Cheukting/mathqa huggingface dataset:
Question (gain): in a recent election , geoff received 1 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3000 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 54 , c ) 56 , d ) 51 , e ) 63
Rationale: "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 60 votes he needs 3571 more votes so : 60 + 3000 = 3060 now what ' s the problem wants ? ? a x % . . . . . . . . 3060 is what % of total votes 6000 . . . . . . . . translating : 3060 = x / 100 * 6000 - - - x = 51 % . . . . . . . . . . d"
Answer: d
Question (probability): two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability e that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability e = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Question (gain): if 40 % of a certain number is 160 , then what is 20 % of that number ?
Options: a ) 75 , b ) 100 , c ) 120 , d ) 30 , e ) 80
Rationale: "explanation : 40 % = 40 * 4 = 160 20 % = 20 * 4 = 80 answer : option e"
Answer: e
Question (general): workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.15 lacs . how many workers were they ?
Options: a ) 300 , b ) 230 , c ) 500 , d ) 560 , e ) 590
Rationale: "n * 50 = ( 315000 - 300000 ) = 15000 n = 15000 / 50 = 300 a"
Answer: a
Question (general): 1 ^ 2 – 2 ^ 2 + 3 ^ 2 – 4 ^ 2 + 5 ^ 2 – 6 ^ 2 + 7 ^ 2 – 8 ^ 2 + 9 ^ 2 – 10 ^ 2 = ?
Options: a ) - 21 , b ) - 53 , c ) - 35 , d ) - 55 , e ) - 58
Rationale: 1 - 4 + 9 - 16 + 25 - 36 + 49 - 64 + 81 - 100 = - 55 answer : d
Answer: d
Question (general): there are 7 players in a bowling team with an average weight of 112 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 115 kg . , b ) 110 kg . , c ) 106 kg . , d ) 105 kg . , e ) 100 kg .
Rationale: "the new average will be = ( 112 * 7 + 110 + 60 ) / 9 = 106 kgs c is the answer"
Answer: c
Question (gain): fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 25 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 3.12 kg , d ) 10 kg , e ) none of these
Rationale: the weight of non - water in 25 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 25 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 3.12 answer : c .
Answer: c
Question (physics): anna left for city a from city b at 5.20 a . m . she traveled at the speed of 80 km / hr for 2 hrs 15 min . after that the speed was reduced to 60 km / hr . if the distance between two cities is 350 kms , at what time did anna reach city a ?
Options: a ) 10.21 , b ) 10.27 , c ) 10.25 , d ) 10.23 , e ) 60.25
Rationale: distance covered in 2 hrs 15 min i . e . , 2 1 / 4 hrs = 80 * 9 / 4 = 180 hrs . time taken to cover remaining distance = ( 350 - 180 ) / 60 = 17 / 6 hrs = 2 5 / 6 = 2 hrs 50 min total time taken = ( 2 hrs 15 min + 2 hrs 50 min ) = 5 hrs 5 min . so , anna reached city a at 10.25 a . m . answer : e
Answer: e
Question (general): at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 155 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 155 male associates implies 55 female associates which means the remaining 35 females must be managers e . 35"
Answer: e
Question (other): pencils , pens and exercise books in a shop are in the ratio of 10 : 2 : 3 . if there are 120 pencils , the number of exercise books in the shop is :
Options: a ) 26 , b ) 36 , c ) 46 , d ) 56 , e ) 66
Rationale: "explanation : let pencils = 10 x , pens = 2 x & exercise books = 3 x . now , 10 x = 120 hence x = 12 . number of exercise books = 3 x = 36 . answer : b"
Answer: b
Question (general): in a group of ducks and cows , the total number of legs are 26 more than thrice the number of heads . find the total number of cows .
Options: a ) a ) 14 , b ) b ) 13 , c ) c ) 16 , d ) d ) 8 , e ) e ) 6
Rationale: "explanation : let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 26 more than twice the number of heads = > 2 ( d + 2 c ) = 26 + 2 ( c + d ) = > d + 2 c = 13 + c + d = > 2 c = 13 + c = > c = 13 i . e . , total number of cows = 13 answer : b"
Answer: b
Question (physics): working alone at its constant rate , machine a produces x boxes in 5 minutes and working alone at its constant rate , machine b produces 2 x boxes in 10 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 3 x boxes ?
Options: a ) 3 minutes , b ) 7.5 minutes , c ) 5 minutes , d ) 6 minutes , e ) 12 minutes
Rationale: "rate = work / time given rate of machine a = 2 x / 10 min machine b produces 2 x boxes in 10 min hence , machine b produces 2 x boxes in 10 min . rate of machine b = 2 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = 2 x / 10 min + rate of machine b = 2 x / 10 = 4 x / 10 now combine time = combine work needs to be done / combine rate = 3 x / 4 x * 10 = 7.5 min ans : b"
Answer: b
Question (general): a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 35 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 190,000 , d ) $ 207,500 , e ) $ 205,000
Rationale: "30 % of 1000 = 300 worked for 20 hours payment @ 5 / hr total payment = 300 * 35 * 5 = 52500 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 52500 + 100000 + 40000 + 15000 = 207500 hence , answer is d"
Answer: d
Question (other): solution a is 20 % sugar and solution b is 80 % sugar . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % sugar solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 20 ) = 1 / 1 so the volume of the two solutions will be equal . answer has to be 4 : 4 = c
Answer: c
Question (other): 12 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1600 , e ) 1848
Rationale: no . of ways of picking 2 biology books ( from 12 books ) = 12 c 2 = ( 12 * 11 ) / 2 = 66 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 66 * 28 = 1848 ( option e )
Answer: e
Question (general): the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 3 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 3 of that new total price : p = 1 / 3 * $ 3,000 = $ 1000 plug this value in the first equation : c + 1000 = $ 2,500 - - > c = $ 1,500 . answer : a ."
Answer: a
Question (gain): a baseball card decreased in value 20 % in its first year and 20 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.8 = 80 after second year price = 80 * 0.8 = 64 final decrease = [ ( 100 - 64 ) / 100 ] * 100 = 36 % correct answer - d"
Answer: d
Question (gain): 2 is what percent of 50
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) none of these
Rationale: "explanation : 2 / 50 * 100 = 1 / 25 * 100 = 4 % option b"
Answer: b
Question (general): the contents of a certain box consist of 14 apples and 26 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 26 oranges , so to get to 6 oranges , we should remove 26 - 6 = 20 oranges . answer e"
Answer: e
Question (general): light glows for every 20 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 381 times , c ) 382 times , d ) 248 times , e ) 482 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 20 ) = 248 times . answer : d"
Answer: d
Question (general): each week , harry is paid x dollars per hour for the first 18 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 34 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 18 x + 1.5 x ( h - 18 ) = = > 42 = 18 + 1.5 ( h - 18 ) = = > h - 18 = 24 / 1.5 = 16 = = > h = 34 answer is a"
Answer: a
Question (general): the average of first five multiples of 2 is ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 7
Rationale: "average = 2 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 30 / 5 = 6 . answer : a"
Answer: a
Question (physics): in an intercollegiate competition that lasted for 3 days , 157 students took part on day 1 , 111 on day 2 and 98 on day 3 . if 89 took part on day 1 and day 2 and 56 took part on day 2 and day 3 and 32 took part on all three days , how many students took part only on day 1 ?
Options: a ) 40 , b ) 44 , c ) 35 , d ) 49 , e ) 38
Rationale: "day 1 & 2 = 89 ; only day 1 & 2 ( 89 - 32 ) = 57 , day 2 & 3 = 56 ; only day 2 & 3 ( 56 - 32 ) = 24 , only day 1 = 157 - ( 57 + 24 + 32 ) = 44 answer : b"
Answer: b
Question (other): a student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "xc 1 * ( x - 1 ) c 1 = 72 x ^ 2 - x - 72 = 0 ( x - 9 ) ( x + 8 ) = 0 x = 9 , - 8 - 8 ca n ' t possible . 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 3 m , the volume of the box ( in m 3 ) is :
Options: a ) 3780 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960
Rationale: "clearly , l = ( 48 - 6 ) m = 42 m , b = ( 36 - 6 ) m = 30 m , h = 8 m . volume of the box = ( 42 x 30 x 3 ) m 3 = 3780 m 3 . answer : option a"
Answer: a
Question (general): find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 21 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 9 , 3,32 , d ) 9 , 6,12 , e ) 9 , 2,23
Rationale: let the numbers be a , b and c . a : b : c = 3 : 2 : 4 given , ( a + b ) + ( c - b ) = 21 = > a + c = 21 = > 3 x + 4 x = 21 = > x = 3 a , b , c are 3 x , 2 x , 4 x a , b , c are 9 , 6 , 12 . answer : d
Answer: d
Question (gain): in a certain village , 20 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 2000 litres of water last ?
Options: a ) 5 , b ) 2 , c ) 10 , d ) 1 , e ) 12
Rationale: i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 20 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 20 * 10 = 200 ( m * n ) water available is 2000 ( p ) it will last 10 months ( p / m * n ) ans : c
Answer: c
Question (general): if x + | x | + y = 5 and x + | y | - y = 6 what is x + y = ?
Options: a ) 1 , b ) - 1 , c ) 3 , d ) 12 , e ) 13
Rationale: if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 12 hence answer should be d
Answer: d
Question (general): a certain clock rings two notes at quarter past the hour , 4 notes at half past , and 6 notes at 3 - quarters past . on the hour , it rings 8 notes plus an additional number of notes equal to whatever hour it is . how many notes will the clock ring from 1 : 00 p . m . through 5 : 00 p . m . , including the rings at 1 : 00 and 5 : 00 ?
Options: a ) 87 , b ) 95 , c ) 102 , d ) 103 , e ) 115
Rationale: form 1 pm to 5 pm . excluding the actual hour chime we have 20 ( 1 pm ) + 20 ( 2 pm ) + 20 ( 3 pm ) + 20 ( 4 pm ) + 8 ( 5 pm ) = 88 now the hour chimes are 1 + 2 + 3 + 4 + 5 = 15 total = 88 + 15 = 103 answer d .
Answer: d
Question (general): on an order of 9 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "clearly , the retailer gets 1 dozen out of 10 dozens free . equivalent discount = 1 / 10 * 100 = 10 % . answer a ) 10 %"
Answer: a
Question (general): the total age of a and b is 13 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 13 , b ) 24 , c ) c is elder than a , d ) data inadequate , e ) none
Rationale: "solution [ ( a + b ) - ( b + c ) ] = 13 â € ¹ = â € º a - c = 13 . answer a"
Answer: a
Question (general): rs . 1200 is divided so that 5 times the first share , 10 times the 2 nd share and fifteen times third share amount to the same . what is the value of the second share ?
Options: a ) s 525 , b ) s 527 , c ) s 598 , d ) s 400 , e ) s 500
Rationale: "a + b + c = 1200 5 a = 10 b = 15 c = x a : b : c = 1 / 5 : 1 / 10 : 1 / 15 = 3 : 2 : 1 2 / 6 * 1200 = rs 400 answer : d"
Answer: d
Question (gain): jackie has two solutions that are 4 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 4 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 36 , e ) 26.25
Rationale: "let a = amount of 4 % acid and b = amount of 12 % acid . now , the equation translates to , 0.04 a + . 12 b = . 05 ( a + b ) but a + b = 60 therefore . 04 a + . 12 b = . 05 ( 60 ) = > 4 a + 12 b = 300 but b = 60 - a therefore 4 a + 12 ( 60 - a ) = 300 = > 16 a = 420 hence a = 26.25 . answer : e"
Answer: e
Question (general): if the product of 6 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "product of even number of - ve numbers is positive so it cant be 6 . answer : d"
Answer: d
Question (probability): there is a 50 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ?
Options: a ) 25.0 % , b ) 50.0 % , c ) 62.5 % , d ) 75.0 % , e ) 80.0 %
Rationale: "p ( chile and not madagascar ) = 0.5 * 0.5 = 0.25 p ( madagascar and not chile ) = 0.5 * 0.5 = 0.25 total probability = 0.25 + 0.25 = 0.5 = 50 % the answer is b ."
Answer: b
Question (physics): a pipe takes a hours to fill the tank . but because of a leakage it took 7 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min
Rationale: pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 420 x = 70 min answer : e
Answer: e
Question (general): at chennai it rained as much on tuesday as on all the others days of the week combined . if the average rainfall for the whole week was 3 cm . how much did it rain on tuesday ?
Options: a ) 2.625 cm , b ) 3 cm , c ) 10.5 cm , d ) 15 cm , e ) none of these
Rationale: total rainfall = 3 x 7 = 21 cm hence , rainfall received on tuesday = 21 / 2 ( as it rained as much on tuesday as on all the others days of the week combined ) = 10.5 cm . answer : c
Answer: c
Question (gain): a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 2 a rupee . find his net profit or loss percent ?
Options: a ) 100 % , b ) 200 % , c ) 250 % , d ) 300 % , e ) 50 %
Rationale: "the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3 he selling at 2 a rupee , his sp = 4 profit = sp - cp = 4 - 2 = 2 profit percent = 2 / 2 * 100 = 100 % answer : a"
Answer: a
Question (general): ( 3 * 10 ^ 2 ) * ( 4 * 10 ^ - 2 ) = ?
Options: a ) 14 , b ) 12 , c ) 1200 , d ) 1.2 , e ) 14.11
Rationale: 3 * 10 ^ 2 = 300 4 * 10 ^ - 2 = 0.04 ( 3 * 10 ^ 2 ) * ( 4 * 10 ^ - 2 ) = 300 * 0.04 = 12.00 the answer is option b
Answer: b
Question (other): the ratio of three numbers is 1 : 2 : 3 and their sum is 60 . the second number of the three numbers is ?
Options: a ) 24 , b ) 26 , c ) 20 , d ) 29 , e ) 30
Rationale: "1 : 2 : 3 total parts = 6 6 parts - - > 60 1 part - - - - > 10 the second number of the three numbers is = 2 * 10 = 20 answer : c"
Answer: c
Question (physics): natasha climbs up a hill , and descends along the same way she went up . it takes her 3 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.75 , d ) 5 , e ) 7.5
Rationale: "lets assume distance to top as x , so the total distance travelled by natasha = 2 x total time taken = 3 + 2 = 5 hrs avg speed = total dist / total time taken = 2 x / 5 avg speed of complete journey is given as = 3 hrs 2 x / 5 = 3 x = 7.5 miles avg speed while climbing = distance / time = 7.5 / 3 = 2.5 option b"
Answer: b
Question (general): the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years k in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) 20 , b ) k = 25 , c ) 30 , d ) k = 35 , e ) 40
Rationale: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
Answer: d
Question (geometry): susan made a block with small cubes of 8 cubic cm volume to make a block , 3 small cubes long , 9 small cubes wide and 5 small cubes deep . she realizes that she has used more small cubes than she really needed . she realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions , if it were made hollow . what is the minimum number of cubes that she needs to make the block ?
Options: a ) 113
b ) 114
c ) 115
d ) 116
e ) 117
Rationale: the total volume ( in terms of number of cubes ) of the solid = 3 * 9 * 5 = 135 the total volume ( in terms of number of cubes ) of the hollow = ( 3 - 2 ) * ( 9 - 2 ) * ( 5 - 2 ) = 21 so number of cubes required = 135 - 21 = 114 answer : b
Answer: b
Question (general): a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of pupils in the class is :
Options: a ) 32 , b ) 50 , c ) 40 , d ) 20 , e ) 10
Rationale: "let there be x pupils in the class . total increase in marks = x x 1 / 2 = x / 2 x / 2 = ( 83 - 63 ) x / 2 = 20 x = 40 . answer : c"
Answer: c
Question (probability): in how many ways can 21 books on english and 19 books on french be placed in a row on a shelf so that two books on french may not be together ?
Options: a ) 3990 , b ) 1540 , c ) 1995 , d ) 3672 , e ) none of these
Rationale: "in order that two books on french are never together , we must place all books as under x e x e x e x e x e . . . . . x e x where e denotes the position of an english book and x that of a french book . since there are 21 books on english , the number of places marked x are therefore , 22 . now , 19 places out of 22 can be chosen in 22 c 19 = 22 c 3 = ( 22 x 21 x 20 ) / ( 3 x 2 x 1 ) = 1540 ways answer b ."
Answer: b
Question (gain): 120 is what percent of 40 ?
Options: a ) 5 % , b ) 20 % , c ) 50 % , d ) 300 % , e ) 500 %
Rationale: "40 * x = 120 - - > x = 3 - - > 3 expressed as percent is 300 % . answer : d ."
Answer: d
Question (general): an alloy of copper and zinc contains copper and zinc in the ratio 9 : 6 . another alloy of copper and zinc contains copper and zinc in the ratio 6 : 9 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 2
Rationale: "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 9 x / 15 , and fraction of zinc in alloy _ 1 = 6 x / 15 similarly , fraction of copper in alloy _ 2 = 6 y / 15 , and fraction of zinc in alloy _ 2 = 9 y / 15 . mixing them , we get copper = 9 x / 15 + 6 y / 15 ; zinc = 6 x / 15 + 9 y / 15 so , 9 x + 6 y = 6 x + 9 y - > 3 x = 3 y - > x / y = 3 / 3 = 1 / 1 so , they must be mixed in the ratio 1 : 1 answer : d"
Answer: d