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 ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | b | floor(divide(95, 6)) | on dividing 95 by a number , the quotient is 6 and the remainder is 5 . find the divisor . | "d = ( d - r ) / q = ( 95 - 5 ) / 6 = 90 / 6 = 15 b" | a = 95 / 6
b = math.floor(a)
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a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000 | d | divide(multiply(multiply(add(const_2, const_3), const_1000), 6), const_2) | if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 54 / r years . if joe ' s parents invested $ 5,000 in a long - term bond that pays 6 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when joe is ready for college ? | "since investment doubles in 54 / r years , then for r = 6 it ' ll double in 54 / 6 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 2 = $ 10,000 . answer : d ." | a = 2 + 3
b = a * 1000
c = b * 6
d = c / 2
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a ) 16 , b ) 25 , c ) 81 , d ) 26 , e ) 17 | c | power(divide(17, subtract(const_2, divide(const_1, add(const_4, const_1)))), const_2) | find out the square of a number which when doubled exceeds its one nineth by 17 ? | "let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 9 ) + 17 = > 18 p = p + 153 = > p = 9 p ^ 2 = 9 ^ 2 = 81 answer : c" | a = 4 + 1
b = 1 / a
c = 2 - b
d = 17 / c
e = d ** 2
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a ) 165 m , b ) 120 m , c ) 100 m , d ) 190 m , e ) 220 m | a | add(25, divide(divide(880, const_pi), const_2)) | the inner circumference of a circular race track , 25 m wide , is 880 m . find radius of the outer circle ? | "let inner radius be r metres . then , 2 Ο r = 880 β r = ( 880 x ( 7 / 44 ) ) = 140 m . radius of outer circle = ( 140 + 25 ) m = 165 m . hence a" | a = 880 / math.pi
b = a / 2
c = 25 + b
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a ) $ 40 , b ) $ 400 , c ) $ 840 , d ) $ 800 , e ) $ 80 | a | subtract(multiply(800, power(add(const_1, divide(10, const_100)), 1)), 800) | find the compound interest on $ 800 for 1 year at 10 % p . a . if ci is component yearly ? | "a = p ( 1 + r / 100 ) ^ t = 800 ( 1 + 10 / 100 ) ^ 1 = 800 * 21 / 20 = $ 840 ci = a - p = 840 - 800 = $ 40 answer is a" | a = 10 / 100
b = 1 + a
c = b ** 1
d = 800 * c
e = d - 800
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a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | e | divide(1080, const_12) | how many boxes do you need if you have to pack 1080 apples into cases that each hold one dozen apples ? | e 90 1080 apples = 90 dozens the required number of boxes = 90 . answer : e | a = 1080 / 12
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a ) s . 440 , b ) s . 500 , c ) s . 720 , d ) s . 740 , e ) s . 840 | c | subtract(820, multiply(divide(subtract(1020, 820), 4), 2)) | a sum of money lent out at s . i . amounts to rs . 820 after 2 years and to rs . 1020 after a further period of 4 years . the sum is ? | s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 4 * 2 = rs . 100 . principal = ( 820 - 100 ) = rs . 720 . answer : c | a = 1020 - 820
b = a / 4
c = b * 2
d = 820 - c
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['a ) 3.84', 'b ) 1.75', 'c ) 3.36', 'd ) 2.72', 'e ) none of these'] | c | divide(divide(multiply(4, add(multiply(3, 900), multiply(2, 750))), add(3, 2)), const_1000) | the weights of one liter vegetable ghee packet of two brands β a β and β b β are 900 gm and 750 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ? | here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . eachpartis 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 750 * 2 * ( 4 / 5 ) = 1200 2160 + 1200 = 3360 solving for units gives us 3.36 so the answer is c | a = 3 * 900
b = 2 * 750
c = a + b
d = 4 * c
e = 3 + 2
f = d / e
g = f / 1000
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a ) 288 , b ) 660 , c ) 500 , d ) 267 , e ) 298 | c | divide(800, multiply(subtract(78, 1), const_0_2778)) | a train 800 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ? | "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 800 + x ) / 60 = 65 / 3 x = 500 m . answer : c" | a = 78 - 1
b = a * const_0_2778
c = 800 / b
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a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 183 cm | e | multiply(multiply(const_2, divide(multiply(subtract(42, const_3), const_2), add(const_4, const_3))), 42) | the sector of a circle has radius of 42 cm and central angle 135 o . find its perimeter ? | "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 42 ) + 2 ( 42 ) = 99 + 84 = 183 cm answer : e" | a = 42 - 3
b = a * 2
c = 4 + 3
d = b / c
e = 2 * d
f = e * 42
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a ) 105 , b ) 140 , c ) 175 , d ) 210 , e ) 245 | d | multiply(35, divide(multiply(divide(72, const_60), 35), subtract(42, 35))) | car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 42 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ? | "in 72 minutes , car x travels 42 miles . car y gains 7 miles each hour , so it takes 6 hours to catch car x . in 6 hours , car x travels 210 miles . the answer is d ." | a = 72 / const_60
b = a * 35
c = 42 - 35
d = b / c
e = 35 * d
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a ) 10 / 16 , b ) 6 / 16 , c ) 7 / 11 , d ) 6 / 10 , e ) 4 / 10 | c | divide(divide(subtract(18, 4), add(const_1, const_1)), add(divide(subtract(18, 4), add(const_1, const_1)), 4)) | there are 4 more women than there are men on a local co - ed softball team . if there are a total of 18 players on the team , what is the ratio of men to women ? | "w = m + 4 w + m = 18 m + 4 + m = 18 2 m = 14 m = 7 w = 11 ratio : 7 : 11 ans : c" | a = 18 - 4
b = 1 + 1
c = a / b
d = 18 - 4
e = 1 + 1
f = d / e
g = f + 4
h = c / g
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a ) 75 % , b ) 70 % , c ) 45 % , d ) 55 % , e ) 65 % | b | subtract(multiply(60, const_3), add(50, 60)) | a student gets 50 % in one subject , 60 % in the other . to get an overall of 60 % how much should get in third subject . | "let the 3 rd subject % = x 50 + 60 + x = 3 * 60 110 + x = 180 x = 180 - 110 = 70 answer : b" | a = 60 * 3
b = 50 + 60
c = a - b
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a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours | b | divide(const_1, subtract(const_1, divide(const_1, multiply(6, const_2)))) | one pump drains one - half of a pond in 6 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ? | "first pump drains 1 / 2 of the tank in 6 hours so 12 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 12 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 12 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 12 + 1 / a ) = 1 / 2 solving u get a = 12 / 11 = 1.1 hence answer is b" | a = 6 * 2
b = 1 / a
c = 1 - b
d = 1 / c
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a ) 360 , b ) 358 , c ) 356 , d ) 514 , e ) 504 | e | multiply(divide(1638, add(add(2, 3), 4)), 4) | an amount of rs . 1638 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of b ? | "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of b = 4 / 13 * 1638 = rs . 504 answer : e" | a = 2 + 3
b = a + 4
c = 1638 / b
d = c * 4
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a ) 22 , b ) 77 , c ) 15 , d ) 12 , e ) 88 | d | subtract(multiply(40, divide(80, const_100)), multiply(divide(4, 5), 25)) | how much is 80 % of 40 is greater than 4 / 5 of 25 ? | ( 80 / 100 ) * 40 β ( 4 / 5 ) * 25 32 - 20 = 12 answer : d | a = 80 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
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a ) 291 , b ) 292 , c ) 293 , d ) 384 , e ) 285 | c | divide(add(add(const_2, 47), multiply(add(20, add(const_2, const_60)), const_60)), 17) | light glows for every 17 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 / 17 = 292 . so total 293 times light ll glow answer : c" | a = 2 + 47
b = 2 + const_60
c = 20 + b
d = c * const_60
e = a + d
f = e / 17
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a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20 | a | divide(660, multiply(add(90, 108), const_0_2778)) | two trains of length 100 meters and 200 meters are 660 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 108 km / h . after how many seconds will the trains meet ? | "the speeds are 90000 / 3600 = 25 m / s and 108000 / 3600 = 30 m / s the relative speed is 55 m / s . time = 660 / 55 = 12 seconds the answer is a ." | a = 90 + 108
b = a * const_0_2778
c = 660 / b
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a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 35 % . | e | multiply(divide(add(multiply(divide(25, const_100), 2), multiply(divide(50, const_100), 6)), 10), const_100) | a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 50 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ? | "25 % of 2 litres = 0.5 litres 50 % of 6 litres = 3.0 litres therefore , total quantity of alcohol is 3.5 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 35 % answer : e" | a = 25 / 100
b = a * 2
c = 50 / 100
d = c * 6
e = b + d
f = e / 10
g = f * 100
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a ) 8876 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 6100 | e | multiply(multiply(const_1, const_12), divide(18300, add(add(multiply(const_1, const_12), multiply(subtract(const_12, 6), const_2)), multiply(subtract(const_12, 8), const_3)))) | a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18300 . a ' s share is ? | "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18300 = 6100 answer : e" | a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d
f = 12 - 8
g = f * 3
h = e + g
i = 18300 / h
j = a * i
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a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 18 | d | add(add(const_4, const_3), const_1) | how many different positive integers exist between 10 ^ 7 and 10 ^ 8 , the sum of whose digits is equal to 2 ? | so , the numbers should be from 10 , 000,000 to 100 , 000,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 10 , 000,001 10 , 000,010 10 , 000,100 10 , 001,000 10 , 010,000 10 , 100,000 11 , 000,000 7 numbers . 2 . one 2 and the rest are 0 ' s : 20 , 000,000 1 number . total = 8 numbers . answer : d | a = 4 + 3
b = a + 1
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a ) 160 , b ) 220 , c ) 312 , d ) 360 , e ) 420 | c | add(divide(multiply(divide(55, const_100), 26), subtract(divide(60, const_100), divide(55, const_100))), 26) | the workforce of company x is 60 % female . the company hired 26 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ? | "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 26 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 26 ) 0.05 x = 14.3 x = 286 - this is quantity of employees before adding 26 men so after adding it will be 312 answer is c" | a = 55 / 100
b = a * 26
c = 60 / 100
d = 55 / 100
e = c - d
f = b / e
g = f + 26
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a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) 74 | e | add(multiply(divide(11, 9), 33.3), 33.3) | zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 33.3 kg of zinc has been consumed in it ? | "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 33.3 kg zinc , mixture , melted = [ 20 / 9 x 33.3 ] kg = 74 kg . answer e" | a = 11 / 9
b = a * 33
c = b + 33
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a ) 600 , b ) 300 , c ) 400 , d ) 500 , e ) 200 | d | subtract(multiply(add(const_60, add(const_4, const_1)), divide(const_60, const_3)), 800) | a good train 800 metres long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 minute , then the length of the tunnel ( in meters ) is : | speed = 78 * 5 / 18 m / sec = = > 65 / 3 length of the tunnel be x then 800 + x / 60 = 65 / 3 3 ( 800 + x ) = 3900 x = 500 answer d | a = 4 + 1
b = const_60 + a
c = const_60 / 3
d = b * c
e = d - 800
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a ) 15.75 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32 | a | divide(add(add(multiply(30, 11.50), multiply(20, 14.25)), multiply(divide(add(multiply(30, 11.50), multiply(20, 14.25)), const_100), 25)), add(30, 20)) | arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 25 % profit ? | "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 125 % of rs . 630 = 125 / 100 * 630 = rs . 787.5 s . p . per kg = 787.5 / 50 = 15.75 . answer : a" | a = 30 * 11
b = 20 * 14
c = a + b
d = 30 * 11
e = 20 * 14
f = d + e
g = f / 100
h = g * 25
i = c + h
j = 30 + 20
k = i / j
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a ) 205 , b ) 305 , c ) 3025 , d ) 5540 , e ) 315 | a | subtract(multiply(2000, multiply(add(const_1, divide(const_0_25, const_4)), add(const_1, divide(const_0_25, const_4)))), 2000) | find the c . i . on a sum of rs . 2000 for 6 months at 20 % per annum , interest being compounded quarterly ? | "c . i . = 2000 ( 21 / 20 ) ^ 2 - 1800 = 205 answer : a" | a = const_0_25 / 4
b = 1 + a
c = const_0_25 / 4
d = 1 + c
e = b * d
f = 2000 * e
g = f - 2000
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a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8 | b | divide(const_2, add(const_1, divide(const_1, const_3))) | ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio q of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ? | "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio q of ann ' s time to bob ' s time is 3 : 2 . answer : b ." | a = 1 / 3
b = 1 + a
c = 2 / b
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a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5 | d | add(subtract(add(12, 18), subtract(30, 3)), subtract(18, 12)) | of 30 applicants for a job , 12 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ? | "d . 7 30 - 3 = 27 27 - 12 - 18 = - 7 then 7 are in the intersection between 4 years experience and degree . answer d" | a = 12 + 18
b = 30 - 3
c = a - b
d = 18 - 12
e = c + d
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a ) 18 , b ) 17 , c ) 16 , d ) 15 , e ) 14 | b | add(divide(subtract(100, 10), 5), const_1) | how many multiples of 5 are there between 10 and 100 , exclusive ? | "5 * 2 = 10 5 * 20 = 100 total multiples = ( 20 - 2 ) + 1 = 19 exclude 10 and 100 = 19 - 2 = 17 answer is b" | a = 100 - 10
b = a / 5
c = b + 1
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a ) 4 , b ) 5 , c ) 6 , d ) 10 , e ) none of these | d | multiply(subtract(const_1, divide(9, 15)), 25) | suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 25 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ? | "the part of job that suresh completes in 9 hours = 9 Γ’ Β β 15 = 3 Γ’ Β β 5 remaining job = 1 - 3 Γ’ Β β 5 = 2 Γ’ Β β 5 remaining job can be done by ashutosh in 2 Γ’ Β β 5 Γ£ β 25 = 10 hours answer d" | a = 9 / 15
b = 1 - a
c = b * 25
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a ) 470 , b ) 468 , c ) 630 , d ) 463 , e ) 520 | c | add(divide(divide(35, divide(divide(divide(divide(divide(35, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(35, divide(divide(divide(divide(divide(35, const_2), const_2), const_2), const_2), const_2)), const_2)))) | find the sum of first 35 natural numbers | "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 35 ( 35 + 1 ) / 2 = 35 ( 36 ) / 2 = 630 answer : option c" | a = 35 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 35 / e
g = f / 2
h = 35 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 35 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o
q = g + p
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a ) 3 / 4 , b ) 1 , c ) 4 / 5 , d ) 2 , e ) 7 / 2 | c | divide(4, 5) | a line that passes through ( β 1 , β 4 ) and ( 5 , k ) has a slope = k . what is the value of k ? | slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 5 + 1 ) = > 6 k = k + 4 = > k = 4 / 5 ans c it is ! | a = 4 / 5
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a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 30.33 | e | divide(add(211.00, divide(multiply(15, 211.00), const_100)), 8) | total dinning bill for 8 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share | "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 8 = 30.33 answer : e" | a = 15 * 211
b = a / 100
c = 211 + 0
d = c / 8
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a ) 18 , b ) 99 , c ) 13 , d ) 55 , e ) 71 | c | subtract(divide(multiply(50, 56), const_100), divide(multiply(30, 50), const_100)) | how much 50 % of 56 is greater than 30 % of 50 ? | "( 50 / 100 ) * 56 β ( 30 / 100 ) * 50 28 - 15 = 13 answer : c" | a = 50 * 56
b = a / 100
c = 30 * 50
d = c / 100
e = b - d
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a ) s . 665 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 720 | a | subtract(815, divide(multiply(subtract(865, 815), 3), 4)) | a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 865 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 865 - 815 ) = rs . 50 . s . i . for 3 years = rs . ( 50 x 3 ) = rs . 150 . principal = rs . ( 815 - 150 ) = rs . 665 . answer : option a" | a = 865 - 815
b = a * 3
c = b / 4
d = 815 - c
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a ) 18.94 % , b ) 18.93 % , c ) 18.92 % , d ) 18.91 % , e ) none of these | b | subtract(const_100, multiply(divide(add(7, const_100), add(32, const_100)), const_100)) | a shopkeeper fixes the marked price of an item 32 % above its cost price . the percentage of discount allowed to gain 7 % is | "explanation : let the cost price = rs 100 then , marked price = rs 132 required gain = 7 % , so selling price = rs 107 discount = 132 - 107 = 25 discount % = ( 25 / 132 ) * 100 = 18.93 % option b" | a = 7 + 100
b = 32 + 100
c = a / b
d = c * 100
e = 100 - d
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a ) 5 : 89 , b ) 7 : 96 , c ) 4 : 25 , d ) 5 : 84 , e ) 8 : 96 | c | divide(divide(power(2, const_2), const_2), divide(power(5, const_2), const_2)) | the diagonals of the two squares are in the ratio of 2 : 5 find the ratio of their area . | "let the diagonals of the square be 2 x and 5 x respectively . ratio of their areas = 1 / 2 ( 2 x ) ^ 2 : 1 / 2 ( 5 x ) = 4 x ^ 2 : 25 x ^ 2 = 4 : 25 answer ( c )" | a = 2 ** 2
b = a / 2
c = 5 ** 2
d = c / 2
e = b / d
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a ) 6 : 5 , b ) 6 : 3 , c ) 4 : 4 , d ) 4 : 8 , e ) 4 : 1 | b | divide(sqrt(36), sqrt(9)) | two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 36 hours respectively . the ratio of their speeds is ? | "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = β b : β a = β 36 : β 9 = 6 : 3 answer : b" | a = math.sqrt(36)
b = math.sqrt(9)
c = a / b
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a ) 2 , b ) 2 1 / 4 , c ) 42 3 / 3 , d ) 4 1 / 2 , e ) 5 | c | multiply(divide(const_60, add(divide(const_1, 6), divide(const_1, 7))), add(divide(const_1, 6), divide(const_1, 7))) | carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 7 hours . how many hours will it take for both of them working together to wash all the windows ? | "work hrs = ab / ( a + b ) = 42 / 13 = 42 3 / 3 answer is c" | a = 1 / 6
b = 1 / 7
c = a + b
d = const_60 / c
e = 1 / 6
f = 1 / 7
g = e + f
h = d * g
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a ) 23 / 20 , b ) 5 , c ) 23 / 30 , d ) 23 / 12 , e ) 2 | c | subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 2)) | a can do a work in 15 days and b in 20 days . if they work on it together for 2 days , then the fraction of the work that is left is : | "ans is : c a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 2 day ' s work = ( 7 / 60 * 2 ) = 7 / 30 therefore , remaining work = ( 1 - 7 / 30 ) = 23 / 30 . ans : c" | a = 1 / 15
b = 1 / 20
c = a + b
d = c * 2
e = 1 - d
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a ) 50 , b ) 55 , c ) 60 , d ) 70 , e ) 90 | e | lcm(15, 18) | find the common factors of 15 and 18 . | first of all we need to find the prime factors of 15 and 18 15 = 5 x 3 18 = 3 x 3 x 2 lcm is the product of highest exponent of all the factors . lcm ( 15,18 ) = 5 x 3 ^ 2 x 2 = 90 answer : 90 | a = math.lcm(15, 18)
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a ) 3 , b ) 12 , c ) 9 , d ) 8 , e ) 7 | a | divide(subtract(subtract(divide(42, const_2), const_1), subtract(42, add(divide(42, const_2), divide(42, 6)))), const_2) | half of the workers in palabras bookstore have read the latest book by j . saramago , and 1 / 6 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 42 workers in the palabras bookstore , how many of them have read both books ? | there are total 42 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 21 have read saramago . 1 / 6 of the workers have read the latest book by h . kureishi . so ( 1 / 6 ) * 42 = 7 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 21 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 42 = 21 + 7 - b + ( 21 - b - 1 ) b = 3 answer ( a ) | a = 42 / 2
b = a - 1
c = 42 / 2
d = 42 / 6
e = c + d
f = 42 - e
g = b - f
h = g / 2
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a ) 15840 , b ) 3388 , c ) 2667 , d ) 8112 , e ) 66711 | d | multiply(square_perimeter(square_edge_by_area(24336)), 13) | find the length of the wire required to go 13 times round a square field containing 24336 m 2 . | "a 2 = 24336 = > a = 156 4 a = 624 624 * 13 = 8112 answer : d" | a = square_perimeter * (
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a ) β 7 , b ) 7 , c ) 20 , d ) 12 , e ) 14 | c | multiply(3, 4) | the sum of all solutions for x in the equation x ^ 2 β 8 x + 21 = | x β 4 | + 3 is equal to : | "x ^ 2 - 8 x + 18 = | x - 4 | rhs can be - ve or + ve x ^ 2 - 9 x + 22 = 0 x ^ 2 - 7 x + 14 = 0 x = 11 , 7,2 we test all 3 values in original equation , all ok . thus , sum = 11 + 7 + 2 = 20 ans ( c )" | a = 3 * 4
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a ) s . 528 , b ) s . 542 , c ) s . 528 , d ) s . 540 , e ) s . 660 | e | multiply(4, divide(1430, add(add(4, 2), const_3))) | rs . 1430 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ? | "a + b + c = 1430 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1430 = rs . 660 answer : e" | a = 4 + 2
b = a + 3
c = 1430 / b
d = 4 * c
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a ) 136 % , b ) 140 % , c ) 144 % , d ) 148 % , e ) 152 % | c | multiply(const_100, divide(5, multiply(add(20, const_100), divide(6, const_100)))) | last year a worker saved 5 % of her annual salary . this year , she made 20 % more money than last year and she saved 6 % of her salary . the amount she saved this year was what percent of the amount she saved last year ? | "let x be the worker ' s salary last year . last year , she saved 0.05 x . this year , she saved 0.06 ( 1.2 x ) = 0.072 x 0.072 x / 0.05 x = 144 % the answer is c ." | a = 20 + 100
b = 6 / 100
c = a * b
d = 5 / c
e = 100 * d
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a ) 7.16 , b ) 7.16 , c ) 7.12 , d ) 7.15 , e ) 7.2 | e | divide(add(125, 165), multiply(add(80, 65), const_0_2778)) | two trains 125 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? | "t = ( 125 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.2 answer : e" | a = 125 + 165
b = 80 + 65
c = b * const_0_2778
d = a / c
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a ) rs . 49 , b ) rs . 40 , c ) rs . 44 , d ) rs . 42 , e ) rs . 66 | e | multiply(25, subtract(circle_area(add(20, 2)), circle_area(20))) | a circular path of 20 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 25 p per m 2 ? | "explanation : Ο ( 22 ^ 2 - 20 ^ 2 ) = 22 / 7 * ( 484 - 400 ) = 264 264 * 1 / 4 = rs . 66 answer : option e" | a = 20 + 2
b = circle_area - (
c = 25 * b
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a ) 9 , b ) 27 , c ) 10 , d ) 8.5 , e ) 6 | b | divide(81, 3) | stacy has a 81 page history paper due in 3 days . how many pages per day would she have to write to finish on time ? | "81 / 3 = 27 answer : b" | a = 81 / 3
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a ) 13 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these | a | subtract(23, 10) | the area of a rectangular plot is 23 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ? | "l Γ b = 23 Γ b β΄ l = 23 m and l β b = 10 β΄ b = 23 β 10 = 13 m answer a" | a = 23 - 10
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a ) 6 , b ) 8 , c ) 10 , d ) 4 , e ) 12 | a | divide(12, const_2) | in a group of ducks and cows , the total number of legs are 12 more than twice the no . of heads . find the total no . of buffaloes . | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 12 = > 2 x = 12 = > x = 6 a" | a = 12 / 2
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a ) 72 , b ) 85 , c ) 94 , d ) 106 , e ) 108 | d | subtract(add(subtract(193, 59), 23), 47) | there are 193 items that are members of set u . of these items , 47 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ? | "you had the answer almost right . the x = 83 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 85 + set ab = 83 + 23 = 106 d" | a = 193 - 59
b = a + 23
c = b - 47
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a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 7 / 25 | e | divide(subtract(divide(multiply(800, 2), 5), 96), 800) | in a group of 800 people , 2 / 5 play at least one instrument , 96 play two or more . what is the probability that one student play exactly one instrument ? | "p ( playing 2 or more instruments ) = 96 / 800 = 3 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 2 / 5 - 3 / 25 = 7 / 25 . answer e ." | a = 800 * 2
b = a / 5
c = b - 96
d = c / 800
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a ) 3 , b ) 1.5 , c ) 2.3 , d ) 1.8 , e ) 6 | b | divide(12, subtract(16, 8)) | a person can swim in still water at 16 km / h . if the speed of water 8 km / h , how many hours will the man take to swim back against the current for 12 km ? | "m = 16 s = 8 us = 16 - 8 = 8 d = 12 t = 12 / 8 = 1.5 answer : b" | a = 16 - 8
b = 12 / a
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a ) 4300 , b ) 4500 , c ) 5120 , d ) 9600 , e ) 5366 | d | subtract(subtract(15000, multiply(15000, divide(20, const_100))), multiply(subtract(15000, multiply(15000, divide(20, const_100))), divide(20, const_100))) | the population of a town is 15000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ? | 15000 Γ 80 / 100 Γ 80 / 100 = 9600 answer : d | a = 20 / 100
b = 15000 * a
c = 15000 - b
d = 20 / 100
e = 15000 * d
f = 15000 - e
g = 20 / 100
h = f * g
i = c - h
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a ) rs . 14705.24 , b ) rs . 14602.25 , c ) rs . 14822.26 , d ) rs . 14322.10 , e ) rs . 15350.23 | a | subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(11, const_100)), 3)), multiply(multiply(const_4, const_100), const_100)) | what will be the compound interest on a sum of rs . 40,000 after 3 years at the rate of 11 p . c . p . a . ? | explanation : amount after 3 years = p ( 1 + r / 100 ) t = 40000 ( 1 + 11 / 100 ) 3 = 40000 ( 111 / 100 ) 3 = 40000 Γ 111 Γ 111 Γ 111 / 100 Γ 100 Γ 100 = 4 Γ 111 Γ 111 Γ 111 / 100 = 54705.24 compound interest = 54705.24 - 40000 = rs . 14705.24 answer : option a | a = 4 * 100
b = a * 100
c = 11 / 100
d = 1 + c
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
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a ) 22 kmph , b ) 77 kmph , c ) 144 kmph , d ) 71 kmph , e ) 88 kmph | c | multiply(const_3_6, divide(640, 16)) | a train 640 m in length crosses a telegraph post in 16 seconds . the speed of the train is ? | "s = 640 / 16 * 18 / 5 = 144 kmph answer : c" | a = 640 / 16
b = const_3_6 * a
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a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 18 | e | divide(subtract(multiply(76, 3), multiply(69, 2)), subtract(multiply(3, 3), multiply(2, 2))) | if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 76 , how much does one shirt cost ? | "3 j + 2 s = 69 2 j + 3 s = 76 - - - - - - - - - - - - - - - - 5 j + 5 s = 145 - - - - ( divide by 5 ) - - - > j + s = 29 3 j + 2 s = j + 2 ( j + s ) = j + 58 = 69 - - - > j = 11 3 * 11 + 2 s = 69 33 + 2 s = 69 2 s = 36 s = 18 answer : e" | a = 76 * 3
b = 69 * 2
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
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a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 16 , e ) 5 and 14 | d | add(multiply(add(floor(sqrt(15)), const_1), const_100), subtract(floor(sqrt(270)), const_1)) | in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 15 and 270 , then the least and greatest integer on the card would be | "given : 15 < x ( x + 1 ) < 270 . now , it ' s better to test the answer choices here rather than to solve : if x = 4 then x ( x + 1 ) = 20 > 15 - - > so , the least value is 4 . test for the largest value : if x = 16 then x ( x + 1 ) = 16 * 17 = 272 > 270 answer : d ." | a = math.sqrt(15)
b = math.floor(a)
c = b + 1
d = c * 100
e = math.sqrt(270)
f = math.floor(e)
g = f - 1
h = d + g
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a ) 10,10 , b ) 30,40 , c ) 70 , 50 , d ) 20,20 , e ) 10,15 | d | subtract(multiply(3, 100), divide(320, const_10)) | a total of 320 chocolates were distributed among 100 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates . find the respective number of boys and girls ? | "let the number of boys be x . number of girls is 100 - x . total number of chocolates received by boys and girls = 2 x + 3 ( 100 - x ) = 320 = > 300 - x = 320 = > x = 20 . so , the number of boys or girls is 20 . answer : d" | a = 3 * 100
b = 320 / 10
c = a - b
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a ) 2 / 6 , b ) 3 / 6 , c ) 4 / 6 , d ) 6 / 4 , e ) 5 / 6 | b | divide(subtract(subtract(subtract(11, 3), 3), 2), 6) | harry started a 7 - mile hike with a full 11 - cup canteen of water and finished the hike in 3 hours with 2 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 3 cups of water during the last mile , how many cups did he drink per mile during the first 6 miles of the hike ? | "no of cups leaked during the trip = 3 cups . no of cups harry drank = 6 cups . no of cups harry drank during the first 6 miles = 3 . drink / mile = 3 / 6 answer : b" | a = 11 - 3
b = a - 3
c = b - 2
d = c / 6
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a ) 75 , b ) 100 , c ) 125 , d ) 135 , e ) 225 | d | divide(subtract(multiply(divide(810, const_3), const_4), 810), const_2) | there are 810 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? | "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 810 . hence , we have m + f = 810 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 810 / 3 = 270 solving the three equations yields the solution f = 270 , m = 540 , and d = 270 . the number of female democratic participants equals half the female participants equals 270 / 2 = 135 . answer : d" | a = 810 / 3
b = a * 4
c = b - 810
d = c / 2
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['a ) 32 cm 2', 'b ) 16 cm 2', 'c ) 20 cm 2', 'd ) 64 cm 2', 'e ) none of these'] | a | divide(power(4, const_2), divide(const_1, const_2)) | a square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely . if a side of the first square is 4 cm , determine the sum of the areas all the square . | solution : side of the first square is 4 cm . side of second square = 2 β 2 cm . side of third square = 2 cm . and so on . i . e . 4 , 2 β , 2 , β 2 , 1 . . . . . . thus , area of these square will be , = 16 , 8 , 4 , 2 , 1 , 1 / 2 . . . . . . . hence , sum of the area of first , second , third square . . . . . . = 16 + 8 + 4 + 2 + 1 + . . . . . = [ 16 / { 1 - ( 1 / 2 ) } ] = 32 cm 2 . answer : option a | a = 4 ** 2
b = 1 / 2
c = a / b
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a ) a ) 13050 , b ) b ) 12960 , c ) c ) 10025 , d ) d ) 11080 , e ) e ) 12080 | b | multiply(const_4, multiply(multiply(12, 15), 18)) | find the greatest number of 5 digits which is exactly divisible by 12 , 15 and 18 ? | the largest five digit numbers are 13050 , 12960,12080 13050 is not divisible by 12 12960 is divisible by 18 , 12 and 15 answer : b | a = 12 * 15
b = a * 18
c = 4 * b
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a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25 | a | divide(4, choose(8, 2)) | kim has 4 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 8 shoes , what is the probability that she will select 2 shoes of the same color ? | "total pairs = 8 c 2 = 28 ; same color pairs = 4 c 1 * 1 c 1 = 4 ; prob = 1 / 7 ans a" | a = math.comb(8, 2)
b = 4 / a
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a ) 18 , b ) 16 , c ) 15 , d ) 14 , e ) 13 | a | add(add(add(const_4, 3), add(3, const_2)), 3) | the number 110 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? | "7 ^ 2 + 5 ^ 2 + 6 ^ 2 = 49 + 25 + 36 = 110 7 + 5 + 6 = 18 hence answer is a" | a = 4 + 3
b = 3 + 2
c = a + b
d = c + 3
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a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 % | b | subtract(const_100, subtract(add(20, 70), 10)) | in an examination , 20 % of total students failed in hindi , 70 % failed in english and 10 % in both . the percentage of these who passed in both the subjects is : | "pass percentage = 100 - ( 20 + 70 - 10 ) = 100 - 80 = 20 answer : b" | a = 20 + 70
b = a - 10
c = 100 - b
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a ) 18 , b ) 16 , c ) 10 , d ) 15 , e ) 14 | d | subtract(const_100, multiply(multiply(add(const_1, divide(13, 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 13 % . the effect on revenue is ? | "100 * 100 = 10000 75 * 113 = 8475 - - - - - - - - - - - 10000 - - - - - - - - - - - 1525 100 - - - - - - - - - - - ? = > 15 % decrease answer : d" | a = 13 / 100
b = 1 + a
c = 25 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
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a ) 10 sec , b ) 11 sec , c ) 12 sec , d ) 13 sec , e ) 14 sec | a | multiply(divide(add(divide(1, 6), divide(1, 6)), add(50, 70)), const_3600) | the famous denali star train starts from anchorge & travels towards fair banksat speed 50 mph . after some time another train glacier discovery train ( at parallel track ) at fair banks and moves towards anchorge at a speed of 70 mph . both the trains denali star & glacier discovery have a length 1 / 6 miles each . after the trains meet how many seconds will faster train take to overtake the slower one ? | total distance = ( 1 / 6 ) + ( 1 / 6 ) = 1 / 3 miles relative speed = ( 50 + 70 ) mph = 120 mph time taken = ( 1 / 3 ) / ( 120 ) hours = 10 seconds answer : a | a = 1 / 6
b = 1 / 6
c = a + b
d = 50 + 70
e = c / d
f = e * 3600
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a ) 14 , b ) 16 , c ) 17 , d ) 13 , e ) 15 | a | divide(subtract(300, 1), 21) | how many positive integers between 1 and 300 are there such that they are multiples of 21 ? | "multiples of 21 = 21 , 42,63 , - - - - - 294 number of multiples of 21 = > 21 * 14 = 294 answer is a" | a = 300 - 1
b = a / 21
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a ) 5 , b ) 11 , c ) 13 , d ) 21 , e ) 23 | b | add(reminder(divide(221, add(const_1, const_12)), const_10), add(const_1, reminder(add(const_1, const_12), const_10))) | if p , q , and r are distinct positive digits and the product of the two - digit integers pq and pr is 221 , what is the sum of the digits p , q , and r ? | factor out 221 221 = 13 * 17 thus pq = 13 & pr = 17 or vice versa thus p = 1 , q = 3 & r = 7 sum = 1 + 3 + 7 = 11 answer : b | a = 1 + 12
b = 221 / a
c = reminder + (
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a ) 30000 , b ) 66666 , c ) 40000 , d ) 20000 , e ) 60000 | b | multiply(divide(50000, 3), 4) | p and q invested in a business . the profit earned was divided in the ratio 3 : 4 . if p invested rs 50000 , the amount invested by q is | "let the amount invested by q = q 50000 : q = 3 : 4 β 50000 Γ 4 = 3 q β q = ( 50000 Γ 4 ) / 3 = 66666 answer is b ." | a = 50000 / 3
b = a * 4
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a ) 200 Ο , b ) 240 Ο , c ) 600 Ο , d ) 480 Ο , e ) 1,200 Ο | c | multiply(multiply(multiply(multiply(divide(20, add(multiply(const_2, const_100), multiply(add(const_2, const_3), const_1000))), const_2), divide(add(const_2, multiply(const_2, const_10)), add(const_3, const_4))), 1,320), const_60) | the end of a blade on an airplane propeller is 20 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet ) | "distance traveled in 1 revolution = 2 Ο r = 2 Ο 20 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 Ο 20 / 5280 = 600 Ο c is the answer" | a = 2 * 100
b = 2 + 3
c = b * 1000
d = a + c
e = 20 / d
f = e * 2
g = 2 * 10
h = 2 + g
i = 3 + 4
j = h / i
k = f * j
l = k * 1
m = l * const_60
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a ) 10 : 4 , b ) 10 : 7 , c ) 13 : 7 , d ) 14 : 6 , e ) 13 : 9 | c | divide(multiply(65, 8), multiply(70, 4)) | car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ? | "sol . distance travelled by car a = 65 Γ 8 = 520 km distance travelled by car b = 70 Γ 4 = 280 km ratio = 520 / 280 = 13 : 7 c" | a = 65 * 8
b = 70 * 4
c = a / b
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a ) 2 / 109 , b ) 7 / 109 , c ) 8 / 223 , d ) 14 / 263 , e ) 13 / 102 | e | multiply(divide(multiply(divide(52, const_4), divide(52, const_4)), multiply(52, 52)), const_2) | two cards are drawn together from a pack of 52 cards . the probability that one is a spade and one is a heart , is : | "n ( s ) = ( 52 x 51 ) / ( 2 x 1 ) = 1326 . let e = event of getting 1 spade and 1 heart . n ( e ) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = ( 13 x 13 ) = 169 . p ( e ) = n ( e ) / n ( s ) 169 / 1326 = 13 / 102 answer e" | a = 52 / 4
b = 52 / 4
c = a * b
d = 52 * 52
e = c / d
f = e * 2
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a ) 5 , b ) 6 , c ) 4 , d ) 8 , e ) 3 | a | divide(factorial(subtract(add(const_4, 9), const_1)), multiply(factorial(9), factorial(subtract(const_4, const_1)))) | how many positive integers less than 50 are there such that they are multiples of 9 ? | "number of multiples of 9 = > 45 - 9 / 9 + 1 = 5 answer is a" | a = 4 + 9
b = a - 1
c = math.factorial(b)
d = math.factorial(9)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
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a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 105 | e | multiply(divide(189, add(add(1, const_2), multiply(const_2, 3))), subtract(multiply(const_2, 3), 1)) | pat , kate and mark charged a total of 189 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate . | "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 189 - total hours charged for , x = 21 . mat charged 6 x - x or 5 x for more hours than kate , or for 105 hours . e is correct" | a = 1 + 2
b = 2 * 3
c = a + b
d = 189 / c
e = 2 * 3
f = e - 1
g = d * f
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a ) 4 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 4 : 0 , e ) 4 : 9 | b | multiply(divide(18, const_100), 9) | a part of certain sum of money is invested at 9 % per annum and the rest at 18 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ? | "18 : 9 = 2 : 1 answer : b" | a = 18 / 100
b = a * 9
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a ) 3377 , b ) 6160 , c ) 5460 , d ) 1976 , e ) 1671 | b | divide(multiply(divide(multiply(5000, add(const_100, 10)), const_100), add(const_100, 12)), const_100) | find the amount on rs . 5000 in 2 years , the rate of interest being 10 % per first year and 12 % for the second year ? | 5000 * 110 / 100 * 112 / 100 = > 6160 answer : b | a = 100 + 10
b = 5000 * a
c = b / 100
d = 100 + 12
e = c * d
f = e / 100
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a ) 2 , b ) 8 , c ) 9 , d ) 3 , e ) 5 | b | divide(subtract(18, 3), 3) | ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the sum of the digits of the number . | "let the two digit number be xy . 4 ( x + y ) + 3 = 10 x + y - - - ( 1 ) 10 x + y + 18 = 10 y + x - - - ( 2 ) solving 1 st equation , 4 x + 4 y + 3 = 10 x + y 3 y + 3 = 6 x 6 x β 3 y = 3 therefore , 2 x β y = 1 - - - ( 3 ) solving 2 nd equation , xy + 18 = yx β β ( 10 x + b ) + 18 = 10 y + x β β 18 = 9 y β 9 x β β 2 = y β x we get y - x = 2 - - - ( 4 ) adding 3 and 4 , we get x = 3 by substituting in ( 4 ) , we get y = 5 so the given number is 35 . sum of the digits = 8 . answer : b" | a = 18 - 3
b = a / 3
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a ) 10.5 , b ) 12.5 , c ) 13.5 , d ) 11.5 , e ) 11 | b | divide(multiply(15, 1000), add(1000, 200)) | 1000 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ? | "1000 * 15 = 1200 * x x = 12.5 answer b" | a = 15 * 1000
b = 1000 + 200
c = a / b
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a ) 216 Β° , b ) 222 Β° , c ) 228 Β° , d ) 234 Β° , e ) 240 Β° | d | subtract(const_360, divide(multiply(add(add(add(add(15, 9), 5), 4), 2), const_360), const_100)) | a circle graph shows how the budget of a certain company was spent : 15 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 - ( 15 + 9 + 5 + 4 + 2 ) = 65 % 100 % of the circle is 360 degrees . then ( 65 % / 100 % ) * 360 = 234 degrees the answer is d ." | a = 15 + 9
b = a + 5
c = b + 4
d = c + 2
e = d * 360
f = e / 100
g = 360 - f
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['a ) 5', 'b ) 10', 'c ) 15', 'd ) 20', 'e ) 25'] | e | divide(subtract(divide(110, const_2), sqrt(subtract(multiply(divide(110, const_2), divide(110, const_2)), multiply(const_4, 750)))), const_2) | the area of a rectangular field is equal to 750 square meters . its perimeter is equal to 110 meters . find the width of this rectangle . | l * w = 750 : area , l is the length and w is the width . 2 l + 2 w = 110 : perimeter l = 55 - w : solve for l ( 55 - w ) * w = 750 : substitute in the area equation w = 25 and l = 30 correct answer e | a = 110 / 2
b = 110 / 2
c = 110 / 2
d = b * c
e = 4 * 750
f = d - e
g = math.sqrt(f)
h = a - g
i = h / 2
|
a ) 200 , b ) 300 , c ) 500 , d ) 600 , e ) 400 | d | divide(660, add(const_1, divide(10, const_100))) | a number increased by 10 % gives 660 . the number is ? | "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 10 % = 110 % 110 % - - - - - - - > 660 ( 110 Γ£ β 6 = 660 ) 100 % - - - - - - - > 600 ( 100 Γ£ β 6 = 600 ) option ' d '" | a = 10 / 100
b = 1 + a
c = 660 / b
|
a ) 14 , b ) 15 , c ) 18 , d ) 20 , e ) 22 | d | multiply(multiply(10, 3), divide(4, 6)) | working simultaneously and independently at an identical constant rate , 10 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ? | "the rate of 10 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 10 * ( x / 4 ) = x / 40 units per day ; now , again as { time } * { combined rate } = { job done } then 6 * ( m * x / 40 ) = 3 x - - > m = 20 . answer : d ." | a = 10 * 3
b = 4 / 6
c = a * b
|
a ) 32.2 , b ) 10.6 , c ) 32.3 , d ) 32.8 , e ) 32.4 | b | add(3, const_1) | the average of first five prime numbers greater than 3 is ? | "5 + 7 + 11 + 13 + 17 = 53 / 5 = 10.60 answer = b" | a = 3 + 1
|
a ) 299 , b ) 266 , c ) 299 , d ) 750 , e ) 261 | d | divide(divide(multiply(90, const_1000), divide(const_60, const_1)), const_2) | the length of a train and that of a platform are equal . if with a speed of 90 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ? | "speed = [ 90 * 5 / 18 ] m / sec = 25 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 25 Γ¨ x = 25 * 60 / 2 = 750 answer : d" | a = 90 * 1000
b = const_60 / 1
c = a / b
d = c / 2
|
a ) 3 : 7 , b ) 7 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 2 : 4 | a | divide(subtract(15.7, 15.4), subtract(16.4, 15.7)) | the average age of students of a class is 15.7 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ? | "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.7 = ( 16.4 - 15.7 ) k = ( 15.7 - 15.4 ) = k = 0.3 / 0.7 = 3 / 7 required ratio = 3 / 7 : 1 = 3 : 7 . answer : a" | a = 15 - 7
b = 16 - 4
c = a / b
|
a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above | b | sqrt(power(5, const_2)) | in the rectangular coordinate system , points ( 5 , 0 ) and ( β 5 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ? | "the answer is b it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 5 b" | a = 5 ** 2
b = math.sqrt(a)
|
a ) 150 , b ) 170 , c ) 190 , d ) 210 , e ) 230 | d | multiply(divide(multiply(30, const_2), subtract(42, 30)), 42) | train a leaves the station traveling at 30 miles per hour . two hours later train Π² leaves the same station traveling in the same direction at 42 miles per hour . how many miles from the station was train a overtaken by train b ? | "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 12 miles per hour . the time to catch up is 60 / 12 = 5 hours . in 5 hours , train a travels another 30 * 5 = 150 miles for a total of 210 miles . the answer is d ." | a = 30 * 2
b = 42 - 30
c = a / b
d = c * 42
|
a ) 400 , b ) 500 , c ) 367 , d ) 368 , e ) 339 | a | divide(70, divide(multiply(5, add(3, divide(1, 2))), const_100)) | what sum of money will produce rs . 70 as simple interest in 5 years at 3 1 / 2 percent ? | "70 = ( p * 5 * 7 / 2 ) / 100 p = 400 answer : a" | a = 1 / 2
b = 3 + a
c = 5 * b
d = c / 100
e = 70 / d
|
a ) 1 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 8 / 45 , e ) 9 / 45 | a | divide(2, 5) | what is the hcf of 2 / 3 , 5 / 9 and 6 / 5 | "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 5 , 6 ) / ( lcm of 3 , 9 , 5 ) = 1 / 45 answer : option a" | a = 2 / 5
|
a ) 678 , b ) 456 , c ) 234 , d ) 476 , e ) 432 | b | multiply(38, 10) | the h . c . f . of two numbers is 38 and the other two factors of their l . c . m . are 12 and 10 . the larger of the two numbers is : | ": explanation : clearly , the numbers are ( 38 x 12 ) and ( 38 x 10 ) . { \ color { blue } \ therefore } larger number = ( 38 x 12 ) = 456 . answer : b ) 456" | a = 38 * 10
|
a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2 | b | subtract(9, 2) | robert ate 9 chocolates , nickel ate 2 chocolates . how many more chocolates did robert ate than nickel ? | 9 - 2 = 7 . answer is b | a = 9 - 2
|
a ) 100 % , b ) 200 % , c ) 300 % , d ) 600 % , e ) 800 % | e | multiply(const_100, divide(const_2, const_2)) | the area of a circle is increased by 800 % . by what percent has the diameter of the circle increased ? | "a diameter of 2 it ' s radius = 1 it ' s area = ( 1 ^ 2 ) pi = 1 pi answer a : if we increase that diameter 100 % , we have . . . . a diameter of 4 it ' s radius = 2 it ' s area = ( 2 ^ 2 ) pi = 4 pi this area has increased ( 4 pi - 1 pi ) / 1 pi = 3 pi / 1 pi = 3 = 300 % answer b : if we increase the diameter 200 % , we have . . . a diameter of 6 it ' s area = 3 it ' s area = ( 3 ^ 2 ) pi = 9 pi this area has increased ( 9 pi - 1 pi ) / 1 pi = 8 pi / 1 pi = 8 = 800 % answer : e" | a = 2 / 2
b = 100 * a
|
a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 9 , d ) 1 / 4 , e ) 1 / 2 | a | subtract(divide(5, 9), divide(4, 9)) | 3 boys are ages 4 , 6 and 7 respectively . 3 girls are ages 5 , 8 and 9 , respectively . if two of the boys and two of the girls are randomly selected and the sum of the selected children ' s ages is q , what is the difference between the probability that q is even and the probability that q is odd ? | age of boys q : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 13,11 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 17,14 9 combinations of sum between sets ( 10 , 12,11 ) ( 13 , 17,14 ) = 23 , 27,24 - 16 , 30,17 - 24 , 28,25 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9 | a = 5 / 9
b = 4 / 9
c = a - b
|
a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 28 | b | add(4, multiply(8, 2)) | if 4 xz + yw = 4 and xw + yz = 8 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ? | ( 2 x + y ) * ( 2 z + w ) = 4 + 2 ( 8 ) = 20 answer : b | a = 8 * 2
b = 4 + a
|
a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 4 , e ) 4 / 5 | c | divide(subtract(divide(40, const_100), divide(50, const_100)), subtract(divide(25, const_100), divide(50, const_100))) | some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ? | "40 % is 15 % - points above 25 % and 10 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 2 : 3 . 2 / 5 of the original paint was replaced . the answer is c ." | a = 40 / 100
b = 50 / 100
c = a - b
d = 25 / 100
e = 50 / 100
f = d - e
g = c / f
|
a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42 | b | add(multiply(const_2, 10), add(7, 10)) | in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 7 years older than b , the present age of b is | explanation : let b ' s age = x years . then , as age = ( x + 7 ) years . ( x + 7 + 10 ) = 2 ( x β 10 ) hence x = 37 . present age of b = 37 years answer : option b | a = 2 * 10
b = 7 + 10
c = a + b
|
a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m . | d | add(divide(add(2, 10), add(9, 10)), 1000) | the distance between 2 cities a and b is 1000 km . a train starts from a at 9 a . m . and travels towards b at 100 km / hr . another starts from b at 10 a . m . and travels towards a at 150 km / hr . at what time do they meet ? | "suppose they meet x hrs after 9 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 9 + 5 = 2 p . m . answer is d" | a = 2 + 10
b = 9 + 10
c = a / b
d = c + 1000
|
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