Cheukting/mathqa huggingface dataset:
Question (general): zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 33.3 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) 74
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 33.3 kg zinc , mixture , melted = [ 20 / 9 x 33.3 ] kg = 74 kg . answer e"
Answer: e
Question (physics): a good train 800 metres long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 minute , then the length of the tunnel ( in meters ) is :
Options: a ) 600 , b ) 300 , c ) 400 , d ) 500 , e ) 200
Rationale: speed = 78 * 5 / 18 m / sec = = > 65 / 3 length of the tunnel be x then 800 + x / 60 = 65 / 3 3 ( 800 + x ) = 3900 x = 500 answer d
Answer: d
Question (gain): arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 25 % profit ?
Options: a ) 15.75 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 125 % of rs . 630 = 125 / 100 * 630 = rs . 787.5 s . p . per kg = 787.5 / 50 = 15.75 . answer : a"
Answer: a
Question (gain): find the c . i . on a sum of rs . 2000 for 6 months at 20 % per annum , interest being compounded quarterly ?
Options: a ) 205 , b ) 305 , c ) 3025 , d ) 5540 , e ) 315
Rationale: "c . i . = 2000 ( 21 / 20 ) ^ 2 - 1800 = 205 answer : a"
Answer: a
Question (general): ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio q of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio q of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: b
Question (general): of 30 applicants for a job , 12 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "d . 7 30 - 3 = 27 27 - 12 - 18 = - 7 then 7 are in the intersection between 4 years experience and degree . answer d"
Answer: d
Question (general): how many multiples of 5 are there between 10 and 100 , exclusive ?
Options: a ) 18 , b ) 17 , c ) 16 , d ) 15 , e ) 14
Rationale: "5 * 2 = 10 5 * 20 = 100 total multiples = ( 20 - 2 ) + 1 = 19 exclude 10 and 100 = 19 - 2 = 17 answer is b"
Answer: b
Question (physics): suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 25 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 10 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 25 = 10 hours answer d"
Answer: d
Question (general): find the sum of first 35 natural numbers
Options: a ) 470 , b ) 468 , c ) 630 , d ) 463 , e ) 520
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 35 ( 35 + 1 ) / 2 = 35 ( 36 ) / 2 = 630 answer : option c"
Answer: c
Question (general): a line that passes through ( – 1 , – 4 ) and ( 5 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 5 , d ) 2 , e ) 7 / 2
Rationale: slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 5 + 1 ) = > 6 k = k + 4 = > k = 4 / 5 ans c it is !
Answer: c
Question (general): total dinning bill for 8 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 30.33
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 8 = 30.33 answer : e"
Answer: e
Question (gain): how much 50 % of 56 is greater than 30 % of 50 ?
Options: a ) 18 , b ) 99 , c ) 13 , d ) 55 , e ) 71
Rationale: "( 50 / 100 ) * 56 – ( 30 / 100 ) * 50 28 - 15 = 13 answer : c"
Answer: c
Question (gain): a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 865 in 4 years . the sum is :
Options: a ) s . 665 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 720
Rationale: "s . i . for 1 year = rs . ( 865 - 815 ) = rs . 50 . s . i . for 3 years = rs . ( 50 x 3 ) = rs . 150 . principal = rs . ( 815 - 150 ) = rs . 665 . answer : option a"
Answer: a
Question (gain): a shopkeeper fixes the marked price of an item 32 % above its cost price . the percentage of discount allowed to gain 7 % is
Options: a ) 18.94 % , b ) 18.93 % , c ) 18.92 % , d ) 18.91 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 132 required gain = 7 % , so selling price = rs 107 discount = 132 - 107 = 25 discount % = ( 25 / 132 ) * 100 = 18.93 % option b"
Answer: b
Question (geometry): the diagonals of the two squares are in the ratio of 2 : 5 find the ratio of their area .
Options: a ) 5 : 89 , b ) 7 : 96 , c ) 4 : 25 , d ) 5 : 84 , e ) 8 : 96
Rationale: "let the diagonals of the square be 2 x and 5 x respectively . ratio of their areas = 1 / 2 ( 2 x ) ^ 2 : 1 / 2 ( 5 x ) = 4 x ^ 2 : 25 x ^ 2 = 4 : 25 answer ( c )"
Answer: c
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 36 hours respectively . the ratio of their speeds is ?
Options: a ) 6 : 5 , b ) 6 : 3 , c ) 4 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 36 : √ 9 = 6 : 3 answer : b"
Answer: b
Question (physics): carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 7 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 42 3 / 3 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 42 / 13 = 42 3 / 3 answer is c"
Answer: c
Question (physics): a can do a work in 15 days and b in 20 days . if they work on it together for 2 days , then the fraction of the work that is left is :
Options: a ) 23 / 20 , b ) 5 , c ) 23 / 30 , d ) 23 / 12 , e ) 2
Rationale: "ans is : c a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 2 day ' s work = ( 7 / 60 * 2 ) = 7 / 30 therefore , remaining work = ( 1 - 7 / 30 ) = 23 / 30 . ans : c"
Answer: c
Question (other): find the common factors of 15 and 18 .
Options: a ) 50 , b ) 55 , c ) 60 , d ) 70 , e ) 90
Rationale: first of all we need to find the prime factors of 15 and 18 15 = 5 x 3 18 = 3 x 3 x 2 lcm is the product of highest exponent of all the factors . lcm ( 15,18 ) = 5 x 3 ^ 2 x 2 = 90 answer : 90
Answer: e
Question (other): half of the workers in palabras bookstore have read the latest book by j . saramago , and 1 / 6 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 42 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 3 , b ) 12 , c ) 9 , d ) 8 , e ) 7
Rationale: there are total 42 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 21 have read saramago . 1 / 6 of the workers have read the latest book by h . kureishi . so ( 1 / 6 ) * 42 = 7 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 21 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 42 = 21 + 7 - b + ( 21 - b - 1 ) b = 3 answer ( a )
Answer: a
Question (physics): find the length of the wire required to go 13 times round a square field containing 24336 m 2 .
Options: a ) 15840 , b ) 3388 , c ) 2667 , d ) 8112 , e ) 66711
Rationale: "a 2 = 24336 = > a = 156 4 a = 624 624 * 13 = 8112 answer : d"
Answer: d
Question (general): the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 4 | + 3 is equal to :
Options: a ) – 7 , b ) 7 , c ) 20 , d ) 12 , e ) 14
Rationale: "x ^ 2 - 8 x + 18 = | x - 4 | rhs can be - ve or + ve x ^ 2 - 9 x + 22 = 0 x ^ 2 - 7 x + 14 = 0 x = 11 , 7,2 we test all 3 values in original equation , all ok . thus , sum = 11 + 7 + 2 = 20 ans ( c )"
Answer: c
Question (general): rs . 1430 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 528 , d ) s . 540 , e ) s . 660
Rationale: "a + b + c = 1430 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1430 = rs . 660 answer : e"
Answer: e
Question (gain): last year a worker saved 5 % of her annual salary . this year , she made 20 % more money than last year and she saved 6 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 136 % , b ) 140 % , c ) 144 % , d ) 148 % , e ) 152 %
Rationale: "let x be the worker ' s salary last year . last year , she saved 0.05 x . this year , she saved 0.06 ( 1.2 x ) = 0.072 x 0.072 x / 0.05 x = 144 % the answer is c ."
Answer: c
Question (physics): two trains 125 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.16 , c ) 7.12 , d ) 7.15 , e ) 7.2
Rationale: "t = ( 125 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.2 answer : e"
Answer: e
Question (general): in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 12 , − 8 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: "slope = rise / run = 11 / 22 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
Answer: a
Question (physics): a circular path of 20 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 25 p per m 2 ?
Options: a ) rs . 49 , b ) rs . 40 , c ) rs . 44 , d ) rs . 42 , e ) rs . 66
Rationale: "explanation : π ( 22 ^ 2 - 20 ^ 2 ) = 22 / 7 * ( 484 - 400 ) = 264 264 * 1 / 4 = rs . 66 answer : option e"
Answer: e
Question (physics): stacy has a 81 page history paper due in 3 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 27 , c ) 10 , d ) 8.5 , e ) 6
Rationale: "81 / 3 = 27 answer : b"
Answer: b
Question (geometry): the side of a square is increased by 20 % then how much % does its area increases ?
Options: a ) 44.00 % , b ) 45.25 % , c ) 48.75 % , d ) 50.00 % , e ) 40.00 %
Rationale: "a = 100 a 2 = 10000 a = 120 a 2 = 14400 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 4400 100 - - - - - - - ? = > 44.00 % answer : a"
Answer: a
Question (geometry): the area of a rectangular plot is 23 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 13 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 23 × b ∴ l = 23 m and l – b = 10 ∴ b = 23 – 10 = 13 m answer a"
Answer: a
Question (general): in a group of ducks and cows , the total number of legs are 12 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 4 , e ) 12
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 12 = > 2 x = 12 = > x = 6 a"
Answer: a
Question (other): there are 193 items that are members of set u . of these items , 47 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 94 , d ) 106 , e ) 108
Rationale: "you had the answer almost right . the x = 83 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 85 + set ab = 83 + 23 = 106 d"
Answer: d
Question (general): in a group of 800 people , 2 / 5 play at least one instrument , 96 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 7 / 25
Rationale: "p ( playing 2 or more instruments ) = 96 / 800 = 3 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 2 / 5 - 3 / 25 = 7 / 25 . answer e ."
Answer: e
Question (physics): a person can swim in still water at 16 km / h . if the speed of water 8 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 3 , b ) 1.5 , c ) 2.3 , d ) 1.8 , e ) 6
Rationale: "m = 16 s = 8 us = 16 - 8 = 8 d = 12 t = 12 / 8 = 1.5 answer : b"
Answer: b
Question (gain): the population of a town is 15000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 5120 , d ) 9600 , e ) 5366
Rationale: 15000 × 80 / 100 × 80 / 100 = 9600 answer : d
Answer: d
Question (gain): what will be the compound interest on a sum of rs . 40,000 after 3 years at the rate of 11 p . c . p . a . ?
Options: a ) rs . 14705.24 , b ) rs . 14602.25 , c ) rs . 14822.26 , d ) rs . 14322.10 , e ) rs . 15350.23
Rationale: explanation : amount after 3 years = p ( 1 + r / 100 ) t = 40000 ( 1 + 11 / 100 ) 3 = 40000 ( 111 / 100 ) 3 = 40000 × 111 × 111 × 111 / 100 × 100 × 100 = 4 × 111 × 111 × 111 / 100 = 54705.24 compound interest = 54705.24 - 40000 = rs . 14705.24 answer : option a
Answer: a
Question (physics): a train 640 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 22 kmph , b ) 77 kmph , c ) 144 kmph , d ) 71 kmph , e ) 88 kmph
Rationale: "s = 640 / 16 * 18 / 5 = 144 kmph answer : c"
Answer: c
Question (general): if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 76 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 18
Rationale: "3 j + 2 s = 69 2 j + 3 s = 76 - - - - - - - - - - - - - - - - 5 j + 5 s = 145 - - - - ( divide by 5 ) - - - > j + s = 29 3 j + 2 s = j + 2 ( j + s ) = j + 58 = 69 - - - > j = 11 3 * 11 + 2 s = 69 33 + 2 s = 69 2 s = 36 s = 18 answer : e"
Answer: e
Question (general): what is the least common multiple of 1227 and 40
Options: a ) 8521 , b ) 1080 , c ) 368 , d ) 8979 , e ) 6584
Rationale: factors of 12 = 2 * 2 * 3 factors of 27 = 3 * 3 * 3 factors of 40 = 2 * 2 * 2 * 5 thus the l . c . m is 2 ^ 3 * 3 ^ 3 * 5 = 1080 the answer is b
Answer: b
Question (general): in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 15 and 270 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 16 , e ) 5 and 14
Rationale: "given : 15 < x ( x + 1 ) < 270 . now , it ' s better to test the answer choices here rather than to solve : if x = 4 then x ( x + 1 ) = 20 > 15 - - > so , the least value is 4 . test for the largest value : if x = 16 then x ( x + 1 ) = 16 * 17 = 272 > 270 answer : d ."
Answer: d
Question (general): a total of 320 chocolates were distributed among 100 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates . find the respective number of boys and girls ?
Options: a ) 10,10 , b ) 30,40 , c ) 70 , 50 , d ) 20,20 , e ) 10,15
Rationale: "let the number of boys be x . number of girls is 100 - x . total number of chocolates received by boys and girls = 2 x + 3 ( 100 - x ) = 320 = > 300 - x = 320 = > x = 20 . so , the number of boys or girls is 20 . answer : d"
Answer: d
Question (physics): harry started a 7 - mile hike with a full 11 - cup canteen of water and finished the hike in 3 hours with 2 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 3 cups of water during the last mile , how many cups did he drink per mile during the first 6 miles of the hike ?
Options: a ) 2 / 6 , b ) 3 / 6 , c ) 4 / 6 , d ) 6 / 4 , e ) 5 / 6
Rationale: "no of cups leaked during the trip = 3 cups . no of cups harry drank = 6 cups . no of cups harry drank during the first 6 miles = 3 . drink / mile = 3 / 6 answer : b"
Answer: b
Question (general): there are 810 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 135 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 810 . hence , we have m + f = 810 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 810 / 3 = 270 solving the three equations yields the solution f = 270 , m = 540 , and d = 270 . the number of female democratic participants equals half the female participants equals 270 / 2 = 135 . answer : d"
Answer: d
Question (geometry): a square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely . if a side of the first square is 4 cm , determine the sum of the areas all the square .
Options: a ) 32 cm 2
b ) 16 cm 2
c ) 20 cm 2
d ) 64 cm 2
e ) none of these
Rationale: solution : side of the first square is 4 cm . side of second square = 2 √ 2 cm . side of third square = 2 cm . and so on . i . e . 4 , 2 √ , 2 , √ 2 , 1 . . . . . . thus , area of these square will be , = 16 , 8 , 4 , 2 , 1 , 1 / 2 . . . . . . . hence , sum of the area of first , second , third square . . . . . . = 16 + 8 + 4 + 2 + 1 + . . . . . = [ 16 / { 1 - ( 1 / 2 ) } ] = 32 cm 2 . answer : option a
Answer: a
Question (general): find the greatest number of 5 digits which is exactly divisible by 12 , 15 and 18 ?
Options: a ) a ) 13050 , b ) b ) 12960 , c ) c ) 10025 , d ) d ) 11080 , e ) e ) 12080
Rationale: the largest five digit numbers are 13050 , 12960,12080 13050 is not divisible by 12 12960 is divisible by 18 , 12 and 15 answer : b
Answer: b
Question (probability): kim has 4 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 8 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25
Rationale: "total pairs = 8 c 2 = 28 ; same color pairs = 4 c 1 * 1 c 1 = 4 ; prob = 1 / 7 ans a"
Answer: a
Question (geometry): the number 110 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 18 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "7 ^ 2 + 5 ^ 2 + 6 ^ 2 = 49 + 25 + 36 = 110 7 + 5 + 6 = 18 hence answer is a"
Answer: a
Question (general): in an examination , 20 % of total students failed in hindi , 70 % failed in english and 10 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 20 + 70 - 10 ) = 100 - 80 = 20 answer : b"
Answer: b
Question (general): the tax on a commodity is diminished by 25 % and its consumption increased by 13 % . the effect on revenue is ?
Options: a ) 18 , b ) 16 , c ) 10 , d ) 15 , e ) 14
Rationale: "100 * 100 = 10000 75 * 113 = 8475 - - - - - - - - - - - 10000 - - - - - - - - - - - 1525 100 - - - - - - - - - - - ? = > 15 % decrease answer : d"
Answer: d
Question (physics): the famous denali star train starts from anchorge & travels towards fair banksat speed 50 mph . after some time another train glacier discovery train ( at parallel track ) at fair banks and moves towards anchorge at a speed of 70 mph . both the trains denali star & glacier discovery have a length 1 / 6 miles each . after the trains meet how many seconds will faster train take to overtake the slower one ?
Options: a ) 10 sec , b ) 11 sec , c ) 12 sec , d ) 13 sec , e ) 14 sec
Rationale: total distance = ( 1 / 6 ) + ( 1 / 6 ) = 1 / 3 miles relative speed = ( 50 + 70 ) mph = 120 mph time taken = ( 1 / 3 ) / ( 120 ) hours = 10 seconds answer : a
Answer: a
Question (geometry): the area of a square is equal to twice the area of a rectangle of dimensions 32 cm * 64 cm . what is the perimeter of the square ?
Options: a ) 236
b ) 256
c ) 456
d ) 656
e ) 756
Rationale: area of the square = s * s = 2 ( 32 * 64 ) = > s = 64 cm perimeter of the square = 4 * 64 = 256 cm . answer : option b
Answer: b
Question (general): how many positive integers between 1 and 300 are there such that they are multiples of 21 ?
Options: a ) 14 , b ) 16 , c ) 17 , d ) 13 , e ) 15
Rationale: "multiples of 21 = 21 , 42,63 , - - - - - 294 number of multiples of 21 = > 21 * 14 = 294 answer is a"
Answer: a
Question (general): if p , q , and r are distinct positive digits and the product of the two - digit integers pq and pr is 221 , what is the sum of the digits p , q , and r ?
Options: a ) 5 , b ) 11 , c ) 13 , d ) 21 , e ) 23
Rationale: factor out 221 221 = 13 * 17 thus pq = 13 & pr = 17 or vice versa thus p = 1 , q = 3 & r = 7 sum = 1 + 3 + 7 = 11 answer : b
Answer: b
Question (gain): p and q invested in a business . the profit earned was divided in the ratio 3 : 4 . if p invested rs 50000 , the amount invested by q is
Options: a ) 30000 , b ) 66666 , c ) 40000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 50000 : q = 3 : 4 ⇒ 50000 × 4 = 3 q ⇒ q = ( 50000 × 4 ) / 3 = 66666 answer is b ."
Answer: b
Question (physics): the end of a blade on an airplane propeller is 20 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 240 π , c ) 600 π , d ) 480 π , e ) 1,200 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 20 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 π 20 / 5280 = 600 π c is the answer"
Answer: c
Question (physics): car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 10 : 4 , b ) 10 : 7 , c ) 13 : 7 , d ) 14 : 6 , e ) 13 : 9
Rationale: "sol . distance travelled by car a = 65 × 8 = 520 km distance travelled by car b = 70 × 4 = 280 km ratio = 520 / 280 = 13 : 7 c"
Answer: c