Cheukting/mathqa huggingface dataset:
Question (general): ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 2.0 = ?
Options: a ) - 0.71 , b ) - 2.13 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 2.0 = - 2.13 answer b"
Answer: b
Question (probability): the probability that a number selected at random from the first 50 natural numbers is a composite number is
Options: a ) 17 / 26 , b ) 17 / 25 , c ) 17 / 20 , d ) 17 / 22 , e ) 17 / 21
Rationale: the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . nswer : b
Answer: b
Question (gain): a retailer buys 80 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 110 , b ) 115 , c ) 112 , d ) 118 , e ) 120
Rationale: "let the market price of each pen be $ 1 then , cost price of 80 pens = $ 36 selling price of 80 pens = 99 % of $ 80 = $ 79.20 profit % = ( ( 43.20 * 100 ) / 36 ) % = 120 % answer e ) 120"
Answer: e
Question (general): if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 66 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 16 , e ) 17
Rationale: "four wheeler = 16 * 4 = 64 ( max ) 2 wheel = 1 so no of 4 wheeler = 16 answer : d"
Answer: d
Question (physics): a train running at the speed of 27 km / hr crosses a post in 20 seconds . what is the length of the train ?
Options: a ) 200 , b ) 150 , c ) 300 , d ) 175 , e ) 250
Rationale: "speed = ( 27 x 5 / 18 ) = 7.5 m / sec . length of the train = ( speed x time ) . length of the train = 7.5 x 20 m = 150 m . answer : b"
Answer: b
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 128 in 4 years ?
Options: a ) 5 % , b ) 3 % , c ) 4 % , d ) 9 % , e ) 1 %
Rationale: "128 = ( 800 * 4 * r ) / 100 r = 4 % answer : c"
Answer: c
Question (gain): a restaurant spends one quarter of its monthly budget for rent and half of the rest for food and beverages . what percentage of the budget does the restaurant spend for food and beverages ?
Options: a ) 23.5 % , b ) 32.5 % , c ) 35 % , d ) 37.5 % , e ) 75 %
Rationale: "let the total budget be 100 as per the question , restaurant spends one quarter of its monthly budget for rent = 25 half of the rest for food and beverages = 75 / 2 = 37.5 therefore , percentage spent on food and beverage = 37.5 answer : d"
Answer: d
Question (general): if a is a positive integer , and if the units digit of a ^ 2 is 4 and the units digit of ( a + 1 ) ^ 2 is 1 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: if the units digit of a ^ 2 is 4 , then the units digit of a is either 2 or 8 . if the units digit of ( a + 1 ) ^ 2 is 1 , then the units digit of a + 1 is either 1 or 9 . to satisfy both conditions , the units digit of a must be 8 . then a + 2 has the units digit of 0 , thus the units digit of ( a + 2 ) ^ 2 will be 0 . the answer is a .
Answer: a
Question (geometry): the ratio of the volumes of two cubes is 125 : 512 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 25 : 64 , c ) 729 : 1331 , d ) 27 : 121 , e ) none of these
Rationale: "ratio of the sides = â ³ â ˆ š 125 : â ³ â ˆ š 512 = 5 : 8 ratio of surface areas = 5 ^ 2 : 8 ^ 2 = 25 : 64 answer : b"
Answer: b
Question (gain): an error 1 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 2.01 , b ) 30.1 , c ) 3.01 , d ) 25.01 , e ) 4.05
Rationale: "explanation : 100 cm is read as 101 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 101 × 101 ) cm 2 = 10609 ( a 2 - a 1 ) = 10201 - 10000 = 201 = > 201 / 10000 * 100 = 2.01 answer : a"
Answer: a
Question (general): george went to a fruit market with certain amount of money . with this money he can buy either 40 oranges or 40 mangoes . he retains 10 % of the money for taxi fare and buys 20 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 4 he decides to retain 10 % of 200 = 20 for taxi fare , so he is left with 180 he buys 20 mangoes ( @ 4 ) so he spends 80 money left is 100 ( 180 - 80 ) no of oranges he can buy = 100 / 4 = > 25 so , george can buy 25 oranges . a"
Answer: a
Question (general): the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 60 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 22 , b ) 27 , c ) 15 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 60 ) = 90 ( x - 5 ) 150 = 10 x = > x = 15 . answer : c"
Answer: c
Question (general): ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio w of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio w of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: b
Question (general): if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units u digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : u . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Question (general): find the value of 72515 x 9999 = m ?
Options: a ) 345434667 , b ) 246465757 , c ) 465767867 , d ) 725077485 , e ) 645354643
Rationale: "72515 x 9999 = 72515 x ( 10000 - 1 ) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 d"
Answer: d
Question (physics): a can give b 50 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 157.89 , b ) 157.13 , c ) 157.22 , d ) 111.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 950 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 950 = 842.10 m . b can give c = 1000 - 842.10 = 157.89 m . answer : a"
Answer: a
Question (gain): the present population of a town is 1240 . population increase rate is 4 % p . a . find the population of town after 1 years ?
Options: a ) 990 , b ) 1215 , c ) 1345 , d ) 1142 , e ) 1290
Rationale: "p = 1240 r = 4 % required population of town = p * ( 1 + r / 100 ) ^ t = 1240 * ( 1 + 4 / 100 ) = 1240 * ( 26 / 25 ) = 1290 ( approximately ) answer is e"
Answer: e
Question (general): sandy bought 65 books for $ 1080 from one shop and 55 books for $ 840 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 14 , b ) $ 16 , c ) $ 18 , d ) $ 20 , e ) $ 22
Rationale: "average price per book = ( 1080 + 840 ) / ( 65 + 55 ) = 1920 / 120 = $ 16 the answer is b ."
Answer: b
Question (gain): a merchant marks goods up by 80 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 35 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.8 p ) * x = 1.35 p x = 1.35 / 1.8 = 0.75 which is a discount of 25 % . the answer is b ."
Answer: b
Question (general): the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?
Options: a ) 174.75 cm , b ) 174.25 cm , c ) 173.75 cm , d ) 173.25 cm , e ) 172.75 cm
Rationale: the total height was 15 cm too much . the average height should be reduced by 15 cm / 20 = 0.75 cm the answer is b .
Answer: b
Question (gain): the cost price of a radio is rs . 3300 and it was sold for rs . 1230 , find the loss % ?
Options: a ) 62.7 % , b ) 65 % , c ) 88 % , d ) 65 % , e ) 62 %
Rationale: "3300 - - - - 2070 100 - - - - ? = > 62.7 % answer : a"
Answer: a
Question (gain): at what rate percent per annum will the simple interest on a sum of money be 3 / 5 of the amount in 10 years ?
Options: a ) 6 % , b ) 7 % , c ) 9 % , d ) 3 % , e ) 1 %
Rationale: "let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 3 x ) / ( x * 5 * 10 ) = 6 % answer : a"
Answer: a
Question (general): ( 3220 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 335 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9380 ) / 28 = 335 option c"
Answer: c
Question (general): working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 2 days ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 20
Rationale: "the rate of 5 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 5 * ( x / 4 ) = x / 20 units per day ; now , again as { time } * { combined rate } = { job done } then 2 * ( m * x / 20 ) = 2 x - - > m = 20 . answer : e ."
Answer: e
Question (gain): heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many litres of tomato puree will be obtained from 20 litres of tomato juice ?
Options: a ) 2 litres , b ) 2.4 litres , c ) 2.5 litres , d ) 6 litres , e ) 4 litres
Rationale: "tomato juice has 90 % water and 10 % tomato tomato puree has 20 % water and 80 % tomato so 20 liter of tomato juice has 20 * 90 / 100 = 18 liters of water and 2 liters of tomato . as tomato puree has 80 % content of tomato , so 2 liters of tomato from 20 liter juice corresponds to 80 % so tomato purees that can be obtained = 100 * 2 / 80 = 2.5 answer : c"
Answer: c
Question (gain): if a speaks the truth 40 % of the times , b speaks the truth 80 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.18 , b ) 0.12 , c ) 1.02 , d ) 1.2 , e ) 1.3
Rationale: "probability of a speaks truth p ( a ) = 4 / 10 ; false = 6 / 10 probability of b speaks truth p ( b ) = 8 / 10 ; false = 2 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 6 / 10 ) * ( 2 / 10 ) ] = 1 - 12 / 100 = 1 - 0.88 = 0.12 answer : b"
Answer: b
Question (general): a seller of used cars has 12 cars to sell and each of his clients selected 4 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "ifno caris selected more than once then the number of clients = 12 / 4 = 3 but since every car is being selected three times so no . of clients must be thrice as well = 3 * 3 = 9 answer : option a"
Answer: a
Question (geometry): the length of a rectangular landscape is 3 times its breadth . there is a playground in it whose area is 1600 square mtr & which is 1 / 3 rd of the total landscape . what is the length of the landscape ?
Options: a ) 90 , b ) 160 , c ) 150 , d ) 120 , e ) 140
Rationale: "sol . x * 3 x = 3 * 2500 x = 50 length = 3 * 50 = 150 c"
Answer: c
Question (general): set a contains all the even numbers between 2 and 50 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 1500 , b ) 3100 , c ) 4400 , d ) 6200 , e ) 7400
Rationale: "each term in set b is 60 more than the corresponding term in set a . the difference of the sums = 25 * 60 = 1500 . the answer is a ."
Answer: a
Question (gain): the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % , then the value of x is :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 25 , e ) 27
Rationale: "explanation : let the cost price of 1 article be z . so , the cost price of 20 article = 20 z - - - - - - - - - - - - - - - - - - - - - - - - - ( 1 ) selling price of 20 articles = 20 z + 25 % of 20 z = 25 z = > selling price of 1 article = 25 z / 20 = ( 5 / 4 ) * z = > selling price of x articles = ( 5 / 4 ) * z * x - - - - - - - - - - - - - - - - - - - - - - - - - ( 2 ) given that selling price ( s . p . ) of x articles = cost price ( c . p . ) of 20 articles = > ( 5 / 4 ) * z * x = 20 z = > x = 16 answer : b"
Answer: b
Question (geometry): the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one fourth of the males and 3 / 4 th of the females in the class ?
Options: a ) a ) 160 degree
b ) b ) 198 degree
c ) c ) 191 degree
d ) d ) 192 degree
e ) e ) 204 degree
Rationale: let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 / 4 of m = 2 x / 4 and 3 / 4 of f = 9 / 4 x . . total preferring that carrer = x / 2 + 9 x / 4 = 11 x / 4 now 5 x = 360 , so x = 360 / 5 = 72 . . so 72 * 11 / 4 = 198 ans 198 b
Answer: b
Question (gain): at what price must an article costing rs . 47.50 be marked in order that after deducting 20 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 62.3 , c ) 62.7 , d ) 74.2 , e ) 62.9
Rationale: cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 80 / 100 ) = 59.375 mp = 74.2 answer : d
Answer: d
Question (physics): a mail handler needs 3 hours to sort the mail . his assistant takes 6 hours to sort the mail . how many hours will it take for both of them working together to sort the mail ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 2 1 / 2 , e ) 1 1 / 5
Rationale: work hrs = ab / ( a + b ) = 18 / 9 = 2 answer is b
Answer: b
Question (other): a bag contains 7 black and 8 white balls . if two balls are drawn simultaneously , what is the probability that both are of the same color is ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 7 / 15
Rationale: drawing two balls of same color from seven black balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = ⁷ c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 7 / 15 answer is e
Answer: e
Question (gain): if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 240 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 240 x = 400 the answer is a ."
Answer: a
Question (general): the average of first five multiples of 7 is :
Options: a ) 9 , b ) 16 , c ) 15 , d ) 8 , e ) 21
Rationale: "explanation : ( 7 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 7 x 15 / 5 = 21 answer : e"
Answer: e
Question (physics): a does half as much work as b in 3 - fourth of the time . if together they take 18 days to complete the work , how much time shall b take to do it ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days
Rationale: explanation : let ‘ x ’ be the number of days taken by b alone to finish the whole work then , a alone will finish the whole work in 3 x / 4 × 2 days = 3 x / 2 days . then , working together , 3 x / 2 × x / 3 x / 2 + x = 18 days 3 x × x / 5 x = 18 3 x / 5 = 18 therefore , the number of days taken by b = x = 18 × 5 / 3 = 30 days . answer : option a
Answer: a
Question (general): a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 56 , find the sum of money ?
Options: a ) 288 , b ) 287 , c ) 72 , d ) 205 , e ) 267
Rationale: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 56 41 - - - - ? = > rs . 287 answer : b"
Answer: b
Question (physics): in what time will a train 80 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.0 sec , b ) 2.8 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 80 / 40 = 2.0 sec . answer : a"
Answer: a
Question (general): john purchased 1375 large bottles at $ 1.75 per bottle and 690 small bottles at $ 1.35 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.62 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.76
Rationale: "( 1375 * 1.75 + 690 * 1.35 ) / ( 1375 + 690 ) = ~ 1.62 option ( a )"
Answer: a
Question (gain): an investor deposited $ 5,000 to open a new savings account that earned 8 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 5050 , b ) $ 5101 , c ) $ 5202 , d ) $ 5303 , e ) $ 5404
Rationale: "the amount in the account after 6 months is 1.02 * 1.02 ( $ 5,000 ) = $ 5202 the answer is c ."
Answer: c
Question (general): 1 , 8 , 27 , 64 , . . .
Options: a ) 25 , b ) 48 , c ) 59 , d ) 63 , e ) 125
Rationale: "explanation : numbers are 1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 17 5 ^ 3 = 125 answer : e"
Answer: e
Question (other): a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 11 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 44 : 55 , e ) 4 : 6
Rationale: say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 11 - - > x ( a - b ) = 11 . since 11 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 11 . the above implies that either x = 1 and ( a - b ) = 11 or x = 11 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 11 . for the original question only option which fits is e , 4 : 5 . cats = 11 * 4 = 44 and dogs = 11 * 5 = 55 . answer : d .
Answer: d
Question (gain): john makes $ 60 a week from his job . he earns a raise and now makes $ 90 a week . what is the % increase ?
Options: a ) 16 % , b ) 50 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 30 / 60 ) * 100 = ( 3 / 6 ) * 100 = 50 % . b"
Answer: b
Question (general): a rope of which a calf is tied is increased from 12 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 2989 , b ) 2789 , c ) 1210 , d ) 1288 , e ) 1211
Rationale: "π ( 232 – 122 ) = 1210 answer : c"
Answer: c
Question (physics): x can finish a work in 21 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "work done by x in 1 day = 1 / 21 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 21 ) = 7 c"
Answer: c
Question (gain): a sells a bicycle to b and makes a profit of 25 % . b sells the same bicycle to c at a profit of 50 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 120
Rationale: explanation : let cp be 100 a sells at 25 % profit so sp = 125 b sells at 50 % profit = 125 x ( 1 + 50 / 100 ) = 187.5 cp - - - sp 100 - - - 187.5 x - - - 225 cp = 225 x 100 / 187.5 = 120 answer : e
Answer: e
Question (general): two trains of equal are running on parallel lines in the same direction at 18 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 21
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 18 = 25 / 9 = > x = 25 . answer : a"
Answer: a
Question (general): the average marks of a class of 12 students is 40 and that of another class of 28 students is 60 . find the average marks of all the students ?
Options: a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 54.0
Rationale: "sum of the marks for the class of 12 students = 12 * 40 = 480 sum of the marks for the class of 28 students = 28 * 60 = 1680 sum of the marks for the class of 40 students = 480 + 1680 = 2160 average marks of all the students = 2160 / 40 = 54 answer : e"
Answer: e
Question (general): if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 20 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 36 % , e ) 50 %
Rationale: official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.20 = 8 gallons of grape juice . 40 × 0.80 = 32 gallons of other components . if we add 10 gallons of grape juice , we will end up with 18 gallons of grape juice and 32 gallons of other components , and we will have a total of 50 gallons of the mixture . so 18 / 50 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 18 / 50 = 36 / 100 = 36 % . the correct answer is choice ( d )
Answer: d
Question (gain): a shopkeeper has 280 kg of apples . he sells 85 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 85 x 20 % + 60 x 30 % = 85 this profit will remain same for any total quantity unless the % of products remains the same . hence ' e ' is the answer"
Answer: e
Question (physics): 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 5 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 16 , d ) 26 , e ) 36
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 6 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 5 * ( 2 / 3 ) ) days = > 36 days answer : e"
Answer: e
Question (general): ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio e of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio e of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: b