Cheukting/mathqa huggingface dataset:
Question (physics): the distance between a & b is 600 km . a person is traveling from a to b at 70 km / hr started at 10 am and another person is traveling from b to a at 80 km / hr and started at same time . then at what time they meet together .
Options: a ) 2 pm , b ) 4 pm , c ) 1 pm , d ) 3 pm , e ) 5 pm
Rationale: let x hours be they will meet together distance covered by 1 st person + distance covered by 2 nd person = 600 km 70 x + 80 x = 600 x = 4 hr they will meet = 10 am + 4 hr = 2 pm answer is a
Answer: a
Question (physics): a train running at 1 / 4 of its own speed reached a place in 12 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 9 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "time taken if run its own speed = 1 / 4 * 12 = 3 hrs time saved = 12 - 3 = 9 hrs answer : a"
Answer: a
Question (general): when a merchant imported a certain item , he paid a 9 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 67.50 , what was the total value of the item ?
Options: a ) $ 1,150 , b ) $ 1,450 , c ) $ 1,750 , d ) $ 2,150 , e ) $ 2,450
Rationale: "let x be the value in excess of $ 1,000 . 0.09 x = 67.5 x = $ 750 the total value was $ 750 + $ 1,000 = $ 1,750 . the answer is c ."
Answer: c
Question (general): the average weight of a group of boys is 30 kg . after a boy of weight 37 kg joins the group , the average weight of the group goes up by 1.00001 kg . find the number of boys in the group originally ?
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 1
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 37 kg joins the group , total weight of boys = 30 x + 37 so 30 x + 37 = 31 ( x + 1 ) = > x = 6 . answer : c"
Answer: c
Question (general): of 55 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 49 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 55 thrower = 37 rest = 55 - 37 = 18 left handed = 18 / 3 = 6 right handed = 12 if all thrower are right handed then total right handed is 37 + 12 = 49 so a . 49 is the right answer"
Answer: a
Question (other): a person want to give his money of $ 900 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 400 , b ) $ 300 , c ) $ 500 , d ) $ 180 , e ) $ 200
Rationale: "b ' s share = 900 * 3 / 9 = $ 300 answer is b"
Answer: b
Question (physics): a can do a piece of work in 21 days and b in 28 days . together they started the work and b left after 4 days . in how many days can a alone do the remaining work ?
Options: a ) 22 , b ) 88 , c ) 27 , d ) 14 , e ) 99
Rationale: "let a worked for x days . x / 21 + 4 / 28 = 1 = > x / 21 = 6 / 7 = > x = 18 a worked for 18 days . so , a can complete the remaining work in 18 - 4 = 14 days . answer : d"
Answer: d
Question (general): if a and b are the two values of t that satisfy the equation t ^ 2 â € “ 12 t + 20 = 0 , with a > b , what is the value of a â € “ b ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: factor the left side of the equation : t ^ 2 â € “ 12 t + 20 = 0 ( t â € “ 2 ) ( t â € “ 10 ) = 0 t = 2 , t = 10 thus , a = 10 and b = 2 . so a â € “ b = 10 â € “ 2 = 8 . the answer is d .
Answer: d
Question (general): the average ( arithmetic mean ) of 4 different integers is 74 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 29 , d ) 30 , e ) 33
Rationale: "total of integers = 74 * 4 = 296 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 296 - ( 90 + 89 + 88 ) = 296 - 267 = 29 answer : c"
Answer: c
Question (general): how many numbers from 2 to 11 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 11 / 2 = 5 5 - 1 = 4 4 + 1 = 5 numbers . answer : c"
Answer: c
Question (other): if w is the set of all the integers between 35 and 64 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 18 , b ) 19 , c ) 61 , d ) 31 , e ) 11
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 63 , the smallest is 36 ) : 63 - 36 = 27 step 2 . divide by 3 : 27 / 3 = 9 step 3 . add 1 : 9 + 1 = 10 . so there are 10 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 64 , the smallest is 36 ) : 64 - 36 = 28 step 2 . divide by 2 : 28 / 2 = 14 step 3 . add 1 : 14 + 1 = 15 . so there are 15 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 10 multiples of 3 and the 15 multiples of 2 : 10 + 15 = 25 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 10 + 15 = 25 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 25 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 60 - 30 = 30 step 2 . divide by 6 : 30 / 6 = 5 step 3 . add 1 : 5 + 1 = 6 . so there are 6 multiples of 6 within the range : we counted 6 numbers twice . subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3 : = 10 + 15 - 6 = 25 - 6 = 19 therefore , the final number of multiples of 2 , 3 or 6 is 19 . hence , this is the correct answer . ( b )"
Answer: b
Question (general): 4 milkmen rented a pasture . a grazed 24 cows for 3 months ; b 10 for 5 months ; c 35 cows for 4 months and d 21 cows for 3 months . if a ' s share of rent is rs . 1440 , find the total rent of the field .
Options: a ) 6500 , b ) 3550 , c ) 4250 , d ) 2250 , e ) 3250
Rationale: ratio of shares of a , b , c , d = ( 24 x 3 ) : ( 10 x 5 ) : ( 35 x 4 ) : ( 21 x 3 ) = 72 : 50 : 140 : 63 . let total rent be rs . x . then , a ’ s share = rs . ( 72 x ) / 325 ( 72 x ) / 325 = 1440 = x = ( 1440 x 325 ) / 72 = 6500 hence , total rent of the field is rs . 6500 . answer is a .
Answer: a
Question (general): how many multiples of 4 are there between 12 and 108 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 3 up to 4 * 27 . 27 - 3 + 1 = 25 . the answer is e ."
Answer: e
Question (general): 123 : 36 : : 221 : ?
Options: a ) 52 , b ) 69 , c ) 72 , d ) 25 , e ) 32
Rationale: "( 1 + 2 + 3 ) ^ 2 = 36 ( 2 + 2 + 1 ) ^ 2 = 25 answer : d"
Answer: d
Question (gain): an inspector rejects 0.02 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 10000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 3100
Rationale: "let the number of meters to be examined be x then , 0.02 % of x = 2 ( 2 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 10000 answer is b"
Answer: b
Question (general): if a - b = 10 and a ^ 2 + b ^ 2 = 150 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 25 , d ) 18 , e ) 19
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 150 - 100 = 50 = > ab = 25 answer : c"
Answer: c
Question (physics): eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 900 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 4 / 1 , e ) 5 / 3
Rationale: "distance traveled by eddy = 900 km time taken by eddy = 3 hours average speed of eddy = 900 / 3 = 300 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 300 / 75 = 4 / 1 answer d"
Answer: d
Question (physics): if 40 honey bees make 40 grams of honey in 40 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 40 , d ) 49 , e ) 30
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 40 : : 40 : x honey 40 : 1 = > 1 x 40 x x = 40 x 1 x 40 = > x = 40 . answer : c"
Answer: c
Question (other): a dog takes 5 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 5 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 25 : 10 , b ) 25 : 8 , c ) 25 : 9 , d ) 8 : 25 , e ) 24 : 8
Rationale: "explanation : dog : hare = ( 5 * 5 ) leaps of hare : 8 leaps of hare = 25 : 8 answer : b"
Answer: b
Question (general): of the families in city x in 2001 , 25 percent owned a personal computer . the number of families in city x owning a computer in 2008 was 15 percent greater than it was in 2001 , and the total number of families in city x was 6 percent greater in 2008 than it was in 2001 . what percent of the families in city x owned a personal computer in 2008 ?
Options: a ) 27.12 % , b ) 23.12 % , c ) 25.55 % , d ) 31.22 % , e ) 56.22 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 25 number of families owning computer in 1998 = 25 * 115 / 100 = 28.75 number of families in 1998 = 106 the percentage = 28.75 / 106 * 100 = 27.12 % . answer : a"
Answer: a
Question (geometry): the mass of 1 cubic meter of a substance is 100 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "100 kg - 1 cubic meter ; 100,000 g - 1 cubic meter ; 100,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 100,000 = 10 / 1 = 10 cubic centimeters . answer : c ."
Answer: c
Question (physics): two pipes a and b can fill a tank in 12 and 24 minutes respectively . if both the pipes are used together , how long will it take to fill the tank ?
Options: a ) 9 min , b ) 8 min , c ) 4 min , d ) 6 min , e ) none of these
Rationale: "explanation : tank can be filled by pipe a in 12 minutes and pipe b in 24 minutes . = > part filled by a in 1 minute = 1 / 12 = > part filled by b in 1 minute = 1 / 24 = > part filled by both in 1 minute = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 time taken to fill the entire tank = 8 minutes answer b"
Answer: b
Question (general): what number is obtained by adding the units digits of 734 ^ 99 and 347 ^ 82 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "the units digit of 734 ^ 99 is 4 because 4 raised to the power of an odd integer ends in 4 . the units digit of 347 ^ 82 is 9 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 82 is in the form 4 n + 2 , the units digit is 9 . then 4 + 9 = 13 . the answer is d ."
Answer: d
Question (other): the ratio between the number of sheep and the number of horses at the stewar farm is 3 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 56 , e ) 58
Rationale: et no of sheep and horses are 3 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 3 * 8 ) = 24 answer : a
Answer: a
Question (physics): a pump can fill a tank with a water in 2 hours . because of a leak , it took 2 and 4 / 5 hours to fill the tank . the leak can drain all the water of the full tank in how many hours ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: the rate of the pump + leak = 5 / 14 1 / 2 - leak ' s rate = 5 / 14 leak ' s rate = 1 / 2 - 5 / 14 = 1 / 7 the leak will empty the tank in 7 hours . the answer is d .
Answer: d
Question (general): the sum of number of boys and girls in a school is 100 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 70
Rationale: "we have x + x % of 100 = 100 x + x / 100 * 100 = 100 2 * x = 100 x = 50 answer is a"
Answer: a
Question (physics): the food in a camp lasts for 20 men for 50 days . if 20 more men join , how many days will the food last ?
Options: a ) 22 days , b ) 25 days , c ) 28 days , d ) 16 days , e ) 27 days
Rationale: one man can consume the same food in 20 * 50 = 1000 days . 20 more men join , the total number of men = 40 the number of days the food will last = 1000 / 40 = 25 days . answer : b
Answer: b
Question (other): three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 264 . what is their h . c . f . ?
Options: a ) 18 , b ) 22 , c ) 24 , d ) 28 , e ) 32
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 264 x = 22 hcf of 2 x , 3 x and 4 x = x = 22 the answer is b ."
Answer: b
Question (general): in a class of students , 1 / 2 of the number of girls is equal to 1 / 3 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 3 / 4
Rationale: "( 1 / 2 ) g = ( 1 / 3 ) ( b + g ) 3 g = 2 b + 2 g g = 2 b b / g = 1 / 2 . the answer is a ."
Answer: a
Question (geometry): two circles are there one with arc area 60 digree equal to 45 digree of another circle find the area of circle 1 : circle 2 ratio
Options: a ) 3 : 4
b ) 1 : 4
c ) 1 : 2
d ) 2 : 3
e ) 1 : 3
Rationale: area for first circle = ( 3.14 * r ^ 2 ) / 6 area of second circke = ( 3.14 * r ^ 2 ) / 8 therefore , ratio = 3 : 4 answer : a
Answer: a
Question (general): in a recent head - to - head run - off election , 12,000 absentee ballets were cast . 1 / 6 of the absentee ballets were thrown out and 3 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 4,000 , d ) 8,000 , e ) 9,000
Rationale: 5 / 6 * 2 / 5 ( total absentee votes ) = 1 / 3 ( total votes ) = 1 / 3 * 12000 = 4000 answer is c
Answer: c
Question (physics): a train 300 m long can cross an electric pole in 30 sec and then find the speed of the train ?
Options: a ) 76 kmph , b ) 54 kmph , c ) 72 kmph , d ) 36 kmph , e ) 91 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 30 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : d"
Answer: d
Question (gain): at what rate percent of simple interest will a sum of money double itself in 66 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 1.51 % , d ) 1.94 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 66 ) = 100 / 66 = 1.51 % answer : c"
Answer: c
Question (general): an = 2 an - 1 + 4 and qn = 4 qn - 1 + 8 for all n > 1 . if a 5 = q 4 and a 7 = 316 , what is the first value of n for which qn is an integer ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: assuming i have understood the symbols used correctly answer is c - 3 a 7 = 2 s 6 + 4 = 316 a 6 = 312 / 2 = 156 = 2 a 5 + 4 a 5 = 152 / 2 = 76 = q 4 q 4 = 4 q 3 + 8 = 76 q 3 = 68 / 4 = 17 q 3 = 4 q 2 + 8 = 17 q 2 = 9 / 4 = 2.25 q 2 = 4 q 1 + 8 q 1 will not be integer = c
Answer: c
Question (physics): courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?
Options: a ) 22 , b ) 77 , c ) 877 , d ) 99 , e ) 88
Rationale: 3.78 meters = 378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters = 525 cm = 5 × 5 × 3 × 7 hence common factors are 3 and 7 hence lcm = 3 × 7 = 21 hence largest size of square tiles that can be paved exactly with square tiles is 77 cm . answer : b
Answer: b
Question (other): in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 160 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 452 , d ) 416 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 160 x = 32 total number of students = 13 x = 13 * 32 = 416 answer is d"
Answer: d
Question (general): x is a positive integer less than 500 . when x is divided by 5 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 5 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 500 n = 24.42 or n = 24 answer : - d"
Answer: d
Question (other): john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 4 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 45 , b ) 62 , c ) 70 , d ) 77 , e ) 98
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 4 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 4 x 60 ) = 15 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 15 x + 20 x + 15 x + 12 x ) = 62 x . for minimum number of pencils x = 1 . the person should have at least 62 pencils . b )"
Answer: b
Question (general): tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next 5 weeks be to increase his average weekly income to $ 500 over the 10 - week period ?
Options: a ) $ 570 , b ) $ 586 , c ) $ 630 , d ) $ 686 , e ) $ 715
Rationale: official solution : ( b ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 500 over 10 weeks , the salesman would need to earn : $ 500 × 10 = $ 5000 . subtract $ 2070 from $ 5000 to determine how much he would need to earn , in total , over the next 5 weeks to average $ 500 for the 10 weeks : $ 5000 – $ 2070 = $ 2930 . dividing $ 2930 by 5 will give us the amount he needs to earn on average over the next 5 weeks : $ 2930 / 5 = $ 586 . the correct answer is choice ( b ) .
Answer: b
Question (general): when a random experiment is conducted , the probability that event a occurs is 1 / 3 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 8 / 27 , b ) 10 / 31 , c ) 12 / 37 , d ) 14 / 41 , e ) 16 / 49
Rationale: "one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 = 4 / 81 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 4 / 81 ) = 8 / 27 the answer is a ."
Answer: a
Question (gain): if 16 % of 40 % of a number is 6 , then the number is
Options: a ) 200 , b ) 225 , c ) 93.75 , d ) 320 , e ) none of these
Rationale: explanation : let 16 / 100 × 40 / 100 × a = 6 a = 6 × 100 × 100 / 16 × 40 = 93.75 correct option : c
Answer: c
Question (general): one day a car rental agency rented 2 / 3 of its cars , including 3 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 18 / 25 , b ) 17 / 20 , c ) 11 / 15 , d ) 7 / 10 , e ) 3 / 5
Rationale: "the cars with cd players which were not rented is ( 2 / 5 ) ( 3 / 5 ) = 6 / 25 of all the cars . the cars which were not rented is 1 / 3 of all the cars . the percent of non - rented cars which had cd players is ( 6 / 25 ) / ( 1 / 3 ) = 18 / 25 the answer is a ."
Answer: a
Question (general): a certain number when divided by 39 leaves a remainder 19 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 4
Rationale: explanation : 39 + 19 = 58 / 13 = 6 ( remainder ) answer : d
Answer: d
Question (general): if the price of gasoline increases by 20 % and a driver intends to spend only 8 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.08 ( p * x ) y = ( 1.08 / 1.2 ) x = 0.9 x which is a reduction of 10 % . the answer is e ."
Answer: e
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ?
Options: a ) 70 kg , b ) 80 kg , c ) 85 kg , d ) 90 kg , e ) 95 kg
Rationale: "total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 50 + 20 ) kg = 70 kg . a )"
Answer: a
Question (physics): machine a can finish a job in 4 hours , machine в can finish the job in 2 hours , and machine с can finish the job in 6 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 4 / 3 , b ) 6 / 5 , c ) 8 / 7 , d ) 10 / 9 , e ) 12 / 11
Rationale: "the combined rate is 1 / 4 + 1 / 2 + 1 / 6 = 11 / 12 of the job per hour . the time to complete the job is 12 / 11 hours . the answer is e ."
Answer: e
Question (geometry): a cubical block of metal weighs 3 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 12
Rationale: "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 3 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 3 pounds = 24 pounds so answer is c and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 3 * 8 = 24 so answer is c"
Answer: c
Question (probability): two coins are tossed . find the probability of at most 2 tails ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 , e ) 3 / 4
Rationale: "n ( s ) = 2 ^ 2 = 4 . . . . ( 2 coins are tossed ) let e is the event of getting at most 2 tails n ( e ) = hh , tt , ht , th = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 4 = 1 ans - d"
Answer: d
Question (physics): a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 35 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 21 , b ) 28 , c ) 90 , d ) 26 , e ) 70
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 35 = rs . 70 . answer : e"
Answer: e
Question (physics): how many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 35 sec , c ) 25 sec , d ) 18 sec , e ) 17 sec
Rationale: "d = 200 + 150 = 350 s = 36 * 5 / 18 = 10 mps t = 350 / 10 = 35 sec answer : b"
Answer: b