options stringlengths 37 300 | correct stringclasses 5 values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
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a ) 2 : 1 , b ) 14 : 3 , c ) 7 : 2 , d ) 1 : 2 , e ) none | a | divide(add(add(3, 4), 7), 7) | if a : b : c = 3 : 4 : 7 , then the ratio ( a + b + c ) : c is equal to | solution : ( a + b + c ) = 3 + 4 + 7 = 14 and c = 7 then , ( a + b + c ) : c = 2 : 1 . answer : option a | a = 3 + 4
b = a + 7
c = b / 7
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a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00 | b | add(multiply(multiply(multiply(0.05, const_2), const_2), const_2), 0.3) | a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.05 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ? | 1 st day fine - 0.05 2 nd day fine - 0.05 * 2 = 0.1 ( as doubling gives lower value ) 3 rd day fine - 0.1 * 2 = 0.2 ( as doubling gives lower value ) 4 th day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value we add 0.3 this time ) 5 th day fine - 0.4 + 0.3 = 0.7 ( as doubling gives higher value we add 0.3 this time ) answer : b . | a = 0 * 5
b = a * 2
c = b * 2
d = c + 0
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a ) $ 900 , b ) $ 800 , c ) $ 1000 , d ) $ 920 , e ) $ 1500 | d | divide(230, subtract(const_1, divide(3, 4))) | linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 230 , what were her original savings ? | "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 230 . so 1 / 4 of her savings is $ 230 . so her original savings are 4 times $ 230 = $ 920 correct answer d" | a = 3 / 4
b = 1 - a
c = 230 / b
|
a ) 2 , b ) 4 , c ) 5 , d ) 500 , e ) none | a | divide(multiply(divide(10, const_100), 900), 45) | 45 x ? = 10 % of 900 | answer let 45 x a = ( 10 x 900 ) / 100 ∴ a = ( 10 x 9 ) / 45 = 2 correct option : a | a = 10 / 100
b = a * 900
c = b / 45
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['a ) 90 °', 'b ) 135 °', 'c ) 216 °', 'd ) 240 °', 'e ) 270 °'] | c | subtract(const_360, divide(multiply(add(add(add(add(20, 9), 5), 4), 2), const_360), const_100)) | a circle graph shows how the budget of a certain company was spent : 20 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ? | the percent of the budget for salaries is 100 - ( 20 + 9 + 5 + 4 + 2 ) = 60 % 100 % of the circle is 360 degrees . then ( 60 % / 100 % ) * 360 = 216 degrees the answer is c . | a = 20 + 9
b = a + 5
c = b + 4
d = c + 2
e = d * 360
f = e / 100
g = 360 - f
|
a ) 24 , b ) 33 , c ) 39 , d ) 40 , e ) 42 | a | subtract(44, divide(44, add(const_1, divide(120, const_100)))) | sales price is $ 44 , gross profit is 120 % of cost , what is the value of gross profit ? | cost + profit = sales cost + ( 120 / 100 ) cost = 44 cost = 20 profit = 44 - 20 = 24 answer ( a ) | a = 120 / 100
b = 1 + a
c = 44 / b
d = 44 - c
|
a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.67 % | b | divide(subtract(30, add(25, const_1)), subtract(divide(40, const_100), divide(add(25, const_1), const_100))) | seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ? | "x - wt of mix x added y - wt of mix y added 0.4 x + 0.25 y = 0.3 ( x + y ) 0.1 x = 0.05 y x / y = 5 / 10 = 1 / 2 y / x = 2 ( y + x ) / x = 3 = > x / ( y + x ) * 100 = 100 / 3 = 33.33 % answer : b" | a = 25 + 1
b = 30 - a
c = 40 / 100
d = 25 + 1
e = d / 100
f = c - e
g = b / f
|
a ) 4 metres , b ) 5 metres , c ) 7 metres , d ) 6 metres , e ) 8 metres | c | subtract(divide(divide(88, const_4), const_2), const_4) | a circular road runs around a circular garden . if the sum of the circumferences of the inner and outer circles is 88 metres and the radius of the inner circle is one - third of the outer circle , then the width of the road is : | let radius of inner circle = r 1 radius of outer circle = r 2 also r 1 = 1 / 3 * r 2 3 * r 1 = r 2 circumference of inner circle = 2 * pi * r 1 circumference of outer circle = 2 * pi * r 2 = 6 * pi * r 1 ( since r 2 = 3 * r 1 ) 2 * pi * r 1 + 6 * pi * r 1 = 88 ( as per question ) r 1 = 3.5 m r 2 = 3 * 3.5 = 10.5 m width of road = 10.5 - 3.5 = 7 m ans . answer : c | a = 88 / 4
b = a / 2
c = b - 4
|
a ) 24 / 256 , b ) 53 / 512 , c ) 105 / 512 , d ) 459 / 512 , e ) 47 / 256 | b | divide(add(add(multiply(add(5, 4), const_10), multiply(3, 5)), const_1), power(const_2, const_10)) | in a multiple choice test comprising 5 questions , each with 4 choices , what is the probability of a student getting 3 or more questions correct ? each question has only one correct answer and the student is equally likely to choose any of the 4 choices . | probability for choosing correct answer is 1 / 4 and incorrect answer is 3 / 4 for 3 correct answers , c ( 5,3 ) * ( 1 / 4 ) ^ 3 * ( 3 / 4 ) ^ 2 = 90 / ( 4 ^ 5 ) for 4 correct answers , c ( 5,4 ) * ( 1 / 4 ) ^ 4 * ( 3 / 4 ) ^ 1 = 15 / ( 4 ^ 5 ) for 5 correct answers , c ( 5,5 ) * ( 1 / 4 ) ^ 5 * ( 3 / 4 ) ^ 0 = 1 / ( 4 ^ 5 ) so total probability = 106 / 1024 = 53 / 512 ans b | a = 5 + 4
b = a * 10
c = 3 * 5
d = b + c
e = d + 1
f = 2 ** 10
g = e / f
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a ) 5 , b ) 4 , c ) 10 , d ) 11 , e ) 12 | c | multiply(subtract(inverse(6), inverse(15)), const_100) | p and q together can do a work in 6 days . if p alone can do it in 15 days . in how many days can q alone do it ? | 1 / 6 - 1 / 15 = = > 1 / 10 = = > 10 answer c | a = 1/(6)
b = 1/(15)
c = a - b
d = c * 100
|
a ) 15 , b ) 45 , c ) 30 , d ) 45 , e ) 60 | b | multiply(15, divide(12, subtract(11, 7))) | in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 12 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ? | this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 12 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 12 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 12 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 12 ) ( 1 ) 11 x = 7 x + 12 4 x = 12 x = 3 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 3 ) = 45 final answer : b | a = 11 - 7
b = 12 / a
c = 15 * b
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a ) 23 , b ) 1 : 2 , c ) 4 : 5 , d ) 3 : 5 , e ) 25 | c | divide(subtract(9, 5), 5) | the ratio between the sale price and the cost price of an article is 9 : 5 . what is the ratio between the profit and the cost price of that article ? | "c . p . = rs . 5 x and s . p . = rs . 9 x . then , gain = rs . 4 x required ratio = 4 x : 5 x = 4 : 5 c" | a = 9 - 5
b = a / 5
|
a ) s . 7.7 , b ) s . 7.4 , c ) s . 7.5 , d ) s . 7.1 , e ) s . 7.9 | c | multiply(divide(divide(multiply(divide(20, const_100), 300), 10), multiply(divide(20, const_100), 300)), const_100) | a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 300 , find the original price per kg ? | "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 300 - - - 80 ? - - - 2 = > rs . 7.5 answer : c" | a = 20 / 100
b = a * 300
c = b / 10
d = 20 / 100
e = d * 300
f = c / e
g = f * 100
|
a ) 3 / 8 , b ) 8 / 15 , c ) 9 / 16 , d ) 12 / 25 , e ) 16 / 27 | c | divide(multiply(divide(6, 8), const_100), multiply(divide(8, 6), const_100)) | 8 is 6 % of a , and 6 is 8 % of b . c equals b / a . what is the value of c ? | "6 a / 100 = 8 a = 400 / 3 8 b / 100 = 6 b = 75 c = b / a = 75 * 3 / 400 = 9 / 16 the answer is c ." | a = 6 / 8
b = a * 100
c = 8 / 6
d = c * 100
e = b / d
|
a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30 | a | subtract(65, add(add(subtract(50, 35), subtract(40, 35)), 35)) | of the 65 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ? | neither car nor garage = total - garage - ( swim - common ) = 65 - 50 - ( 40 - 35 ) = 65 - 55 = 10 answer a | a = 50 - 35
b = 40 - 35
c = a + b
d = c + 35
e = 65 - d
|
a ) 21 , b ) 36 , c ) 39 , d ) 60 , e ) 65 | b | divide(multiply(multiply(8, 12), 3), 8) | exactly 3 / 8 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ? | "the total number of the people in the room must be a multiple of both 8 and 12 ( in order 3 / 7 and 5 / 13 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 8 and 12 , which is 96 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 96 people in the room . therefore there are 3 / 8 * 96 = 36 people in the room under the age of 21 . answer : b ." | a = 8 * 12
b = a * 3
c = b / 8
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a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30 | c | divide(subtract(50, 10), const_2) | we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 10 , and the difference between the total number of strawberries and the total number of blueberries would increase by 50 . each blue box contains how many blueberries ? | "let x be the number of blueberries in each blue box . then there are x + 10 strawberries in each red box . x + ( x + 10 ) = 50 x = 20 the answer is c ." | a = 50 - 10
b = a / 2
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a ) – 3 , b ) 9 / 2 , c ) 1 , d ) 2 , e ) 3 | b | divide(multiply(const_3, const_3), 2) | if x / y = 3 and ( 2 a - x ) / ( 3 b - y ) = 3 , then the value of a / b is ? | x = 3 y 2 a - 3 y = 3 ( 3 b - y ) 2 a - 3 y = 9 b - 3 y 2 a = 9 b a / b = 9 / 2 answer : b | a = 3 * 3
b = a / 2
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it depends on z . | a | multiply(subtract(divide(power(divide(9702, const_3), 2), 4), add(add(add(multiply(multiply(const_1000, subtract(4, 2)), const_100), multiply(multiply(const_1000, subtract(4, 2)), const_10)), multiply(2, const_100)), subtract(const_100, 2))), 4) | if z is a multiple of 9702 , what is the remainder when z ^ 2 is divided by 4 ? | "2 is a factor of 9702 , so 2 is a factor of z . then 2 ^ 2 = 4 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 4 is 0 . the answer is a ." | a = 9702 / 3
b = a ** 2
c = b / 4
d = 4 - 2
e = 1000 * d
f = e * 100
g = 4 - 2
h = 1000 * g
i = h * 10
j = f + i
k = 2 * 100
l = j + k
m = 100 - 2
n = l + m
o = c - n
p = o * 4
|
a ) rs . 1200 , b ) rs . 890 , c ) rs . 600 , d ) rs . 1190 , e ) rs . 450 | d | divide(multiply(subtract(const_100, 15), 1400), const_100) | a man buys a cycle for rs . 1400 and sells it at a loss of 15 % . what is the selling price of the cycle ? | "explanation : s . p . = 85 % of rs . 1400 = rs . ( 85 / 100 * 1400 ) = rs . 1190 answer : d" | a = 100 - 15
b = a * 1400
c = b / 100
|
a ) 76 days , b ) 48 days , c ) 98 days , d ) 31 days , e ) 24 days | e | inverse(subtract(inverse(12), inverse(24))) | a and b can finish a work in 12 days while a alone can do the same work in 24 days . in how many days b alone will complete the work ? | "b = 1 / 12 – 1 / 24 = 1 / 24 = > 24 days answer : e" | a = 1/(12)
b = 1/(24)
c = a - b
d = 1/(c)
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | subtract(power(subtract(add(5, 3), 2), 2), multiply(floor(divide(power(subtract(add(5, 3), 2), 2), 5)), 5)) | when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 2 ) ^ 2 is divided by 5 ? | "n = 5 x + 3 , for some integer x ( n + 2 ) ^ 2 = ( 5 x + 5 ) ^ 2 = 5 y , for some integer y when we divide this by 5 , the remainder is 0 . the answer is a ." | a = 5 + 3
b = a - 2
c = b ** 2
d = 5 + 3
e = d - 2
f = e ** 2
g = f / 5
h = math.floor(g)
i = h * 5
j = c - i
|
a ) 3072 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536 | a | multiply(add(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(0.3, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), 0.3), const_10) | if an average hard drive had a capacity of 0.3 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ? | "0.3 * 2 ^ 10 = 0.3 * 1024 = 307.2 the answer is a ." | a = 0 * 3
b = a * 2
c = b * 2
d = c * 2
e = d * 2
f = e * 2
g = f * 2
h = g * 2
i = h * 2
j = i * 2
k = j + 0
l = k * 10
|
a ) 277 m , b ) 704 m , c ) 352 m , d ) 288 m , e ) 378 m | c | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 250), const_100) | the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 250 resolutions ? | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 250 resolutions . = 250 * 2 * 22 / 7 * 22.4 = 35200 cm = 352 m answer : c" | a = 3 + 4
b = a * 3
c = b + 1
d = 3 + 4
e = c / d
f = e * 22
g = f * 2
h = g * 250
i = h / 100
|
a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108 | b | divide(multiply(divide(subtract(const_100, 16), const_100), 8), divide(subtract(const_100, 93), const_100)) | if grapes are 93 % water and raisins are 16 % water , then how many kilograms did a quantity of raisins , which currently weighs 8 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . ) | let x be the original weight . the weight of the grape pulp was 0.07 x . since the grape pulp is 84 % of the raisins , 0.07 x = 0.84 ( 8 ) . then x = 12 * 8 = 96 kg . the answer is b . | a = 100 - 16
b = a / 100
c = b * 8
d = 100 - 93
e = d / 100
f = c / e
|
a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23 | a | subtract(subtract(25, const_2), add(add(10, const_4), const_1)) | set a consists of all the prime numbers between 10 and 25 . what is the range of set a ? | "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 23 lowest number = 11 range = highest - lowest = 23 - 11 = 12 option a" | a = 25 - 2
b = 10 + 4
c = b + 1
d = a - c
|
a ) 19 , b ) 27 , c ) 29 , d ) 47 , e ) 49 | e | divide(add(370, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36)) | a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 370 m long platform ? | let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 370 ) / 36 * 5 / 18 = 49 min . answer : e | a = const_0_2778 * 36
b = a * 12
c = 370 + b
d = const_0_2778 * 36
e = c / d
|
a ) 4 , b ) 3 , c ) 5 , d ) 7 , e ) 9 | a | add(divide(multiply(add(25, const_1), 60), const_1000), 2.5) | a train of 25 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 2.5 km long ? | "d = 25 * 60 + 2500 = 4000 m t = 4000 / 60 * 18 / 5 = 240 sec = 4 mins answer : a" | a = 25 + 1
b = a * 60
c = b / 1000
d = c + 2
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a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 65 % | c | multiply(divide(subtract(multiply(const_3, divide(const_1, const_2)), const_1), const_1), const_100) | the length of a rectangle is halved , while its breadth is tripled . what is the % change in area ? | "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c" | a = 1 / 2
b = 3 * a
c = b - 1
d = c / 1
e = d * 100
|
a ) 776 , b ) 864 , c ) 299 , d ) 257 , e ) 125 | b | divide(multiply(divide(288, divide(subtract(60, subtract(const_100, 60)), const_100)), 60), const_100) | there were two candidates in an election . winner candidate received 60 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ? | "w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 288 60 % - - - - - - - - ? = > 864 answer : b" | a = 100 - 60
b = 60 - a
c = b / 100
d = 288 / c
e = d * 60
f = e / 100
|
a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 355 | c | multiply(23, 14) | the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is : | "clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer : option c" | a = 23 * 14
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a ) 225 , b ) 500 , c ) 75 , d ) 800 , e ) none 0 of them | a | multiply(divide(const_1, add(add(const_4, 3), const_1)), 600) | a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of b . | "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is a" | a = 4 + 3
b = a + 1
c = 1 / b
d = c * 600
|
a ) 700 , b ) 704 , c ) 704 , d ) 706 , e ) 707 | b | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 500), const_100) | the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : option b" | a = 3 + 4
b = a * 3
c = b + 1
d = 3 + 4
e = c / d
f = e * 22
g = f * 2
h = g * 500
i = h / 100
|
a ) 280 , b ) 270 , c ) 260 , d ) 250 , e ) 240 | a | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 220) | a 220 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ? | "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 220 ) / 9 = 500 / 9 = > x = 280 . answer : option a" | a = 120 + 80
b = a * const_0_2778
c = b * 9
d = c - 220
|
a ) 14,550 , b ) 18,550 , c ) 22,550 , d ) 26,550 , e ) 30,550 | c | multiply(divide(add(500, 402), const_2), add(divide(subtract(500, 402), const_2), const_1)) | the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 402 to 500 inclusive ? | "2 + 4 + 6 + 8 + . . . + 100 = 2550 402 + 404 + . . . + 500 = 50 ( 400 ) + ( 2 + 4 + . . . + 100 ) = 20,000 + 2550 = 22,550 the answer is c ." | a = 500 + 402
b = a / 2
c = 500 - 402
d = c / 2
e = d + 1
f = b * e
|
a ) 10 , b ) 9 , c ) 8 , d ) 7 , e ) 6 | e | multiply(subtract(4, 3), divide(432, add(multiply(4, 9), multiply(3, 12)))) | we run a business that rents out canoes and kayaks . a canoe rental costs $ 9 per day , and a kayak rental costs $ 12 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 432 in revenue . how many more canoes than kayaks were rented out ? | "let x be the number of canoes . then 3 x / 4 is the number of kayaks . 9 x + ( 3 x / 4 ) * 12 = 432 9 x + 9 x = 432 18 x = 432 x = 24 ( canoes ) 3 x / 4 = 18 ( kayaks ) there were 24 - 18 = 6 more canoes rented out . the answer is e ." | a = 4 - 3
b = 4 * 9
c = 3 * 12
d = b + c
e = 432 / d
f = a * e
|
a ) 16 % , b ) 17.5 % , c ) 18.2 % , d ) 58.5 % , e ) 13 % | b | multiply(divide(subtract(72900, add(48000, 14000)), add(48000, 14000)), const_100) | ramu bought an old car for rs . 48000 . he spent rs . 14000 on repairs and sold it for rs . 72900 . what is his profit percent ? | "total cp = rs . 48000 + rs . 14000 = rs . 62000 and sp = rs . 72900 profit ( % ) = ( 72900 - 62000 ) / 62000 * 100 = 17.5 % answer : b" | a = 48000 + 14000
b = 72900 - a
c = 48000 + 14000
d = b / c
e = d * 100
|
a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 2000 | a | divide(subtract(140, divide(multiply(6, 2600), const_100)), subtract(divide(5, const_100), divide(6, const_100))) | rs . 2600 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ? | "( x * 5 * 1 ) / 100 + [ ( 2600 - x ) * 6 * 1 ] / 100 = 140 x = 1600 answer : a" | a = 6 * 2600
b = a / 100
c = 140 - b
d = 5 / 100
e = 6 / 100
f = d - e
g = c / f
|
a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252 | d | divide(const_2, choose(add(6, 6), 6)) | a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? | "first , total ways to select for all boys and girls , i . e 12 ! / ( 6 ! * 6 ! ) = 12 * 11 * 10 * 9 * 8 * 7 / 6 * 5 * 4 * 3 * 2 = 924 then there are one two way girls can have all same colors , either white or black . the number of ways in which 6 girls can select 6 white balls = 6 c 6 = 1 the number of ways in which 6 girls can select 6 black balls = 6 c 6 = 1 therefore , total favorable outcomes / total outcomes = 2 / 924 = 1 / 462 d" | a = 6 + 6
b = math.comb(a, 6)
c = 2 / b
|
a ) 74 kg , b ) 78.5 kg , c ) 99.5 kg , d ) data inadequate , e ) none of these | c | add(multiply(7, 3.5), 75) | the average weight of 7 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ? | "total weight increased = ( 7 x 3.5 ) kg = 24.5 kg . weight of new person = ( 75 + 24.5 ) kg = 99.5 kg . answer : option c" | a = 7 * 3
b = a + 75
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a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35 | a | divide(30, divide(32, 16)) | in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 32 people were made to stand in a column , how many columns could be formed ? | "16 * 30 = 32 * n n = 15 the answer is a ." | a = 32 / 16
b = 30 / a
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a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | e | subtract(427398, multiply(floor(divide(427398, 10)), 10)) | what least number must be subtracted from 427398 so that remaining no . is divisible by 10 | "explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted answer : option e" | a = 427398 / 10
b = math.floor(a)
c = b * 10
d = 427398 - c
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a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34 | c | add(subtract(add(10, 8), subtract(10, 8)), const_1) | the average age of applicants for a new job is 10 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ? | minimum age = average - 1 standard deviation = 10 - 8 = 2 maximum age = average + 1 standard deviation = 10 + 8 = 18 maximum number of different ages of the applicants = 18 - 2 + 1 = 17 answer c | a = 10 + 8
b = 10 - 8
c = a - b
d = c + 1
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a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs | e | divide(900, 50) | ajay can ride 50 km in 1 hour . in how many hours he can ride 900 km ? | 1 hour he ride 50 km he ride 900 km in = 900 / 50 * 1 = 18 hours answer is e | a = 900 / 50
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a ) 32 : 99 , b ) 8 : 21 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21 | b | divide(add(multiply(6000, 4), multiply(divide(12000, const_3), multiply(2, 4))), add(multiply(12000, multiply(2, const_3)), multiply(subtract(12000, divide(12000, const_3)), multiply(2, const_3)))) | a and b invests rs . 6000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ? | "a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 48000 : 126000 8 : 21 answer : b" | a = 6000 * 4
b = 12000 / 3
c = 2 * 4
d = b * c
e = a + d
f = 2 * 3
g = 12000 * f
h = 12000 / 3
i = 12000 - h
j = 2 * 3
k = i * j
l = g + k
m = e / l
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a ) 80 , b ) 90 , c ) 56 , d ) 70 , e ) 60 | c | multiply(add(7, const_1), 7) | tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 7 even numbers . his mother immediately worked out the answer . how much had he scored in math ? | "c 56 sum = ( n x n ) + n hence , 7 x 7 = 49 + 7 = 56" | a = 7 + 1
b = a * 7
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a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 12 seconds , e ) 18 seconds | a | divide(80, multiply(add(15, 3), const_0_2778)) | the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 80 metres ? | "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 80 m = 80 / 5 = 16 seconds . answer : a" | a = 15 + 3
b = a * const_0_2778
c = 80 / b
|
a ) a . 72 , b ) b . 50 , c ) c . 92 , d ) d . 46 , e ) e . 44 | c | multiply(divide(44, add(6, add(const_1, const_4))), add(12, add(6, add(const_1, const_4)))) | a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 44 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ? | at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 44 seconds . thus x = 4 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 92 seconds . answer c | a = 1 + 4
b = 6 + a
c = 44 / b
d = 1 + 4
e = 6 + d
f = 12 + e
g = c * f
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a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39 | a | add(divide(subtract(add(40, 2), 21), 1.5), 21) | each week , harry is paid x dollars per hour for the first 21 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 ? | "42 x = 21 x + 1.5 x ( h - 21 ) = = > 42 = 21 + 1.5 ( h - 21 ) = = > h - 21 = 21 / 1.5 = 14 = > h = 35 answer is a" | a = 40 + 2
b = a - 21
c = b / 1
d = c + 21
|
a ) 1 / 35 , b ) 1 / 9 , c ) 1 / 10 , d ) 1 / 20 , e ) 1 / 30 | a | divide(const_2, choose(add(4, 4), 4)) | a bag contains 4 white marbles and 4 black marbles . if each of 4 girls and 4 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? | "first , total ways to select for all boys and girls , i . e 8 ! / ( 4 ! * 4 ! ) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1 = 70 then there are one two way girls can have all same colors , either white or black . the number of ways in which 4 girls can select 4 white balls = 4 c 4 = 1 the number of ways in which 4 girls can select 4 black balls = 4 c 4 = 1 therefore , total favorable outcomes / total outcomes = 2 / 70 = 1 / 35 a" | a = 4 + 4
b = math.comb(a, 4)
c = 2 / b
|
a ) 4 days , b ) 2 days , c ) 4 1 ⁄ 2 days , d ) 3 days , e ) none of these | a | inverse(divide(add(inverse(3), inverse(6)), const_2)) | a can knit a pair of socks in 3 days . b can knit the same thing in 6 days . if they are knitting together , in how many days will they knit two pairs of socks ? | explanationa ’ s one day ’ s work = 1 ⁄ 3 rd work . b ’ s one day ’ s work = 1 ⁄ 6 rd work . ( a + b ) ’ s one day ’ s work = 1 ⁄ 3 + 1 ⁄ 6 = 1 ⁄ 2 nd work . ∴ a and b together can complete the work ( knit a pair of socks ) in 2 days . ∴ they together knit two pair of socks in 4 days . answer a | a = 1/(3)
b = 1/(6)
c = a + b
d = c / 2
e = 1/(d)
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a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 % | b | sqrt(72) | the difference between c . i . and s . i . on an amount of $ 20,000 for 2 years is $ 72 . what is the rate of interest per annum ? | "$ 72 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 20000 * x . the interest on the first year ' s interest is 20000 * x * x 20000 * x ^ 2 = 72 x = 0.06 the answer is b ." | a = math.sqrt(72)
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a ) 8 , b ) 6 , c ) 4 , d ) 10 , e ) 12 | a | divide(subtract(multiply(multiply(3, 4), 6), multiply(3, 4)), 6) | running at their respective constant rates , machine x takes 6 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 2 w widgets ? | "together they make 5 / 4 w widgets in 3 days . so they make w widgets in 3 * 4 / 5 = 12 / 5 days . 1 / ( t + 2 ) + 1 / t = 5 / 12 now , calculating this is really cumbersome so try to plug in options to get to the answer . if machine x takes 12 days to produce 2 w widgets , it would take 6 days to make w widgets , t would be 4 . 1 / 6 + 1 / 4 = 5 / 12 it works so t = 4 . answer : a" | a = 3 * 4
b = a * 6
c = 3 * 4
d = b - c
e = d / 6
|
a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9 | a | subtract(power(subtract(73, multiply(add(const_3, const_4), const_10)), subtract(353, multiply(floor(divide(353, const_4)), const_4))), multiply(const_2, const_10)) | find the ones digit of 73 ^ 353 | "the units digit of 73 ^ 353 will be the same as the units digit of 3 ^ 353 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 353 = 352 + 1 = ( multiple of 4 ) + 1 , then the units digit of 3 ^ 353 will be the first number in the pattern thus 3 . answer : a ." | a = 3 + 4
b = a * 10
c = 73 - b
d = 353 / 4
e = math.floor(d)
f = e * 4
g = 353 - f
h = c ** g
i = 2 * 10
j = h - i
|
a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4 | e | divide(add(divide(subtract(multiply(26, 2), 10), subtract(multiply(2, 2), const_1)), subtract(26, multiply(2, divide(subtract(multiply(26, 2), 10), subtract(multiply(2, 2), const_1))))), 3) | if 2 x + y = 26 and x + 2 y = 10 , then ( x + y ) / 3 = | "we have two equations : 2 x + y = 26 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 36 divide both sides by 3 to get : x + y = 12 so , ( x + y ) / 3 = 12 / 3 = 4 answer : e" | a = 26 * 2
b = a - 10
c = 2 * 2
d = c - 1
e = b / d
f = 26 * 2
g = f - 10
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 26 - k
m = e + l
n = m / 3
|
a ) 2998 , b ) 2799 , c ) 2890 , d ) 1485 , e ) 1584 | e | multiply(volume_cylinder(divide(3, const_2), 14), 16) | find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 16 per cubic meter ? | "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 16 = 1584 answer : e" | a = 3 / 2
b = volume_cylinder * (
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a ) 34 , b ) 76 , c ) 29 , d ) 12 , e ) 20 | a | divide(subtract(subtract(subtract(1015, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6) | alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1015 . find the cost of each ice - cream cup ? | "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1015 96 + 225 + 490 + 6 x = 1015 6 x = 204 = > x = 34 . answer : a" | a = 16 * 6
b = 1015 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 6
|
a ) 14700 , b ) 14703 , c ) 37798 , d ) 13777 , e ) 14778 | a | multiply(35000, divide(add(divide(subtract(50000, add(add(5000, 4000), 5000)), const_3), add(5000, 4000)), 50000)) | a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more thanc . out of a total profit of rs . 35000 , a receives : | explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 * 21 / 50 ) = rs . 14,700 . answer : a ) 14700 | a = 5000 + 4000
b = a + 5000
c = 50000 - b
d = c / 3
e = 5000 + 4000
f = d + e
g = f / 50000
h = 35000 * g
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a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,700 , e ) $ 21,100 | d | multiply(const_2, const_10) | a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,000 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ? | "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 2000 = $ 20700 correct option : d" | a = 2 * 10
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a ) 12 days , b ) 16 days , c ) 18 days , d ) 11.5 days , e ) 38 days | d | add(divide(subtract(const_1, multiply(add(divide(const_1, 24), divide(const_1, 30)), 6)), add(divide(const_1, multiply(add(const_2, const_3), multiply(const_2, 6))), add(divide(const_1, 24), divide(const_1, 30)))), 6) | a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 6 days before the completion of the work . in how many days was the work completed ? | "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 6 days = 6 * ( 1 / 24 + 1 / 30 ) = 9 / 20 remaining work = 11 / 20 the number of days required for this initial work = 5.5 days . the total number of days required = 6 + 5.5 = 11.5 days . answer : d" | a = 1 / 24
b = 1 / 30
c = a + b
d = c * 6
e = 1 - d
f = 2 + 3
g = 2 * 6
h = f * g
i = 1 / h
j = 1 / 24
k = 1 / 30
l = j + k
m = i + l
n = e / m
o = n + 6
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a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1800 , e ) $ 1900 | a | divide(300, subtract(const_1, divide(3, 4))) | linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ? | "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 300 . so 1 / 4 of her savings is $ 300 . so her original savings are 4 times $ 300 = $ 1200 correct answer a" | a = 3 / 4
b = 1 - a
c = 300 / b
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a ) 22 , b ) 28 , c ) 99 , d ) 42 , e ) 66 | d | multiply(6, 7) | walking 7 / 6 of his usual rate , a boy reaches his school 6 min early . find his usual time to reach the school ? | "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 6 - - - - - - - - - ? = 42 m answer : d" | a = 6 * 7
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a ) 3.6 sec , b ) 18 sec , c ) 35 sec , d ) 72 sec , e ) none of these | c | multiply(multiply(divide(divide(add(230, 120), const_1000), subtract(45, 9)), const_60), const_60) | a jogger running at 9 kmph along side a railway track is 230 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? | "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 230 + 120 ) m = 350 m . ∴ time taken = ( 350 ⁄ 10 ) sec = 35 sec . answer c" | a = 230 + 120
b = a / 1000
c = 45 - 9
d = b / c
e = d * const_60
f = e * const_60
|
a ) 300 m , b ) 1000 m , c ) 120 m , d ) 200 m , e ) 500 m | e | divide(36, subtract(divide(36, 12), 10)) | a train covers a distance of 36 km in 12 min . if it takes 10 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 36 / 12 * 60 ) km / hr = ( 180 * 5 / 18 ) m / sec = 50 m / sec . length of the train = 50 * 10 = 500 m . answer : e" | a = 36 / 12
b = a - 10
c = 36 / b
|
a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.24 | e | add(214.18, divide(const_3, const_100)) | 8 people decided to split the restaurant bill evenly . if the bill was $ 214.18 dollars , how much money did they 1 cent is the smallest unit ? | "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 418 not divisible by a hence , we need to add 6 to this number for it to be divisible by 8 correct option : e" | a = 3 / 100
b = 214 + 18
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a ) 2 days , b ) 3 days , c ) 1 day , d ) 4 days , e ) 5 days | c | divide(36, multiply(6, divide(48, multiply(4, 2)))) | if 4 women can color 48 m long cloth in 2 days , then 6 women can color 36 m long cloth in | "the length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 women = 36 / 6 × 6 = 1 day . c" | a = 4 * 2
b = 48 / a
c = 6 * b
d = 36 / c
|
['a ) 16', 'b ) 20', 'c ) 36', 'd ) 32', 'e ) 28'] | d | multiply(multiply(multiply(const_2, const_2), const_2), 4) | a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 4 cubic feet . if a large block has twice the width , twice the depth , and twice the length of a normal block , what is the volume of cheese in a large block in cubic feet ? | volume of cube = lbh = 4 new cube l , b , h are increases of 2 l , 2 b , 2 h new volume of cube = 2 l * 2 b * 2 h = 8 * lbh = 8 * 4 = 32 answer : d | a = 2 * 2
b = a * 2
c = b * 4
|
a ) 26 years , b ) 27 years , c ) 28 years , d ) 29 years , e ) 30 years | a | divide(subtract(32, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | a man is 32 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is | "explanation : let ' s son age is x , then father age is x + 32 . = > 2 ( x + 6 ) = ( x + 32 + 6 ) = > 2 x + 12 = x + 38 = > x = 26 years answer : option a" | a = 2 * 2
b = a - 2
c = 32 - b
d = 2 - 1
e = c / d
|
['a ) 48', 'b ) 56', 'c ) 68', 'd ) 87', 'e ) 92'] | a | multiply(add(const_10, const_2), divide(1440, rectangle_area(20, 18))) | the monthly rent of a shop of dimension 20 feet × 18 feet is rs . 1440 . what is the annual rent per square foot of the shop ? | sol . monthly rent per square feet = 1440 / ( 20 * 18 ) = 4 & annual rent per square feet = 12 * 4 = 48 answer : a | a = 10 + 2
b = 1440 / rectangle_area
c = a * b
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a ) 72 : 107 , b ) 4 : 5 , c ) 17 : 23 , d ) 3 : 4 , e ) 68 : 95 | a | divide(multiply(9000, 24), add(multiply(9000, 3), multiply(add(9000, 5000), subtract(24, 3)))) | ashley and betty start a business with $ 9000 each , and after 3 months , betty adds another $ 5000 . how should they share the profits at the end of the 24 months ? | ashley invests $ 9000 for 24 months , but betty invests $ 9000 for the first 3 months and then adds $ 5000 . so , the investment of betty for remaining 21 months is $ 14000 . ashley : betty 9000 * 24 : ( 9000 * 3 ) + ( 14000 * 21 ) 216000 : 321000 a : b = 72 : 107 answer : a | a = 9000 * 24
b = 9000 * 3
c = 9000 + 5000
d = 24 - 3
e = c * d
f = b + e
g = a / f
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a ) 23 , b ) 37 , c ) 28 , d ) 40 , e ) 50 | e | subtract(const_100, subtract(add(25, 50), 25)) | in an examination , 25 % of total students failed in hindi , 50 % failed in english and 25 % in both . the percentage of these who passed in both the subjects is : | "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 25 + 50 â € “ 25 = 50 therefore students who passed = 100 â € “ 50 = 50 . answer : e" | a = 25 + 50
b = a - 25
c = 100 - b
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a ) 140 sq . units , b ) 170 sq . units , c ) 190 sq . units , d ) 168 sq . units , e ) 149 sq . units | d | multiply(12, multiply(const_2, divide(sqrt(1225), divide(12, const_2)))) | the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 12 units ? | "explanation : given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 12 units area of the rectangle = lb = 14 * 12 = 168 sq . units answer : option d" | a = math.sqrt(1225)
b = 12 / 2
c = a / b
d = 2 * c
e = 12 * d
|
a ) 6 , b ) 7 , c ) 5 , d ) 3 , e ) 2 | c | divide(subtract(51, multiply(const_4, 9)), 6) | a pineapple costs rs 9 each and a watermelon costs rs . 6 each . if i spend rs 51 on total what is the number of pineapple i purchased ? | "5 * 9 + 6 = 51 5 pineapples answer : c" | a = 4 * 9
b = 51 - a
c = b / 6
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a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these | a | divide(4000, divide(multiply(const_1, const_1), add(multiply(const_3, const_2), multiply(const_1, const_1)))) | a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4000 as profit , what is their total profit ? | "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4000 = > total profit = 4000 * 7 = 28000 . answer : option a" | a = 1 * 1
b = 3 * 2
c = 1 * 1
d = b + c
e = a / d
f = 4000 / e
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a ) 22 , b ) 15 , c ) 77 , d ) 266 , e ) 182 | b | divide(multiply(subtract(26, 6), 3), 4) | ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age ? | "present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : b" | a = 26 - 6
b = a * 3
c = b / 4
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a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25 | e | add(multiply(divide(3, 5), divide(3, 5)), add(multiply(divide(3, 5), divide(const_2, 5)), multiply(divide(3, 5), divide(const_2, 5)))) | a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability j that you can still row the canoe ? | simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability j of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer : 1 – 4 / 25 = 21 / 25 . answer choice e . | a = 3 / 5
b = 3 / 5
c = a * b
d = 3 / 5
e = 2 / 5
f = d * e
g = 3 / 5
h = 2 / 5
i = g * h
j = f + i
k = c + j
|
a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 44 | c | add(divide(subtract(343, 14), 7), const_1) | how many multiples of 7 are there between 14 and 343 , exclusive ? | "7 * 2 = 14 7 * 49 = 343 total multiples = ( 49 - 2 ) + 1 = 48 exclude 7 343 = 48 - 2 = 46 answer is ( c )" | a = 343 - 14
b = a / 7
c = b + 1
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a ) 16 seconds , b ) 76 seconds , c ) 10.8 seconds , d ) 12 seconds , e ) 18 seconds | c | divide(60, multiply(add(15, 5), const_0_2778)) | the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 5 kmph , what time will he take to cover 60 metres ? | "speed of the boat downstream = 15 + 5 = 20 kmph = 20 * 5 / 18 = 50 / 9 m / s hence time taken to cover 60 m = 60 * 9 / 50 = 10.8 seconds . answer : c" | a = 15 + 5
b = a * const_0_2778
c = 60 / b
|
a ) 250 miles , b ) 240 miles , c ) 230 miles , d ) 235 miles , e ) 75 miles | a | multiply(divide(350, 70), 50) | david and lewis leave chennai for hyderabad simultaneously at 8 p . m in the night driving in two cars at speeds of 50 mph and 70 mph respectively . as soon as lewis reaches hyderabad he returns back to chennai along the same route and meets david on the way back . if the distance between the two cities is 350 miles , how far from chennai did david and lewis meet ? | time taken by lewis to reach hyderabad = 350 / 70 = 5 hours in 5 hours , david travels 50 * 5 = 250 miles so distance at which they meet should be greater than 250 miles . only a satisfies . answer is a . | a = 350 / 70
b = a * 50
|
a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600 | e | divide(600, 1) | divide $ 600 among a , b in the ratio 1 : 2 . how many $ that a get ? | sum of ratio terms = 1 + 2 = 3 a = 600 * 1 / 3 = $ 200 answer is e | a = 600 / 1
|
a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22 | b | add(subtract(subtract(const_1000, const_10), multiply(multiply(const_10, multiply(78, 78)), multiply(const_4, const_2))), const_10) | how many three digit numbers w are divisible by 78 or 91 ? | "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples w - - 11 + 9 - 1 = 19 . hence answer is 19 . b" | a = 1000 - 10
b = 78 * 78
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
|
a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 5 | e | divide(subtract(5, 4), subtract(10, 5)) | cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 4 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ? | "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 4 ) / ( 10 - 5 ) = 1 / 5 so they should be mixed in the ratio 1 : 5 answer - e" | a = 5 - 4
b = 10 - 5
c = a / b
|
a ) 7 / 45 , b ) 2 / 45 , c ) 1 / 9 , d ) 8 / 45 , e ) 9 / 45 | c | divide(2, 18) | what is the hcf of 2 / 3 , 4 / 9 and 6 / 18 | explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 9 , 18 ) = 2 / 18 = 1 / 9 answer : option c | a = 2 / 18
|
a ) 12 , b ) 39 , c ) 54 , d ) 156 , e ) none | d | sqrt(multiply(234, 104)) | the mean proportional between 234 and 104 is | "sol . required mean proportional = √ 234 x 104 = √ 13 x 9 x 2 x 13 x 8 = ( 13 x 3 x 4 ) = 156 . answer d" | a = 234 * 104
b = math.sqrt(a)
|
a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70 | a | divide(multiply(6.30, const_100), subtract(add(25, const_100), divide(multiply(add(30, const_100), subtract(const_100, 20)), const_100))) | a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 6.30 less , he would have gained 30 % . find the cost of the article . | "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 6.30 when c . p = ( 100 * 6.30 ) / 21 = 30 answer : a" | a = 6 * 30
b = 25 + 100
c = 30 + 100
d = 100 - 20
e = c * d
f = e / 100
g = b - f
h = a / g
|
a ) 15 , b ) 30 , c ) 36 , d ) 72 , e ) 46 | d | multiply(const_3, add(16, 8)) | a bus starts from city x . the number of women in the bus is half of the number of men . in city y , 16 men leave the bus and 8 women enter . now , number of men and women is equal . in the beginning , how many passengers entered the bus ? | explanation : originally , let number of women = x . then , number of men = 2 x . so , in city y , we have : ( 2 x - 16 ) = ( x + 8 ) or x = 24 . therefore total number of passengers in the beginning = ( x + 2 x ) = 3 x = 72 . answer : d | a = 16 + 8
b = 3 * a
|
a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8 | a | divide(multiply(4, 2), add(multiply(3, 3), multiply(4, 2))) | at tea factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ? | at tea factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a . | a = 4 * 2
b = 3 * 3
c = 4 * 2
d = b + c
e = a / d
|
a ) 160 , b ) 210 , c ) 260 , d ) 310 , e ) 360 | c | multiply(divide(subtract(subtract(power(multiply(6, divide(add(const_100, 50), const_100)), const_2), power(multiply(4, divide(subtract(const_100, 25), const_100)), const_2)), subtract(power(6, const_2), power(4, const_2))), subtract(power(6, const_2), power(4, const_2))), const_100) | there are two concentric circles with radii 6 and 4 . if the radius of the outer circle is increased by 50 % and the radius of the inner circle decreased by 25 % , by what percent does the area between the circles increase ? | "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 36 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 20 pi . when the big circle ' s radius increases , the new area is 81 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 72 pi . the ratio of a 2 / a 1 is 72 / 20 = 3.6 which is an increase of 260 % . the answer is c ." | a = 100 + 50
b = a / 100
c = 6 * b
d = c ** 2
e = 100 - 25
f = e / 100
g = 4 * f
h = g ** 2
i = d - h
j = 6 ** 2
k = 4 ** 2
l = j - k
m = i - l
n = 6 ** 2
o = 4 ** 2
p = n - o
q = m / p
r = q * 100
|
a ) 1 / 8 , b ) 1 / 7 , c ) 1 / 2 , d ) 1 / 4 , e ) 1 / 6 | c | divide(6, multiply(6, const_2)) | john works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 6 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ? | first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 6 x total tips for all months = 6 * x + 6 x = 12 x tips for august / total tips for all months = 6 x / 12 x = 1 / 2 answer : c | a = 6 * 2
b = 6 / a
|
a ) $ 960 , b ) $ 1,350 , c ) $ 1,500 , d ) $ 2,050 , e ) $ 2,250 | c | divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 7.50), const_1000) | a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 192,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ? | "number of boxes = total volume / volume of one box = 192,000 / ( 8 * 10 * 12 ) = 200 one box costs 7.50 , so 200 box will cost = 200 * 7.5 = 1500 c is the answer" | a = 3 * 100
b = 8 * 10
c = a + b
d = c + 4
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 7
j = i / 1000
|
a ) 10 , b ) 12 , c ) 20 , d ) 11.25 , e ) 15 | d | inverse(add(divide(const_1, 15), divide(const_1, 45))) | x does a work in 15 days . y does the same work in 45 days . in how many days they together will do the same work ? | "x ' s 1 day ' s work = 1 / 15 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 15 + 1 / 45 ) = 1 / 11.25 both together will finish the work in 11.25 days . correct option is d" | a = 1 / 15
b = 1 / 45
c = a + b
d = 1/(c)
|
a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 % | a | multiply(divide(subtract(add(multiply(divide(15, const_100), 2), multiply(divide(75, const_100), 3)), add(subtract(3, multiply(divide(75, const_100), 3)), subtract(2, multiply(divide(15, const_100), 2)))), add(3, 2)), const_100) | in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 75 percent of the republicans and 15 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ? | "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 3 : 2 = = 60 : 40 represents the number ratio of republicans : democrats . if 75 % of republicans ( which is ( 60 * 0.75 ) = 45 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 51 ( 45 + 6 ) voters voted for candidate x and 49 voted for candidate y . thus we can infer that candidate x is expected to win the election by 2 ( 51 - 49 ) votes . therefore candidate x is expected to win the election by ( 2 / 100 ) votes which is equivalent to 2 % . i think the answer is a ." | a = 15 / 100
b = a * 2
c = 75 / 100
d = c * 3
e = b + d
f = 75 / 100
g = f * 3
h = 3 - g
i = 15 / 100
j = i * 2
k = 2 - j
l = h + k
m = e - l
n = 3 + 2
o = m / n
p = o * 100
|
a ) 500 , b ) 1,600 / 3 , c ) 1,000 , d ) 1,500 , e ) 2,500 | c | multiply(divide(4000, 2), divide(const_1, 2)) | the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 4000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ? | "st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 4000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 4000 2 = 2000 d = s * t d = 2000 * ( 1 / 2 ) d = 1000 answer : c" | a = 4000 / 2
b = 1 / 2
c = a * b
|
a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 % | c | multiply(divide(multiply(500, power(10, add(const_3, const_3))), multiply(10, power(10, 9))), const_100) | a corporation that had $ 10 billion in profits for the year paid out $ 500 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 ) | "required answer = [ employee benefit / profit ] * 100 = [ ( 500 million ) / ( 10 billion ) ] * 100 = [ ( 500 * 10 ^ 6 ) / ( 10 * 10 ^ 9 ) ] * 100 = ( 50 / 1000 ) * 100 = 5 % so answer is ( c )" | a = 3 + 3
b = 10 ** a
c = 500 * b
d = 10 ** 9
e = 10 * d
f = c / e
g = f * 100
|
a ) a ) 2.12 , b ) b ) 2.2 , c ) c ) 1.25 , d ) d ) 1.3 , e ) e ) 2.0 | e | divide(multiply(0.75, 8), 3) | if 0.75 : x : : 3 : 8 , then x is equal to : | ( x * 3 ) = ( 0.75 * 8 ) x = 6 / 3 x = 2 answer = e | a = 0 * 75
b = a / 3
|
a ) 88 kmph , b ) 89 kmph , c ) 72 kmph , d ) 50 kmph , e ) 18 kmph | d | divide(divide(280, const_1000), divide(20, const_3600)) | a train 280 m long can cross an electric pole in 20 sec and then find the speed of the train ? | "length = speed * time speed = l / t s = 280 / 20 s = 14 m / sec speed = 14 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 50 kmph answer : d" | a = 280 / 1000
b = 20 / 3600
c = a / b
|
a ) 12 % decrease , b ) 18 % decrease , c ) 19 % decrease , d ) 13.75 % decrease , e ) 12.5 % decrease | c | subtract(const_100, multiply(multiply(add(const_1, divide(15, const_100)), subtract(const_1, divide(25, const_100))), const_100)) | the tax on a commodity is diminished by 25 % and its consumption increased by 15 % . the effect on revenue is ? | "100 * 100 = 10000 75 * 115 = 9200 - - - - - - - - - - - 10000 - - - - - - - - - - - 1375 100 - - - - - - - - - - - ? = > 13.75 % decrease answer : c" | a = 15 / 100
b = 1 + a
c = 25 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
|
a ) 81000 , b ) 81028 , c ) 105300 , d ) 29889 , e ) 22312 | c | add(add(83200, multiply(divide(1, 8), 83200)), multiply(divide(1, 8), add(83200, multiply(divide(1, 8), 83200)))) | every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 83200 ? | 83200 * 9 / 8 * 9 / 8 = 105300 . answer : c | a = 1 / 8
b = a * 83200
c = 83200 + b
d = 1 / 8
e = 1 / 8
f = e * 83200
g = 83200 + f
h = d * g
i = c + h
|
a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | b | multiply(2, multiply(const_3, const_2)) | the length of a side of a hexagon is 2 inches . what is the perimeter ? | "hexagon . it means 6 equal sides . p = 2 + 2 + 2 + 2 + 2 + 2 = 4 + 4 + 4 = 8 + 4 = 12 inches answer b" | a = 3 * 2
b = 2 * a
|
a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22 | b | subtract(add(12, 6), const_1) | a student is ranked 12 th from right and 6 th from left . how many students are there in totality ? | "from right 12 , from left 6 total = 12 + 6 - 1 = 17 answer : b" | a = 12 + 6
b = a - 1
|
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