Cheukting/mathqa huggingface dataset:
Question (general): a lady has fine gloves and hats in her closet - 18 blue , 32 red , and 25 yellow . the lights are out and it is totally dark . in spite of darkness , she can make out the difference between a hat and a glove . she takes out an item out of the closet only if she is sure that it is a glove . how many gloves must she take out to make sure she has a pair of each color ?
Options: a ) 60 , b ) 65 , c ) 70 , d ) 75 , e ) 80
Rationale: "32 r + 24 y + 1 y + 1 b + 2 b = 60 answer : a"
Answer: a
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 40 percent on clothing , 30 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 3.6 % , c ) 4 % , d ) 5.2 % , e ) 6.0 %
Rationale: "let amount spent by jill = 100 clothing = 40 , food = 30 , others = 30 tax on clothing = 1.6 tax on others = 2.4 percentage = 4 / 100 = 4 % answer : c"
Answer: c
Question (general): a student chose a number , multiplied it by 5 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 48 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "solution : let xx be the number he chose , then 5 ⋅ x − 138 = 102 5 x = 240 x = 48 answer a"
Answer: a
Question (other): in a class , 30 students pass in english and 20 students in maths , while some students among these pass in both . how many students do only english as compared to those doing only maths ?
Options: a ) 10 , b ) 15 , c ) 4 , d ) 12 , e ) indeterminate
Rationale: "for doing union or intersection we would need three values . in this question the missing information in this question is total no . of students in the class . answer : e"
Answer: e
Question (general): if 31 / 198 = 0.1565 , what is the 97 nd digit to the right of the decimal point of the fraction ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 7 , e ) 9
Rationale: "we are not concerned what 31 / 198 means . . we have to look at the decimal . . 0.1565 means 0.1565656 . . . . so leaving girst and second digit to the right of decimal , all odd numbered are 6 and all even numbered are 5 . . here 97 is odd , so ans is 6 c"
Answer: c
Question (general): 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 ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 24 , d ) 19 / 30 , e ) 11 / 15
Rationale: 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
Answer: c
Question (gain): robert spent $ 100 in buying raw materials , $ 125 in buying machinery and 10 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 150 , b ) $ 210 , c ) $ 250 , d ) $ 160 , e ) $ 200
Rationale: let the total amount be x then , ( 100 - 10 ) % of x = 100 + 125 90 % of x = 225 90 x / 100 = 225 x = $ 250 answer is c
Answer: c
Question (gain): a 12 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 150 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 12 , investment = rs . ( 100 / 8 x 12 ) = rs . 150 ∴ market value of rs . 100 stock = rs . 150 answer b"
Answer: b
Question (geometry): there is a square with sides of 13 . what is the area of the biggest circle that can be cut out of this square ?
Options: a ) 132.73 , b ) 231.92 , c ) 530.93 , d ) 113.1 , e ) 204.33
Rationale: "area of a circle = a = ï € r ^ 2 square is 13 wide , so circle ' s diameter would be 13 , and radius would be 6.5 a = ï € 6.5 ^ 2 which is approximately 132.73 answer is a"
Answer: a
Question (physics): how long does a train 130 m long running at the speed of 98 km / hr takes to cross a bridge 160 m length ?
Options: a ) 13.9 sec , b ) 13.1 sec , c ) 17.9 sec , d ) 61.9 sec , e ) 47.98 sec
Rationale: "speed = 98 * 5 / 18 = 27 m / sec total distance covered = 130 + 160 = 290 m . required time = 290 / 22 = 13.1 sec . answer : b"
Answer: b
Question (gain): a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 5500 . what is the share of b ?
Options: a ) 1000 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 5500 x ( 2 / 11 ) ) = rs . 1000 . answer is a"
Answer: a
Question (general): if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 14 } + { 12 } ?
Options: a ) 23 , b ) 20 , c ) 15 , d ) 5 , e ) 2
Rationale: "soln : { 14 } + { 12 } = 14 * { 12 } + { 12 } = 15 * { 12 } answer : c"
Answer: c
Question (general): if x + ( 1 / x ) = 5 , what is the value of w = x ^ 2 + ( 1 / x ) ^ 2 ?
Options: a ) w = 21 , b ) w = 22 , c ) w = 23 , d ) w = 24 , e ) 27
Rationale: "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c"
Answer: c
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 7 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5236 , c ) 6420 , d ) 8960 , e ) 7960
Rationale: "clearly , l = ( 48 - 14 ) m = 34 m , b = ( 36 - 14 ) m = 22 m , h = 8 m . volume of the box = ( 34 x 22 x 7 ) m 3 = 5236 m 3 . answer : option b"
Answer: b
Question (general): if the price of a certain computer increased 30 percent from d dollars to 351 dollars , then 2 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 270 i . e . 2 d = 2 * 270 = 540 answer : option a"
Answer: a
Question (physics): a certain number of men can do a work in 54 days . if there were 6 men more it could be finished in 6 days less . how many men were there in the beginning ?
Options: a ) 50 , b ) 48 , c ) 70 , d ) 40 , e ) 50
Rationale: "explanation : m ( 54 ) = ( m + 6 ) ( 48 ) 9 m - 8 m = 48 m = 48 answer : option b"
Answer: b
Question (physics): in traveling from a dormitory to a certain city , a student went 1 / 2 of the way by foot , 3 / 5 of the way by bus , and the remaining 4 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 10 , e ) 12
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 3 / 5 x + 4 x - 1 / 2 x - 3 / 5 x = 4 x = 20 km option : a"
Answer: a
Question (general): a small pool filled only with water will require an additional 500 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 500 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1875
Rationale: "since pumping in additional 500 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 500 = 0.8 * { total } - - > { total } = 1,875 answer : e ."
Answer: e
Question (other): a certain bag contains 60 balls — 22 white , 18 green , 17 yellow , 3 red , and 1 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.85 , e ) 0.95
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 17 ) / 60 = 57 / 60 = 0.95 . answer : e ."
Answer: e
Question (gain): if a speaks the truth 40 % of the times , b speaks the truth 20 % of the times . what is the probability that at least one will tell the truth
Options: a ) 1.8 , b ) 2.0 , c ) 1.52 , d ) 0.52 , e ) 1.3
Rationale: "probability of a speaks truth p ( a ) = 4 / 10 ; false = 6 / 10 probability of b speaks truth p ( b ) = 2 / 10 ; false = 8 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 6 / 10 ) * ( 8 / 10 ) ] = 1 - 48 / 100 = 1 - 0.48 = 0.52 answer : d"
Answer: d
Question (other): find the number of zeroes in 58 ! ( 58 factorial )
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "no of zeroes is 58 / 5 = 11 11 / 5 = 2 11 + 2 = 13 answer : b"
Answer: b
Question (physics): find the cost of fencing around a circular field of diameter 36 m at the rate of rs . 3.50 a meter ?
Options: a ) 438 , b ) 395 , c ) 378 , d ) 279 , e ) 222
Rationale: "2 * 22 / 7 * 18 = 113 113 * 3 1 / 2 = rs . 395 answer : b"
Answer: b
Question (general): a number when divided by 342 gives a remainder 47 . when the same number ift divided by 19 , what would be the remainder ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 21 , e ) 14
Rationale: "sol . on dividing the given number by 342 , let k be the quotient and 47 as remainder . then , number – 342 k + 47 = ( 19 x 18 k + 19 x 2 + 9 ) = 19 ( 18 k + 2 ) + 9 . the given number when divided by 19 , gives ( 18 k + 2 ) as quotient and 9 as remainder . option c"
Answer: c
Question (general): which is the least number that must be subtracted from 1100 so that the remainder when divided by 7 , 12 , 16 is 4 ?
Options: a ) 58 , b ) 68 , c ) 78 , d ) 88 , e ) 90
Rationale: "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1100 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 88 d"
Answer: d
Question (other): two integers are in the ratio of 1 to 4 . if 12 is added to the smaller number , the ratio becomes 1 to 1 . find the larger integer .
Options: a ) 8 , b ) 16 , c ) 32 , d ) 48 , e ) 54
Rationale: "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 12 to the smaller integer makes the ratio 1 to 1 , then x + 12 = y . substituting y = 4 x into the second equation yields x + 12 = 4 x . so , x = 4 ( smaller integer ) and , y = 4 x = 16 ( larger integer ) so b is the correct answer . another option is to test the answer choices . a ) the larger number is 8 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 2 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 2 ) , we get 14 . so , the new ratio is 14 to 8 which is the same as 7 to 4 . no good . we want a resulting ratio of 1 to 1 eliminate a b ) the larger number is 16 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 4 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 4 ) , we get 16 so , the new ratio is 16 to 16 which is 1 to 1 . therefore ( b ) is correct . c ) the larger number is 32 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 8 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 8 ) , we get 20 so , the new ratio is 20 to 32 which is 5 to 8 . no good . we want a resulting ratio of 1 to 1 eliminate c d ) the larger number is 48 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 12 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 12 ) , we get 24 so , the new ratio is 24 to 48 . this is the same as the ratio of 1 to 2 no good . we want a resulting ratio of 1 to 1 eliminate d e ) the larger number is 54 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 13.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 54 . eliminate e therefore b is the only correct choice ."
Answer: b
Question (gain): the salaries of a and b together amount to $ 4000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 3000 , e ) $ 1200
Rationale: let a ' s salary is x b ' s salary = 4000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 4000 - x ) x = $ 3000 answer is d
Answer: d
Question (general): 1 / 2 + [ ( 2 / 3 * 3 / 8 ) + 4 ] - 8 / 16 =
Options: a ) 29 / 16 , b ) 19 / 16 , c ) 15 / 16 , d ) 17 / 4 , e ) 0
Rationale: 1 / 2 + [ ( 2 / 3 * 3 / 8 ) + 4 ] - 8 / 16 = 1 / 2 + [ ( 1 / 4 ) + 4 ] - 8 / 16 = 1 / 2 + [ 17 / 4 ] - 9 / 16 = 8 / 16 + 68 / 16 - 8 / 16 = 68 / 16 = 17 / 4 d
Answer: d
Question (gain): michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 6 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %
Rationale: "since michelle earns 6 % interest compounded semiannually , then she earns 3 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 3 % * 5 = 15 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 15 % , only answer choice a fits . answer : a"
Answer: a
Question (general): a company producing fruit juice changed its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters . if the price of a box did not change and all boxes are full of juice , by approximately what percent did the price of the juice decrease ?
Options: a ) 12.00 % , b ) 16.67 % , c ) 18.33 % , d ) 20.00 % , e ) 21.50 %
Rationale: suppose when v = 5 x 10 x 20 = 1000 cm , the price is $ 1200 per cm price = $ 1.2 the price is $ 1200 if v = 6 x 10 x 20 = 1000 cm . per cm price = $ 1.0 so the price is decreased by $ 0.2 so the % price decreased by $ 0.2 / 1.20 = 16.67 % answer : b
Answer: b
Question (gain): if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 19,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 950 , e ) $ 900
Rationale: "- > 250 / 5,000 = 5 % and 19,000 * 5 % = 950 . thus , d is the answer ."
Answer: d
Question (general): a man can row 4.2 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.4 , d ) 1.5 , e ) 1.1
Rationale: "speed of boat in still water ( b ) = 4.2 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.4 km / hr . answer : c"
Answer: c
Question (other): divide rs . 116000 among 3 persons a , b and c such that the ratio of the shares of a and b is 3 : 4 and that of b : c is 5 : 6 . find the share of a ?
Options: a ) 29491 , b ) 28491 , c ) 39491 , d ) 49491 , e ) 59491
Rationale: compound ratio of a : b : c a : b = 3 : 4 b : c = 5 : 6 - - - - - - - - - - a : b : c = 15 : 20 : 24 we can divide rs . 116000 in this ratio . share of a = 15 / 59 * 116000 = 29491 answer : a
Answer: a
Question (geometry): the diagonal of a rhombus are 40 m and 30 m . its area is :
Options: a ) 600
b ) 450
c ) 350
d ) 500
e ) 620
Rationale: area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 40 ã — 30 ) cm ( power ) 2 = 40 ã — 15 = 600 cm ( power ) 2 answer is a .
Answer: a
Question (other): in a certain corporation , there are 300 male employees and 150 female employees . it is known that 40 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 7 / 10 , e ) 11 / 15
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.4 * 300 / 450 = 120 / 450 = 4 / 15 the sum of the probabilities is 9 / 15 = 3 / 5 the answer is c ."
Answer: c
Question (gain): in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 20 ducks and in the larger pond there are 80 ducks . if 20 % of the ducks in the smaller pond are green and 15 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: "number of ducks in small pond = 20 green ducks in small pond = 20 % of 20 = 4 ducks number of ducks in large pond = 80 green ducks in large pond = 15 % of 80 = 12 ducks total number of ducks = 20 + 80 = 100 total number of green ducks = 4 + 12 = 16 ducks percentage of green ducks = 16 / 100 * 100 = 16 % answer : d"
Answer: d
Question (physics): the current of a stream runs at the rate of 5 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7.63 , b ) b ) 2.6 , c ) c ) 8.83 , d ) d ) 6.69 , e ) e ) 3
Rationale: "s = 5 m = x ds = x + 5 us = x - 5 6 / ( x + 5 ) + 6 / ( x - 5 ) = 2 x = 8.83 answer : c"
Answer: c
Question (physics): if two projectiles are launched at the same moment from 1386 km apart and travel directly towards each other at 445 km per hour and 545 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "the projectiles travel a total of 990 km per hour . the time to meet is 1386 / 990 = 1.4 hours = 84 minutes the answer is c ."
Answer: c
Question (general): find the average of all the numbers between 11 and 21 which are divisible by 2 .
Options: a ) 15 , b ) 18 , c ) 16 , d ) 22 , e ) none
Rationale: "sol . average = ( 12 + 14 + 16 + 18 + 20 / 5 ) = 80 / 5 = 16 . answer c"
Answer: c
Question (physics): a train speeds past a pole in 15 sec and a platform 140 m long in 25 sec , its length is ?
Options: a ) 238 , b ) 150 , c ) 988 , d ) 210 , e ) 171
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 140 ) / 25 = x / 15 = > x = 210 m . answer : d"
Answer: d
Question (gain): a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
Options: a ) rs . 25000 , b ) rs . 20000 , c ) rs . 15000 , d ) rs . 22000 , e ) none of these
Rationale: let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 400 = > x = 20000 answer : b
Answer: b
Question (general): the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 12 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 21 / 26 , b ) 25 / 26 , c ) 11 / 26 , d ) 6 / 26 , e ) 22 / 33
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 12 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 12 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 12 * 2 b * b 3 b - 2 b ^ 2 = 24 b ^ 2 3 b = 26 b ^ 2 b = 3 / 26 = 3 / 26 so , a = 2 b = 6 / 26 the correct answer is d ."
Answer: d
Question (geometry): a snooker tournament charges $ 40.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 212 , b ) 200 , c ) 220 , d ) 230 , e ) 240
Rationale: "let no of sits in vip enclosure is x then x * 40 + 15 ( 320 - x ) = 7500 or 25 x = 7500 - 4800 , x = 2700 / 25 = 108 vip = 108 general 212 a"
Answer: a
Question (general): a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money r did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ r = 20 answer : b"
Answer: b
Question (general): a ’ s speed is 20 / 12 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 6 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 12 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 8 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 8 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 12 meters ) to reach the finish line . so b should get a head start of 8 / 20 th of the race . answer ( d )"
Answer: d
Question (physics): a train speeds past a pole in 15 seconds and a platform 130 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 175 , b ) 185 , c ) 195 , d ) 205 , e ) 215
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 130 = 25 * ( x / 15 ) 10 x = 1950 x = 195 meters the answer is c ."
Answer: c