Cheukting/mathqa huggingface dataset:
Question (gain): by selling 8 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 10 % ?
Options: a ) 6.54 , b ) 9.45 , c ) 7.34 , d ) 6.67 , e ) 5.09
Rationale: "90 % - - - 8 110 % - - - ? 90 / 110 * 8 = 6.54 answer : a"
Answer: a
Question (geometry): if the sum of a number and its square is 132 , what is the number ?
Options: a ) 15 , b ) 11 , c ) 28 , d ) 91 , e ) none of these
Rationale: let the number be x . then , x + x 2 = 132 ( x + 12 ) ( x - 11 ) = 0 x = 11 answer : b
Answer: b
Question (physics): during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 180 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 480
Rationale: "easy 480 is the answer . 3 / 4 ( x / 2 ) = 180 x = 180 * 8 / 3 = 480 . answer e"
Answer: e
Question (gain): a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 25 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 260 before any discount ?
Options: a ) $ 136.50 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 210.00
Rationale: since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 25 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 260 would be . . . . . ( $ 260 ) ( . 7 ) ( . 75 ) = ( $ 260 ) ( . 525 ) = 136.5 final answer : a
Answer: a
Question (general): if 2464 / 1.12 = 2200 , then 246.4 / 11.2 is equal to ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 25
Rationale: "answer given expression 246.4 / 11.2 = 2464 / 112 = 2464 / ( 1.12 x 100 ) = 2200 / 100 = 22 correct option : c"
Answer: c
Question (physics): if 4 men can paint 60 m long wall in 3 days , then 5 men can paint 50 m long wall in
Options: a ) 3 days , b ) 2 days , c ) 5 days , d ) 6 days , e ) 1 day
Rationale: the length of wall painted by one man in one day = 60 / 4 ã — 3 = 5 m no . of days required to paint 50 m wall by 5 men = 50 / 5 ã — 5 = 2 day . b
Answer: b
Question (gain): a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 10 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 22.22 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 110 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 110 - 90 ) / 90 * 100 = ~ 22.22 % answer : d ."
Answer: d
Question (general): a cricketer scored 152 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 60.52 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 152 - ( 12 x 4 + 2 x 6 ) = 152 - ( 60 ) = 92 now , we need to calculate 92 is what percent of 152 . = > 92 / 152 * 100 = 60.52 % answer : c"
Answer: c
Question (other): what is the square root of 96,721 ?
Options: a ) 476 , b ) 489 , c ) 289 , d ) 511 , e ) 311
Rationale: "1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) c = 489 ^ 2 and e = 511 ^ 2 c = ( 300 - 11 ) ^ 2 and e = ( 300 + 11 ) ^ 2 since we need the answer less than 90000 = > c is out . thus we have e as the ans ."
Answer: e
Question (gain): a profit of rs . 20000 is to be distributed among a , b , c in the proportion 2 : 3 : 5 . what will be the difference between b ’ s and c ’ s shares
Options: a ) 4000 , b ) 3000 , c ) 5500 , d ) 4500 , e ) none of these
Rationale: explanation : b ' s share = rs 20000 * ( 3 / 10 ) = rs 6000 c ' s share = rs 20000 * ( 5 / 10 ) = rs 10000 difference in b ' s and c ' s shares = rs 4000 answer : a
Answer: a
Question (other): find the first term and the common ratio of a g . p whose fourth term is 250 and seventh term is 31,250
Options: a ) 2 / 5,25 , b ) 4,5 / 2 , c ) 1,16 , d ) 2,5 , e ) 1,5
Rationale: a * r ^ 3 = 250 , a * r ^ 6 = 31,250 , r ^ 3 = 31,250 / 250 = 125 r = 5 , a * 125 = 250 , a = 2 answer : d
Answer: d
Question (gain): a sum of money deposited at c . i . amounts to rs . 6000 in 6 years and to rs . 7500 in 7 years . find the rate percent ?
Options: a ) 25 % , b ) 20 % , c ) 15 % , d ) 10 % , e ) 5 %
Rationale: "6000 - - - 1500 100 - - - ? = > 25 % answer : a"
Answer: a
Question (gain): a dog breeder would like to make the largest profit off of his latest litter of puppies . puppies with more than 4 spots sell for more money . the last litter had 10 puppies ; 6 had 5 spots , 3 had 4 spots , and 1 had 2 spots . what % of puppies can the dog breeder expect to sell for a greater profit ?
Options: a ) 90 % , b ) 65 % , c ) 50 % , d ) 85 % , e ) 80 %
Rationale: number of dogs with profitable spots = ( 6 + 3 ) = 6 + 3 = 9 now , we need to calculate 9 is what percent of 10 . = > 9 / 10 * 100 = 90 % a
Answer: a
Question (general): paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings .
Options: a ) 25 , b ) 35 , c ) 50 , d ) 20 , e ) 15
Rationale: let the original income = $ 100 . then , expenditure = $ 75 and savings = $ 25 new income = $ 120 , new expenditure = $ ( ( 110 / 100 ) * 75 ) = rs . 165 / 2 new savings = $ ( 120 - ( 165 / 2 ) ) = $ 75 / 2 increase in savings = $ ( ( 75 / 2 ) - 25 ) = $ 25 / 2 increase % = ( ( 25 / 2 ) * ( 1 / 25 ) * 100 ) % = 50 % . answer c ) 50 .
Answer: c
Question (general): on the average mr . jackson has 2 hours to plan for an long hour meeting he talk to his assistant 7 hours to prepare the paper work needed . how much hours should jackson and assistant has t plan for 30 min meeting ?
Options: a ) 4.5 hr , b ) 4.8 hr , c ) 4.9 hr , d ) 5.5 hr , e ) 6.5 hr
Rationale: for a 1 hour talk he took total of 9 hr time 1 hr = 9 hr ( 2 + 7 ) 30 min = 1 / 2 hr = ? so 9 * 1 / 2 div by 1 4.5 hr answer : a
Answer: a
Question (general): there are 4 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 50 , e ) e ) 100
Rationale: using anagram method : 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ r _ r _ b _ b so . . 6 ! / number of repeated letters ( 4 ! ) ( 2 ! ) = 5 ans : d
Answer: d
Question (general): the sum of the first 50 positive even integers is 2550 . what is the sum t of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : t = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Question (geometry): what should be added to 4440 so that it may become a perfect square ?
Options: a ) 44
b ) 45
c ) 46
d ) 47
e ) 49
Rationale: 67 x 67 = 4489 4489 - 4440 = 49 if added to 49 get perfect square answer = e
Answer: e
Question (gain): a chemist mixes one liter of pure water with x liters of a 50 % salt solution , and the resulting mixture is a 10 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: concentration of salt in pure solution = 0 concentration of salt in salt solution = 50 % concentration of salt in the mixed solution = 10 % the pure solution and the salt solution is mixed in the ratio of - - > ( 50 - 10 ) / ( 10 - 0 ) = 4 / 1 1 / x = 4 / 1 x = 1 / 4 answer : a
Answer: a
Question (general): how many positive even integers less than 100 contain digits 3 or 9 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 10
Rationale: "two digit numbers : 3 at tens place : 30 , 32,34 , 36,38 9 at tens place : 90 , 92,94 , 96,98 if 3 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer e"
Answer: e
Question (other): a can contains a mixture of two liquids a and b in the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many litres of liquid a was contained by the can initially ?
Options: a ) 25 , b ) 21 , c ) 20 , d ) 10 , e ) 15
Rationale: suppose the can initially contains 7 x and 5 x litres mixtures a and b respectively quantity of a in mix . left = [ 7 x – 7 / 12 * 9 ] = [ 7 x – 21 / 4 ] quantity of b in mix . left = [ 5 x – 5 / 12 * 9 ] = [ 5 x - 15 / 4 ] therefore [ 7 x - 21 / 4 ] = 7 / 9 or 28 x - 21 = 7 / 9 [ 5 x - 15 / 4 ] + 9 20 x + 21 252 x - 189 = 140 x + 147 or 112 x = 336 , x = 3 . quantity of a in the can initially = 7 * 3 = 21 answer : b
Answer: b
Question (general): in a company of 12 employees , 5 employees earn $ 36,000 , 4 employees earn $ 45,000 , and the 3 highest - paid employees earn the same amount . if the average annual salary for the 12 employees is $ 47,500 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 60,000 , b ) $ 65,000 , c ) $ 70,000 , d ) $ 75,000 , e ) $ 80,000
Rationale: 5 * 36,000 + 4 * 45,000 + 3 x = 12 * 47,500 3 x = 570,000 - 180,000 - 180,000 3 x = 210,000 x = 70,000 the answer is c .
Answer: c
Question (general): if y is 75 % greater than x , than x is what % less than y ?
Options: a ) 30.6 % , b ) 34.4 % , c ) 38.7 % , d ) 42.9 % , e ) 46.5 %
Rationale: "y = 1.75 x x = y / 1.75 = 100 y / 175 = 4 y / 7 x is 3 / 7 less which is about 42.9 % less than y . the answer is d ."
Answer: d
Question (physics): a 250 m long train is running at a speed of 55 km / hr . it crossed a platform of length 300 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 36 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 250 m + 300 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 550 m time = distance / speed = 550 x 18 / ( 5 x 55 ) = 36 sec ans is : c"
Answer: c
Question (general): arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 40 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: suppose anoop joined after 3 months . then , 20000 * 12 = 40000 * ( 12 – x ) = > = > x = 6 . answer : d
Answer: d
Question (general): when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 36 ?
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 5
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 36 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 5 more to make it 36 m + 36 answer - e"
Answer: e
Question (geometry): a cubical block of metal weighs 5 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48
b ) 40
c ) 24
d ) 18
e ) 12
Rationale: for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 5 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 5 pounds = 40 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 5 * 8 = 40 so answer is b
Answer: b
Question (probability): a box contains 3 red balls and 3 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 2 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 3 black balls be bbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 3 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 2 black ( bb ) and 3 red ( rrr ) they can be arranged in ( 5 ! ) / ( 2 ! x 3 ! ) hence required probability = [ ( 6 ! ) / ( 3 ! x 3 ! ) ] / [ ( 5 ! ) / ( 2 ! x 3 ! ) ] = 2 d"
Answer: d
Question (gain): 3 candidates in an election and received 1136 , 5636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55 % , c ) 57 % , d ) 63.2 % , e ) 62 %
Rationale: "total number of votes polled = ( 1136 + 5636 + 11628 ) = 18400 so , required percentage = 11628 / 18400 * 100 = 63.2 % d"
Answer: d
Question (general): the population of a town increased from 1 , 75,000 to 2 , 62,500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 262500 - 175000 ) = 87500 . increase % = ( 87500 / 175000 × 100 ) % = 50 % . required average = ( 50 / 10 ) % = 5 % . answer b"
Answer: b
Question (general): there are 14 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 87 , b ) 91 , c ) 95 , d ) 99 , e ) 103
Rationale: "14 c 2 = 91 the answer is b ."
Answer: b
Question (general): the decimal 0.1 is how many times greater than the decimal ( 0.0001 ) ^ 3 ?
Options: a ) 10 ^ 9 , b ) 10 ^ 10 , c ) 10 ^ 11 , d ) 10 ^ 12 , e ) 10 ^ 13
Rationale: "0.1 = 10 ^ - 1 ( 0.0001 ) ^ 3 = ( 10 ^ - 4 ) ^ 3 = 10 ^ - 12 10 ^ 11 * 10 ^ - 12 = 10 ^ - 1 the answer is c ."
Answer: c
Question (general): when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: "for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 4 digits after decimal total no . of decimals = 6 req . no . of digits = ( n - 1 ) = ( 6 - 1 ) = 5 answer : a"
Answer: a
Question (general): two employees a and b are paid a total of rs . 450 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?
Options: a ) 130 , b ) 140 , c ) 150 , d ) 170 , e ) 180
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 450 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 450 ⇒ y [ 15 / 10 + 1 ] = 450 ⇒ 25 y / 10 = 450 ⇒ 25 y = 4500 ⇒ y = 4500 / 25 = rs . 180 e"
Answer: e
Question (probability): what is the probability of getting only 1 head in a single throw of four fair coins ?
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 1 / 4 , d ) 1 / 5 , e ) 5 / 8
Rationale: "one possible case is httt . p ( httt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 there are 4 c 1 = 4 possible cases . p ( 1 head ) = 4 * 1 / 16 = 1 / 4 the answer is c ."
Answer: c
Question (general): a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 18 sec , c ) 36 sec , d ) 72 sec , e ) none
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 10 = 36 sec answer : c"
Answer: c
Question (gain): 4 is what percent of 50 ?
Options: a ) 0.2 % , b ) 8 % , c ) 10 % , d ) 20 % , e ) 500 %
Rationale: "4 = x * 50 / 100 x = 8 % ans ; b"
Answer: b
Question (geometry): the ratio of the radius of two circles is 2 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 7
b ) 2 : 9
c ) 4 : 9
d ) 3 : 7
e ) 3 : 4
Rationale: r 1 : r 2 = 2 : 3 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 4 : 9 answer : c
Answer: c
Question (gain): the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 55 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 992 , d ) $ 870 , e ) $ 660
Rationale: "c let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 155 % of $ 640 = 150 / 100 * 640 = $ 992 ."
Answer: c
Question (general): what is the units digit of the expression 14 ^ 7 − 18 ^ 4 ?
Options: a ) 0 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "units digit of 14 ^ 7 − 18 ^ 4 : consider the following unit digits : 4 ^ 1 : 4 4 ^ 2 : 6 4 ^ 3 : 4 4 ^ 4 : 6 ⇒ unit digit of 4 ^ 7 is : 4 the unit digit of 14 ^ 7 will also be 4 also : 8 ^ 1 : 8 8 ^ 2 : 4 8 ^ 3 : 2 8 ^ 4 : 6 ⇒ unit digit of 8 ^ 4 is : 6 the unit digit of 18 ^ 4 will also be 6 finally , 4 - 6 ( or 14 - 6 ) = 8 answer : e )"
Answer: e
Question (general): for 6 - digit integer 46 x , y 12 , when x and y are drawn at random from { 3 , 58 } , what is the probability w that the integer drawn is divisible by 8 ? * a solution will be posted in two days .
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: in general , the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8 . thus , in order for 46 , x , y 12 to be divided by 8 , y 12 should be divided by 8 . amongst 3 , 5,8 , 3 and 5 can be divided by 8 . therefore , w = two out of three can be divided and the answer is d .
Answer: d
Question (general): the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 75 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 48 , b ) 51 , c ) 60 , d ) 71 , e ) 96
Rationale: "the total sum of the numbers should be increased by 50 . then the average will increase by 50 / 10 = 5 . the correct average is 51 . the answer is b ."
Answer: b
Question (physics): a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "otal time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 8 = 10 gallons - - - > 2 / 10 = 20 % of the fuel used . b is the correct answer ."
Answer: b
Question (general): all the students of class are told to sit in circle shape . here the boy at the 10 th position is exactly opposite to 40 th boy . total number of boys in the class ?
Options: a ) 50 , b ) 45 , c ) 60 , d ) 55 , e ) 53
Rationale: "as half the circle shape consist of 40 - 10 = 30 boys , so total number of boys in full circle = 2 * 30 = 60 answer : c"
Answer: c
Question (physics): in what time will a train 120 metres long cross an electric pole , if its speed be 72 km / hr ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 9 sec , e ) 5 sec
Rationale: "solution speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec time taken = ( 120 / 20 ) sec = 6 sec . answer b"
Answer: b
Question (physics): a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1850 ?
Options: a ) s . 125 , b ) s . 108 , c ) s . 100 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1850 74 x = 1850 = > x = 25 5 x = 125 rs . answer : a"
Answer: a
Question (physics): a worker ' s daily wage is increased by 50 % and the new wage is $ 42 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 28 , d ) $ 32 , e ) $ 36
Rationale: "let x be the daily wage before the increase . 1.5 x = $ 42 x = $ 28 the answer is c ."
Answer: c
Question (general): 5 ltr of water is added with 15 ltr of a solution containing 26 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 17.25 % , b ) 19 , c ) 19.5 % , d ) 21.5 % , e ) 22 %
Rationale: we have a 15 litre solution containing 26 % alcohol in water . = > quantity of alcohol in the solution = 15 ã — 26 / 100 now 5 litre of water is added to the solution . = > total quantity of the new solution = 15 + 5 = 20 percentage of alcohol in the new solution = 15 ã — 26 / 100 20 ã — 100 = 15 ã — 26 / 10020 ã — 100 = 15 ã — 1.3 / 100 = 19.5 % c
Answer: c
Question (physics): a 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 177 , b ) 166 , c ) 350 , d ) 198 , e ) 161
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 39 = 50 / 3 3 ( x + 300 ) = 1950 è x = 350 m . answer : c"
Answer: c
Question (general): anne bought doughnuts for a class breakfast party . she bought 15 chocolate doughnuts , 12 coconut doughnuts , and 14 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 41 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: add the numbers of doughnuts . 15 + 12 + 14 = 41 . answer is a .
Answer: a
Question (general): following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 , c ) 13 , d ) 14 , e ) 14.5
Rationale: "let the candy and soda before the increase be c and s respectively so increased price of can = c ( 1 + 25 / 100 ) = 10 - - - - - - - - - - - > c = 8 increase price of soda : s ( 1 + 1 / 2 ) = 6 - - - - - - - - - - - > s = 4 hence total = 8 + 4 = 12 . . hence answer : b"
Answer: b
Question (physics): if a boat is rowed downstream for 500 km in 5 hours and upstream for 240 km in 6 hours , what is the speed of the boat and the river ?
Options: a ) 70 , 30 , b ) 30 , 70 , c ) 70 , 70 , d ) 30 , 30 , e ) 80 , 50
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 100 ; us = 40 x = ( 100 + 40 ) / 2 = 140 / 2 = 70 km / hr y = ( 100 - 40 ) / 2 = 60 / 2 = 30 km / hr answer : a"
Answer: a
Question (gain): the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8215 for a computer table , then what was the cost price of the computer table ?
Options: a ) 7297 , b ) 6625 , c ) 2871 , d ) 6725 , e ) 2981
Rationale: "explanation : cp = sp * ( 100 / ( 100 + profit % ) ) = 8215 ( 100 / 124 ) = rs . 6625 . answer : b"
Answer: b
Question (general): set d consists of all the prime numbers between 10 and 25 . what is the range of set d ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23
Rationale: answer of set d is 12 = a
Answer: a