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a ) 0 , b ) 4.3 , c ) 2.5 , d ) 4.67 , e ) 10 | b | divide(subtract(64, subtract(multiply(const_4, divide(12, const_2)), 12)), 12) | the area of one square is x ^ 2 + 12 x + 36 and the area of another square is 4 x ^ 2 β 12 x + 9 . if the sum of the perimeters of both squares is 64 , what is the value of x ? | spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 6 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 6 l 2 = 2 x - 3 p 1 = 4 ( x + 6 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 64 4 ( x + 6 ) + 4 ( 2 x - 3 ) = 64 . . . . . . . . . . . . . . > x = 4.3 answer : b | a = 12 / 2
b = 4 * a
c = b - 12
d = 64 - c
e = d / 12
|
a ) 4 , b ) 5 , c ) 8 , d ) 9 , e ) 10 | a | divide(add(6, 2), const_2) | in one hour , a boat goes 6 km along the stream and 2 km against the stream . the sped of the boat in still water ( in km / hr ) is : | "solution speed in still water = 1 / 2 ( 6 + 2 ) km / hr = 4 kmph . answer a" | a = 6 + 2
b = a / 2
|
a ) 45 , b ) 55 , c ) 60 , d ) 65 , e ) 50 | e | divide(subtract(350, 200), 3) | on the first day of her vacation , louisa traveled 200 miles . on the second day , traveling at the same average speed , she traveled 350 miles . if the 200 - mile trip took 3 hours less than the 350 - mile trip , what was the average speed , in miles per hour ? | "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 200 / t = 350 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 200 / 4 = 50 answer : e" | a = 350 - 200
b = a / 3
|
a ) 2 hr , b ) 2 hr 20 min , c ) 2 hr 40 min , d ) 5 hr 40 min , e ) 6 hr | c | add(multiply(const_2, const_100), multiply(const_60, subtract(divide(480, add(divide(480, 4), divide(480, 8))), const_2))) | while working alone at their respective constant rates , server g uploads 480 files in 4 hours and server y uploads 480 files in 8 hours . if all files uploaded by these servers are the same size , how long would it take the two servers , working at the same time and at their respective constant rates , to process a total of 480 files ? | server g processes 480 / 4 files per hour = 120 per hour server y processes 180 / 8 files per hour = 60 per hour total files processed per hour when g and y work together = 120 + 60 per hour = 180 files per hour 480 / 180 = 2 2 / 3 hours = c | a = 2 * 100
b = 480 / 4
c = 480 / 8
d = b + c
e = 480 / d
f = e - 2
g = const_60 * f
h = a + g
|
a ) 72 % , b ) 87.5 % , c ) 63.7 % , d ) 56.9 % , e ) 90 % | b | subtract(const_100, multiply(divide(add(40, const_100), add(60, const_100)), const_100)) | two numbers are respectively 40 % and 60 % more than a third number . what percentage is the first of the second ? | "required answer = ( 100 + x ) / ( 100 + y ) * 100 = 140 * 100 / 160 = 87.5 % answer is b" | a = 40 + 100
b = 60 + 100
c = a / b
d = c * 100
e = 100 - d
|
a ) s . 300 , b ) s . 408 , c ) s . 389 , d ) s . 368 , e ) s . 323 | b | divide(578, add(add(multiply(divide(2, 3), divide(1, 4)), divide(1, 4)), 1)) | if rs . 578 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ? | "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 578 * 2 / 17 = rs . 68 b ' s share = 578 * 3 / 17 = rs . 102 c ' s share = 578 * 12 / 17 = rs . 408 . answer : b" | a = 2 / 3
b = 1 / 4
c = a * b
d = 1 / 4
e = c + d
f = e + 1
g = 578 / f
|
a ) 18 , b ) 28 , c ) 32 , d ) 48 , e ) 58 | d | multiply(divide(divide(12880, 230), 7), 6) | the ratio between the number of sheep and the number of horses at the stewar farm is 6 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ? | "et no of sheep and horses are 6 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 6 * 8 ) = 48 answer : d" | a = 12880 / 230
b = a / 7
c = b * 6
|
a ) 6 , b ) 24 , c ) 8 , d ) 12 , e ) 44 | a | divide(add(divide(56, 8), divide(40, 8)), const_2) | a man swims downstream 40 km and upstream 56 km taking 8 hours each time , what is the speed of the man in still water ? | "40 - - - 8 ds = 5 ? - - - - 1 56 - - - - 8 us = 7 ? - - - - 1 m = ? m = ( 5 + 7 ) / 2 = 6 answer : a" | a = 56 / 8
b = 40 / 8
c = a + b
d = c / 2
|
a ) 28 % , b ) 41 % , c ) 45 % , d ) 64 % , e ) 78 % | d | multiply(divide(multiply(divide(70, const_100), divide(subtract(6, 4), 6)), add(multiply(divide(subtract(const_100, 80), const_100), divide(4, 6)), multiply(divide(70, const_100), divide(subtract(6, 4), 6)))), const_100) | 4 / 6 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is | "total population = 60 ( assume ) . 4 / 6 * 60 = 40 people from montague . 2 / 6 * 60 = 20 people from capulet . 0.2 * 40 = 8 people from montague support juliet . 0.7 * 20 = 14 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 14 / ( 8 + 14 ) = ~ 64 . answer : d" | a = 70 / 100
b = 6 - 4
c = b / 6
d = a * c
e = 100 - 80
f = e / 100
g = 4 / 6
h = f * g
i = 70 / 100
j = 6 - 4
k = j / 6
l = i * k
m = h + l
n = d / m
o = n * 100
|
a ) 3 , b ) 5 , c ) 6 , d ) 16 , e ) 18 | e | add(5, 3) | if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 3 is divided by 41 ? | "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . x + 3 = 82 k + 5 + 3 = 82 k + 8 or x + 3 = 8 , 90,172 etc . when divided by 41 , we will get the remainder 8 . e" | a = 5 + 3
|
a ) 5.45 % , b ) 6.23 % , c ) 7 % , d ) 8.12 % , e ) 11.5 % | e | multiply(divide(subtract(5800, add(4400, 800)), add(4400, 800)), const_100) | alfred buys an old scooter for $ 4400 and spends $ 800 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ? | "c . p . = 4400 + 800 = $ 5200 s . p . = $ 5800 gain = 5800 - 5200 = $ 600 gain % = 600 / 5200 * 100 = 11.5 % answer is e" | a = 4400 + 800
b = 5800 - a
c = 4400 + 800
d = b / c
e = d * 100
|
a ) 288 , b ) 190 , c ) 188 , d ) 180 , e ) 12 | d | divide(add(1100, 700), divide(1100, 110)) | a 1100 m long train crosses a tree in 110 sec , how much time will it take to pass a platform 700 m long ? | l = s * t s = 1100 / 110 s = 10 m / sec . total length ( d ) = 1800 m t = d / s t = 1800 / 10 t = 180 sec answer : d | a = 1100 + 700
b = 1100 / 110
c = a / b
|
a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 580 , e ) s . 585 | c | subtract(multiply(subtract(540, 440), 6), subtract(540, 440)) | if rs . 440 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ? | "80 = ( 440 * 4 * r ) / 100 r = 5.68 % i = ( 440 * 6 * 5.68 ) / 100 = 150 440 + 150 = 590 answer : c" | a = 540 - 440
b = a * 6
c = 540 - 440
d = b - c
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | b | subtract(divide(5, const_2), multiply(43, 43)) | what is the remainder when 43 ^ 92 is divided by 5 ? | "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 92 has the form 4 k so the units digit of 43 ^ 92 is 1 . the remainder when dividing by 5 is 1 . the answer is b ." | a = 5 / 2
b = 43 * 43
c = a - b
|
a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) 23 kg | a | subtract(multiply(add(29, const_1), 27.8), multiply(29, 28)) | the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.8 kg . the weight of the new student is | "the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.8 weight of the new student = ( 30 * 27.8 β 29 * 28 ) = 834 - 812 = 22 answer : a" | a = 29 + 1
b = a * 27
c = 29 * 28
d = b - c
|
a ) - 12 , b ) - 6 , c ) 12 , d ) 6 , e ) 24 | a | multiply(divide(12, const_3), negate(divide(12, const_4))) | in the quadratic equation ax 2 - x - 12 = 0 , if the sum of two roots is 1 , what is the product of the two roots ? | explanation : the sum of the roots of the quadratic equation ax 2 + bx + c = 0 are ( - b / a ) and the product of the roots are ( c / a ) . thus , in the equation ax 2 - 11 x + 40 = 0 , where a = a , b = - 1 and c = - 12 . we get , sum of the roots = 1 / a = 1 a = 1 product of the roots = - 12 / 1 = - 12 answer : a | a = 12 / 3
b = 12 / 4
c = a * negate
|
a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11 | b | multiply(divide(subtract(63, 60), 60), const_100) | a book is bought for $ 60 and sold for $ 63 . what is the profit in percentage ? | "63 / 60 = 1.05 the answer is b ." | a = 63 - 60
b = a / 60
c = b * 100
|
a ) none , b ) one , c ) two , d ) three , e ) four | a | divide(add(factorial(6), 6), add(factorial(6), 6)) | for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers e are there between 6 * + 2 and 6 * + 6 , inclusive ? | "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes e in this range . answer : a ." | a = math.factorial(6)
b = a + 6
c = math.factorial(6)
d = c + 6
e = b / d
|
a ) + 20 % , b ) - 25 % , c ) + 305 , d ) - 30 % , e ) can not determined | a | divide(subtract(multiply(add(const_100, 50), subtract(const_100, 20)), multiply(const_100, const_100)), const_100) | in the science city , kolkata the rate of the ticket is increased by 50 % to increased the revenue but simultaneously 20 % of the visitor decreased . what is percentage change in the revenue . if it is known that the science city collects one revenue only from the visitors and it has no other financial supports : | solution : let the initial revenue be 100 . 100 - - - - - 50 % β ( ticket up ) - - - - - > 150 - - - - - 20 % β ( visitors down ) - - - - - > 120 . there is 20 % increase in the revenue . answer : option a | a = 100 + 50
b = 100 - 20
c = a * b
d = 100 * 100
e = c - d
f = e / 100
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | multiply(add(const_3, const_4), const_2) | 81 * 82 * 83 * 84 * 85 * 86 * 87 * 89 . what should be in the unit place in this product ? | it should be zero in the unit place in this product . 85 * 82 will give zero in unit place . answer : a | a = 3 + 4
b = a * 2
|
a ) 201 , b ) 240 , c ) 124 , d ) 125 , e ) 180 | c | add(add(divide(500, add(const_4, const_1)), divide(subtract(500, add(const_4, const_1)), power(add(const_4, const_1), const_2))), divide(subtract(500, add(const_4, const_1)), power(add(const_4, const_1), const_3))) | how many zeros does 500 ! end with ? | "according to above 500 ! has 500 / 5 + 500 / 25 + 500 / 125 = 100 + 20 + 4 = 124 trailing zeros . answer : c ." | a = 4 + 1
b = 500 / a
c = 4 + 1
d = 500 - c
e = 4 + 1
f = e ** 2
g = d / f
h = b + g
i = 4 + 1
j = 500 - i
k = 4 + 1
l = k ** 3
m = j / l
n = h + m
|
a ) 32 , b ) 119 , c ) 128 , d ) 135 , e ) 143 | a | multiply(divide(subtract(12, divide(48, 12)), divide(48, 12)), add(divide(subtract(12, divide(48, 12)), divide(48, 12)), divide(48, 12))) | if the sum of two positive integers is 12 and the difference of their squares is 48 , what is the product of the two integers ? | "let the 2 positive numbers x and y x + y = 12 - - 1 x ^ 2 - y ^ 2 = 48 = > ( x + y ) ( x - y ) = 48 - - 2 using equation 1 in 2 , we get = > x - y = 4 - - 3 solving equation 1 and 3 , we get x = 8 y = 4 product = 8 * 4 = 32 answer a" | a = 48 / 12
b = 12 - a
c = 48 / 12
d = b / c
e = 48 / 12
f = 12 - e
g = 48 / 12
h = f / g
i = 48 / 12
j = h + i
k = d * j
|
a ) 16 % , b ) 16.66 % , c ) 17.9 % , d ) 18.12 % , e ) 60 % | e | multiply(divide(subtract(80, 50), 50), const_100) | john makes $ 50 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ? | "increase = ( 30 / 50 ) * 100 = ( 3 / 5 ) * 100 = 60 % . e" | a = 80 - 50
b = a / 50
c = b * 100
|
a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9 | a | divide(divide(add(16, 10), const_2), const_2) | a man can row downstream at 16 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ? | "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 16 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 26 = > x = 13 , y = 3 . answer : a" | a = 16 + 10
b = a / 2
c = b / 2
|
a ) $ 10.00 , b ) $ 11.20 , c ) $ 14.40 , d ) $ 25.20 , e ) $ 18.00 | d | multiply(divide(subtract(const_100, 20), const_100), multiply(divide(subtract(const_100, 30), const_100), 45.00)) | a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer β s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer β s suggested retail price o f $ 45.00 ? | "for retail price = $ 45 first maximum discounted price = 45 - 30 % of 45 = 45 - 13.5 = 31.5 price after additional discount of 20 % = 31.5 - 20 % of 31.5 = 31.5 - 6.3 = 25.2 answer : option d" | a = 100 - 20
b = a / 100
c = 100 - 30
d = c / 100
e = d * 45
f = b * e
|
a ) 0.4 , b ) 0.5 , c ) 0.65 , d ) 0.75 , e ) 0.85 | a | divide(subtract(150, 90), 150) | in a group of 150 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ? | "number of people whose age is less than 20 is given by 150 - 90 = 60 probability p that a person selected at random from the group is less than 20 is given by 60 / 150 = 0.4 correct answer a" | a = 150 - 90
b = a / 150
|
a ) 5,150 , b ) 7,550 , c ) 10,150 , d ) 12,550 , e ) 20,150 | d | multiply(divide(add(300, 202), const_2), add(divide(subtract(300, 202), const_2), const_1)) | the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 202 to 300 inclusive ? | "2 + 4 + 6 + 8 + . . . + 100 = 2550 202 + 204 + . . . + 300 = 50 ( 200 ) + ( 2 + 4 + . . . + 100 ) = 10,000 + 2550 = 12,550 the answer is d ." | a = 300 + 202
b = a / 2
c = 300 - 202
d = c / 2
e = d + 1
f = b * e
|
a ) 60 kg , b ) 70 kg , c ) 80 kg , d ) 89 kg , e ) 95 kg | d | add(multiply(8, 3), 65) | the average weight of 8 person ' s increases by 3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | "total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 65 + 24 ) kg = 89 kg . d )" | a = 8 * 3
b = a + 65
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a ) 46.85 % , b ) 43.75 % , c ) 50 % , d ) 56.25 % , e ) 36 % | b | multiply(subtract(divide(add(const_100, 15), subtract(const_100, 20)), const_1), const_100) | a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 15 % impurities to the product . find the net profit percentage of the dealer ? | the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 20 % impurities to the product . it means that he is selling $ 5 worth of product for $ 5.75 . so his profit is $ 5.75 - $ 4 = $ 1.75 and his profit percent is ( 1.75 / 4 ) * 100 = 43.75 % answer : - b | a = 100 + 15
b = 100 - 20
c = a / b
d = c - 1
e = d * 100
|
a ) 400 , b ) 420 , c ) 461.5 , d ) 500 , e ) 600 | c | divide(300, divide(65, const_100)) | if it is assumed that 65 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ? | "minimum no of mail to be sent for getting 300 responses at 65 % = 300 / 0.65 = 461.5 option c" | a = 65 / 100
b = 300 / a
|
['a ) 90 , 85,60', 'b ) 85 , 75,60', 'c ) 90 , 75,70', 'd ) 90 , 75,60', 'e ) none'] | d | multiply(6, sqrt(divide(33300, multiply(add(multiply(6, 4), add(multiply(6, 5), multiply(5, 4))), const_2)))) | if the length , breadth and the height of a cuboid are in the ratio 6 : 5 : 4 and if the total surface area is 33300 cm 2 cm 2 , then the length , breadth and height in cms , are respectively . | explanation : let length = 6 x , breadth = 5 x and height = 4 x in cm 2 ( 6 x Γ 5 x + 5 x Γ 4 x + 6 x Γ 4 x ) = 33300 148 x 2 = 33300 β x 2 = 33300 / 148 = 225 β x = 15 length = 90 cm , breadth = 75 cm and height = 60 cm correct option : d | a = 6 * 4
b = 6 * 5
c = 5 * 4
d = b + c
e = a + d
f = e * 2
g = 33300 / f
h = math.sqrt(g)
i = 6 * h
|
a ) m , b ) m , c ) m , d ) m , e ) m | c | divide(14, subtract(divide(14, 10), 6)) | a train covers a distance of 14 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 14 / 10 * 60 ) km / hr = ( 84 * 5 / 18 ) m / sec = 70 / 3 m / sec . length of the train = 70 / 3 * 6 = 140 m . answer : c" | a = 14 / 10
b = a - 6
c = 14 / b
|
a ) 450 , b ) 750 , c ) 1,800 , d ) 5,900 , e ) 7,500 | a | subtract(multiply(2, 360), multiply(2, divide(multiply(5, 360), add(const_4, const_4)))) | eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 2 hours ? | "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 2 hours ) = 450 cans . the answer is a ." | a = 2 * 360
b = 5 * 360
c = 4 + 4
d = b / c
e = 2 * d
f = a - e
|
a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 16 | e | multiply(divide(subtract(31, 3), add(3, 4)), 4) | one hour after yolanda started walking from x to y , a distance of 31 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob Ρ ' s was 4 miles per hour , how many miles had bob walked when they met ? | "when b started walking y already has covered 3 miles out of 31 , hence the distance at that time between them was 31 - 3 = 28 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 28 / 7 = 4 hours . in 6 hours b walked 4 * 4 = 16 miles . answer : e ." | a = 31 - 3
b = 3 + 4
c = a / b
d = c * 4
|
a ) 5 / 18 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 6 | a | multiply(5, add(divide(const_1, 30), divide(const_1, 45))) | two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 5 days ? | "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 5 days = 5 ( 1 / 18 ) = 5 / 18 . answer a" | a = 1 / 30
b = 1 / 45
c = a + b
d = 5 * c
|
a ) $ 198 , b ) $ 216 , c ) $ 220 , d ) $ 180 , e ) $ 240 | d | subtract(add(200, multiply(divide(200, const_100), 20)), multiply(divide(add(200, multiply(divide(200, const_100), 20)), const_100), 25)) | a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 25 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ? | wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 25 emlpoyee paid = . 75 * 240 = 180 $ answer d | a = 200 / 100
b = a * 20
c = 200 + b
d = 200 / 100
e = d * 20
f = 200 + e
g = f / 100
h = g * 25
i = c - h
|
a ) 899.015 , b ) 752.804 , c ) 714.642 , d ) 629.906 , e ) none of these | d | subtract(multiply(divide(789.009, const_100), 56.84), multiply(divide(const_1, const_3), multiply(divide(789.009, const_100), 56.84))) | 789.009 - ? + 56.84 = 215.943 | "explanation : 629.906 answer : option d" | a = 789 / 9
b = a * 56
c = 1 / 3
d = 789 / 9
e = d * 56
f = c * e
g = b - f
|
a ) 19 , b ) 22 , c ) 25 , d ) 20 , e ) 36 | e | multiply(subtract(15, 3), 3) | an seller earns an income of re 3 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 15 th day of business , he earns an income of : | 2 nd day he earns = 3 ( 2 β 3 ) 3 rd day he earns = 3 ( 3 β 3 ) on 15 th day he earns 3 ( 15 - 3 ) = 36 rupees answer : e | a = 15 - 3
b = a * 3
|
a ) 18 , b ) 99 , c ) 19 , d ) 18 , e ) 17 | e | subtract(divide(multiply(80, 40), const_100), divide(multiply(10, 15), const_100)) | how much 80 % of 40 is greater than 10 % of 15 ? | "( 80 / 100 ) * 40 β ( 10 / 100 ) * 15 32 - 15 = 17 answer : e" | a = 80 * 40
b = a / 100
c = 10 * 15
d = c / 100
e = b - d
|
a ) 400 , b ) 625 , c ) 250 , d ) 2,500 , e ) 10,000 | c | divide(50, divide(10, 50)) | in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 10 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ? | "total fish = x percentage of second catch = ( 10 / 50 ) * 100 = 20 % so , x * 20 % = 50 x = 250 ans . c" | a = 10 / 50
b = 50 / a
|
a ) 10 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 5 days | e | multiply(divide(const_1, add(divide(const_1, 9), divide(const_1, 2))), 3) | a can finish a work in 12 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ? | b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done by a in 12 * 5 / 12 = 5 days answer is e | a = 1 / 9
b = 1 / 2
c = a + b
d = 1 / c
e = d * 3
|
a ) 160 , b ) 170 , c ) 180 , d ) 190 , e ) 200 | c | divide(multiply(multiply(24, const_2), 75), 20) | 75 boys can complete a job in 24 days . how many men need to complete the job twice in 20 days | one man can complete the job in 24 * 75 = 1800 days to complete the job twice he would need 3600 days . thus , to complete the job in 20 days , 3600 / 20 = 180 men are needed . answer : c | a = 24 * 2
b = a * 75
c = b / 20
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a ) 8 , b ) 12 , c ) 20 , d ) 44 , e ) 36 | d | multiply(subtract(const_10, 1), 4) | on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on december 1 than were in stock on january 1 ? | "jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 nov 1 = c - 40 dec 1 = c - 44 difference between stock on december 1 than were in stock on january 1 will be - c - ( c - 44 ) = 44 hence answer will be ( d )" | a = 10 - 1
b = a * 4
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a ) 320 , b ) 345 , c ) 425 , d ) 475 , e ) 400 | d | multiply(divide(760, 5), 3) | there are 760 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ? | "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 760 . hence 3 x + 5 x = 760 solve for x 8 x = 760 x = 95 number of boys 3 x = 3 Γ 95 = 285 number of girls 5 x = 5 Γ 95 = 475 d" | a = 760 / 5
b = a * 3
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a ) 5 , b ) 10 , c ) 17 , d ) 25 , e ) 30 | b | subtract(30, divide(add(multiply(30, 7.50), 425), add(25, 7.50))) | a contractor is engaged for 30 days on the condition that he receives rs . 25 for eachday he works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was heabsent ? | "30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b" | a = 30 * 7
b = a + 425
c = 25 + 7
d = b / c
e = 30 - d
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a ) 3.56 , b ) 4.16 , c ) 4.86 , d ) 5.1 , e ) 5.2 | b | divide(multiply(10, 5), add(10, const_2)) | if a dozen of oranges cost $ 5 , what would be the cost of 10 oranges ? | the cost of one orange = 5 / 12 = 0.416 the cost of ten oranges = 0.416 x 10 = $ 4.16 answer : b | a = 10 * 5
b = 10 + 2
c = a / b
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a ) 13 β 4 , b ) 13 β 2 , c ) 23 β 2 , d ) 12 β 4 , e ) 15 β 2 | e | sqrt(multiply(add(power(divide(48, const_4), const_2), power(divide(36, const_4), const_2)), const_2)) | the perimeter of one square is 48 cm and that of another is 36 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ? | "4 a = 48 4 a = 36 a = 12 a = 9 a 2 = 144 a 2 = 81 combined area = a 2 = 225 = > a = 15 d = 15 β 2 answer : e" | a = 48 / 4
b = a ** 2
c = 36 / 4
d = c ** 2
e = b + d
f = e * 2
g = math.sqrt(f)
|
a ) 381 , b ) 382 , c ) 383 , d ) 384 , e ) 355 | e | divide(add(add(const_2, 47), multiply(add(20, add(const_2, const_60)), const_60)), 14) | light glows for every 14 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am | "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 14 = 354 so total 355 times light ll glow answer : e" | a = 2 + 47
b = 2 + const_60
c = 20 + b
d = c * const_60
e = a + d
f = e / 14
|
a ) 22 , b ) 48 , c ) 60 , d ) 88 , e ) 72 | b | divide(multiply(36, 20), 15) | if 36 men can do a piece of work in 20 hours , in how mwny hours will 15 men do it ? | "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 20 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 20 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 20 } { 15 } = 48 hence , 15 men can do it in 48 hours . answer : b ) 48" | a = 36 * 20
b = a / 15
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a ) 2 . , b ) z = 4 . , c ) z = 5 . , d ) 6 . , e ) 8 . | c | divide(multiply(3, 20), 12) | 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours z will it take 12 beavers that work at the same pace , to build the same dam ? | "c . 5 hrs if there were 10 beavers it qould have taken double z = 6 hrs . . so closest to that option is 5 ." | a = 3 * 20
b = a / 12
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a ) 574 , b ) 270 , c ) 566 , d ) 266 , e ) 121 | a | multiply(580, divide(11, const_100)) | find the simple interest on rs . 580 for 11 months at 9 paisa per month ? | "i = ( 580 * 11 * 9 ) / 100 = 574 answer : a" | a = 11 / 100
b = 580 * a
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a ) 108 , b ) 111 , c ) 114 , d ) 117 , e ) 120 | d | multiply(add(add(subtract(multiply(2, const_10), 2), 1), multiply(2, const_10)), 3) | every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` rat ' ' ? | ` ` rat ' ' = ( 18 + 1 + 20 ) * 3 = 117 . the answer is d . | a = 2 * 10
b = a - 2
c = b + 1
d = 2 * 10
e = c + d
f = e * 3
|
a ) 36 , b ) 405 , c ) 200 , d ) 302 , e ) 404 | b | subtract(multiply(2, multiply(125, const_0_2778)), 100) | a train 100 m long crosses a platform 125 m long in 2 sec ; find the speed of the train ? | "d = 100 + 125 = 225 t = 2 s = 225 / 2 * 18 / 5 = 405 kmph answer : b" | a = 125 * const_0_2778
b = 2 * a
c = b - 100
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a ) 0.05 , b ) 0.005 , c ) 0.5 , d ) 5 , e ) 50 | c | multiply(divide(0.0015, 0.003), const_100) | 0.0015 Γ· ? = 0.003 | "let 0.0015 / x = 0.003 x = 0.0015 / 0.003 = 0.5 answer : c" | a = 0 / 15
b = a * 100
|
a ) 3 , b ) 14 , c ) 9 , d ) 21 , e ) none of these | c | sqrt(power(9, 2)) | β ( 9 ) ^ 2 | "explanation β ( 9 ) ^ 2 = ? or , ? = 9 answer c" | a = 9 ** 2
b = math.sqrt(a)
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a ) $ 54,000 , b ) $ 57,000 , c ) $ 60,000 , d ) $ 63,000 , e ) $ 66,000 | d | divide(multiply(const_100, multiply(const_100, add(const_1, 4))), add(divide(25, const_100), multiply(multiply(divide(25, const_100), subtract(const_1, divide(25, const_100))), const_2))) | the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 39,375 , how much profit did the business make ? | "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = $ 39,375 p = $ 63,000 the answer is d ." | a = 1 + 4
b = 100 * a
c = 100 * b
d = 25 / 100
e = 25 / 100
f = 25 / 100
g = 1 - f
h = e * g
i = h * 2
j = d + i
k = c / j
|
a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718 | e | multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, 3)), multiply(3, multiply(4, 3))), 3) | the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e" | a = 2 * 12
b = 15 + 25
c = a * b
d = 6 * 3
e = c - d
f = 4 * 3
g = 3 * f
h = e - g
i = h * 3
|
a ) 189 km , b ) 225 km , c ) 255 km , d ) 199 km , e ) none | b | multiply(divide(multiply(50, divide(45, const_60)), subtract(60, 50)), 60) | a car that moves at an average speed of 60 kmph , reaches its destination on time . when its average speed becomes 50 kmph , then it reaches its destination 45 minutes late . find the length of journey . | sol . difference between timings = 45 min = 3 / 4 hr . let the length of journey be x km . then , x / 50 - x / 60 = 1 / 4 Γ’ β‘ β 6 x - 5 x = 225 Γ’ β‘ β x = 225 km . answer b | a = 45 / const_60
b = 50 * a
c = 60 - 50
d = b / c
e = d * 60
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a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70 | d | inverse(subtract(divide(const_1, 15), divide(const_1, 20))) | one pipe can fill a tank in 15 hour . but because of hole in a tank , this tank fill in 20 hour . so in how much time this hole will empty the full tank ? | in 1 hour hole empty = [ 1 / 15 - 1 / 20 ] = 1 / 60 so total time taken to empty the full tank through hole = 60 hour . answer d | a = 1 / 15
b = 1 / 20
c = a - b
d = 1/(c)
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a ) 81 : 121 , b ) 9 : 11 , c ) 25 : 144 , d ) 27 : 121 , e ) none of these | c | power(divide(125, 1728), divide(const_1, const_3)) | the ratio of the volumes of two cubes is 125 : 1728 . what is the ratio of their total surface areas ? | "ratio of the sides = Γ’ Β³ Γ’ Λ Ε‘ 125 : Γ’ Β³ Γ’ Λ Ε‘ 1728 = 5 : 12 ratio of surface areas = 5 ^ 2 : 12 ^ 2 = 25 : 144 answer : c" | a = 125 / 1728
b = 1 / 3
c = a ** b
|
a ) 36 , b ) 34 , c ) 38 , d ) 32 , e ) 31 | d | subtract(subtract(164, 120), add(10, const_2)) | moli buys 3 ribbons , 7 clips and 1 soap for rs . 120 exactly . at the same place it would cost rs . 164 for 4 ribbons , 10 clips and one soap . how much would it cost for one ribbon , one clip and one soap ? | explanation : let us consider , ribbon is denoted by r clips is denoted by c soaps is denoted by s now according to the question , = > 3 r + 7 c + s = 120 - - - - - - - - ( 1 ) = > 4 r + 10 c + s = 164 - - - - - - - - ( 2 ) ( 1 ) - ( 2 ) = > ( 3 r - 4 r ) + ( 7 c - 10 c ) + ( s - s ) = 120 - 164 = > - r - 3 c = - 44 multily the equation by - 1 , it becomes = > r + 3 c = 44 - - - - - - - ( 3 ) now perform this operation 2 * ( 1 ) - ( 2 ) = > 2 r + 4 c + s = 76 - - - - - - - ( 4 ) finaly ( 4 ) - ( 3 ) = > r + c + s = 32 hence , the cost of 1 ribbon , 1 clip and 1 saop would be 32 rs . answer : d | a = 164 - 120
b = 10 + 2
c = a - b
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a ) 7.5 , b ) 66 , c ) 77 , d ) 52 , e ) 42 | a | multiply(divide(5, const_60), 90) | the speed of a train is 90 kmph . what is the distance covered by it in 5 minutes ? | "90 * 5 / 60 = 7.5 kmph answer : a" | a = 5 / const_60
b = a * 90
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a ) 51 , b ) 48 , c ) 55 , d ) 63 , e ) 65 | a | divide(divide(multiply(140, const_100), 80), const_2) | a rainstorm increased the amount of water stored in state j reservoirs from 124 billion gallons to 140 billion gallons . if the storm increased the amount of water in the reservoirs to 80 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ? | "let total capacity be x we know 140 = 0.80 x x = 140 / 0.80 = 175 prior to storm , we had 124 bn gallons 175 - 124 = 51 answer : a" | a = 140 * 100
b = a / 80
c = b / 2
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a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16 | b | subtract(8, divide(24, 8)) | if ( m - 8 ) is a factor of m ^ 2 - km - 24 , then k = | "( m - 8 ) ( m - a ) = m ^ 2 - km - 24 a = - 3 k = 8 + a = 5 = b" | a = 24 / 8
b = 8 - a
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a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 30 % | e | subtract(add(60, 70), const_100) | a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 70 % have red flags , what percentage of children have flags of both the colors ? | solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 70 % = 70 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 70 - c = 100 c = 30 option e . | a = 60 + 70
b = a - 100
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a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9 | c | divide(const_5, 6) | a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability w that both selected dogs are not littermates ? | we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) w = 5 / 6 . answer : c | a = 5 / 6
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a ) 1236 , b ) 3024 , c ) 4096 , d ) 4608 , e ) 6561 | b | multiply(multiply(add(4, 4), add(4, 4)), multiply(add(4, 4), multiply(4, 4))) | how many 4 - digit positive integers are there , where each digit is positive , and no 4 adjacent digits are same ? | "first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities fourth digit , 6 possibilities . 9 * 8 * 7 * 6 = 3024 . b" | a = 4 + 4
b = 4 + 4
c = a * b
d = 4 + 4
e = 4 * 4
f = d * e
g = c * f
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a ) 6 / 15 , b ) 7 / 13 , c ) 8 / 15 , d ) 9 / 17 , e ) 2 / 13 | c | divide(subtract(const_60, multiply(divide(const_60, 15), add(divide(const_60, 15), divide(const_60, 20)))), const_60) | p can do a work in 15 days and q cando the same work in 20 days . if they can work together for 4 days , what is the fraction of work left ? | amount of work p can do in 1 day = 1 / 15 amount of work q can do in 1 day = 1 / 20 amount of work p and q can do in 1 day = 1 / 15 + 1 / 20 = 7 / 60 amount of work p and q can together do in 4 days = 4 Γ ( 7 / 60 ) = 7 / 15 fraction of work left = 1 β 7 / 15 = 8 / 15 c | a = const_60 / 15
b = const_60 / 15
c = const_60 / 20
d = b + c
e = a * d
f = const_60 - e
g = f / const_60
|
a ) 35 , b ) 90 , c ) 11 , d ) 10 , e ) 9 | a | divide(subtract(95, 25), const_2) | how many of the integers between 25 and 95 are even ? | "number start between 25 to 95 is 70 numbers half of them is even . . which is 35 answer : a" | a = 95 - 25
b = a / 2
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a ) 280 , b ) 290 , c ) 342 , d ) 250 , e ) 253 | c | subtract(400, add(divide(multiply(400, 10), const_100), divide(multiply(5, 400), const_100))) | the sale price shirts listed for rs . 400 after successive discount is 10 % and 5 % is ? | 400 * ( 90 / 100 ) * ( 95 / 100 ) = 342 c | a = 400 * 10
b = a / 100
c = 5 * 400
d = c / 100
e = b + d
f = 400 - e
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a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13 | d | divide(subtract(78000, 42000), add(800, 1200)) | village x has a population of 78000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ? | "let the population of two villages be equal after p years then , 78000 - 1200 p = 42000 + 800 p 2000 p = 36000 p = 18 answer is d ." | a = 78000 - 42000
b = 800 + 1200
c = a / b
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a ) 3500 , b ) 1200 , c ) 1650 , d ) 3700 , e ) 1800 | e | multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 4000) | in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 4000 , the number of valid votes that the other candidate got , was : | "number of valid votes = 80 % of 4000 = 3200 . valid votes polled by other candidate = 45 % of 4000 = ( 45 / 100 ) x 4000 = 1800 answer = e" | a = 20 / 100
b = 1 - a
c = 55 / 100
d = 1 - c
e = b * d
f = e * 4000
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a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 50 | b | multiply(100, subtract(const_1, divide(divide(200, const_2), add(300, divide(200, const_2))))) | a invested $ 300 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ? | "a : b = 300 * 12 : 200 * 6 a : b = 3 : 1 a ' s share = 100 * 3 / 4 = $ 75 answer is b" | a = 200 / 2
b = 200 / 2
c = 300 + b
d = a / c
e = 1 - d
f = 100 * e
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a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,625 , e ) $ 2,250 | d | 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 β s latest order required a truck with at least 336,000 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 = 336,000 / ( 8 * 10 * 12 ) = 350 one box costs 7.50 , so 350 box will cost = 350 * 7.5 = 2625 d 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 ) 139 , b ) 141 , c ) 143 , d ) 145 , e ) 147 | a | add(add(power(add(add(divide(subtract(subtract(77, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(77, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(77, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(77, const_10), const_2), const_4), const_2), const_2))) | the sum of 77 consecutive integers is 7777 . what is the greatest integer in the set ? | "let x be the first integer in the set . then x + 76 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 76 ) = 77 x + 76 * 77 / 2 = 77 ( x + 38 ) then x + 38 = 101 x = 63 the largest integer in the set is 63 + 76 = 139 the answer is a ." | a = 77 - 10
b = a - 2
c = b / 4
d = c + 2
e = d + 2
f = e ** 2
g = 77 - 10
h = g - 2
i = h / 4
j = i + 2
k = j + 2
l = k + 2
m = l ** 2
n = f + m
o = 77 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 77 - 10
t = s - 2
u = t / 4
v = u + 2
w = v ** 2
x = r + w
y = n + x
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a ) 79 , b ) 81 , c ) 82 , d ) 83 , e ) 85 | d | multiply(divide(subtract(80, divide(multiply(40, 75), const_100)), subtract(const_100, 40)), const_100) | a group of boy scouts and girls scouts is going on a rafting trip . 80 % of the scouts arrived with signed permission slips . if 40 % of the scouts were boy scouts and 75 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent . | "40 % were boy scouts so 60 % ( 100 - 40 = 60 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 75 % of 40 % of the total going ) + ( ? % of 60 % of the total going ) = 80 % of the total going we can let the ` ` total going ' ' = 100 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 75 * . 40 * 100 + x * . 60 * 100 = . 80 * 100 30 + x * 60 = 80 60 x = 50 x = 50 / 60 x = . 833333 converting this to a percent , we have 83 % d" | a = 40 * 75
b = a / 100
c = 80 - b
d = 100 - 40
e = c / d
f = e * 100
|
a ) 122762 , b ) 132877 , c ) 122882 , d ) 133875 , e ) 132887 | d | divide(divide(multiply(4016.25, const_100), 1), 3) | a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 3 years . what is the sum ? | "principal = ( 100 * 4016.25 ) / ( 1 * 3 ) = rs . 133875 . answer : d" | a = 4016 * 25
b = a / 1
c = b / 3
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a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 36 | e | multiply(subtract(divide(30, 12), const_1), 24) | pipe a can fill a tank in 12 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ? | "let the pipe b be closed after x minutes . 30 / 12 - x / 24 = 1 = > x / 24 = 30 / 12 - 1 = 3 / 2 = > x = 3 / 2 * 24 = 36 . answer : e" | a = 30 / 12
b = a - 1
c = b * 24
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a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70 | d | multiply(divide(7, subtract(9, 7)), 18) | sandy is younger than molly by 18 years . if the ratio of their ages is 7 : 9 , how old is sandy ? | "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 18 x = 9 sandy is 63 years old . the answer is d ." | a = 9 - 7
b = 7 / a
c = b * 18
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a ) 30 , b ) 32 , c ) 31 th ( 80 - 89 ) , d ) 34 , e ) 36 | c | subtract(70, 79) | score interval - - - - - - - - - - - - - - - - number of scores 50 - 59 - - - - - - - - - - - - - - - - - - - - - - - - - - 2 60 - 69 - - - - - - - - - - - - - - - - - - - - - - - - - - 4 70 - 79 - - - - - - - - - - - - - - - - - - - - - - - - - - 10 80 - 89 - - - - - - - - - - - - - - - - - - - - - - - - - - 27 90 - 99 - - - - - - - - - - - - - - - - - - - - - - - - - - 18 the table above shows the distribution of test scores for a group of management trainees . which score interval contains the median of the 61 scores ? | total scores = 2 + 4 + 10 + 27 + 18 = 61 , which is odd , therefore the median is the floor ( 61 / 2 ) + 1 = 31 th score . and the 31 th score is in the 80 - 89 range , because 50 - 79 only reference 28 scores . c | a = 70 - 79
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a ) 191 , b ) 355 , c ) 800 , d ) 840 , e ) 900 | c | divide(multiply(640, const_100), subtract(const_100, 20)) | a side of beef lost 20 percent of its weight in processing . if the side of beef weighed 640 pounds after processing , how many pounds did it weigh before processing ? | "let weight of side of beef before processing = x ( 80 / 100 ) * x = 640 = > x = ( 640 * 100 ) / 80 = 800 answer c" | a = 640 * 100
b = 100 - 20
c = a / b
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a ) 3 / 7 , b ) 3 / 2 , c ) 3 / 5 , d ) 3 / 1 , e ) 3 / 3 | b | divide(subtract(27, 23), subtract(23, 17)) | two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds . the ratio of their speeds is ? | "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 23 = = > 27 x + 17 y = 23 x + 23 y = = > 4 x = 6 y = = > x / y = 3 / 2 . answer : b" | a = 27 - 23
b = 23 - 17
c = a / b
|
a ) 30 % , b ) 32.50 % , c ) 33 1 / 3 % , d ) 40 % , e ) 50 % | c | divide(multiply(16, const_4), add(const_4, const_1)) | the cost price of 16 articles is the same as the selling price of 12 articles . find the loss / profit percentages . | "explanation : the gain is 4 out of 12 articles . therefore , gain percentage = 4 x 100 / 12 = 100 / 3 = 33 1 / 3 % answer : option c" | a = 16 * 4
b = 4 + 1
c = a / b
|
a ) 8 % , b ) 10 % , c ) 11 % , d ) 17 % , e ) 20 % | d | multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(30, const_100))), divide(multiply(30, const_100), add(30, const_100))), const_100) | selling an kite for rs . 30 , a shop keeper gains 30 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ? | "explanation : marked price = rs . 30 c . p . = 100 / 130 * 30 = rs . 23.07 sale price = 90 % of rs . 30 = rs . 27 required gain % = 3.92 / 23.07 * 100 = 17 % . answer : d" | a = 30 / 100
b = 100 - 10
c = a * b
d = 30 * 100
e = 30 + 100
f = d / e
g = c - f
h = 30 * 100
i = 30 + 100
j = h / i
k = g / j
l = k * 100
|
a ) s 222 , b ) s 216 , c ) s 220 , d ) s 270 , e ) s 217 | d | add(add(220, divide(500, 100)), multiply(divide(20, 100), add(220, divide(500, 100)))) | the manufacturing cost of a shoe is rs . 220 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains | "explanation : total cost of a watch = 220 + ( 500 / 100 ) = 225 . gain = 20 % = > sp = 1.2 cp = 1.2 x 225 = 270 answer : d" | a = 500 / 100
b = 220 + a
c = 20 / 100
d = 500 / 100
e = 220 + d
f = c * e
g = b + f
|
a ) 4079 , b ) 4579 , c ) 5579 , d ) 5679 , e ) 5779 | b | subtract(multiply(add(5, const_1), 5400), add(add(add(add(5124, 5366), 5808), 5399), 6124)) | a grocer has a sale of rs . 5124 , rs . 5366 , rs . 5808 , rs . 5399 and rs . 6124 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5400 ? | "total sale for 5 months = rs . ( 5124 + 5366 + 5808 + 5399 + 6124 ) = rs . 27821 . required sale = rs . [ ( 5400 x 6 ) - 27821 ] = rs . ( 32400 - 27821 ) = rs . 4579 . answer : b" | a = 5 + 1
b = a * 5400
c = 5124 + 5366
d = c + 5808
e = d + 5399
f = e + 6124
g = b - f
|
a ) 1 million , b ) 2 million , c ) 4 million , d ) 8 million , e ) none of these | a | divide(power(divide(8, const_2), subtract(8, const_2)), power(divide(8, const_2), subtract(8, const_2))) | one bacterium splits into 8 bacteria of the next generation . but due to environment , only 50 % of one generation can produced the next generation . if the seventh generation number is 4096 million , what is the number in first generation ? | solution : let the number of bacteria in the 1 st generation be x , then number of bacteria in 2 nd , 3 rd , 4 th . . . . . generation would be 8 ( x / 2 ) , 8 ( 4 x / 2 ) , 8 ( 16 x / 2 ) . . . . and so on . as x , 4 x , 16 x , 64 x . . . . . it is in gp with common ratio 4 . hence , 7 th term of gp , x ( 4 ) 6 = 4096 or , x = 1 or 1 million . answer : option a | a = 8 / 2
b = 8 - 2
c = a ** b
d = 8 / 2
e = 8 - 2
f = d ** e
g = c / f
|
a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64 | a | multiply(multiply(divide(1, 4), divide(1, 3)), subtract(1, divide(5, 8))) | xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 1 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ? | "p ( xavier will solve ) = 1 / 4 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 4 ) * ( 1 / 3 ) * ( 3 / 8 ) = 1 / 32 . ans . a ." | a = 1 / 4
b = 1 / 3
c = a * b
d = 5 / 8
e = 1 - d
f = c * e
|
a ) 7 , b ) 6 , c ) 9 , d ) 21 , e ) 63 | d | multiply(add(add(7, 6), 3), 3) | a class has a ratio of 3 : 6 : 7 of children with red hair , blonde hair and black hair respectively . if the class has 9 kids with red hair , how many kids are there with black hair ? | "since there is a 3 : 7 ratio between red haired children and black - haired children , if there are 9 children with red hair , then there must be 3 times the amount of black - haired children . therefore , are 21 children with black hair . answer : d )" | a = 7 + 6
b = a + 3
c = b * 3
|
a ) 100 km , b ) 150 km , c ) 50 km , d ) 120 km , e ) 200 km | a | multiply(5, 20) | a walks at 10 kmph and 5 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ? | "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 5 hours . x / 10 - x / 20 = 5 x = 100 km answer is a" | a = 5 * 20
|
a ) 220.3 , b ) 224.5 , c ) 190.3 , d ) 150 , e ) none of these | b | add(divide(multiply(400, 28), const_100), divide(multiply(45, 250), const_100)) | evaluate : 28 % of 400 + 45 % of 250 | explanation : 28 % of 400 + 45 % of 250 = ( 28 / 100 * 400 + 45 / 100 * 250 ) = ( 112 + 112.5 ) = 224.5 answer b | a = 400 * 28
b = a / 100
c = 45 * 250
d = c / 100
e = b + d
|
a ) 540 , b ) 128 , c ) 100 , d ) 942 , e ) 942.86 | e | multiply(subtract(power(20, const_2), power(10, const_2)), divide(add(multiply(10, const_2), const_2), add(const_4, const_3))) | a rope of which a calf is tied is increased from 10 m to 20 m , how much additional grassy ground shall it graze ? | "Ο ( 202 β 102 ) = 942.86 answer : e" | a = 20 ** 2
b = 10 ** 2
c = a - b
d = 10 * 2
e = d + 2
f = 4 + 3
g = e / f
h = c * g
|
a ) 1 / 26 , b ) 1 / 52 , c ) 2 / 62 , d ) 2 / 26 , e ) 3 / 26 | a | divide(subtract(52, multiply(const_4, const_4)), 52) | a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is : | "here , n ( s ) = 52 . let e = event of getting a queen of club or a king of heart . then , n ( e ) = 2 . p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 answer should be a" | a = 4 * 4
b = 52 - a
c = b / 52
|
a ) 8.2 km , b ) 6.7 km , c ) 7.6 km , d ) 7.4 km , e ) 6.3 km | c | multiply(divide(multiply(add(8, 1.8), subtract(8, 1.8)), add(add(8, 1.8), subtract(8, 1.8))), const_2) | a man can row 8 kmph in still water . when the river is running at 1.8 kmph , it takes him 2 hour to row to a place and back . what is the total distance traveled by the man ? | "m = 8 s = 1.8 ds = 9.8 us = 6.2 x / 9.8 + x / 6.2 = 1 x = 3.8 d = 2.88 * 2 = 7.6 answer : c" | a = 8 + 1
b = 8 - 1
c = a * b
d = 8 + 1
e = 8 - 1
f = d + e
g = c / f
h = g * 2
|
['a ) 9', 'b ) 61', 'c ) 98', 'd ) 54', 'e ) 64'] | d | add(divide(surface_cube(5), const_3), const_4) | a cube of side 5 cm is painted on all its side . if it is sliced into 1 cubic centimer cubes , how many 1 cubic centimeter cubes will have exactly one of their sides painted ? | explanatory answer when a 5 cc cube is sliced into 1 cc cubes , we will get 5 * 5 * 5 = 125 cubes of 1 cubic centimeter . in each side of the larger cube , the smaller cubes on the edges will have more than one of their sides painted . therefore , the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted . in each face of the larger cube , there will be 5 * 5 = 25 cubes . of these , the cubes on the outer rows will be on the edge . 16 such cubes exist on each face . if we count out the two outer rows on either side of a face of the cube , we will be left with 3 * 3 = 9 cubes which are not on the edge in each face of the cube . therefore , there will be 9 cubes of 1 - cc volume per face that will have exactly one of their sides painted . in total , there will be 9 * 6 = 54 such cubes . choice d is the correct answer . | a = surface_cube / (
b = a + 3
|
a ) 896 , b ) 890 , c ) 990 , d ) 789 , e ) 740 | c | add(800, multiply(800, divide(12, const_100))) | a person buys an article at $ 800 . at what price should he sell the article so as to make a profit of 12 % ? | "a 896 cost price = $ 800 profit = 12 % of 800 = $ 96 selling price = cost price + profit = 800 + 96 = 896" | a = 12 / 100
b = 800 * a
c = 800 + b
|
a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | b | add(floor(divide(25, 3)), floor(divide(25, power(3, const_2)))) | if m = 3 ^ n , what is the greatest value of n for which m is a factor of 25 ! | "we should find the highest power of 3 in 25 ! : 25 / 3 + 25 / 3 ^ 2 = 8 + 2 = 10 ( take only the quotient into account ) . . so the highest power of 3 in 25 ! is 10 . answer : b ." | a = 25 / 3
b = math.floor(a)
c = 3 ** 2
d = 25 / c
e = math.floor(d)
f = b + e
|
a ) 20 % , b ) 60 % , c ) 100 % , d ) 180 % , e ) 200 % | b | multiply(divide(10, subtract(subtract(const_100, 44), 10)), const_100) | jane makes toy bears . when she works with an assistant , she makes 44 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane β s output of toy bears per hour by what percent ? | "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 57.6 bears per 36 hours a week or 1.6 bears / hr ( [ 40 bears * 1.44 ] / [ 40 hrs * . 90 ] ) . [ ( 1.6 - 1 ) / 1 ] * 100 % = 60 % answer : b" | a = 100 - 44
b = a - 10
c = 10 / b
d = c * 100
|
a ) 270 m , b ) 340 m , c ) 310 m , d ) 350 m , e ) 327 m | b | multiply(divide(subtract(108, 36), const_3_6), 17) | two trains are moving in the same direction at 108 kmph and 36 kmph . the faster train crosses the slower train in 17 seconds . find the length of the faster train in meters . | relative speed = ( 108 - 36 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in 17 sec = 17 * 20 = 340 m . the length of the faster train = 340 m . answer : b | a = 108 - 36
b = a / const_3_6
c = b * 17
|
a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 55 | b | divide(500, multiply(const_0_2778, subtract(63, 3))) | how many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | "solution speed of train relative to man = ( 63 - 3 ) km / hr = 60 km / hr = ( 60 x 5 / 18 ) m / sec = 50 / 3 m / sec time taken to pass the man = ( 500 x 3 / 50 ) sec = 30 sec answer b" | a = 63 - 3
b = const_0_2778 * a
c = 500 / b
|
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