Cheukting/mathqa huggingface dataset:
Question (general): in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 42 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 24
Rationale: "12 * 42 = 504 504 % 21 = 24 answer : e"
Answer: e
Question (general): in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 7,4 ) , and ( 7,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 2 / 7 , d ) 4 / 9 , e ) 7 / 10
Rationale: "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 28 . p ( x + y < 4 ) = 8 / 28 = 2 / 7 the answer is c ."
Answer: c
Question (gain): the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 750 , b ) 650 , c ) 625 , d ) 115 , e ) 400
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 160 ) = rs . 625 . answer : b"
Answer: b
Question (gain): one - third of 1206 is what percent of 200 ?
Options: a ) 3 , b ) 201 , c ) 300 , d ) none of these , e ) can not be determined
Rationale: "answer let one - third of 1206 is n % of 200 . ∵ 1206 / 3 = ( n x 200 ) / 100 ∴ n = ( 402 x 100 ) / 200 = 201 correct option : b"
Answer: b
Question (gain): machine p and machine q are each used to manufacture 660 sprockets . it takes machine p 10 hours longer to produce 660 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 6
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 660 / x = 660 / 1.1 x + 10 1.1 ( 660 ) = 660 + 11 x 11 x = 66 x = 6 the answer is e ."
Answer: e
Question (physics): a train 280 m long is running at a speed of 54 km / hr . in what time will it pass a bridge 200 m long ?
Options: a ) 32 sec , b ) 42 sec , c ) 45 sec , d ) 18 sec , e ) 49 sec
Rationale: "total length = 280 + 200 = 480 speed = 54 km / h = ( 54 * 5 ) / 18 = 15 / 1 m / s time = ( 480 * 1 ) / 15 = 32 sec . answer : a"
Answer: a
Question (other): a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 10,500 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 3000 , c ) 3600 , d ) 4200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 10500 = > 7 x = 10500 = > x = 1500 total number of motorcycles = 2 x = 2 * 1500 = 3000 answer b"
Answer: b
Question (general): what is the sum of the 1 st 6 prime numbers greater than 10 ?
Options: a ) 112 , b ) 111 , c ) 212 , d ) 115 , e ) 113
Rationale: required numbers are = ( 11 + 13 + 17 + 19 + 23 + 29 ) = 112 note : 1 is not a prime number answer a
Answer: a
Question (gain): $ 8,000 is deposited in a savings account that pays 12 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 8288.55 , b ) $ 8985.10 , c ) $ 8988.80 , d ) $ 8977.14 , e ) $ 8964.95
Rationale: "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 12 / 2 = 6 % now , ca = 8000 ( 1 + 6 / 100 ) ^ 2 = $ 8988.80 hence answer is c"
Answer: c
Question (physics): a , b and c can do a piece of work in 9 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ?
Options: a ) 4.12 days , b ) 4.52 days , c ) 3.52 days , d ) 2.52 days , e ) 4.92 days
Rationale: 1 / 9 + 1 / 14 + 1 / 28 = 55 / 252 = > 252 / 55 days = > 4.52 days answer : b
Answer: b
Question (general): in a division sum , the divisor is 12 times the quotient and 6 times the remainder . if the remainder is 24 , what is the divident ?
Options: a ) 1738 , b ) 1752 , c ) 1846 , d ) 1648 , e ) none
Rationale: "solution : dividend = [ divisor * quotient ] + remainder - - - - > ( 1 ) . given divisor = 6 * 24 = 144 . 12 * quotient = 144 = > quotient = 144 / 12 = 12 . substitute these values in the ( 1 ) then we get 1752 as dividend . answer b"
Answer: b
Question (general): to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 775 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 194 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 775 . as per question we need to take 1 / 4 of 775 to be considered for top 10 movies = 193.75 approximate the value we 194 . imo option b is the correct answer . . ."
Answer: b
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean a . if 68 % of the distribution lies one standard deviation d of the mean , what percent of the distribution is less than a + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ a + d 34 % ________________________________________________ a 34 % ________________________________________________ a - d 16 % since 68 % lies one standard deviation from mean a , = > 50 % of 68 % lies on either side as it is symmetric about a . thus 16 % lie below a - d and 16 % lie above a + d now below a + d = 16 + 34 + 34 = 84 % hence d"
Answer: d
Question (general): if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 8 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 16 , e ) 1 / 4
Rationale: "say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 8 - - > f = 16 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 16 ) = 3 / 16 . answer : d ."
Answer: d
Question (other): share rs . 4320 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1440
Rationale: "amount received by sanjay . 4 / 12 x 4320 = 1440 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1440 . e"
Answer: e
Question (physics): a man rows his boat 78 km downstream and 56 km upstream , taking 4 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 5 , c ) 7 , d ) 8 , e ) 3
Rationale: "speed downstream = d / t = 78 / ( 4 ) = 20 kmph speed upstream = d / t = 56 / ( 4 ) = 14 kmph the speed of the stream = ( 20 - 14 ) / 2 = 3 kmph answer : e"
Answer: e
Question (gain): tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1040 , b ) 1045 , c ) 1055 , d ) 1060 , e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 . c )"
Answer: c
Question (physics): a car traveling at a certain constant speed takes 10 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 40 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 35 , b ) 35.5 , c ) 36 , d ) 36.5 , e ) 37
Rationale: "40 * t = 1 km = > t = 1 / 40 km / h v * ( t + 10 / 3600 ) = 1 v ( 1 / 40 + 10 / 3600 ) = 1 v ( 100 / 3600 ) = 1 v = 36 km / h the answer is c ."
Answer: c
Question (general): a camera lens filter kit containing 5 filters sells for $ 87.50 . if the filters are purchased individually , 2 of them are priced at $ 16.45 each , 2 at $ 14.05 each , 1 at $ 19.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 7 % , b ) 8 % , c ) 9 % , d ) 10 % , e ) 11 %
Rationale: "cost of kit = $ 87.50 if filters are purchased individually - $ 16.45 * 2 + $ 14.05 * 2 + $ 19.50 = $ 80.50 amount saved = $ 87.50 - $ 80.50 = $ 7 required % age = ( $ 7 / $ 87.50 ) * 100 = 8 % so , the correct answer is b ."
Answer: b
Question (physics): a man swims downstream 30 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 3 , b ) 8 , c ) 9 , d ) 4 , e ) 2
Rationale: 30 - - - 3 ds = 10 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 10 + 6 ) / 2 = 8 answer : b
Answer: b
Question (gain): if a speaks the truth 75 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.45 , d ) 0.482 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 75 / 100 = 0.75 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.75 × 0.6 = 0.45 answer : c"
Answer: c
Question (general): what is the dividend . divisor 16 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 134 , c ) c ) 149 , d ) d ) 158 , e ) e ) 160
Rationale: "d = d * q + r d = 16 * 9 + 5 d = 144 + 5 d = 149 answer c"
Answer: c
Question (general): what is the positive difference between the sum of the squares of the first 3 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 24 , e ) 27
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 = 14 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 14 is 27 . so the answer is ( e ) ."
Answer: e
Question (gain): the charge for a single room at hotel p is 40 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) e . 150 %
Rationale: "p = 0.6 r = 0.9 g r = 0.9 g / 0.6 = 1.5 * g thus r is 50 % greater than g . the answer is d ."
Answer: d
Question (general): sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6800 ?
Options: a ) 4966 , b ) 6791 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6800 x 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 answer : b"
Answer: b
Question (other): in a group of cheerleaders , the group made of 10 males and 16 females . every cheerleader gets to choose between a coke or malt . the number of those that choose malt is double the number that chose coke , if all the 6 males choose malt , how many females chose malt ?
Options: a ) 30 , b ) 5 , c ) 8 , d ) 20 , e ) 10
Rationale: number of cheerleaders = 27 number of male = 10 number of female = 17 coke = 9 maly = 17 female who chose malt = 17 - 9 = 8 answer = c
Answer: c
Question (general): if a certain number is divided by 5 , the quotient , dividend , and divisor , added together , will amount to 65 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 50
Rationale: "let x = the number sought . then x / 5 + x + 5 = 65 . x = 50 . e"
Answer: e
Question (general): if t = 5 / 9 * ( k - 32 ) , and if t = 105 , then what is the value of k ?
Options: a ) 209 , b ) 212 , c ) 215 , d ) 218 , e ) 221
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 105 ) / 5 + 32 = 221 the answer is e ."
Answer: e
Question (general): a camera lens filter kit containing 5 filters sells for $ 57.50 . if the filters are purchased individually , 2 of them are priced at $ 10.45 each , 2 at $ 12.05 each , 1 at $ 17.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 7 % , b ) 8 % , c ) 8.5 % , d ) 10 % , e ) 11 %
Rationale: "cost of kit = $ 57.50 if filters are purchased individually - $ 10.45 * 2 + $ 12.05 * 2 + $ 17.50 = $ 62.50 amount saved = $ 62.50 - $ 57.50 = $ 5 required % age = ( $ 5 / $ 62.50 ) * 100 = 8 % so , the correct answer is b ."
Answer: b
Question (gain): there were two candidates in an election . winner candidate received 75 % of votes and won the election by 500 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 744 , c ) 750 , d ) 199 , e ) 231
Rationale: "w = 75 % l = 25 % 75 % - 25 % = 50 % 50 % - - - - - - - - 500 75 % - - - - - - - - ? = > 750 answer : c"
Answer: c
Question (general): if 170 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 47 , b ) 46 , c ) 41 , d ) 48 , e ) 45
Rationale: "the question actually asks the highest power of 10 which divides 300 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 170 factorial will have 41 as - 170 / 5 = 34 34 / 5 = 6 6 / 5 = 1 so answer will be ( c ) 41"
Answer: c
Question (other): the ratio of spinsters to cats is 2 to 7 . if there are 35 more cats than spinsters , how many spinsters are there ?
Options: a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42
Rationale: let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 35 x = 7 and the number of spinsters is 2 ( 7 ) = 14 . the answer is a .
Answer: a
Question (general): chris mixed 3 pounds of raisins with 3 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7
Rationale: "1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 3 3 lbs of nuts = $ 9 total value of mixture = 9 + 3 = 12 fraction of the value of raisin = 3 / 12 = 1 / 4 ans : c"
Answer: c
Question (gain): in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 9 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 72 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,09 = 9 / 100 x = 80 * 9 / 100 x = 7.2 7.2 / 10 = 0.72 = 72 % , answer b"
Answer: b
Question (physics): how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 4 m x 2 m x 25 cm ?
Options: a ) 5600 , b ) 6000 , c ) 1185 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 400 x 200 x 25 ) / ( 25 x 11.25 x 6 ) = 1185 . answer : option c"
Answer: c
Question (general): a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220
Rationale: orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : option b
Answer: b
Question (general): what is the sum of natural numbers between 40 and 100
Options: a ) 4800 , b ) 4270 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 40 and 100 numbers = 61 = > 100 - 40 = 60 + 1 = 61 sn = 61 / 2 ã — 140 = 61 ã — 70 = 4270 answer : b"
Answer: b
Question (probability): if 4 consecutive letters are selected at random from the english alphabet , then the probability that one of the letters is a vowel is ?
Options: a ) 13 / 23 , b ) 16 / 23 , c ) 11 / 23 , d ) 17 / 23 , e ) 18 / 23
Rationale: total no . of ways of selecting 4 consecutive letters = > 23 [ like abcd , bcde , efgh , . . etc ] no . of ways of having one is a vowel = > abcd , bcde , cdef , defg , efgh , fghi , ghij , hijk , ijkl , lmno , mnop , nopq , opqr , rstu , stuv , tuvw , uvwx . . . = 17 p ( one of letter is vowel ) = 17 / 23 answer : d
Answer: d
Question (general): a man is 36 years older than his son . in three years , his age will be thrice the age of his son . the present age of this son is
Options: a ) 28 years , b ) 22 years , c ) 18 years , d ) 16 years , e ) 15 years
Rationale: "let ' s son age is x , then father age is x + 36 . = > 3 ( x + 3 ) = ( x + 36 + 3 ) = > 3 x + 9 = x + 39 = > 2 x = 30 years = 15 years answer : e"
Answer: e
Question (gain): how much 60 % of 50 is greater than 50 % of 30 ?
Options: a ) 18 , b ) 91 , c ) 11 , d ) 17 , e ) 15
Rationale: "( 60 / 100 ) * 50 – ( 50 / 100 ) * 30 30 - 15 = 15 answer : e"
Answer: e
Question (gain): a pair of articles was bought for $ 50 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 22.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 90 % of x = 25 x = 25 * . 9 = $ 22.50 answer is b"
Answer: b
Question (general): a meal cost $ 37.25 adn there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 42 - 45 , b ) 41 - 43 , c ) 39 - 41 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 37.25 ) = 3.725 15 % ( 37.25 ) = 5.5875 total amount could have been 37.25 + 3.725 and 37.25 + 5.5875 = > could have been between 40.975 and 42.8375 = > approximately between 41 and 43 answer is b ."
Answer: b
Question (physics): a train moves at average speed of 40 kmph reaches its destination on time . what its average speed becomes 35 kmph , then it reaches its destination 15 late . find the length of the journey ?
Options: a ) 70 km , b ) 85 km , c ) 38 km , d ) 14 km , e ) 1 km
Rationale: difference between timings = 15 mis = 1 / 4 hr let the length of the journey be x km . then x / 35 - x / 40 = 1 / 4 8 x - 7 x = 70 x = 70 km answer ( a )
Answer: a
Question (gain): evaluate 25 % of 450 + 45 % of 250
Options: a ) 225 , b ) 242 , c ) 252 , d ) 262 , e ) 272
Rationale: "explanation : = ( 25 / 100 ) * 450 + ( 45 / 100 ) * 250 = 225 option a"
Answer: a
Question (gain): if a lends rs . 3500 to b at 10 % p . a . and b lends the same sum to c at 11.5 % p . a . , then the gain of b ( in rs . ) in a period of 3 years is
Options: a ) rs . 154.50 , b ) rs . 155.50 , c ) rs . 156.50 , d ) rs . 157.50 , e ) none of these
Rationale: explanation : we need to calculate the profit of b . it will be , si on the rate b lends - si on the rate b gets gain of b = 3500 × 11.5 × 3 / 100 − 3500 × 10 × 3 / 100 = 157.50 option d
Answer: d
Question (general): at a certain high school , the senior class is twice the size of the junior class . if 1 / 8 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 3 / 8 , b ) 3 / 4 , c ) 1 / 3 , d ) 4 / 5 , e ) 1 / 2
Rationale: start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 8 ) * 200 = 25 and ( 3 / 4 ) * 100 = 75 . 25 + 75 = 100 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 100 total students in japanese , so 100 students in japanese / 300 total students equals 1 / 3 of the students in both classes that study japanese . answer : c
Answer: c
Question (geometry): the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 25 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 25 % , c ) 10 % , d ) 45 % , e ) 180 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 25 percent to make square c length of each side of square c = 1.25 * 20 = 25 area of c = 25 ^ 2 = 625 difference in areas of c and cummulative areas of a and b = 625 - ( 400 + 100 ) = 225 percent is the area of square c greater than the sum of the areas of squares a and b = ( 225 / 500 ) * 100 % = 45 % answer d"
Answer: d
Question (general): the sum of ages of 5 children born 3 years different each is 55 yrs . what is the age of the elder child ?
Options: a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . x + 12 = 5 + 12 = 17 a"
Answer: a
Question (probability): there are 7 girls and 3 chairs . in how many ways girls can occupy the chairs ?
Options: a ) 760 , b ) 210 , c ) 560 , d ) 740 , e ) 800
Rationale: "total girls = 7 total chairs = 3 1 st chair can be occupy in 7 ways 2 nd chair can be occupy in 6 ways 3 rd chair can be occupy in 5 ways total number of ways = 7 * 6 * 5 = 210 ways correct option is b"
Answer: b
Question (general): in a mixed college 160 students are there in one class . out of this 160 students 3 / 5 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 64 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 3 / 5 = 96 total boys : 160 - 96 = 64 answer is b"
Answer: b
Question (physics): a train running at 7 / 11 of its own speed reached a place in 22 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 4 hrs , b ) 6 hrs , c ) 8 hrs , d ) 9 hrs , e ) 11 hrs
Rationale: "new speed = 7 / 11 of usual speed new time = 11 / 7 of usual time 11 / 7 of usual time = 22 hrs usual time = 22 * 7 / 11 = 14 hrs time saved = 22 - 44 = 8 hrs answer is c"
Answer: c
Question (physics): a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3300 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1980 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 132 so , a ’ s amount = 120 × 15 = rs . 1980 . answer : option c"
Answer: c
Question (general): a line that passes through ( – 2 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 3 + 2 ) = > 5 k = k + 4 = > k = 1 ans b it is !"
Answer: b