Bluel0la/Set_1 · Datasets at Hugging Face

Instruction stringclasses 5 values	Input stringlengths 43 704	response stringlengths 1 1.77k
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.

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"