Datasets:
Bluel0la
/
Set_1

Dataset card Data Studio Files
xet
Community
Instruction
stringclasses
5 values
Input
stringlengths
43
704
response
stringlengths
1
1.77k
Provide a detailed solution to the given mathematical problem.
find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 13 cm a) 178 cm 2 , b) 179 cm 2 , c) 285 cm 2 , d) 247 cm 2 , e) 197 cm 2
"area of a trapezium = 1 / 2 (sum of parallel sides) * (perpendicular distance between them) = 1 / 2 (20 + 18) * (13) = 247 cm 2 answer : d"
Work through the equation methodically, ensuring clarity at each step.
natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3 kilometers per hour , what was her average speed (in kilometers per hour) while climbing to the top ? a) 1.75 , b) 2.25 , c) 2.5 , d) 2.75 , e) 3.25
let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 3 km / hour x / 3 = 3 x = 9 km the average speed while climbing = distance / time = 9 / 4 = 2.25 km / h the answer is b .
Solve the problem systematically, showing each step clearly.
water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 135 grams of water ? a) 120 , b) 116 , c) 112 , d) 108 , e) 104
"(16 / 18) * 144 = 120 grams the answer is a ."
Explain the solution process for the given equation.
if 12 % of x is equal to 6 % of y , then 18 % of x will be equal to how much % of y ? a) 7 % , b) 9 % , c) 11 % , d) 12 % , e) none of these
we have , 12 % of x = 6 % of y = > 2 % of x = 1 % of y = > (2 x 9) % of x = (1 x 9) % of y thus , 18 % of x = 9 % of y . answer : b
Provide a detailed solution to the given mathematical problem.
if the numbers 1 to 100 are written on 100 pieces of paper , (one on each) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ? a) 1 / 50 , b) 1 / 25 , c) 1 / 100 , d) 1 , e) 2
"there are 25 primes , 74 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 100 . answer : c"
Provide a detailed solution to the given mathematical problem.
john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 8,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ? a) 10000 , b) 12000 , c) 16160.8 , d) 14000 , e) 15000
"a = p (1 + r / n) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x (1 + 0.02 / 2) ^ 2 - x = 8,000 (1 + 0.04 / 4) ^ 4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal) = > x [ (1.01) ^ 2 - 1 ] = 8,000 [ (1.01) ^ 4 - 1 ] = > x [ (1.01) ^ 2 - 1 ] = 8,000 [ (1.01) ^ 2 + 1 ] [ (1.01) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 8,000 (1.0201 + 1) = 16160.8 hence answer is c ."
Break down and solve the equation step by step.
a can do a job in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is ? a) 2 / 15 , b) 8 / 15 , c) 3 / 11 , d) 5 / 12 , e) 6 / 13
"a' s 1 day work = 1 / 15 b' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 5 days work = 7 / 60 * 5 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is d"
Provide a detailed solution to the given mathematical problem.
on the first day of her vacation , louisa traveled 240 miles . on the second day , traveling at the same average speed , she traveled 420 miles . if the 240 - mile trip took 3 hours less than the 420 - mile trip , what was the average speed , in miles per hour ? a) 65 , b) 50 , c) 55 , d) 60 , e) 58
"(time) * (rate) = (distance) - - > (rate) = (distance) / (time) - - > given : (rate) = 240 / t = 420 / (t + 3) - - > 4 / t = 7 / (t + 3) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > (rate) = 240 / 4 = 60 answer : d"
Explain the solution process for the given equation.
hillary and eddy are climbing to the summit of mt . everest from a base camp 5,100 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1100 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ? a) 14.0 , b) 9.0 , c) 10.0 , d) 11.0 , e) 12.0
"solution : h stopped 800 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance between them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . e"
Explain the solution process for the given equation.
a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 18 km / hr . what is the length of the platform ? a) 80 , b) 240 , c) 288 , d) 277 , e) 221
"speed = 18 * 5 / 18 = 5 m / sec . length of the train = 5 * 20 = 100 m . let the length of the platform be x m . then , (x + 100) / 36 = 5 = > x = 80 m . answer : a"
Work through the equation methodically, ensuring clarity at each step.
if 2 x = 4 y = z , what is x - y , in terms of z ? a) z / 4 , b) z / 2 , c) z , d) 2 z , e) 4 z
"2 x = 4 y = z i . e . x = z / 2 and y = z / 4 x - y = z / 2 - z / 4 = z / 4 answer : option a"
Provide a detailed solution to the given mathematical problem.
sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 8 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ? a) 11 / 30 , b) 29 / 60 , c) 17 / 24 , d) 19 / 30 , e) 11 / 15
let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 8 x = 7 / 8 x so if gold card balance is transferred then the rest unspent will be 7 / 8 x - x / 6 = 17 / 24 x so the ans is c
Explain the solution process for the given equation.
1396 x 1396 a) 1948816 , b) 1981709 , c) 18362619 , d) 2031719 , e) none of these
"1396 x 1396 = (1396) 2 = (1400 - 2) 2 = (1400) 2 + (4) 2 - (4 x 1400 x 4) = 1948816 . answer : option a"
Work through the equation methodically, ensuring clarity at each step.
at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 11 charts have been brought to the meeting , how many people are present ? a) 6 , b) 7 , c) 8 , d) 9 , e) 10
"say there are' a' associate professors . so we have 2 a pencils and a charts . say there are' b' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 21 so a + b = 7 total number of people = 7 answer : b"
Provide a detailed solution to the given mathematical problem.
five 6 faced dice are thrown together . the probability that all the three show the same number on them is ? a) 1 / 32 , b) 1 / 1296 , c) 1 / 33 , d) 1 / 38 , e) 1 / 34
the three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways . hence the probability is 6 / 7776 = 1 / 1296 answer : b
Work through the equation methodically, ensuring clarity at each step.
each factor of 210 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 40 ? a) 1 / 16 , b) 5 / 42 , c) 1 / 8 , d) 3 / 16 , e) 1 / 4
"210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is (1 + 1) (1 + 1) (1 + 1) (1 + 1) = 16 (see below) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 16 . answer : a"
Explain the solution process for the given equation.
a worker earns $ 24 on the first day and spends $ 18 on the second day . the worker earns $ 24 on the third day and spends $ 18 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 72 ? a) 9 , b) 12 , c) 17 , d) 21 , e) 24
"every two days , the net total is $ 6 . after 16 days , the worker will have $ 48 . on day 17 , the worker will receive $ 24 for a net total of $ 72 . the answer is c ."
Break down and solve the equation step by step.
in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each 100 m in length both trains running with a speed of 80 kmph ? a) 4.5 sec , b) 4.8 sec , c) 4.2 sec , d) 5.0 sec , e) 5.2 sec
d = 100 m + 100 m = 200 m * 1 / 1000 = 0.2 kms rs = 80 + 80 = 160 kmph t = (0.2 / 160) * 3600 = 4.5 sec answer : a
Explain the solution process for the given equation.
a cube has four of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ? a) 1 : 4 , b) 1 : 3 , c) 1 : 2 , d) 2 : 5 , e) 2 : 11
"let x be the area of each face of the cube . the area painted red is 4 (x / 2) = 2 x the area painted white is 4 (x / 2) + 2 x = 4 x the ratio of red to white is 2 x : 4 x which is 1 : 2 . the answer is c ."
Explain the solution process for the given equation.
the sum of two numbers is 528 and their h . c . f is 33 . the number of pairs of numbers satisfying the above conditions is : a) 4 , b) 5 , c) 6 , d) 6 , e) 1
"let the required numbers be 33 a and 33 b . then , 33 a + 33 b = 528 = > a + b = 16 . now , co - primes with sum 16 are (1 , 15) , (3 , 13) , (5 , 11) and (7 , 9) . required numbers are (33 * 1 , 33 * 15) , (33 * 3 , 33 * 13) , (33 * 5 , 33 * 11) , (33 * 7 , 33 * 9) . the number of such pairs is 4 . answer : a"
Explain the solution process for the given equation.
solve below question 4 x + 1 = 37 a) - 8 , b) - 9 , c) - 5 , d) 9 , e) 1
1 . subtract 1 from both sides : 4 x + 1 - 1 = 37 - 1 2 . simplify both sides : 4 x = 36 3 . divide both sides by 4 : 4 . simplify both sides : x = 9 d
Provide a detailed solution to the given mathematical problem.
among 400 students , 51 % study sociology , 46 % study mathematics and 40 % study biology . if 34 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ? a) 30 , b) 90 , c) 148 , d) 172 , e) 188
i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 136 using your analysis : we see that the total number of students who study either maths or sociology = 184 + 204 - 136 = 252 so , in the image we know that the number of students in the zone with the black boundary = 252 let' s assume the number of students who studyonlybiology to beb (this is the number that we have to maximize) and , let' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 252 + b + w = 400 or , b + w = 400 - 252 = 148 that is , b = 148 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 148 c
Provide a detailed solution to the given mathematical problem.
wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 3 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? a) 1 / 20 , b) 3 / 40 , c) 13 / 40 , d) 3 / 20 , e) 13 / 22
"p (1 and not 2) = 3 / 8 * (1 - 3 / 5) = 14 / 40 = 3 / 20 . answer : d ."
Break down and solve the equation step by step.
if the cost price of 50 articles is equal to the selling price of 25 articles , then the gain or loss percent is ? a) 16 , b) 127 , c) 12 , d) 18 , e) 100
"percentage of profit = 25 / 25 * 100 = 100 % answer : e"
Explain the solution process for the given equation.
the difference between the ages of two persons is 20 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ? a) 30 , b) 35 , c) 25 , d) 28 , e) 32
let their ages be x years and (x + 20) years then , (x + 20) - 15 = 2 (x - 15) x + 5 = 2 x - 30 x = 35 answer is b
Explain the solution process for the given equation.
how many different pairs of numbers (s , t) such that s = 3 t can be obtained if s and t are selected from the set of number { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } a) 1 , b) 2 , c) 3 , d) 4 , e) 5
given s = 3 t t can take 0,1 , 2,3 , 4 and so s = 0,3 , 6,9 , 12 4 such pairs can be formed . answer e
Break down and solve the equation step by step.
what is the greatest value of x such that 4 ^ x is a factor of 21 ! ? a) 5 , b) 6 , c) 3 , d) 2 , e) 4
pretty simple , really . if m = 6 , then 4 m = 24 , which is 12 x 2 , both of which are included in 21 ! since 6 is the largest number here , its the answer . answer is b
Explain the solution process for the given equation.
there were two candidates in an election . winner candidate received 62 % of votes and won the election by 312 votes . find the number of votes casted to the winning candidate ? a) 806 , b) 744 , c) 912 , d) 1200 , e) 1400
"w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 312 62 % - - - - - - - - ? = > 806 answer : a"
Break down and solve the equation step by step.
a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 50 kmph . when and at what distance from mumbai do the two trains meet ? a) 276 , b) 271 , c) 200 , d) 278 , e) 268
"when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / (50 - 40) = 4 hours so , the two trains meet at 2 p . m . the two trains meet 4 * 50 = 200 km away from mumbai . answer : c"
Provide a detailed solution to the given mathematical problem.
225 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees a) 10 , b) 12 , c) 14 , d) 16 , e) 17
"26 trees have 25 gaps between them , required distance (225 / 25) = 10 a"
Explain the solution process for the given equation.
nitin ranks 15 th in a class of 47 students . what is rank from the last ? a) 33 , b) 38 , c) 32 , d) 28 , e) 19
"explanation : number students behind the nitin in rank = (47 - 15) = 32 nitin is 33 rd from the last answer : a) 33"
Work through the equation methodically, ensuring clarity at each step.
shop offered 25 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop' s original selling price ? a) 500 , b) 550 , c) 746 , d) 700 , e) 750
sp * (75 / 100) = 560 sp = 7.46 * 100 = > cp = 746 answer : c
Explain the solution process for the given equation.
8 x 5.4 - 0.6 x 10 / 1.2 = ? a) 30 , b) 45 , c) 50 , d) 31 , e) 21
"given expression = (43.2 - 6) / 1.2 = 37.2 / 1.2 = 31 answer is d ."
Provide a detailed solution to the given mathematical problem.
what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 7 a) 2 / 15 , b) 3 / 5 , c) 1 / 6 , d) 1 / 7 , e) none of these
explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 7 = . 71 so biggest is 4 / 5 and smallest is 2 / 3 their difference is 4 / 5 - 2 / 3 = 2 / 15 option a
Provide a detailed solution to the given mathematical problem.
if x > 0 , x / 50 + x / 5 is what percent of x ? a) 6 % , b) 25 % , c) 37 1 / 2 % , d) 60 % , e) 75 %
"just plug and chug . since the question asks for percents , pick 100 . (but any number will do .) 100 / 50 + 100 / 5 = 2 + 20 = 25 25 is 25 % of 100 = b"
Provide a detailed solution to the given mathematical problem.
the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling alongthe boundary ofthe park at the speed of 12 km / hr completes one round in 8 min , then the area of the park (in sq . m) is ? a) 13400 m , b) 147600 m , c) 153600 m , d) 187500 m , e) 196700 m
"perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 (3 x + 2 x) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = (480 x 320) m 2 = 153600 m c"
Solve the problem systematically, showing each step clearly.
paul has to secure 50 % marks to clear his exam of class 7 th . he got 50 marks and failed by 10 marks . what is the maximum marks ? a) 100 , b) 110 , c) 120 , d) 210 , e) 200
c 120 to pass the exam ravish needs 50 + 10 = 60 marks . = > (60 / 50) * 100 = 120
Solve the problem systematically, showing each step clearly.
calculate the area of a triangle , if the sides are 13 cm , 12 cm and 5 cm , what is its area ? ['a) 36 cm 2','b) 35 cm 2','c) 30 cm 2','d) 32 cm 2','e) 31 cm 2']
the triangle with sides 13 cm , 12 cm and 5 cm is right angled , where the hypotenuse is 13 cm . area of the triangle = 1 / 2 * 12 * 5 = 30 cm 2 answer : c
Solve the problem systematically, showing each step clearly.
two whales are moving in the same direction at 18 mps and 15 mps . the faster whale crosses the slow whale in 15 seconds . what is the length of the slower whale in meters ? a) 45 m , b) 56 m , c) 39 m , d) 33 m , e) 62 m
relative speed = (18 - 15) = 3 mps . distance covered in 15 sec = 15 * 3 = 45 m . the length of the faster train = 45 m . answer : a
Solve the problem systematically, showing each step clearly.
if a certain number is divided by 2 , the quotient , dividend , and divisor , added together , will amount to 62 . what is the number ? a) 18 , b) 28 , c) 40 , d) 38 , e) 59
"let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c"
Provide a detailed solution to the given mathematical problem.
a train running at the speed of 180 km / hr crosses a pole in 9 seconds . find the length of the train . a) 150 meter , b) 286 meter , c) 186 meter , d) 288 meter , e) 450 meter
"speed = 180 * (5 / 18) m / sec = 50 m / sec length of train (distance) = speed * time (50) * 9 = 450 meter answer : e"
Work through the equation methodically, ensuring clarity at each step.
potato chips are on sale , buy 2 get 1 free . there are only 9 bags of chips left (4 plain and 5 bbq) . a shopper randomly grabs 3 bags . what is the probability the shopper will grab exactly 3 bags of bbq chips ? a) 2 / 3 , b) 1 / 3 , c) 1 / 5 , d) 5 / 42 , e) 7 / 42
combination probability formula : ncr = n ! / [ r ! (n - r) ! ] total possible , select 3 bags from 9 bags = 9 c 3 = 9 ! / [ 3 ! (9 - 3) ! ] = 84 . to have 3 bbq there must be 0 plain , select 0 plain from 4 = 4 c 0 = 1 . and , select 3 bbq from 5 = 5 c 3 = 10 . 3 bbq and 0 plain = (1) (10) = 10 probability = (number outcomes favorable) / (total number outcomes) = 10 / 84 = 5 / 42 answer : d
Break down and solve the equation step by step.
how many even integers n , such that 20 < = n < = 220 are of the form 3 k + 4 , where k is any natural number ? a) 28 , b) 31 , c) 34 , d) 37 , e) 40
"the first number is 22 = 16 + 6 (1) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 220 = 16 + 6 (34) there are 34 numbers in the list . the answer is c ."
Break down and solve the equation step by step.
a person' s present age is two - fifth of the age of his mother . after 6 years , he will be one - half of the age of his mother . how old is the mother at present ? a) a) 25 , b) b) 40 , c) c) 32 , d) d) 45 , e) e) 30
"let the mother' s present age be x years then the person' s present age = 2 x / 5 (2 x / 5) + 6 = 1 / 2 (x + 6) 2 (2 x + 30) = 5 (x + 6) x = 30 answer is e"
Break down and solve the equation step by step.
the proportion of water to alcohol in solution a is 5 : 4 and the proportion of water to alcohol in solution b is 6 : 5 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ? a) 40.9 % , b) 41.9 % , c) 42.9 % , d) 43.9 % , e) 44.9 %
"let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : (4 / 9) (v / 2) + (5 / 11) (v / 2) = 2 v / 9 + 5 v / 22 = 89 v / 198 . the concentration of alcohol is 89 / 198 = 44.9 % the answer is e ."
Explain the solution process for the given equation.
find the average of all the numbers between 6 and 29 which are divisible by 5 ? a) 17 , b) 20 , c) 25 , d) 30 , e) 15
average = (10 + 15 + 20 + 25) 4 = 70 / 4 = 17 answer is a
Solve the problem systematically, showing each step clearly.
the cost price of a radio is rs . 1860 and it was sold for rs . 1340 , find the loss % ? a) 18 % , b) 12 % , c) 22 % , d) 27 % , e) 21
"1860 - - - - 520 100 - - - - ? = > 27 % answer : d"
Explain the solution process for the given equation.
if the cost price of 81 chocolates is equal to the selling price of 45 chocolates , the gain percent is : a) 80 % , b) 85 % , c) 82 % , d) 70 % , e) 75 %
"explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 45 chocolates = rs . 45 ; s . p . of 45 chocolates = rs . 81 . .' . gain % = 36 * 100 / 45 = 80 % answer : a"
Break down and solve the equation step by step.
what is the difference between the place values of two 1' s in the numeral 135.21 a) 99.999 , b) 100.2 , c) 134 , d) 99.99 , e) 99.9
required difference = 100 - 0.01 = 99.99 answer is d
Solve the problem systematically, showing each step clearly.
a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 9 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ? a) 3 , b) 4 , c) 18 / 5 , d) 9 , e) 12
"yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 9 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a (rate of machine r) = 1 / 36 r _ s (rate of machine s) = 1 / 9 lets say x machines are used to attain the desired rate , thus x / 36 + x / 9 = 1 / 2 (desired r = 1 / 2 i . e . to complete the job in 2 hours) (x + 4 x) / 36 = 1 / 2 5 x / 36 = 1 / 2 x = 18 / 5 . qa = 18 / 5 (answer c)"
Break down and solve the equation step by step.
i remember during the school days , the teacher asked the class ` ` can you tell me the sum of the first 50 odd numbers ? ` ` . i ran quickly to the teacher and told her ` ` the answer is 2500'' . the teacher replied ` ` lucky guess'' . she then asked me ` ` can you tell me the sum of first 75 odd numbers ? ` ` . i wait for approx 10 seconds and replied with the correct answer . how can i answer so quickly and whats the correct answer ? a) 5624 , b) 5625 , c) 5626 , d) 5627 , e) none
solution : 5625 n ^ 1 75 * 75 = 5625 (sum of first 75 odd numbers) . 50 * 50 = 2500 (sum of first 50 odd numbers) . answer b
Explain the solution process for the given equation.
the sum of the first 92 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? a) 5,050 , b) 7,500 , c) 10,500 , d) 11,700 , e) 19,600
"101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 92 * 100 + (1 + 3 + 5 + 7 + . . . . . .) sum of 1 st 100 natural numbers = (100 * 101) / 2 = 5050 sum of 1 st 92 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 92 * 100 + (1 + 3 + 5 + 7 + . . . . . .) = 9200 + 2500 = 11700 d is the answer ."
Provide a detailed solution to the given mathematical problem.
a train 250 m long is running at a speed of 58 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ? a) 5 sec , b) 9 sec , c) 12 sec , d) 18 sec , e) 15 sec
"answer : d . speed of the train relative to man = (58 - 8) kmph = (50 * 5 / 18) m / sec = (125 / 9) m / sec time taken by the train to cross the man = time taken by it to cover 250 m at 125 / 9 m / sec = 250 * 9 / 125 sec = 18 sec"
Solve the problem systematically, showing each step clearly.
in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 107800 . how many times did he participate in the competition ? a) 4 , b) 5 , c) 6 , d) 7 , e) 8
"107800 = 2 * 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 8 times . the answer is e ."
Break down and solve the equation step by step.
what is the compound interest paid on a sum of rs . 4500 for the period of 2 years at 10 % per annum . a) 945 , b) 620 , c) 610 , d) 600 , e) none of these
"solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 4500 = 4500 * (21 / 100) = 945 answer a"
Solve the problem systematically, showing each step clearly.
in a class of 30 students , 5 students did not borrow any books from the library , 12 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average (arithmetic mean) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ? a) 5 , b) 8 , c) 15 , d) 18 , e) 20
the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 32 - 12 = 20 books . answer : e .
Break down and solve the equation step by step.
calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 20 % and its breadth is decreased by 5 % ? ['a) 14 percent increase','b) 5 percent increase','c) 24 percent increase','d) 13 percent increase','e) 11 percent increase']
let l and b be 100 each 100 * 100 = 10000 l increase by 20 % = 120 b decrease by 5 % = 95 120 * 95 = 11400 14 percent increase answer : a
Work through the equation methodically, ensuring clarity at each step.
if x , y , and z are positive integers , and 4 x = 5 y = 8 z , then the least possible value of x + y + z is a) 15 , b) 23 , c) 37 , d) 42 , e) 60
"take lcm of 4,5 and 8 = 40 now 4 x = 40 = > x = 10 5 y = 40 = > y = 8 8 z = 40 = > z = 5 10 + 8 + 5 = 23 . option b ."
Provide a detailed solution to the given mathematical problem.
lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 20 more photos than claire . how many photos has claire taken ? a) 6 , b) 8 , c) 10 , d) 12 , e) 14
"l = r l = 3 c r = c + 20 3 c = c + 20 c = 10 the answer is c ."
Provide a detailed solution to the given mathematical problem.
in a group of buffaloes and ducks , the number of legs are 24 more than twice the number of heads . what is the number of buffaloes in the group ? a) 12 , b) 13 , c) 14 , d) 15 , e) 16
let no . of buffaloes be x & no . of ducks be y buffaloes have 4 legs while ducks have 2 4 x + 2 y = 2 * (x + y) + 24 = > 4 x + 2 y - 2 x - 2 y = 24 = > x = 12 number of buffaloes in the group = 12 answer : a
Solve the problem systematically, showing each step clearly.
a firm is comprised of partners and associates in a ratio of 2 : 63 . if 35 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ? a) 12 , b) 14 , c) 16 , d) 18 , e) 20
"the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 7 of the increase in 35 associates . the ratio changed from 14 : 441 to 14 : 476 . thus the number of partners is 14 . the answer is b ."
Explain the solution process for the given equation.
a dishonest dealer professes to sell goods at the cost price but uses a weight of 780 grams per kg , what is his percent ? a) 28 % , b) 25 % , c) 55 % , d) 28 % , e) 28.2 %
"780 - - - 220 100 - - - ? = > 28.2 % answer : e"
Break down and solve the equation step by step.
a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ? a) 180 , b) 270 , c) 360 , d) 500 , e) 550
"12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 870 = 270 answer b"
Provide a detailed solution to the given mathematical problem.
a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9 . in all papers together , the candidate obtained 60 % of the total marks . then the number of papers in which he got more than 50 % marks is a) 2 , b) 3 , c) 4 , d) 5 , e) 1
here we can assume that one subject is of 100 marks so total there are 5 subjects = > 100 * 5 = 500 . now according to the question he secured 60 % of those which is 60 % of 500 = 300 marks in total . the ratio between the marks is given as 5 : 6 : 7 : 8 : 9 , so now we can distribute 300 marks according to the ratio . total ratio = 35 for 6 : (300 / 35) * 6 = 51.4 similarly , we will get for others as 60 , 68.57 , 77.14 hence , there are 5 subject where he secured more that 50 % . the answer is 5 . d
Solve the problem systematically, showing each step clearly.
two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 10 seconds . the length of the faster train is a) 225 m , b) 100 m , c) 120 m , d) 180 m , e) none
"solution relative speed = (36 + 45) km / hr = (81 x 5 / 18) m / sec = (45 / 2) m / sec length of the train = (45 / 2 x 10) m = 225 m . answer a"
Work through the equation methodically, ensuring clarity at each step.
a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 80 inches . find b . ['a) 8','b) 16','c) 24','d) 32','e) 48']
from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 (= 2 ^ 2 * 3) andbis 4 (= 2 ^ 2) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 (2 ^ 2 * 3) andbis 80 (2 ^ 4 * 5) , sob = 2 ^ 4 or 2 ^ 4 * 5 (16 or 80) . combining 2 premises shows the answer is b (16) .
Explain the solution process for the given equation.
find the number of factors of 180 that are in the form (4 * k + 2) , where k is a non - negative integer ? a) 1 , b) 2 , c) 3 , d) 4 , e) 6
make sure to follow posting guidelines (link in my signatures) . title of the thread must mention the first few words of the question itself . as for the question , the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number) . number of factors of 180 (= 2 ^ 2 * 3 ^ 2 * 5) = 18 . so listing the factors gives us : 1 , 180 2 , 90 3 , 60 4 , 45 5 , 36 6 , 30 9 , 20 10 , 18 12 , 15 as the question asks us about the factors of the form 4 k + 2 - - - > eliminate all odd factors . you are now left with 24 , 610 , 1218 , 2030 , 3660 , 90180 for the form 4 k + 2 , the first few values are 2 , 6 , 10 , 14 , 18 , 22 , 26 , 30 . . . already giving you 5 factors (= 2 , 610 , 1830) . you can stop here and mark 6 (6 th one = 90) as the correct answer as 5 is not given . for checking any particular factor whether they conform to the form 4 k + 2 - - - > do the following 4 k + 2 = 36 - - - > 4 k = 34 - - > this will not give you an integer value for k - - - > reject . proceed with others until you find all the values asked . e is thus the correct answer .
Break down and solve the equation step by step.
company x provides bottled water to its employees in 1 liter bottles , $ 2 each . at least how many 1 l bottles must company x buy monthly , so that new contract with $ 50 fixed monthly rate and $ 1 for 10 l bottle each paid off ? (assume that no other costs apply) a) 28 , b) 29 , c) 30 , d) 31 , e) 27
let the no . of 1 liter bottles be x , so the no . of 10 l bottles will be x / 10 (to equate the vol .) since the total cost will be equal , 2 x = 50 + x / 10 so x = 26.31 or 27 . answer is (e) .
Solve the problem systematically, showing each step clearly.
the average age of a group of persons going for picnic is years . fifteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is a) 5 , b) 10 , c) 15 , d) 40 , e) 50
solution let the initial number of persons be x . then 16 x + 15 x 15 = 15.5 (x + 20) = 0.5 x = 7.5 x = 15 . answer c
Work through the equation methodically, ensuring clarity at each step.
when 100 is divided by positive integer x , the remainder is 3 . what is the remainder when 197 is divided by x ? a) 2 , b) 3 , c) 4 , d) 6 , e) 8
if 100 / x leaves a reminder 3 then (100 - 3) i . e . 97 is divisible by x so (100 + 97) / x leaves a reminder rem (100 / x) + rem (97 / x) = > 3 + 0 = 3 answer : b
Explain the solution process for the given equation.
in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates (0 , 7.5) , (8 , 0) , (0 , - 7.5) , (- 8 , 0) ? a) 56 , b) 88 , c) 112 , d) 116 , e) 120
"ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 7.5 + 7.5 = 15 area = 1 / 2 * 16 * 15 = 120 e is the answer"
Break down and solve the equation step by step.
a chemical supply company has 60 liters of a 30 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ? a) 12 , b) 15 , c) 20 , d) 24 , e) 30
60 liters of a 30 % hno 3 solution means hno 3 = 18 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 18 + x = 50 % of (60 + x) or x = 24 . hence , d
Solve the problem systematically, showing each step clearly.
60 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ? a) 80 litres , b) 90 litres , c) 120 litres , d) 170 litres , e) none of these
explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 60 = 80 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 80 = 120 litres . answer c
Break down and solve the equation step by step.
find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 18 per cubic meter ? ['a) 2998','b) 2799','c) 1782','d) 1485','e) 2780']
22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 18 = 1782 answer : c
Provide a detailed solution to the given mathematical problem.
the grade point average of one third of the classroom is 60 ; the grade point average of the rest is 66 . what is the grade point average of the whole class ? a) 55 , b) 56 , c) 64 , d) 65 , e) 66
"let n = total students in class total points for 1 / 3 class = 60 n / 3 = 20 n total points for 2 / 3 class = 66 * 2 n / 3 = 44 n total points for whole class = 20 n + 44 n = 64 n 64 n total class points / n total students = 64 grade point average for total class answer : c"
Solve the problem systematically, showing each step clearly.
(x) + 3612 + 16125 - 6149 = 90189 . calculate the value of x a) 76601 , b) 76600 , c) 76655 , d) 76313 , e) 76723
"x + 3612 + 16125 - 6149 = 90189 = x + 3612 + 16125 = 90189 + 6149 = x + 19737 = 96338 = x = 96338 - 19737 = 76601 answer is a"
Work through the equation methodically, ensuring clarity at each step.
suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 112 runs thereby increasing his average by 6 runs . what is his average after the 17 th innings ? a) 18 , b) 25 , c) 16 , d) 72 , e) 27
"to improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings . thus , the average after the 17 th innings = 112 - 96 = 16 . answer : c"
Provide a detailed solution to the given mathematical problem.
a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 10 pounds of the body weight , by what percent was the prescribed dosage lesser than the typical dosage ? a) 8 % , b) - 37.5 % , c) 11 % , d) 12.5 % , e) 14.8 %
typical dosage per 10 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * (120 / 10) = 2 * 12 = 24 c . c dosage prescribed by doctor for 120 pound patient = 18 c . c % prescribed dosage greater than the typical dosage = (18 - 24 / 16) * 100 % = (- 6 / 16) * 100 % = - 37.5 % answer b
Work through the equation methodically, ensuring clarity at each step.
a reduction of 30 % in the price of oil enables a house wife to obtain 3 kgs more for rs . 700 , what is the reduced price for kg ? a) 70 , b) 50 , c) 60 , d) 80 , e) 65
"700 * (30 / 100) = 210 - - - - 3 ? - - - - 1 = > rs . 70 answer : a"
Work through the equation methodically, ensuring clarity at each step.
in the xy - plane , the point (1 , 3) is the center of a circle . the point (- 2 , 3) lies inside the circle and the point (1 , - 2) lies outside the circle . if the radius r of the circle is an integer , then r = a) 6 , b) 5 , c) 4 , d) 3 , e) 2
"an easy way to solve this question will be just to mark the points on the coordinate plane . you' ll see that the distance between the center (1 , 3) and the point inside the circle (- 2 , 3) is 3 units (both points are on y = 3 line so the distance will simply be 1 - (- 2) = 3) so the radius must be more than 3 units . the distance between the center (1,3) and the point outside the circle (1 , - 2) is 5 units (both points are on x = 1 line so the distance will simply be 3 - (- 2) = 5) so the radius must be less than 5 units , which implies 3 < r < 5 , thus as r is an integer then r = 4 . answer : c ."
Provide a detailed solution to the given mathematical problem.
if it takes a tub 2 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ? a) 48 seconds , b) 1 minute , 12 seconds , c) 1 minute , 50 seconds , d) 2 minutes , 14 seconds , e) 4 minutes , 12 seconds
"if 5 / 7 of tub' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 2 minutes to drain 5 / 7 th of tub it takes 2 * (7 / 5) minutes to drain the entire tub and 2 * (7 / 5) * (2 / 7) min to drain 2 / 7 th of the tub which is 4 / 5 minutes or 48 minutes so answer is a"
Explain the solution process for the given equation.
the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 90 instead of 10 then find the correct average marks ? a) a) 78 , b) b) 82 , c) c) 92 , d) d) 91 , e) e) 85
"correct avg marks = 100 + (10 - 90) / 10 avg = 100 - 8 = 92 answer is c"
Work through the equation methodically, ensuring clarity at each step.
if (a + b) = 4 , (b + c) = 9 and (c + d) = 3 , what is the value of (a + d) ? a) 16 . , b) 8 . , c) 7 , d) 2 . , e) - 2
"given a + b = 4 = > a = 4 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 4 - b + 3 - c = > 7 - (b + c) = > 7 - 9 = - 2 . option e . . ."
Explain the solution process for the given equation.
a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 12 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ? a) 14 , b) 16 , c) 21 , d) 22 , e) 32
"i treat such problems as work ones . work = rate * time mileage (m) = rate (mpg) * gallons (g) x gallons is a full tank { 462 = rx { 336 = (r - 12) x solve for r , r = 44 44 - 12 = 32 mpg e"
Work through the equation methodically, ensuring clarity at each step.
on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 630 , the rate of interest being the same in both the cases . the rate of interest is ? a) 8 % , b) 10 % , c) 12 % , d) 14 % , e) 16 %
"difference in c . i . and s . i for 2 years = $ 630 - $ 600 = $ 30 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 30 rate = (100 * 30) / (300) = 10 % the answer is b ."
Explain the solution process for the given equation.
90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 20 % of the total school population of x students , what is x ? a) 125 , b) 150 , c) 212 , d) 250 , e) 500
90 = x / 100 * 20 / 100 * x = > x ^ 2 = 9 * 10000 / 2 = > x = 212 c
Provide a detailed solution to the given mathematical problem.
how many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 4 percent sugar solution ? a) 12.5 , b) 15.5 , c) 17.5 , d) 21.5 , e) 24.5
"let x be the amount that needs to be evaporated . 0.03 (50) = 0.04 (50 - x) 0.04 x = 2 - 1.5 x = 0.5 / 0.04 = 12.5 liters the answer is a ."
Work through the equation methodically, ensuring clarity at each step.
a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter e of liquid a was contained by the can initially ? a) 10 , b) 20 , c) 21 , d) 25 , e) 27
"as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = (712) * total and b = (5 / 12) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove (7 / 12) * 9 of a - - - > a remaining = 21 - (7 / 12) * 9 = 63 / 4 similarly , for b , you remove (5 / 12) * 9 - - - > b remaining = 15 - (5 / 12) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b (final ratio) = (45 / 4) / (81 / 4) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = (7 x - (7 / 12) * 9) / (5 x - (5 / 12) * 9 + 9) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = (7 x - (7 / 12) * 9) / (5 x - (5 / 12) * 9 + 9) - - - > giving you x = 3 . thus a (original) e = 7 * 3 = 21 . c"
Provide a detailed solution to the given mathematical problem.
the average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? a) 120 kg , b) 130 kg , c) 137 kg , d) 190 kg , e) none
"solution total weight increased = (10 x 7.2) kg = 72 kg . weight of new person = (65 + 72) kg = 137 kg . answer c"
Explain the solution process for the given equation.
a train speeds past a pole in 15 sec and a platform 130 m long in 25 sec , its length is ? a) 195 , b) 150 , c) 160 , d) 170 , e) 180
"let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 (x + 130) / 25 = x / 15 = > x = 195 m . answer : option a"
Provide a detailed solution to the given mathematical problem.
what least number must be subtracted from 427398 so that remaining no . is divisible by 11 a) 3 , b) 4 , c) 6 , d) 7 , e) 8
"explanation : on dividing 427398 by 11 we get the remainder 4 , so 4 should be subtracted answer : option b"
Work through the equation methodically, ensuring clarity at each step.
if each side of a square is increased by 25 % , find the percentage change in its area . a) 46.25 % , b) 56.25 % , c) 56 % , d) 50.25 % , e) 36.25 %
"let each side of the square be a . then , area = a 2 . new side = (125 a / 100) = (5 a / 4) . new area = (5 a / 4) 2 = (25 a 2) / 16 . increase in area = ((25 a 2) / 16) - a 2 = (9 a 2) / 16 . increase % = [ ((9 a 2) / 16) * (1 / a 2) * 100 ] % = 56.25 % . answer b 56.25 %"
Work through the equation methodically, ensuring clarity at each step.
carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 6 inches tall . how tall are the sculpture andbase together ? a) 3.1 feet , b) 3.2 feet , c) 3.3 feet , d) 3.4 feet , e) 3.5 feet
"we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 6 = 40 40 / 12 = 3.3 feet answer : c"
Break down and solve the equation step by step.
if you multiply all the numbers on your mobile phone , what is the answer ? a) 2 , b) 6 , c) 1 , d) 0 , e) 7
d 0 their is a zero in your phone .
Provide a detailed solution to the given mathematical problem.
rectangular tile each of size 20 cm by 30 cm must be laid horizontally on a rectangular floor of size 100 cm by 150 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is : a) 40 , b) 15 , c) 25 , d) 32 , e) 45
"area of tile = 20 * 30 = 600 area of floor = 100 * 150 = 15000 no of tiles = 15000 / 600 = 25 so , the no of tile = 25 answer : c"
Provide a detailed solution to the given mathematical problem.
how many paying stones , each measuring 3 * 2 m are required to pave a rectangular court yard 15 m long and 6 m board ? a) 99 , b) 18 , c) 26 , d) 15 , e) 12
"15 * 6 = 3 * 2 * x = > x = 15 answer : d"
Provide a detailed solution to the given mathematical problem.
if a : b = 4 : 7 and b : c = 5 : 9 , then a : c = ? a) 28 : 37 , b) 18 : 37 , c) 16 : 53 , d) 20 : 63 , e) 15 : 48
a / b = 4 / 7 and b / c = 5 / 9 a / b * b / c = 4 / 7 * 5 / 9 = 20 / 63 so a / c = 20 / 63 20 : 63 answer d
Work through the equation methodically, ensuring clarity at each step.
[ 1 / (1 . 2.3) ] + [ 1 / (2 . 3.4) ] + [ 1 / (3 . 4.5) ] + [ 1 / (4 . 5.6) ] is equal to a) 7 / 30 , b) 11 / 30 , c) 13 / 30 , d) 17 / 30 , e) none
answer given exp . = [ (4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3) ] / [ (2 x 3 x 4 x 5 x 6) ] = 168 / (24 x 30) = 7 / 30 correct option : a
Work through the equation methodically, ensuring clarity at each step.
a shopkeeper sold an article offering a discount of 5 % and earned a profit of 19.7 % . what would have been the percentage of profit earned if no discount was offered ? a) 60 % , b) 26 % , c) 30 % , d) 56 % , e) 73 %
"let c . p . be rs . 100 . then , s . p . = rs . 19.70 let marked price be rs . x . then , 95 / 100 x = 119.70 x = 11970 / 95 = rs . 126 now , s . p . = rs . 126 , c . p . = rs . 100 profit % = 26 % . answer : b"
Work through the equation methodically, ensuring clarity at each step.
a man buys an article for $ 110 . and sells it for $ 125 . find the gain percent ? a) 10 % , b) 13.6 % , c) 25 % , d) 20 % , e) 30 %
"c . p . = $ 110 s . p . = $ 125 gain = $ 15 gain % = 15 / 110 * 100 = 13.6 % answer is b"