of 2.5 inches represents 60 lit / min 1.25 inches represents 60 lit / min 4 inches will represent 60 * 4 / 1.25 = 192 b is the answer
Explain the solution process for the given equation.,"find the average of all the numbers between 6 and 36 which are divisible by 5 . a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 22.5","""solution average = ( 10 + 15 + 20 + 25 + 30 + 35 ) / 6 ) = 135 / 6 = 22.5 answer e"""
Provide a detailed solution to the given mathematical problem.,"an electric pump can fill a tank in 10 hours . because of a leak in the tank , it took 20 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ? a ) 10 hours , b ) 12 hours , c ) 20 hours , d ) 5 hours , e ) 15 hours","""work done by the leak in 1 hour = 1 / 10 - 1 / 20 = 1 / 20 the leak will empty the tank in 20 hours answer is c"""
Break down and solve the equation step by step.,"if shares of two persons in profits are rs . 400 and rs . 500 then ratio of their capitals is a ) 3 : 4 , b ) 4 : 5 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2","""profit = time * capital so 400 : 500 = 4 : 5 answer : b"""
Explain the solution process for the given equation.,"the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 231 the other is a ) 330 , b ) 300 , c ) 270 , d ) 250 , e ) 350","""the other number = l . c . m * h . c . f / given number = 2310 * 30 / 231 = 300 answer is b ."""
"Solve the problem systematically, showing each step clearly.","a train 240 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 240 m long ? a ) 28.8 sec , b ) 20.33 sec , c ) 60 sec , d ) 48 sec , e ) 49 sec","""total length = 240 + 240 = 480 speed = 60 km / h = ( 60 * 5 ) / 18 = 50 / 3 m / s time = ( 480 * 3 ) / 50 = 28.8 sec . answer : a"""
Explain the solution process for the given equation.,"in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number i and the smallest possible number of students that could have taken both geometry and biology ? a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31","official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number i of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."
Provide a detailed solution to the given mathematical problem.,"( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) what is m ? a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36","( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / ( 2 * ( 2 * 5 ) ^ 35 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ ( m + 1 ) = ( 1 / 5 ) ^ 35 ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / [ ( 2 ^ 36 ) * ( 5 ^ 35 ) ] so , m = 34 answer c"
Explain the solution process for the given equation.,"amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.2 km ? a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m","""c 300 m distance covered by amar = 18 / 4.8 ( 1.6 km ) = 3 / 8 ( 1200 ) = 300 m answer is c"""
Provide a detailed solution to the given mathematical problem.,"70 % of the employees of a company are men . 50 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ? a ) 4 % , b ) 10 % , c ) 83.33 % , d ) 90.33 % , e ) 20 %","""no of employees = 100 ( say ) men = 70 women = 30 men speaking french = 0.5 * 70 = 35 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 35 = 5 and women not speaking french = 30 - 5 = 25 % of women not speaking french = 25 / 30 * 100 = 83.33 % answer c"""
Provide a detailed solution to the given mathematical problem.,"for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 120 ? a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30","""4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 120 4 n < 113 n < 28 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 28 ( 48 integers ) and n = - 1 and 0 so 30 integers . e is the answer"""
"Solve the problem systematically, showing each step clearly.","how many integers k greater than 100 and less than 900 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ? a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90","""not sure if this is the shortest . . but this is how i did this there are 7 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . . . . 7 . 708 | 807 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 7 sets with 10 such number in each set will give 7 x 10 = 70 integers . c"""
"Work through the equation methodically, ensuring clarity at each step.","what is the remainder when 7 ^ 74 - 5 ^ 74 is divided by 8 ? a ) 0 , b ) 2 , c ) 0 , d ) 3 , e ) none of these","""easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 48 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : c"""
"Work through the equation methodically, ensuring clarity at each step.","steve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ? a ) 68 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph","""average speed = total distance / total time = ( 50 * 2 + 80 * 3 ) / ( 2 + 3 ) = 68 ans : a"""
Break down and solve the equation step by step.,"three unbiased coins are tossed , what is the probability of getting at least 2 tails ? a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 2 , e ) 1 / 10","""total cases are = 2 ^ 3 = 8 favoured cases = [ tth , tht , htt , ttt ] = 4 probability = 4 / 8 = 1 / 2 answer d"""
"Work through the equation methodically, ensuring clarity at each step.","a can do a job in 45 days and b can do it in 30 days . a and b working together will finish 4 times the amount of work in - - - - - - - days ? a ) 30 days , b ) 45 days , c ) 80 days , d ) 72 1 / 2 days , e ) 72 days",1 / 45 + 1 / 30 = 5 / 90 = 1 / 18 18 / 1 = 18 * 4 = 72 days answer : e
Provide a detailed solution to the given mathematical problem.,"thomas worked in the factory @ 4550 / - per week . owner told him to give the amount after one month . then how much amount will be paid to thomas ? a ) 9500 , b ) 17500 , c ) 18200 , d ) 19500 , e ) 6750",total salary paid to thomas in one week : 4550 / - salary for one day : 4550 / 7 = 650 / - total for one month = 650 / - * 30 days = 19500 / - answer is option ( d )
Explain the solution process for the given equation.,"a train is moving at a speed of 100 km / hour . the length of the train is 100 metre . in how much time will it cross a pole ? a ) 1 second , b ) 2.5 second , c ) 4 second , d ) 3.6 second , e ) 4.5 second","in order to cross the pole , the train will need to cover its own length of 100 meter . to cover 100 x 1000 meter , train takes 60 minutes or 60 x 60 = 3600 second . so , to cover 100 meter , train would take 3600 x 100 / 100 x 1000 = 3.6 second . answer : d ."
"Work through the equation methodically, ensuring clarity at each step.","x , y , and z are all unique numbers . if x is chosen randomly from the set { 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? a ) 1 / 20 , b ) 1 / 12 , c ) 2 / 15 , d ) 3 / 10 , e ) 1 / 7","""p ( x is prime ) = 1 / 3 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 3 * 1 / 4 = 1 / 12 the answer is b ."""
Explain the solution process for the given equation.,"a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 5 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ? a ) 9 : 100 , b ) 100 : 9 , c ) 12 : 100 , d ) 12 : 20 , e ) 13 : 100","""water : soap = 3 : 5 soap : salt = 12 : 20 = > for 12 soap , salt = 20 = > for 5 soap , salt = ( 20 / 12 ) * 5 = 100 / 12 = 25 / 3 so , water : soap : salt = 3 : 5 : 25 / 3 = 9 : 15 : 25 after open container , water : soap : salt = 2.25 : 15 : 25 so , water : salt = 2.25 : 25 = 9 : 100 answer : a"""
Explain the solution process for the given equation.,"a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 12 seconds . what is the length of the train in meters ? a ) 400 meters , b ) 120 meters , c ) 1777 meters , d ) 60 meters , e ) none of these","""train overtakes a bike means that we are talking about total length of the train . ( train' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 12 seconds distance = speed * time 36000 * 12 / 3600 = 120 meters . b is the answer ."""
Provide a detailed solution to the given mathematical problem.,"a train 285 m long , running with a speed of 54 km / hr will pass a tree in a ) 19 sec , b ) 15 sec , c ) 16 sec , d ) 20 sec , e ) none","""sol . speed = ( 54 x 5 / 18 ) m / sec . = 15 m / sec . time taken = ( 285 x 1 / 15 ) sec = 19 sec answer a"""
Explain the solution process for the given equation.,"q' = 3 q - 3 , what is the value of ( 3' )' ? a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 40","""( 3' )' = ( 3 * 3 - 3 )' = 6' = 6 * 6 - 6 = 30 answer d"""
Break down and solve the equation step by step.,"double of quarter of 2 percent written as a decimal is : a ) 0.01 , b ) 0.0005 , c ) 0.25 , d ) 0.005 , e ) none of these","""explanation : solution : ( 2 ) * ( 1 / 4 ) * 2 % = 2 * ( 1 / 4 * 2 / 100 ) = 0.01 . answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 4 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ? a ) 50 , b ) 90 , c ) 100 , d ) 105 , e ) 140","""rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 4 of all one - bedroom : 1 / 4 * { all one bedroom } = 40 - - > { all one - bedroom } = 160 { all two - bedroom } = 490 - 160 = 330 two - bedroom not rented = 330 - 240 = 90 b"""
Provide a detailed solution to the given mathematical problem.,"lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is : a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435",total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 344000 x \ therefore required percentage = \ inline \ frac { 800 x } { 344000 } \ times 100 = 0.23255 a
Break down and solve the equation step by step.,"if w is 40 percent less than x , x is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ? a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %","given w = 0.6 x , x = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer ."
Break down and solve the equation step by step.,"for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - third of his earnings to charity . if the worker' s charitable contributions totaled one - eighth of his earnings for the entire year , what is the value of n ? a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 33 / 25 , e ) 4","""let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 3 = 1 / 8 ( 11 x + nx ) ; 11 / 10 + n / 3 = 1 / 8 ( 11 + n ) 33 + 10 n / 30 = 11 + n / 8 = > 264 + 80 n = 330 + 30 n = > 50 n = 66 n = 66 / 50 = 33 / 25 answer : d ."""
"Solve the problem systematically, showing each step clearly.","in the manufacture of a certain product , 6 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ? a ) 0.125 % , b ) 0.24 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %","""percent of defective produced = 6 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 6 / 100 ) * 100 % = ( 24 / 10000 ) * 100 % = ( 24 / 100 ) % = . 24 % answer b"""
"Work through the equation methodically, ensuring clarity at each step.","the difference between a number and its two - fifth is 510 . what is 40 % of that number ? a ) 342 , b ) 340 , c ) 344 , d ) 346 , e ) 348","""let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 40 % of 850 = 340 . answer : b"""
"Solve the problem systematically, showing each step clearly.","joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 3 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ? a ) 168 , b ) 144 , c ) 175 , d ) 216 , e ) 250","""total paint initially = 360 gallons paint used in the first week = ( 1 / 3 ) * 360 = 120 gallons . remaning paint = 240 gallons paint used in the second week = ( 1 / 5 ) * 240 = 48 gallons total paint used = 168 gallons . option a"""
Break down and solve the equation step by step.,"a bag contains 6 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ? a ) 5 / 14 , b ) 8 / 21 , c ) 12 / 21 , d ) 43 / 91 , e ) 47 / 91",the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 43 / 91 the answer is d .
Explain the solution process for the given equation.,"suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 620 ( before payroll deductions ) ? a ) 670 , b ) 710 , c ) 750 , d ) 790 , e ) 830",total pay = 40 * $ 12.50 + $ 0.16 * x = 620 x = 120 / 0.16 = 750 the answer is c .
"Work through the equation methodically, ensuring clarity at each step.","a sum of money lent out at s . i . amounts to a total of $ 600 after 2 years and to $ 850 after a further period of 5 years . what was the initial sum of money that was invested ? a ) $ 500 , b ) $ 520 , c ) $ 540 , d ) $ 560 , e ) $ 580",s . i for 5 years = $ 850 - $ 600 = $ 250 the s . i . is $ 50 / year s . i . for 2 years = $ 100 principal = $ 600 - $ 100 = $ 500 the answer is a .
"Work through the equation methodically, ensuring clarity at each step.","31 of the scientists that attended a certain workshop were wolf prize laureates , and 13 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 51 of the scientists attended that workshop , how many of them were nobel prize laureates ? a ) a ) 11 , b ) b ) 18 , c ) c ) 24 , d ) d ) 25 , e ) d ) 36","""lets solve by creating equation . . w = 31 . . total = 52 . . not w = 52 - 31 = 21 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 21 or x = 9 . . so who won nobel but not wolf = x + 3 = 12 . . but people who won both w and n = 13 . . so total who won n = 12 + 13 = 25 . . d"""
Provide a detailed solution to the given mathematical problem.,"for all integers x > 1 . < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 . what is the value of < 2 > * < 4 > ? a ) 60 , b ) 116 , c ) 210 , d ) 263 , e ) 360","since < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 = 1 + 2 + . . + ( 2 x - 2 ) + ( 2 x - 1 ) + 2 x then < x > is basically the sum of all integers from 1 to 2 x , inclusive . hence < 2 > is the sum of all integers from 1 to 2 * 2 = 4 and < 4 > is the sum of all integers from 1 to 2 * 4 = 8 - > < 4 > = 36 and < 2 > = 10 - - > < 3 > * < 2 > = 21 * 10 = 360 answer : e"
"Solve the problem systematically, showing each step clearly.","the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 12 minutes is : a ) 9 , b ) 5 , c ) 7 , d ) 6 , e ) 51","""explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 12 / 60 ) ) km = 5 km . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","a dishonest dealer professes to sell goods at the cost price but uses a weight of 840 grams per kg , what is his percent ? a ) 19 , b ) 25 , c ) 77 , d ) 88 , e ) 11","""840 - - - 160 100 - - - ? = > 19 % answer : a"""
Provide a detailed solution to the given mathematical problem.,"find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 50 is a prime number , when each of the given numbers is equally likely to be selected ? a ) 10 / 50 , b ) 15 / 50 , c ) 8 / 50 , d ) 3 / 50 , e ) 7 / 50","let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 } n ( x ) = 15 , n ( s ) = 50 hence , the required probability is 15 / 50 . answer : b"
Explain the solution process for the given equation.,"uncle bruce is baking chocolate chip cookies . he has 72 ounces of dough ( with no chocolate ) and 50 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 40 % chocolate ? a ) 4 , b ) 6 , c ) 8 , d ) 2 , e ) 10","""first , you must find the total weight of the mixture given that 80 % of it will be dough . 60 % * total = 72 = > ( 6 / 10 ) total = 72 = > total = 720 / 6 = > total = 120 oz , from there , you must find 10 % of the total 40 oz of the mixture . 40 % * total = > ( 4 / 10 ) ( 120 ) = 48 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 50 - 48 oz = 2 oz chocolate left over . answer : d"""
Provide a detailed solution to the given mathematical problem.,"a worker' s daily wage is increased by 40 % and the new wage is $ 28 per day . what was the worker' s daily wage before the increase ? a ) $ 18 , b ) $ 20 , c ) $ 22 , d ) $ 24 , e ) $ 25","""let x be the daily wage before the increase . 1.4 x = $ 28 x = $ 20 the answer is b ."""
Break down and solve the equation step by step.,"tom traveled the entire 20 miles trip . if he did the first 10 miles of at a constant rate 12 miles per hour and the remaining trip of at a constant rate 10 miles per hour , what is the his average speed , in miles per hour ? a ) 12.45 mph , b ) 11.25 mph , c ) 10.95 mph , d ) 10.91 mph , e ) 10.56 mph",avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 10 + 10 ) / ( ( 10 / 12 ) + ( 10 / 10 ) = 120 / 11 = 10.91 mph d
"Solve the problem systematically, showing each step clearly.","ratio and proportion 215 : 474 : : 537 : ? a ) 26 , b ) 27 , c ) 25 , d ) 22 , e ) 23",2 + 1 + 5 + 4 + 7 + 4 = 23 5 + 3 + 7 + x = 23 = > x = 8 combination that match 8 is 26 since 2 + 6 = 8 answer : a
"Solve the problem systematically, showing each step clearly.","the average of non - zero number and its square is 5 times the number . the number is : a ) 9 , b ) 7 , c ) 8 , d ) 5 , e ) 3","let the number be x . then , ( x + x 2 ) / 2 = 5 x = > x 2 - 9 x = 0 = > x ( x - 9 ) = 0 = > x = 0 or x = 9 so , the number is 9 . answer : a"
"Work through the equation methodically, ensuring clarity at each step.","what is the remainder when 1003 * 1005 * 1007 is divided by 15 a ) 3 , b ) 17 , c ) 14 , d ) 0 , e ) 7","""1003 / 15 = = > remainder = 13 1005 / 15 = = > remainder = 0 1007 / 15 = = > remainder = 2 13 * 0 * 2 = 0 / 15 = = > remainder = 0 answer : d"""
"Solve the problem systematically, showing each step clearly.","if the average of 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 and x is 750 , what is the value of x ? a ) 750 , b ) 752 , c ) 754 , d ) 755 , e ) 756","""sum of the deviations of the numbers in the set from the mean is always zero 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 mean is 750 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 750 + 5 = 755 d"""
"Solve the problem systematically, showing each step clearly.","express a speed of 16 kmph in meters per second ? a ) 10 mps , b ) 8 mps , c ) 4 mps , d ) 7 mps , e ) 2 mps","""16 * 5 / 18 = 4 mps answer : c"""
Provide a detailed solution to the given mathematical problem.,"find the least number of 5 digits , which is exactly divisible by 89 . a ) 27 , b ) 37 , c ) 932 , d ) 12 , e ) 91",answer : a
"Work through the equation methodically, ensuring clarity at each step.","in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 6 , and the ratio of flour to baking soda is 5 to 1 . if there were 30 more pounds of baking soda in the room , the ratio of flour to baking soda would be 4 to 1 . how many pounds of sugar are stored in the room ? a ) 30 , b ) 50 , c ) 60 , d ) 45 , e ) 70","""sugar : flour = 3 : 6 = 1 : 2 = 5 : 10 flour : soda = 5 : 1 = 10 : 2 ; thus we have that sugar : flour : soda = 5 x : 10 x : 2 x . also given that 10 x / ( 2 x + 30 ) = 4 / 1 - - > x = 60 - - > sugar = 5 x = 30 . answer : a"""
Provide a detailed solution to the given mathematical problem.,"a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price w of the machine ? a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160","""since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let' s start by testing answer c : $ 120 . . . . if . . . . . retail price w = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"""
Explain the solution process for the given equation.,"how many multiples of 7 are there between 700 and 1000 , inclusive ? a ) 43 , b ) 42 , c ) 22 , d ) 21 , e ) 20","""there are exactly 301 numbers between 700 to 1000 . . 701 to 800 = 100 801 to 1000 = 200 . . . total 300 numbers , count 700 too . . 301 / 7 = 43 . . . ans option a ."""
"Solve the problem systematically, showing each step clearly.","the side of a square is increased by 15 % then how much % does its area increases ? ['a ) 52.65','b ) 56.25','c ) 50.75','d ) 32.25','e ) 52.75']",a = 100 a 2 = 10000 a = 115 a 2 = 13225 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 3225 100 - - - - - - - ? = > 32.25 % answer : d
"Work through the equation methodically, ensuring clarity at each step.","one computer can upload 120 megabytes worth of data in 6 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 42 seconds . how long would it take for the second computer , working on its own , to upload 120 megabytes of data ? a ) 6 , b ) 7 , c ) 9.13 , d ) 11 , e ) 13","""since the first computer can upload 120 megabytes worth of data in 6 seconds then in 6 * 7 = 42 seconds it can upload 7 * 120 = 840 megabytes worth of data , hence the second compute in 42 seconds uploads 1300 - 840 = 460 megabytes worth of data . the second computer can upload 120 megabytes of data in 9.13 seconds . answer : c ."""
Provide a detailed solution to the given mathematical problem.,"a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 50 % ? a ) 750 , b ) 882 , c ) 772 , d ) 652 , e ) 271","""cost price = rs . 500 profit = 50 % of 500 = rs . 250 selling price = cost price + profit = 500 + 250 = 750 answer : a"""
"Work through the equation methodically, ensuring clarity at each step.","a certain machine produces 650 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 7 days ? a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 109,200 , e ) 168,000","""since 7 days consist of 24 * 7 hours the total hours of a week is 168 hours . since every hour the machine produces 650 units of product p the total product during 168 hours is 650 * 168 = 109,200 correct option : d"""
"Solve the problem systematically, showing each step clearly.","natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 2 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ? a ) 1.5 , b ) 2.5 , c ) 3.75 , d ) 5 , e ) 7.5","""let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 2 km / hour x / 3 = 2 x = 6 km the average speed while climbing = distance / time = 6 / 4 = 1.5 km / h the answer is a ."""
Explain the solution process for the given equation.,"at what rate of compound interest per annum will a sum of rs . 1200 become rs . 1348.32 in 2 years a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %","""explanation : let rate will be r % 1200 ( 1 + r / 100 ) 2 = 134832 / 100 ( 1 + r / 100 ) 2 = 134832 / 120000 ( 1 + r / 100 ) 2 = 11236 / 10000 ( 1 + r / 100 ) = 106 / 100 = > r = 6 % option d"""
Break down and solve the equation step by step.,"in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 9 , 0 ) , ( 0 , - 3.5 ) , ( - 9 , 0 ) ? a ) 63 , b ) 88 , c ) 112 , d ) 116 , e ) 120","""ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 9 + 9 = 18 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 18 * 7 = 63 a is the answer"""
"Solve the problem systematically, showing each step clearly.","the sum of two numbers is 45 . their difference is 5 . the bigger number is a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 45",x + y = 45 x - y = 5 adding 2 x = 50 = = > x = 25 and y = 45 - 25 = 20 bigger number is x = 25 answer b .
"Solve the problem systematically, showing each step clearly.","suraj has a certain average of runs for 12 innings . in the 13 th innings he scores 96 runs thereby increasing his average by 5 runs . what is his average after the 13 th innings ? a ) 48 , b ) 64 , c ) 36 , d ) 72 , e ) 27","""to improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings . thus , the average after the 13 th innings = 96 - 60 = 36 . answer : c"""
Break down and solve the equation step by step.,"a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 200 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ? a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6","""the distance between the nest and the ditch is 200 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 200 = 6000 . d = st 6000 / 1.5 = t , i think we can take 6000 meters as 6 km , then only we get t = 4 . ( 1000 meters = 1 km ) d )"""
Provide a detailed solution to the given mathematical problem.,"at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 55 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ? a ) 24 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 %","""another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 55 = 25 + b + 25 b / 100 b = 24 answer ( a )"""
"Solve the problem systematically, showing each step clearly.","p , q and r together earn rs . 1800 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ? a ) s . 50 , b ) s . 70 , c ) s . 90 , d ) s . 100 , e ) s . 120","explanation : amount earned by p , q and r in 1 day = 1800 / 9 = 200 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 200 = 50 = > amount earned by r in 1 day = 50 answer : option a"
"Solve the problem systematically, showing each step clearly.","the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is : a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 355","""clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer : option c"""
Explain the solution process for the given equation.,"a man can row 36 kmph in still water . it takes him thrice as long to row up as to row down the river . find the rate of the stream ? a ) 14 kmph , b ) 12 kmph , c ) 18 kmph , d ) 1 kmph , e ) none of these",explanation : let man' s rate upsteam be x kmph then his rate of downstream = 3 x kmph rate still water = 1 / 2 ( 3 x + x ) = 2 x 2 x = 36 x = 18 rate of upstream = 18 rate of downstream = 54 rate of stream 1 / 2 ( 54 - 18 ) = 18 kmph answer : option c
Provide a detailed solution to the given mathematical problem.,"if remainder is 1 , quotient is 54 and dividend is 217 then what is divisor ? a ) 2 , b ) 4 , c ) 6 , d ) 14 , e ) 16","""we know dividend = divisor * quotient + remainder = = = > 217 = divisor * 54 + 1 = = = = = > 216 / 54 = divisor = = = > divisor = 4 ans - b"""
Provide a detailed solution to the given mathematical problem.,"an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many y ways can the assembly line be arranged ? a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720",c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want y = 6 c ! / 2 - > 720 / 2 = 360
"Solve the problem systematically, showing each step clearly.","if a train , travelling at a speed of 360 kmph , crosses a pole in 5 sec , then the length of train is ? a ) 381 m , b ) 112 m , c ) 500 m , d ) 125 m , e ) 433 m","""c c = 360 * 5 / 18 * 5 = 500 m"""
Break down and solve the equation step by step.,"ajay spends 45 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 7.5 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income . a ) rs . 40000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these","""let the monthly income of ajay be rs . x savings of ajay = x - ( 45 + 25 + 7.5 ) / 100 * x = 22.5 / 100 x 22.5 / 100 x = 9000 x = 40000 . answer : a"""
Explain the solution process for the given equation.,"two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1,100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam' s account balance increased from his initial deposit of $ 1,000 ? a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 %","""investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %"""
"Solve the problem systematically, showing each step clearly.","a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2445 ? a ) s . 800 , b ) s . 810 , c ) s . 815 , d ) s . 900 , e ) s . 920","""2445 * 1 / 3 = 815 option c"""
Break down and solve the equation step by step.,"by selling 16 pens for a rupee a woman loses 5 % . how many for a rupee should he sell in order to gain 18 % ? a ) 12 , b ) 14 , c ) 45 , d ) 13 , e ) 65",d 95 % - - - 16 118 % - - - ? 95 / 118 * 16 = 13
"Work through the equation methodically, ensuring clarity at each step.","if the number 892 , 142,24 x is divisible by 11 , what must be the value of x ? a ) 1 , b ) 2 , c ) 3 , d ) 0 , e ) 5","""multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 892 , 142,24 x sum of digits at odd places = 8 + 2 + 4 + 2 + x = 16 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 4 = 16 ( ii ) ( i ) - ( ii ) = 16 + x - 16 = x - 0 hence x should be = 0 to make this a multiple of 11 ( 0 ) option d"""
Explain the solution process for the given equation.,"an individual deposited 20 % of 25 % of 30 % of what he had into his account with a bank . if he deposited rs . 750 , how much was he having initially with him before depositing ? a ) rs . 500000 , b ) rs . 50000 , c ) rs . 5000 , d ) rs . 15000 , e ) rs . 6000",let x amount he has then 20 % of 25 % of 30 % of x = 750 so x = 50000 answer : b
Break down and solve the equation step by step.,"two positive integers differ by 4 , and sum of their reciprocals is 4 . then one of the numbers is a ) a ) 3 , b ) b ) 1 , c ) 2 , d ) d ) 21 , e ) e ) 28","""algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 4 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 4 or ( n ^ 2 + 4 n ) * 4 = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 2 . hence , c"""
"Solve the problem systematically, showing each step clearly.","a pipe can fill a cistern in 66 minutes . find the time in which 1 / 11 part of the cistern will be filled ? a ) 5 min , b ) 2 min , c ) 6 min , d ) 1 min , e ) 10 min","""full cistern filled in = 66 minutes 1 / 11 part filled in = 66 * 1 / 11 = 6 minutes answer is c"""
"Work through the equation methodically, ensuring clarity at each step.","a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ? a ) 11 , b ) 23 , c ) 27 , d ) 22 , e ) 91","""let the son' s present age be x years . then , man' s present age = ( x + 25 ) years . ( x + 25 ) + 2 = 2 ( x + 2 ) x + 27 = 2 x + 4 = > x = 23 . answer : b"""
Provide a detailed solution to the given mathematical problem.,"the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 17 . the larger of the two numbers is : a ) 276 , b ) 299 , c ) 391 , d ) 345 , e ) 355","""clearly , the numbers are ( 23 x 13 ) and ( 23 x 17 ) . larger number = ( 23 x 17 ) = 391 . answer : option c"""
"Work through the equation methodically, ensuring clarity at each step.","a certain article of clothing was discounted during a special sale to 4 / 5 of its original retail price . when the clothing did n' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ? a ) 50 % , b ) 33.33 % , c ) 40 % , d ) 16.66 % , e ) 12.5 %","""say the original retail price of the item was $ 200 . the price after the first sale = 4 / 5 * $ 200 = $ 160 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 160 - 100 ) / 150 = 1 / 3 = 40 % . answer : c ."""
Explain the solution process for the given equation.,"a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 30 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ? a ) 21 % , b ) 22.5 % , c ) 25 % , d ) 30 % , e ) 40 %","""1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.3 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 30 % income the savings increased by 100 % . or s = . 3 i or s = 30 % of income d is the answer"""
"Solve the problem systematically, showing each step clearly.","in a class of 50 students , 18 take chorus , 26 take band , and 2 take both chorus and band . how many students in the class are not enrolled in either chorus or band ? a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 18",16 + 2 + 24 + x = 50 42 + x = 50 x = 8 students a )
Break down and solve the equation step by step.,"find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years a ) 306.09 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01","""a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"""
"Solve the problem systematically, showing each step clearly.","p runs 20 % faster than q so p gives q a 300 meter head start . if the race ends in a tie , how far ( in meters ) did p run in the race ? a ) 1500 , b ) 1600 , c ) 1700 , d ) 1800 , e ) 1900","""let d be the race distance that p ran . let t be the time it took to complete the race . let v be q' s speed . t = d / 1.2 v = ( d - 300 ) / v d = 1.2 d - 360 0.2 d = 360 d = 1800 meters . the answer is d ."""
"Solve the problem systematically, showing each step clearly.","20 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ? a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 17.4 %","""alcohol in the 20 litres of mix . = 20 % of 20 litres = ( 20 * 20 / 100 ) = 4 litres water in it = 20 - 3 = 17 litres new quantity of mix . = 20 + 3 = 23 litres quantity of alcohol in it = 4 litres percentage of alcohol in new mix . = 4 * 100 / 23 = 17.4 % answer is e"""
Provide a detailed solution to the given mathematical problem.,"how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 38 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ? a ) 2 , b ) 5 , c ) 8 , d ) 15 , e ) 25","selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 38 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 40 ) / ( 40 - 38 ) = 5 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 8 lbs . answer ( c )"
"Solve the problem systematically, showing each step clearly.","amanda sees a sale for 30 % off all items , she sees a dress on sale that originally cost $ 50 . how much will it cost amanda to buy the dress after the sale amount of 30 % has been take off ? a ) $ 40 , b ) $ 35 , c ) $ 50 , d ) $ 65 , e ) $ 15",final number = original number - 30 % ( original number ) = 50 - 30 % ( 50 ) = 50 - 15 = $ 35 . answer b
"Solve the problem systematically, showing each step clearly.","from below option 51 is divisible by which one ? a ) a ) 4 , b ) b ) 5 , c ) c ) 6 , d ) d ) 3 , e ) e ) 7","""51 / 3 = 17 d"""
Explain the solution process for the given equation.,"a car is running at a speed of 90 kmph . what distance will it cover in 15 second ? a ) 100 m , b ) 255 m , c ) 375 m , d ) can not be determined , e ) none of these","""explanation : given : speed = 108 kmph = ( 90 x ( 5 / 18 ) ) m / sec = 25 m / sec distance covered in 15 second = ( 25 x 15 ) m = 375 m . answer : c"""
Break down and solve the equation step by step.,"nicky and cristina are running a 100 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ? a ) 30 , b ) 35 , c ) 40 , d ) 25 , e ) 60","""the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . a"""
Provide a detailed solution to the given mathematical problem.,"a trader sells 75 meters of cloth for rs . 4950 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ? a ) 51 , b ) 88 , c ) 90 , d ) 42 , e ) 22","""sp of 1 m of cloth = 4950 / 75 = rs . 66 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 66 - rs . 15 = rs . 51 answer : a"""
Explain the solution process for the given equation.,"at an election 2 candidates are participated a candidate got 30 % of votes and defeated by 5000 votes . 100 votes are invalid . find the total polled votes ? a ) 11520 , b ) 12600 , c ) 15000 , d ) 13560 , e ) 12560",winners votes = 100 - 30 = 70 % invalid votes = 100 polled votes = [ ( 100 * 5000 ) / ( 2 * 70 - 100 ) ] + 100 = 12600 answer is b
Break down and solve the equation step by step.,"two vessels contains equal number of mixtures milk and water in the ratio 4 : 1 and 7 : 3 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ? a ) 2 : 1 , b ) 4 : 1 , c ) 3 : 1 , d ) 2 : 3 , e ) 4 : 3",the ratio of milk and water in the new vessel is = ( 4 / 5 + 7 / 10 ) : ( 1 / 5 + 3 / 10 ) = 3 / 2 : 1 / 2 = 3 : 1 answer is c
"Solve the problem systematically, showing each step clearly.","a train covers a distance of 12 km in 10 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ? a ) 298 , b ) 288 , c ) 120 , d ) 776 , e ) 180","""speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 9 = 180 m . answer : e"""
Provide a detailed solution to the given mathematical problem.,"the number of stamps that p and q had were in the ratio of 7 : 2 respectively . after p gave q 15 stamps , the ratio of the number of p' s stamps to the number of q' s stamps was 2 : 1 . as a result of the gift , p had how many more stamps than q ? a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65","""p started with 7 k stamps and q started with 2 k stamps . ( 7 k - 15 ) / ( 2 k + 15 ) = 2 / 1 3 k = 45 k = 15 p has 7 ( 15 ) - 15 = 90 stamps and q has 2 ( 15 ) + 15 = 45 stamps . the answer is c ."""
Explain the solution process for the given equation.,"the average weight of 8 persons increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 101 kg","""total weight increased = ( 8 x 4.5 ) kg = 36 kg . weight of new person = ( 65 + 36 ) kg = 101 kg . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","a train running at the speed of 60 km / hr crosses a pole in 12 seconds . find the length of the train ? a ) 150 meter , b ) 200 meter , c ) 156 meter , d ) 168 meter , e ) 154 meter","""speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 12 = 200 meter answer : b"""
Break down and solve the equation step by step.,"one week , a certain truck rental lot had a total of 20 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 10 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ? a ) 18 , b ) 20 , c ) 12 , d ) 8 , e ) 4","""n - not rented trucks ; r - rented trucks n + r = 20 n + r / 2 = 10 r = 20 b"""
"Work through the equation methodically, ensuring clarity at each step.","how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 5 - percent solution ? a ) 35 , b ) 22.5 , c ) 27 , d ) 16 2 / 3 , e ) 15","""how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 5 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 5 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 5 x = 7.5 since you need a 15 l solution , you must evaporate 22.5 of the original 50 l solution to get a 5 % solution . answer is b ."""
"Solve the problem systematically, showing each step clearly.","the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 40 per cent . the two reductions together are equal to a single reduction of a ) 45 % , b ) 55 % , c ) 35 % , d ) 32.5 % , e ) 30 %","""price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 40 percent is reduced which means the new price is merely 60 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 3 / 5 ) p = 9 / 20 p is the new price after both deduction which is 45 percent of the original value p . this implies this entire series of deduction is worth having discounted 55 % of p . so answer is b = 55 %"""
"Solve the problem systematically, showing each step clearly.","7386038 is divisible by a ) 3 , b ) 4 , c ) 9 , d ) 11 , e ) 13","""explanation : the given number is 7386038 . the sum of the digits at even places is = 3 + 6 + 3 = 12 . the sum of the digits at odd places is = 7 + 8 + 0 + 8 = 23 . the difference is given by 23 - 12 = 11 answer : d"""
Break down and solve the equation step by step.,"the water level in a rectangular swimming pool measuring 60 feet by 20 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons ) a ) 100 , b ) 250 , c ) 4500 , d ) 1200 , e ) 5625","""6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 20 * 1 / 2 = 600 feet ^ 3 of water must be removed , which equals to 600 * 7.5 = 4500 gallons . answer : c ."""
Explain the solution process for the given equation.,"a watch was sold at a loss of 10 % . if it was sold for rs . 225 more , there would have been a gain of 5 % . what is the cost price ? a ) 1000 , b ) 1500 , c ) 2778 , d ) 2788 , e ) 2991","""90 % 105 % - - - - - - - - 15 % - - - - 225 100 % - - - - ? = > rs . 1500 answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","the compound interest earned by sunil on a certain amount at the end of two years at the rate of 6 % p . a . was rs . 370.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned . a ) rs . 3360.80 , b ) rs . 3370.80 , c ) rs . 3320.70 , d ) rs . 3230.80 , e ) rs . 3130.80",let the sum be rs . p p { [ 1 + 6 / 100 ] 2 - 1 } = 370.80 p ( 6 / 100 ) ( 2 + 6 / 100 ) = 370.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 246 / ( 0.05 ) ( 2.05 ) = 3000 . amount = rs . 3370.80 . answer : b
Provide a detailed solution to the given mathematical problem.,"a train 120 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph","""speed of train relative to man : 120 / 6 * 18 / 5 km / hr = 72 km / hr let speed of train = x therefore x + 6 = 72 x = 72 - 6 x = 66 km / hr answer : c"""
"Work through the equation methodically, ensuring clarity at each step.","bill is golfing with 3 friends and can either buy generic golf tees that are packaged by the dozen or the higher quality aero flight tees that come by the pair . what is the minimum number of packages of aero flight tees bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome , if he will buy no more than 2 packages of the generic golf tees ? a ) 16 , b ) 10 , c ) 28 , d ) 4 , e ) 2","at least 20 golf tees for each member of his foursome = total of at least 4 * 20 = 80 tees . 2 packages of the generic golf tees , that are packaged by the dozen = 2 * 12 = 24 tees . so , bill must by at least 16 aero tees . they come by the pair , hence he must by at least 56 / 2 = 28 packages of aero flight tees . answer : c ."
"Work through the equation methodically, ensuring clarity at each step.","ramesh purchased a refrigerator for rs . 17500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ? a ) 34778 , b ) 26888 , c ) 24475 , d ) 17600 , e ) 12778","""price at which the tv set is bought = rs . 17,500 discount offered = 20 % marked price = 17500 * 100 / 80 = rs . 21875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 21875 + 375 = rs . 22250 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 22250 * 110 / 100 = rs . 24475 answer : c"""
Provide a detailed solution to the given mathematical problem.,"how much space , in cubic units , is left vacant when maximum number of 6 x 6 x 6 cubes are fitted in a rectangular box measuring 12 x 18 x 14 ? a ) 428 , b ) 429 , c ) 430 , d ) 431 , e ) 432","""no of cubes that can be accommodated in box = ( 12 * 18 * 14 ) / ( 6 * 6 * 6 ) 12 * 16 in numerator can be perfectly divided by 6 * 6 in denominator . side with length 14 ca n' t be perfectly divided by 6 and hence is the limiting factor . closet multiple of 6 less that 14 is 12 . so vacant area in cube = = 18 * 12 * ( 14 - 12 ) = 18 * 12 * 2 = 432 ans - e"""
Provide a detailed solution to the given mathematical problem.,"at a summer camp with 1,500 participants , 1 / 2 of the campers are aged 10 to 12 . next year , the number of campers aged 10 to 12 will increase by 1 / 3 . after this change , what percentage of the total 1,500 campers will the 10 to 12 - year - olds represent ? a ) 62 , b ) 64 , c ) 65 , d ) 66 2 / 3 % , e ) 67","""total - 1,500 participants campers are aged 10 to 12 = ( 1 / 2 ) * 1500 = 750 next year , campers are aged 10 to 12 = ( 4 / 3 ) * 750 = 1000 percentage = ( 1000 / 1500 ) * 100 = 66 2 / 3 % answer : option d"""
Provide a detailed solution to the given mathematical problem.,"the difference between the place value and the face value of 6 in the numerical 856973 is a ) 973 , b ) 6973 , c ) 5994 , d ) 9554 , e ) none of them","""= ( place value of 6 ) - ( face value of 6 ) = ( 6000 - 6 ) = 5994 answer is c"""
"Solve the problem systematically, showing each step clearly.","the diagonals of a rhombus are 30 cm and 20 cm . find its area ? a ) 176 , b ) 190 , c ) 150 , d ) 278 , e ) 300","""1 / 2 * 30 * 20 = 300 answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","kareena , saif , and a puppy start walking down a road . they start at the same time , from the same point , in the same direction . the saif walks at 5 miles / hour kareena at 6 miles / hour . the puppy runs from saif to kareena and back again with a constant speed of 10 miles / hour . the puppy does not slow down on the turn . how far does the puppy travel in 1 hour ? a ) 10 miles , b ) 14 miles , c ) 12 miles , d ) 20 miles , e ) 30 miles",a 10 miles speed us 10 miles / hour
"Work through the equation methodically, ensuring clarity at each step.","what is the total number of integers between 100 and 500 ( exclusive ) that are divisible by 5 ? a ) 51 , b ) 63 , c ) 79 , d ) 66 , e ) 42","105 , 110 , 115 , . . . , 490,495 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / (' space' ) + 1 = ( 495 - 105 ) / ( 5 ) + 1 = 78 + 1 = 79 answer is c"
"Solve the problem systematically, showing each step clearly.","what should be the least number to be added to the 11002 number to make it divisible by 11 ? a ) 12 , b ) 9 , c ) 18 , d ) 77 , e ) 26","""answer : 9 option : b"""
Break down and solve the equation step by step.,"circular gears l and r start to rotate at the same time at the same rate . gear l makes 10 complete revolutions per minute and gear r makes 30 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 6 more revolutions than gear l ? a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 12 , e ) e ) 18","""gear l - - 10 rotations per 60 seconds - - 1 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 3 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 2 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 2 units . required net difference should be 6 rotations = > 3 ( 6 seconds later ) = = > 18 seconds . answer : e"""
"Work through the equation methodically, ensuring clarity at each step.","what is the difference between the c . i . on rs . 5000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ? a ) rs . 2.04 , b ) rs . 2.09 , c ) rs . 2.06 , d ) rs . 2.22 , e ) rs . 2.08","""c . i . when interest is compounded yearly = [ 5000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 5000 * 26 / 25 * 51 / 50 = rs . 5304 c . i . when interest is compounded half - yearly = [ 5000 * ( 1 + 2 / 100 ) 2 ] = ( 5000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 5306.04 difference = ( 5306.04 - 5304 ) = rs . 2.04 . answer : a"""
Explain the solution process for the given equation.,"in town x , 64 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town x are females ? a ) 16 % , b ) 25 % , c ) 32 % , d ) 34 % , e ) 52 %","""we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 42 are employed males , hence 22 % are employed females . ( employed females ) / ( total employed people ) = 22 / 64 = 34 % answer : d ."""
Break down and solve the equation step by step.,"ifaequals the sum of the even integers from 2 to 80 , inclusive , andbequals the sum of the odd integers from 1 to 79 , inclusive , what is the value of a - b ? a ) 1 , b ) 10 , c ) 19 , d ) 40 , e ) 21","""this is a solution from beatthegmat : even numbers : ( 80 - 2 ) / 2 + 1 = 40 even integers . ( 80 + 2 ) / 2 = 41 is the average of the even set . sum = avg * ( # of elements ) = 41 * 40 = 1640 = a odd numbers : ( 79 - 1 ) / 2 + 1 = 40 odd integers . ( 79 + 1 ) / 2 = 40 is the average of the odd set . sum = avg * ( # of elements ) = 40 * 40 = 1600 = b a - b = 1640 - 1600 = 40 . answer : d"""
Provide a detailed solution to the given mathematical problem.,"if 2 + 3 = 10 ; 2 + 5 = 27 ; 2 + 7 = 53 then 2 + 11 = ? a ) 124 , b ) 129 , c ) 128 , d ) 125 , e ) 120","""2 ^ 0 + 3 ^ 2 = 1 + 9 = 10 2 ^ 1 + 5 ^ 2 = 2 + 25 = 27 2 ^ 2 + 7 ^ 2 = 4 + 49 = 53 and 2 ^ 3 + 11 ^ 2 = 8 + 121 = 129 answer : b"""
Provide a detailed solution to the given mathematical problem.,"a , band c can do a piece of work in 11 days , 20 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ? a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days","""( a + b )' s 1 day' s work = 1 / 11 + 1 / 20 = 31 / 220 ( a + c )' s 1 day' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day' s = 31 / 220 + 6 / 55 = 55 / 220 = 1 / 4 1 / 4 th work done in 2 days work done = 4 * 2 = 8 days answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 60,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 480,000 , e ) $ 540,000","""the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 60,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 60000 * 2 ^ 3 = 480000 hence , the answer is d ."""
Explain the solution process for the given equation.,"jolene entered an 16 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ? a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24","""if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 920.24 answer : d ."""
Explain the solution process for the given equation.,"irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 170 cookies , what percent of the cookies did nell bake ? a ) 0.125 % , b ) 1.25 % , c ) 11.7 % , d ) 125 % , e ) 0.152 %","""9.18 x + 5.17 x + 2.05 x = 16.4 x = 170 cookies x = 170 / 16.4 = 10 ( approx ) so , nell baked 10 * 2.05 cookies or 20 cookies ( approx ) % share = 20 / 170 = 11.7 approx hence , answer is c ."""
Provide a detailed solution to the given mathematical problem.,"how many factors does 34 ^ 2 have ? a ) 2 , b ) 8 , c ) 20 , d ) 25 , e ) 26","""36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 5 * 4 = 20 answer c ."""
"Work through the equation methodically, ensuring clarity at each step.","two brothers ram and ravi appeared for an exam . the probability of selection of ram is 2 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected . a ) 2 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5","""let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 2 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 2 / 7 x 1 / 5 = 2 / 35 answer : a"""
Provide a detailed solution to the given mathematical problem.,"according to a recent student poll , 5 / 6 out of 30 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ? a ) 1 / 14 , b ) 4 / 49 , c ) 2 / 7 , d ) 28 / 29 , e ) 13 / 14","25 students are interested , 5 are not interested prob = 1 - 5 c 2 / 30 c 2 = 1 - ( 5 * 4 / ( 30 * 29 ) ) = 1 - 20 / 580 = 1 - 1 / 29 = 28 / 29 answer : d"
Provide a detailed solution to the given mathematical problem.,"if a randomly selected non - negative single digit integer is added to { 2 , 3 , 6 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ? a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6","""we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 6 ) / 2 = 4.5 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ."""
Break down and solve the equation step by step.,"a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 210,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ? a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 60,000 , e ) $ 75,000","""another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 7 a * 1 + a * 5 ) / 6 = 12 a / 6 = 2 a = 60000 answer is d . $ 60,000"""
"Work through the equation methodically, ensuring clarity at each step.","sachin is younger than rahul by 5 years . if the ratio of their ages is 7 : 9 , find the age of sachin a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 15.5","""if rahul age is x , then sachin age is x - 5 , so ( x - 5 ) / x = 7 / 9 = > 9 x - 45 = 7 x = > 2 x = 45 = > x = 22.5 so sachin age is 22.5 - 7 = 15.5 answer : e"""
Break down and solve the equation step by step.,"a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 35 adults have their meal , find the total number of children that can be catered with the remaining food . a ) 33 , b ) 54 , c ) 18 , d ) 45 , e ) 01","""explanation : as there is meal for 70 adults and 35 have their meal , the meal left can be catered to 35 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 35 adults = 45 children hence , the meal can be catered to 45 children . answer : d"""
Break down and solve the equation step by step.,"if 75 percent of a class answered the first question on a certain test correctly , 30 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ? a ) 25 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %","""i did n' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 30 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 105 x = 25 ans : a"""
"Work through the equation methodically, ensuring clarity at each step.","how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 145 m length ? a ) 13.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 13.9 sec , e ) 47.98 sec","""speed = 70 * 5 / 18 = 19 m / sec total distance covered = 120 + 145 = 265 m . required time = 265 / 19 = 13.9 sec . answer : d"""
"Work through the equation methodically, ensuring clarity at each step.","harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 4 of her books to their new home . what fraction of millicent' s old library capacity is the new home' s library capacity ? a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 12","""because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h' = 1 / 3 h = 10 books m' = 1 / 4 m = 15 books total = 25 books m' = 25 = 5 / 12 * 60 ratio : 5 / 12 ans : e"""
Break down and solve the equation step by step.,"a bag contains 6 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ? a ) 2 / 7 , b ) 3 / 10 , c ) 5 / 11 , d ) 6 / 13 , e ) 11 / 21","""the total number of ways to draw two balls is 13 c 2 = 78 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 7 c 2 = 21 p ( two balls of the same colour ) = 36 / 78 = 6 / 13 the answer is d ."""
Explain the solution process for the given equation.,"if y is the smallest positive integer such that 4410 multiplied by y is the square of an integer , then y must be ['a ) 2','b ) 5','c ) 6','d ) 7','e ) 10']","4410 = 2 * 3 ^ 2 * 5 * 7 ^ 2 to be perfect square , we need to multiply by at least 2 * 5 = 10 . the answer is e ."
Explain the solution process for the given equation.,"rs . 2080 is divided so that 3 times the first share , thrice the 2 nd share and four times the third share amount to the same . what is the value of the second share ? a ) s 802 , b ) s 208 , c ) s 960 , d ) s 690 , e ) s 906","""a + b + c = 2080 3 a = 2 b = 4 c = x a : b : c = 1 / 3 : 1 / 2 : 1 / 4 = 4 : 6 : 3 6 / 13 * 2080 = rs 960 answer : c"""
Explain the solution process for the given equation.,"a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ? a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 %","""just assume original price is 100 . sale price = 80 then it is marked down by 10 % = 80 - 8 = 72 . hence it is 72 % of the original price . hence answer is a"""
Break down and solve the equation step by step.,"a picnic attracts 240 persons . there are 80 more men than women , and 80 more adults than children . how many men are at this picnic ? a ) 240 , b ) 75 , c ) 110 , d ) 120 , e ) 200","""adult + children = 240 let , children = y then , adult = y + 80 i . e . y + ( y + 80 ) = 240 i . e . y = 80 i . e . adult = 80 + 80 = 160 adults include only men and women i . e . men + women = 160 let women , w = x then men , m = x + 80 i . e . x + ( x + 20 ) = 2 x + 80 = 160 i . e . x = 40 i . e . men , m = 40 + 80 = 120 answer : option d"""
Break down and solve the equation step by step.,"the temperature of a certain cup of coffee 5 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ? a ) 65 , b ) 61.875 , c ) 80 , d ) 85 , e ) 90","""first , we have to find a . we know that after t = 5 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 5 a ) + 60 60 = 120 * ( 2 ^ - 5 a ) 60 / 120 = 2 ^ - 5 a 1 / 2 = 2 ^ - 5 a 2 ^ - 1 = 2 ^ - 5 a - 1 = - 5 a 1 / 5 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 5 * 30 ) + 60 f = 120 * ( 2 ^ - 6 ) + 60 f = 120 * ( 1 / 2 ^ 6 ) + 60 f = 120 * 1 / 64 + 60 f = 1.875 + 60 = 61.875 answer b !"""
Explain the solution process for the given equation.,"two persons a and b can complete a piece of work in 18 days and 24 days respectively . if they work together , what part of the work will be completed in 2 days ? a ) 7 / 36 , b ) 9 / 35 , c ) 4 / 37 , d ) 8 / 35 , e ) 5 / 3","""a' s one day' s work = 1 / 18 b' s one day' s work = 1 / 24 ( a + b )' s one day' s work = 1 / 18 + 1 / 24 = 7 / 72 the part of the work completed in 3 days = 2 ( 7 / 72 ) = 7 / 36 . answer : a"""
Explain the solution process for the given equation.,"the cash difference between the selling prices of an article at a profit of 4 % and 6 % is rs . 3 . the ratio of the two selling prices is ? a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51","""let c . p . of the article be rs . x . then , required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 answer : b"""
"Solve the problem systematically, showing each step clearly.","how many integerskgreater than 100 and less than 1100 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ? a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90","numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ninet pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 9 * 10 = 90 hence e ."
"Solve the problem systematically, showing each step clearly.","if below equation are true 24 $ 6 = 64 35 $ 5 = 87 63 $ 7 = 99 by using same logic what is the value of the below question 88 $ 8 = ? a ) 1621 , b ) 1711 , c ) 1611 , d ) 1511 , e ) 1311",correct answer : c the number on the right side is formed as ( sum of digits of the 1 st number ) no 1 / no 2 ex : 35 $ 5 = 87 ( 3 + 5 = 8 ) ( 35 / 5 = 7 ) 63 $ 7 = 99 ( 6 + 3 = 9 ) ( 63 / 7 = 9 )
Break down and solve the equation step by step.,"a man swims downstream 60 km and upstream 40 km taking 4 hours each time ; what is the speed of the current ? a ) 3 kmph , b ) 2.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph","""explanation : 60 - - - 4 ds = 15 ? - - - - 1 40 - - - - 4 us = 10 ? - - - - 1 s = ? s = ( 15 - 10 ) / 2 = 2.5 answer : option b"""
Provide a detailed solution to the given mathematical problem.,"how many paying stones , each measuring 2 m * 1 m are required to pave a rectangular court yard 30 m long and 16 m board ? ['a ) 240','b ) 18','c ) 26','d ) 17','e ) 12']",30 * 16 = 2 * 1 * x = > x = 240 answer : a
Explain the solution process for the given equation.,"some of 40 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 20 % . what fraction of the original paint was replaced ? a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 1","""let total paint = 1 let amount replaced = x 40 ( 1 - x ) + 20 x = 20 x = 1 / 1 answer : e"""
Break down and solve the equation step by step.,"nicky and cristina are running a 500 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ? a ) 50 , b ) 45 , c ) 40 , d ) 35 , e ) 30","""the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . e"""
Break down and solve the equation step by step.,"a cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm . find the total area of the wet surface . a ) 66 m square , b ) 49 m square , c ) 77 m square , d ) 44 m square , e ) 33 m square","""area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 4 * 1.25 + 6 * 1.25 ) ] + 6 * 4 = 49 m square answer : b"""
Provide a detailed solution to the given mathematical problem.,"the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is : a ) 21 , b ) 20 , c ) 22 , d ) 25 , e ) 40","""let the total number of workers be x . then , 8000 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 42000 = x = 21 . answer a"""
"Solve the problem systematically, showing each step clearly.","walking at 70 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ? a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 56","""speed is inversly proprtional to time walking at 70 % of speed meand 7 / 10 s takes 10 / 7 t . it takes 24 minutes extra to cover the distance . then 10 / 7 t = t + 24 10 t = 7 t + 168 3 t = 168 t = 56 . option e is correct"""
Explain the solution process for the given equation.,"product of two natural numbers is 5 . then , the sum of reciprocals of their squares is a ) 290 / 289 , b ) 26 / 25 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these","""explanation : if the numbers are a , b , then ab = 5 , as 17 is a prime number , so a = 1 , b = 5 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 5 ( 2 ) = 26 / 25 option b"""
Break down and solve the equation step by step.,"a = 5 ^ 15 - 125 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ? a ) none , b ) one , c ) two , d ) three , e ) four","""this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get none different values and answer is a . . . ."""
Provide a detailed solution to the given mathematical problem.,"find value for x from below equation ? x + 1 = 2 a ) - 5 , b ) 1 , c ) 4 , d ) 3 , e ) 2","""1 . subtract 1 from both sides : x + 1 - 1 = 2 - 1 2 . simplify both sides : x = 1 b"""
Explain the solution process for the given equation.,"a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 54 . find the number of notes of rs . 50 denomination . a ) 15 , b ) 21 , c ) 37 , d ) 19 , e ) 21","""total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 54 - x now , 50 * x + 500 * ( 54 - x ) = 10350 50 x + 27000 - 500 x = 10350 - 450 x = - 16650 x = 37 . no . of 50 rupees note = 37 . answer : option c"""
"Work through the equation methodically, ensuring clarity at each step.","a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 10 per sq m ? a ) 6350 , b ) 7357 , c ) 6328 , d ) 6750 , e ) 7560","""area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 10 = rs . 6750 answer : d"""
"Solve the problem systematically, showing each step clearly.","how many 3 digit number contain number 4 ? a ) 352 , b ) 268 , c ) 236 , d ) 252 , e ) 354","""total 3 digit no . = 9 * 10 * 10 = 900 not containing 4 = 8 * 9 * 9 = 648 total 3 digit number contain 4 = 900 - 648 = 252 answer : d"""
"Solve the problem systematically, showing each step clearly.","how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 140 m in length ? a ) 16.5 , b ) 16.0 , c ) 15 , d ) 16.8 , e ) 16.1","""d = 110 + 140 = 250 m s = 60 * 5 / 18 = 50 / 3 t = 250 * 3 / 50 = 15 sec answer : c"""
Break down and solve the equation step by step.,"sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 200 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 4 of the days were hot , then what was the price of 1 cup on a hot day ? a ) $ 1.56 , b ) $ 1.88 , c ) $ 2.25 , d ) $ 2.50 , e ) $ 3.25","""6 regular days - - > sales = 6 * 32 * x = 192 x ; 4 hot days - - > sales = 4 * 32 * ( 1.25 x ) = 160 x ; total sales = 192 x + 160 x = 352 x . total cost = 10 * 32 * 0.75 = 240 . profit = 352 x - 240 = 200 - - > x = 1.25 . 1.25 x = ~ 1.56 . answer : a ."""
Break down and solve the equation step by step.,"find the surface area of a 10 cm * 4 cm * 3 cm brick . ['a ) 154 cm square','b ) 156 cm square','c ) 160 cm square','d ) 164 cm square','e ) none of these']","explanation : surface area of a cuboid = 2 ( lb + bh + hl ) cm square so , surface area of a brick = 2 ( 10 * 4 + 4 * 3 + 3 * 10 ) cm square = 2 ( 82 ) cm square = 164 cm square option d"
Provide a detailed solution to the given mathematical problem.,"a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 27 km / hr in the same direction . in how much time will the train pass the jogger ? a ) 76 sec , b ) 72 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec","""speed of train relative to jogger = 27 - 9 = 18 km / hr . = 18 * 5 / 18 = 5 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 5 = 72 sec . answer : b"""
"Work through the equation methodically, ensuring clarity at each step.","how many positive integers less than 5,000 are evenly divisible by neither 15 nor 23 ? a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349","""integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 23 5000 / 23 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 23 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 23 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4521 answer c ."""
"Solve the problem systematically, showing each step clearly.","a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2430 ? a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920","""2430 * 1 / 3 = 810 option b"""
Provide a detailed solution to the given mathematical problem.,"amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.5 km ? a ) 375 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m","""a 375 m distance covered by amar = 18 / 4.8 ( 1.5 km ) = 3 / 8 ( 1500 ) = 375 m"""
Explain the solution process for the given equation.,"find the perimetri of trapezium with sides 4 , 6,12 and distance between two parallel side is 3 . ['a ) 27','b ) 26','c ) 28','d ) 25','e ) 24']",1 / 2 * ( 6 + 12 ) * 3 = 27 answer : a
Explain the solution process for the given equation.,"in a classroom , the average age of boys ( b ) is g and the average age of girls ( g ) is b . the average age of all is b + g . at the time of calculation , the class teacher , who is 42 years old was also present in the class . can you find the value of b + g ? a ) 8 , b ) 3 , c ) 7 , d ) 9 , e ) 10","a b + g = 8 for b in range ( 199 ) : for g in range ( 199 ) : sum 1 = 2 * b * g + 42 sum 2 = ( b + g ) * ( b + g + 1 ) if ( sum 1 = = sum 2 ) : print ( b , g , sum 1 ) ( b , g ) = ( 35 ) = > b + g = 8"
Explain the solution process for the given equation.,"80 is increased by 50 % . find the final number . a ) 100 , b ) 110 , c ) 120 , d ) 30 , e ) 160","""final number = initial number + 50 % ( original number ) = 80 + 50 % ( 80 ) = 80 + 40 = 120 . answer c"""
Provide a detailed solution to the given mathematical problem.,"real - estate salesman z is selling a house at a 30 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 30 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 30 percent discount . salesman y' s final price is what fraction of salesman x' s final price ? a ) 12 / 13 , b ) 11 / 15 , c ) 11 / 17 , d ) 11 / 14 , e ) 11 / 7","""let the retail price be = x selling price of z = 0.70 x selling price of x = 0.70 * 0.80 x = 0.56 x selling price of y = ( ( 0.70 x + 0.56 x ) / 2 ) * 0.70 = 0.63 x * 0.70 = 0.44 x 0.44 x = k * 0.56 x k = 0.44 / 0.56 = 44 / 56 = 11 / 14 answer : d"""
Explain the solution process for the given equation.,"what is the smallest integer n for which 25 ^ n > 5 ^ 12 ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10","""to solve , we want to get the bases the same . thus we need to break 25 ^ n into prime factors . 25 ^ n = ( 5 ^ 2 ) ^ n = 5 ^ ( 2 n ) ( remember that when we have a power to a power , we multiply the exponents . ) we can use the new value in the given inequality : 5 ^ ( 2 n ) > 5 ^ 12 since we have the same bases on either side of the inequality we can drop the bases and set up an equation involving just the exponents . 2 n > 12 n > 6 because n is greater than 6 , the smallest integer that satisfies the inequality 25 ^ n > 5 ^ 12 is 7 . the answer is b ."""
Provide a detailed solution to the given mathematical problem.,"how many squares are there between 2011 to 2300 ? ? ? ? ['a ) 3','b ) 4','c ) 5','d ) 6','e ) 7']","nos . are 2025 , 2116 , 2209 answers is 3 answer : a"
Explain the solution process for the given equation.,"a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 2 a rupee . find his net profit or loss percent ? a ) 100 % , b ) 200 % , c ) 250 % , d ) 300 % , e ) 50 %","""the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3 he selling at 2 a rupee , his sp = 4 profit = sp - cp = 4 - 2 = 2 profit percent = 2 / 2 * 100 = 100 % answer : a"""
Break down and solve the equation step by step.,"3 * 14 + 3 * 15 + 3 * 18 + 11 = ? a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 152","""3 * 14 + 3 * 15 + 3 * 18 + 11 = 42 + 45 + 54 + 11 = 152 the answer is e ."""
Break down and solve the equation step by step.,"a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 9 brown mice in the experiment , how many mice in total are in the experiment ? a ) 39 , b ) 33 , c ) 27 , d ) 21 , e ) 10","""let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 9 = > m = 27 answer c"""
"Work through the equation methodically, ensuring clarity at each step.","the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 507 sq meters , then what is the width ( in meters ) of the rectangular plot ? a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15","""area = l * w = 3 w ^ 2 = 507 w ^ 2 = 169 w = 13 the answer is c ."""
Explain the solution process for the given equation.,"how many times in a day the hands of a clock are straight ? a ) 21 , b ) 27 , c ) 24 , d ) 22 , e ) 25","""in 12 hours , the hands coincide or are in oppesite direction 22 times . in 24 hours , they are at right angles 22 times . answer is d ."""
Explain the solution process for the given equation.,"s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is a ) 198 , b ) 297 , c ) 320 , d ) 402 , e ) 405","last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is first term = 68 ; total terms = 64 ; difference = 4 68 + ( 63 ) 4 = 320 ans c"
Break down and solve the equation step by step.,"price of a book increases 15 % successively ( 2 times ) what is the new price of the book more compared to that of the old price : a ) 32.25 % , b ) 23.34 % , c ) 36 % , d ) 39 % , e ) 29 %",new price is 1.15 * 1.15 * old price = 1.3225 * old price increase in price = 0.3225 * old price % increase = 100 * 0.3225 * old price / old price = 32.25 % answer : a
"Solve the problem systematically, showing each step clearly.","a can do a piece of work in 8 days . b can do it in 12 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ? a ) 87 days , b ) 20 days , c ) 16 days , d ) 24 days , e ) 36 days","""c = 1 / 4 - 1 / 8 - 1 / 12 = 1 / 24 = > 24 days answer : d"""
Provide a detailed solution to the given mathematical problem.,"a shipment of 250 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ? a . b . c . d . e . a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3",probability of choosing one defective phone from a lot of 250 which ontains 84 defective phones is = ( 84 / 250 ) probability of choosing one defective phone from a lot of 249 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 249 ) combined probability of series of events = product of the probabilities = ( 84 / 250 ) * ( 83 / 249 ) 84 / 250 is close to ( 1 / 3 ) and ( 83 / 249 ) = ( 1 / 3 ) so answer is ( 1 / 3 ) * ( 1 / 3 ) = ( 1 / 9 ) answer : d
Break down and solve the equation step by step.,"how many three digit numbers n are divisible by 78 or 91 ? a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22","""the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b"""
"Work through the equation methodically, ensuring clarity at each step.","if 50 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ? a ) 560 , b ) 540 , c ) 520 , d ) 440 , e ) 500","we know 50 % people study biology , therefore the no of people not studying = 100 - 50 = 50 % > therefore the people not studying biology out of a total 880 people are = 50 % of 880 > ( 50 / 100 ) * 880 = 440 people d"
Explain the solution process for the given equation.,"an ant walks an average of 500 meters in 60 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ? a ) 1.0 , b ) 0.5 , c ) 0.75 , d ) 0.425 , e ) 0.3","""the ant walks an average of 500 meters in 60 minutes 500 meters in 1 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 60 minutes 0.425 km in 1 hours speed = 0.425 * 1 = 0.425 km / h i guess option d should be 0.425"""
Provide a detailed solution to the given mathematical problem.,"12 times a positive integer is more than its square by 36 , then the positive integer is a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 14","""explanation : let the number be x . then , 12 x = x 2 + 36 = > x 2 - 12 x + 36 = 0 = > ( x - 6 ) ( x - 6 ) = 0 = > x = 6 answer : a"""
Break down and solve the equation step by step.,"sides of a rectangular park are in the ratio 4 : 3 and its area is 3750 sq m , the cost of fencing it at 50 ps per meter is ? a ) s . 132.3 , b ) s . 129 , c ) s . 125 , d ) s . 120 , e ) s . 121","""4 x * 3 x = 3750 = > x = 17.7 2 ( 82.3 + 50 ) = 264.6 m 264.6 * 1 / 2 = rs . 132.3 answer : a"""
"Solve the problem systematically, showing each step clearly.","a and b together have $ 1210 . if of a' s amount is equal to of b' s amount , what is the ratio between a and b ? a ) 2 : 3 , b ) 3 : 2 , c ) 4 : 5 , d ) 5 : 3 , e ) can not be determined","""( 4 / 15 ) a = ( 2 / 5 ) b a = ( ( 2 / 15 ) * ( 15 / 4 ) ) b a = ( 3 / 2 ) b a / b = 3 / 2 a : b = 3 : 2 option b"""
Explain the solution process for the given equation.,"find the least number which when divided by 38 and 3 leaves a remainder of 1 in each case . a ) 107 , b ) 109 , c ) 111 , d ) 113 , e ) 115","""the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 38 , 3 ) + 1 = 115 . answer : e"""
Break down and solve the equation step by step.,"a is half good a work man as b and together they finish a job in 18 days . in how many days working alone b finish the job ? a ) 23 , b ) 22 , c ) 27 , d ) 36 , e ) 48","""c 27 wc = 1 : 2 2 x + x = 1 / 18 = > x = 1 / 54 2 x = 1 / 27 = > 27 days"""
"Work through the equation methodically, ensuring clarity at each step.","if the selling price of 100 articles is equal to the cost price of 40 articles , then the loss or gain percent is : a ) 25 % , b ) 40 % , c ) 60 % , d ) 65 % , e ) 50 %","let c . p . of each article be re . 1 . then , c . p . of 100 articles = rs . 100 ; s . p . of 100 articles = rs . 40 . loss % = 60 / 100 * 100 = 60 % answer : c"
Provide a detailed solution to the given mathematical problem.,"what is the sum of all possible 3 - digit numbers that can be constructed using the digits 1 , 2 , and 4 if each digit can be used only once in each number ? a ) 1210 , b ) 1221 , c ) 1332 , d ) 1443 , e ) 1554","there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 111 ) + 2 ( 222 ) + 2 ( 444 ) = 1554 the answer is e ."
Break down and solve the equation step by step.,"the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 47 . what is a possible value for the mean of the distribution ? a ) 46 , b ) 54 , c ) 48 , d ) 49 , e ) 50",the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 47 : { mean } - 3 * { sd } > 47 ; { mean } - 6 > 47 ; { mean } > 53 . answer : b .
Explain the solution process for the given equation.,"mahesh can do a piece of work in 40 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ? a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 60","""work done by mahesh in 60 days = 20 * 1 / 40 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 2 = 60 days answer is e"""
Break down and solve the equation step by step.,"a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 12 km ? a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 6","""m = 4 s = 2 us = 4 - 2 = 2 d = 12 t = 12 / 2 = 6 answer : e"""
Break down and solve the equation step by step.,"a rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ? a ) 44 ft , b ) 88 ft , c ) 74 ft , d ) 11 ft , e ) 66 ft","""given that length and area , so we can find the breadth . length x breadth = area 40 x breadth = 680 breadth = 17 feet area to be fenced = 2 b + l = 2 ( 17 ) + 40 = 74 feet answer : c ) 74 ft"""
Explain the solution process for the given equation.,"the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1250 resolutions ? a ) 1277 m , b ) 1760 m , c ) 1278 m , d ) 1288 m , e ) 1378 v","""in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1250 resolutions . = 1250 * 2 * 22 / 7 * 22.4 = 176000 cm = 1760 m answer : b"""
Provide a detailed solution to the given mathematical problem.,"the percentage increase in the area of rectangle , if each of its side is increased by 10 % is ? a ) 21 % , b ) 30 % , c ) 25 % , d ) 40 % , e ) 50 %","""let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 110 x / 100 new breadth = 110 y / 100 = 11 y / 10 new area = 11 x / 10 * 11 y / 10 = 121 xy / 100 m ^ 2 increase percent = 21 xy / 100 * 1 / xy * 100 = 21 % answer is a"""
Explain the solution process for the given equation.,"what is the probability of getting exactly 2 heads in a single throw of five fair coins ? a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 11 / 32","""one possible case is hhttt . p ( hhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 2 = 10 possible cases . p ( 2 heads ) = 10 * 1 / 32 = 5 / 16 the answer is d ."""
Provide a detailed solution to the given mathematical problem.,"a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ? a ) 30 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .","""let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a"""
Provide a detailed solution to the given mathematical problem.,"the tax on a commodity is diminished by 19 % and its consumption increased by 15 % . the effect on revenue is ? a ) 2 % , b ) 8.85 % , c ) 5.85 % , d ) 6.85 % , e ) 1 %","""100 * 100 = 10000 81 * 115 = 9315 - - - - - - - - - - - 10000 - - - - - - - - - - - 685 100 - - - - - - - - - - - ? = > 6.85 % decrease answer : d"""
Explain the solution process for the given equation.,"sandy leaves her home and walks toward ed' s house . two hours later , ed leaves his home and walks toward sandy' s house . the distance between their homes is 52 kilometers , sandy' s walking speed is 6 km / h , and ed' s walking speed is 4 km / h . how many kilometers will sandy walk before she meets ed ? a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37","sandy walks 12 km in the first two hours so there are 40 km remaining . when ed starts walking , they complete a total of 10 km per hour . they will meet four hours after ed starts walking . since sandy walks for 6 hours , she walks 36 km . the answer is d ."
"Work through the equation methodically, ensuring clarity at each step.","60 % of a number is added to 120 , the result is the same number . find the number ? a ) 300 , b ) 288 , c ) 270 , d ) 129 , e ) 281","""( 60 / 100 ) * x + 120 = x 2 x = 600 x = 300 answer : a"""
Break down and solve the equation step by step.,"a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 6 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ? a ) 27 , b ) 22 , c ) 24 , d ) 26 , e ) 30","""total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : a"""
Provide a detailed solution to the given mathematical problem.,"a certain article of clothing was discounted during a special sale to 2 / 5 of its original retail price . when the clothing did n' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ? a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 16.66 % , e ) 12.5 %","""say the original retail price of the item was $ 200 . the price after the first sale = 3 / 5 * $ 200 = $ 120 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 120 - 100 ) / 120 = 1 / 3 = 16.66 % . answer : d ."""
"Work through the equation methodically, ensuring clarity at each step.","divide $ 1000 among a , b in the ratio 1 : 4 . how many $ that b get ? a ) $ 500 , b ) $ 800 , c ) $ 1000 , d ) $ 200 , e ) $ 750","""sum of ratio terms = 1 + 4 = 5 a = 1000 * 4 / 5 = $ 800 answer is b"""
Provide a detailed solution to the given mathematical problem.,"a person buys an article at $ 800 . at what price should he sell the article so as to make a profit of 12 % ? a ) 896 , b ) 890 , c ) 990 , d ) 789 , e ) 740","""a 896 cost price = $ 800 profit = 12 % of 800 = $ 96 selling price = cost price + profit = 800 + 96 = 896"""
Break down and solve the equation step by step.,"nicky and cristina are running a 300 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ? a ) 40 , b ) 50 , c ) 30 , d ) 60 , e ) 45","""the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . c"""
"Work through the equation methodically, ensuring clarity at each step.","a no . when divided by 125 gives a remainder 40 , what remainder will be obtainedby dividingthe same no . 15 ? a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14","""125 + 40 = 165 / 15 = 11 ( remainder ) b"""
"Work through the equation methodically, ensuring clarity at each step.","in a renowned city , the average birth rate is 8 people every two seconds and the death rate is 6 people every two seconds . estimate the size of the population net increase that occurs in one day . a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 86,400 , e ) 259,200","""every 2 seconds , 2 persons are added ( 8 - 6 ) . every second 1 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option d"""
Explain the solution process for the given equation.,"at an election 2 candidates are participated a candidate got 45 % of votes and defeated by 9000 votes . 83 votes are invalid . find the total polled votes ? a ) 100000 , b ) 85236 , c ) 89562 , d ) 90083 , e ) 95842","""winners votes = 100 - 45 = 55 % invalid votes = 83 polled votes = [ ( 100 * 9000 ) / ( 2 * 55 - 100 ) ] + 83 = 90083 answer is d"""
Provide a detailed solution to the given mathematical problem.,"a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent q of the distribution is less than m + d ? a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %","""d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , q = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d ."""
"Solve the problem systematically, showing each step clearly.","the average of 45 results is 10 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ? a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 560","""23 th result = sum of 45 results - sum of 44 results 10 * 45 - 15 * 22 + 20 * 22 = 450 - 330 + 440 = 560 answer is e"""
Break down and solve the equation step by step.,"income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 18000 , then find his savings ? a ) rs . 3600 , b ) rs . 3629 , c ) rs . 3279 , d ) rs . 3629 , e ) rs . 3283","""let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 18000 = > x = 3600 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3600 . answer : a"""
"Solve the problem systematically, showing each step clearly.","a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 5 feet . how many feet does the squirrel travels if the post is 25 feet tall and 3 feet in circumference ? ['a ) 10 feet','b ) 12 feet','c ) 13 feet','d ) 15 feet','e ) 18 feet']",total circuit = 25 / 5 = 5 total feet squirrel travels = 5 * 3 = 15 feet answer : d
Provide a detailed solution to the given mathematical problem.,"the present worth of rs . 242 due in 2 years at 10 % per annum compound interest is : a ) rs . 200 , b ) rs . 250 , c ) rs . 240 , d ) rs . 220 , e ) rs . 230","""explanation : present worth of rs . x due t years hence is given by present worth ( pw ) = x / ( 1 + r / 100 ) t present worth ( pw ) = 242 / ( 1 + 10 / 100 ) 2 = 242 / ( 11 / 10 ) 2 = rs . 200 answer : option a"""
Break down and solve the equation step by step.,"what is the sum of the multiples of 3 from 33 to 60 , inclusive ? a ) 465 , b ) 470 , c ) 452 , d ) 450 , e ) 460","""the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 60 / 3 ) - ( 33 / 3 ) + 1 multiply these together so what we show average * total numbers = sum ( 33 + 60 ) / 2 * ( 60 / 3 ) - ( 33 / 3 ) + 1 = sum 93 / 2 * 10 = 465 a"""
"Solve the problem systematically, showing each step clearly.","a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 190 . find the original price of petrol ? a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 4.2","""price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 190 / 45 = $ 4.2 answer : e ."""
Break down and solve the equation step by step.,"what is the difference between the largest number and the least number written with the digits 9 , 3 , 5 , 7 ? a ) 6084 , b ) 3788 , c ) 2077 , d ) 2721 , e ) 6174","""explanation : 3579 9753 - - - - - - - - - - - - 6174 answer : e"""
Break down and solve the equation step by step.,"if 3 x = 9 y = z , what is x + y , in terms of z ? a ) z / 2 , b ) 2 z , c ) z / 3 , d ) 3 z / 5 , e ) 4 z / 9","""3 x = 9 y = z x = z / 3 and y = z / 9 x + y = z / 3 + z / 9 = 4 z / 9 answer is e"""
Provide a detailed solution to the given mathematical problem.,"of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents z watch all of the shows ? a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21","oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is z = 3.5 % of 600 , is 21 . d is the correct answer"
"Work through the equation methodically, ensuring clarity at each step.","amar takes as much time in running 12 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.6 km ? a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m","""d 400 m distance covered by amar = 12 / 4.8 ( 1.6 km ) = 2.5 ( 1600 ) = 400 m answer is d"""
Provide a detailed solution to the given mathematical problem.,"the distance from city a to city b is 180 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 60 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ? a ) 42 , b ) 44 , c ) 46 , d ) 36 , e ) 50","""the time it takes cara to drive to city b is 180 / 30 = 6 hours . dan needs to take less than 5 hours for the trip . dan needs to exceed a constant speed of 180 / 5 = 36 miles per hour . the answer is d ."""
Explain the solution process for the given equation.,"at a special sale , 9 tickets can be purchased for the price of 6 tickets . if 9 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 9 tickets ? a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %","""let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 9 tickets cost 900 9 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 300 , % of 9 tickets = ( 300 / 900 ) * 100 = 33.3 % answer : b"""
Break down and solve the equation step by step.,"if grapes are 92 % water and raisins are 20 % water , then how many kilograms did a quantity of raisins , which currently weighs 5 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . ) a ) 50 , b ) 54 , c ) 55 , d ) 56 , e ) 60","""let x be the original weight . the weight of the grape pulp was 0.08 x . since the grape pulp is 80 % of the raisins , 0.08 x = 0.8 ( 5 ) . then x = 50 kg . the answer is a ."""
"Work through the equation methodically, ensuring clarity at each step.","the weights of 3 bags are in the ratio 4 : 5 : 6 . if the sum of the weights of the heaviest and the lightest bag is 45 kg more than the weight of the third bag , what is the weight of the lightest bag ? a ) 45 kg , b ) 38 kg , c ) 66 kg , d ) 36 kg , e ) of these","let the weights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 45 = > 5 k = 45 = > k = 9 therefore the weight of the lightest boy = 4 k = 4 ( 9 ) = 36 kg . answer : d"
Provide a detailed solution to the given mathematical problem.,"3 photographers , lisa , mike and norm , take photos of a wedding . the total of lisa and mikes photos is 60 less than the sum of mike' s and norms . if norms photos number 10 more than twice the number of lisa' s photos , then how many photos did norm take ? a ) 40 , b ) 50 , c ) 60 , d ) 110 , e ) 80",l + m = m + n - 60 / n = 2 l + 10 60 = m + n - l - m 60 = n - l 60 = 2 l + 10 - l 50 = l 2 ( 50 ) + 10 = 110 d
"Solve the problem systematically, showing each step clearly.","three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution q in the liquid in the tank after 3 minutes ? a ) 5 / 8 , b ) 6 / 8 , c ) 4 / 8 , d ) 2 / 8 , e ) 3 / 8","""part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by b in 3 minutes = 3 / 20 required ratio = 3 / 20 * 15 / 6 = 3 / 8 answer : e"""
"Solve the problem systematically, showing each step clearly.","in a group of 100 people , 55 have visited iceland and 43 have visited norway . if 61 people have visited both iceland and norway , how many people have visited neither country ? a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64","""this is an example of a standard overlapping sets question . it has no' twists' to it , so you' ll likely find using the overlapping sets formula to be a fairly easy approach . if you' re not familiar with it , then here is the formula : 100 = 55 + 43 - 61 + ( # in neither group ) = 63 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"""
Break down and solve the equation step by step.,"a 240 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ? a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m","""relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 240 ) / 9 = 500 / 9 x + 240 = 500 x = 260 . c"""
"Solve the problem systematically, showing each step clearly.","if | x + 3 | = 15 , what is the sum of all the possible values of x ? a ) - 16 , b ) - 12 , c ) - 8 , d ) - 3 , e ) 11","""there will be two cases x + 3 = 15 or x + 3 = - 15 = > x = 12 or x = - 18 sum of both the values will be - 18 + 15 = - 3 answer : d"""
Provide a detailed solution to the given mathematical problem.,"the cash difference between the selling prices of an book at a profit of 8 % and 16 % is $ 3 . the ratio of the two selling prices is : a ) 55 : 23 , b ) 52 : 33 , c ) 52 : 53 , d ) 27 : 29 , e ) 51 : 34","""let c . p . of the book be $ x . then , required ratio = 108 % of x / 116 % of x = 108 / 116 = 27 / 29 = 27 : 29 d"""
Explain the solution process for the given equation.,"each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 4 of the slips are the drawn , without replacement , what is the probability that all 4 have a odd number written on it ? a ) 1 / 12 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 42 , e ) 5 / 9","""key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 = 1 / 42 d"""
Provide a detailed solution to the given mathematical problem.,"find the greatest number which on dividing 1428 and 2206 , leaves a reminder of 9 and 13 respectively a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 141","""explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1428 - 9 ) and ( 2206 - 13 ) = hcf ( 1419 , 2193 ) = 129 option c"""
"Solve the problem systematically, showing each step clearly.","the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 33 , what is the perimeter of the garden in feet ? a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44","""let x be the length of one side of the square garden . x ^ 2 = 8 x + 33 x ^ 2 - 8 x - 33 = 0 ( x - 11 ) ( x + 3 ) = 0 x = 11 , - 3 p = 4 ( 11 ) = 44 the answer is e ."""
"Work through the equation methodically, ensuring clarity at each step.","vijay sells a cupboard at 12 % below cost price . had he got rs . 1650 more , he would have made a profit of 12 % . what is the cost price of the cupboard ? a ) 7450 , b ) 14900 , c ) 7400 , d ) 6875 , e ) none of these","""explanation : cost price = 1650 / ( 0.12 + 0.12 ) = 2086 / 0.24 = rs . 6875 answer d"""
"Work through the equation methodically, ensuring clarity at each step.","how many positive integers less than 350 are there such that they are multiples of 17 or multiples of 18 ? a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40","""350 / 17 = 20 ( plus remainder ) so there are 20 multiples of 17 350 / 18 = 19 ( plus remainder ) so there are 19 multiples of 18 we need to subtract 1 because 17 * 18 is a multiple of both so it was counted twice . the total is 20 + 19 - 1 = 38 the answer is c ."""
Explain the solution process for the given equation.,"which greatest possible length can be used to measure exactly 15 meter 75 cm , 11 meter 25 cm and 7 meter 65 cm a ) 45 cm , b ) 255 cm , c ) 244 cm , d ) 55 cm , e ) 280 cm","""explanation : convert first all terms into cm . i . e . 1575 cm , 1125 cm , 765 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 255 . option b"""
Break down and solve the equation step by step.,"a 8 % stock yields 20 % . the market value of the stock is : a ) rs 48 , b ) rs 45 , c ) rs 40 , d ) rs 50 , e ) rs 55","""explanation : for an income of rs . 20 , investment = rs . 100 . for an income of rs 8 , investment = rs . 100 / 20 x 8 = rs 40 market value of rs . 100 stock = rs 40 answer is c"""
"Work through the equation methodically, ensuring clarity at each step.","when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 5 , the remainder is 5 . how many values less than 100 can n take ? a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5","""a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 0 . . a"""
Provide a detailed solution to the given mathematical problem.,"a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 80 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ? a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 76.6","""many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover this distance at regular speed is 45 + 2 = 47 seconds = 47 / 3,600 hours = 5 / 383 hours ; so , we get that to cover 1 kilometer 1 / ( 5 / 383 ) hours is needed - - > regular speed 76.6 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e"""
Provide a detailed solution to the given mathematical problem.,"a light has a rating of 110 watts , it is replaced with a new light that has 30 % higher wattage . how many watts does the new light have ? a ) 143 , b ) 145 , c ) 156 , d ) 134 , e ) 100","""final number = initial number + 30 % ( original number ) = 110 + 30 % ( 110 ) = 110 + 33 = 143 . answer a"""
"Work through the equation methodically, ensuring clarity at each step.","3 persons invested rs . 9000 in a joint business . the second person invested rs . 1000 more than the first and the third rs . 1000 more than second . after two years , they gained rs . 1800 . how much third person will get ? a ) 400 , b ) 800 , c ) 600 , d ) 1200 , e ) 1000",first persons investment = x second persons investment = x + 1000 third persons investments = x + 2000 x + x + 1000 + x + 2000 = 9000 3 x = 6000 x = 2000 ratio = 2000 : 3000 : 4000 2 : 3 : 4 4 / 9 * 1800 = 800 answer : b
"Work through the equation methodically, ensuring clarity at each step.","there is a 5 % chance that tigers will not win at all during the whole season . there is a 5 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ? a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 95 %","""there is a 5 % chance that tigers will not win at all during the whole season we can infer that there is 95 % chance tigers will win . similarly there is a 5 % chance that federer will not play at all in the whole season we can also infer that there is 95 % chance that federer will play . answer e"""
"Work through the equation methodically, ensuring clarity at each step.","youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 12 minutes more to walk to work than to ride his bike to work , then x equals ? a ) 4 , b ) 7 , c ) 10 , d ) 15 , e ) 18","""please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 720 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 7200 - - - - > 40 x = 720 - - > x = 18 . option e"""
Explain the solution process for the given equation.,"having scored 96 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ? a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24","""explanation : let the average score of the first 18 innings be n 18 n + 96 = 19 ( n + 4 ) = > n = 20 so , average score after 19 th innings = x + 4 = 24 . answer : e"""
Explain the solution process for the given equation.,"a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ? a ) 21 , b ) 28 , c ) 90 , d ) 100 , e ) 11","""explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 5 = rs . 100 . answer : d"""
Explain the solution process for the given equation.,"the maximum number of students among them 1230 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : a ) 91 , b ) 10 , c ) 1001 , d ) 1911 , e ) none of these","""explanation : required number of students = h . c . f of 1230 and 920 = 10 . answer : b"""
Break down and solve the equation step by step.,"to fill a tank , 42 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifths of its present ? a ) 102 , b ) 103 , c ) 104 , d ) 105 , e ) 106","""let the capacity of 1 bucket = x . then , the capacity of tank = 42 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 42 x ) / ( 2 x / 5 ) = ( 42 x ) x 5 / 2 x = 210 / 2 = 105 answer is d ."""
Provide a detailed solution to the given mathematical problem.,"the list price of an article is rs . 65 . a customer pays rs . 57.33 for it . he was given two successive discounts , one of them being 10 % . the other discount is ? a ) 8 % , b ) 7 % , c ) 10 % , d ) 12 % , e ) 2 %","""option e explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 57.33 x = 2 %"""
Explain the solution process for the given equation.,"in a division , a student took 42 as divisor instead of 36 . his answer was 24 . the correct answer is - a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38","""x / 42 = 24 . x = 24 * 42 . so correct answer would be , ( 24 * 42 ) / 36 = 38 . answer : e"""
"Solve the problem systematically, showing each step clearly.","when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.12510168 ? a ) 5 , b ) 6 , c ) 10 , d ) 3 , e ) 8","""for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 9 digits after decimal total no . of decimals = 11 req . no . of digits = ( n - 1 ) = ( 11 - 1 ) = 10 answer : c"""
Explain the solution process for the given equation.,"two numbers a and b are such that the sum of 5 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b . a ) 2 : 3 , b ) 1 : 1 , c ) 3 : 4 , d ) 4 : 3 , e ) 5 : 5","""5 / 100 a + 4 / 100 b = 2 / 3 ( 6 / 100 a + 8 / 100 b ) = > 1 / 20 a + 1 / 25 b = 1 / 25 a + 4 / 75 b = > ( 1 / 20 - 1 / 25 ) b = 1 / 25 a + 4 / 75 b ( 1 / 20 - 1 / 25 ) a = ( 4 / 75 - 1 / 25 ) b 1 / 100 a = 1 / 75 b a / b = 100 / 75 = 4 / 3 req ratio = 4 : 3 answer d"""
"Solve the problem systematically, showing each step clearly.","if an object travels at three feet per second , how many feet does it travel in one hour ? a ) 3488 , b ) 10800 , c ) 12788 , d ) 1800 , e ) 2881","explanation : if an object travels at 2 feet per second it covers 3 x 60 feet in one minute , and 3 x 60 x 60 feet in one hour . answer = 10800 answer : b ) 10800"