Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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a car travels uphill at 30 km / hr and downhill at 60 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ? | "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 6 ; avg speed = 150 / ( 10 / 3 + 5 / 6 ) = 36 kmph answer : e" | a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph | e | divide(add(100, 50), add(divide(100, 30), divide(50, 60))) | add(n2,n3)|divide(n2,n0)|divide(n3,n1)|add(#1,#2)|divide(#0,#3)| | general |
a work which could be finished in 11 days was finished 3 days earlier after 10 more men joined . the number of men employed was ? | "x - - - - - - - 11 ( x + 10 ) - - - - 6 x * 11 = ( x + 10 ) 6 x = 12 \ answer : e" | a ) 22 , b ) 20 , c ) 88 , d ) 71 , e ) 12 | e | divide(multiply(multiply(3, const_2), 10), subtract(11, multiply(3, const_2))) | multiply(n1,const_2)|multiply(n2,#0)|subtract(n0,#0)|divide(#1,#2)| | physics |
the ratio of numbers is 3 : 4 and their h . c . f is 5 . their l . c . m is : | "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 5 . so , the numbers are 15 and 20 . l . c . m of 15 and 20 = 60 . answer : d" | a ) 12 , b ) 16 , c ) 24 , d ) 60 , e ) 98 | d | lcm(multiply(3, 5), multiply(4, 5)) | multiply(n0,n2)|multiply(n1,n2)|lcm(#0,#1)| | other |
if the average ( arithmetic mean ) of a and b is 50 and the average of b and c is 70 , what is the value of c β a ? | "- ( a + b = 100 ) b + c = 140 c - a = 40 a . 40" | a ) 40 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given . | a | subtract(multiply(70, const_2), multiply(50, const_2)) | multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | general |
a invested $ 15000 in a business after 6 months b invested $ 18000 in the business . end of the year if they got $ 16000 as profit . find b shares ? | "a : b = 15000 * 12 : 18000 * 6 a : b = 5 : 3 a ' s share = 16000 * 5 / 8 = 10000 b ' s share = 16000 * 3 / 8 = 6000 answer is d" | a ) $ 10000 , b ) $ 12000 , c ) $ 5000 , d ) $ 6000 , e ) $ 7500 | d | multiply(16000, subtract(const_1, divide(divide(18000, const_2), add(15000, divide(18000, const_2))))) | divide(n2,const_2)|add(n0,#0)|divide(#0,#1)|subtract(const_1,#2)|multiply(n3,#3)| | gain |
if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 70 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly... | "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 70 - { both correctly } + 5 { both correctly } = 60 . answer : a ." | a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 % | a | subtract(add(add(85, 70), 5), const_100) | add(n0,n1)|add(n2,#0)|subtract(#1,const_100)| | other |
a number when divided by 44 , gives 400 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 35 | "explanation : p Γ· 44 = 400 = > p = 400 * 44 = 17600 p / 35 = 17600 / 35 = 502 , remainder = 30 answer : option a" | a ) a ) 30 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7 | a | divide(multiply(44, 400), 35) | multiply(n0,n1)|divide(#0,n3)| | general |
what is the area of a square field whose diagonal of length 22 m ? | "d 2 / 2 = ( 22 * 22 ) / 2 = 220 answer : b" | a ) 300 sq m , b ) 220 sq m , c ) 200 sq m , d ) 400 sq m , e ) 800 sq m | b | divide(square_area(22), const_2) | square_area(n0)|divide(#0,const_2)| | geometry |
if p ( a ) = 0.18 , p ( b ) = 0.5 and p ( b | a ) = 0.2 , find p ( a n b ) ? | p ( b | a ) = p ( a n b ) / p ( a ) p ( a n b ) = p ( b | a ) Γ p ( a ) p ( a n b ) = 0.2 Γ 0.18 p ( a n b ) = 0.36 b ) | a ) 0.28 , b ) 0.36 , c ) 0.45 , d ) 0.56 , e ) 0.7 | b | multiply(multiply(0.18, 0.2), const_10) | multiply(n0,n2)|multiply(#0,const_10) | general |
an error 1 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ? | "percentage error in calculated area = ( 1 + 1 + ( 1 Γ£ β 1 ) / 100 ) % = 2.01 % answer : e" | a ) 4.05 % , b ) 4.02 % , c ) 4 % , d ) 3 % , e ) 2.01 % | e | divide(multiply(subtract(square_area(add(const_100, 1)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | gain |
a survey of n people in the town of eros found that 50 % of them preferred brand a . another surveyof 100 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ? | "50 % of n people from eros prefer brand a . 50 % of n is 50 / 100 x n = n / 2 . 60 % of 100 people from angie prefer brand a . 60 % of 100 is 60 / 100 x 100 = 60 . of the total n + 100 people surveyed , n / 2 + 60 prefer brand a . given that this is 55 % , we have ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 solving the eq... | a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250 | d | divide(subtract(multiply(100, divide(60, const_100)), multiply(100, divide(55, const_100))), subtract(divide(55, const_100), divide(50, const_100))) | divide(n2,const_100)|divide(n3,const_100)|divide(n0,const_100)|multiply(n1,#0)|multiply(n1,#1)|subtract(#1,#2)|subtract(#3,#4)|divide(#6,#5)| | general |
325.124 x 12.98 Γ£ Β· 3.001 + 21.21 = ? | "explanation : ? = 325.124 x 12.98 Γ£ Β· 3.001 + 21.21 = ? Γ’ β° Λ ( 325.124 x 13 / 3 ) + 21.21 Γ’ β° Λ 1408.87 + 21.21 Γ’ β° Λ 1430.080 answer : option a" | a ) 1430.08 , b ) 1420.06 , c ) 781.189 , d ) 656.112 , e ) 456.512 | a | multiply(325.124, power(12.98, 3.001)) | power(n1,n2)|multiply(n0,#0)| | general |
gold is 19 times as heavy as water and copper is 9 times heavy . in what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water ? | "? required ratio = 6 ? 4 = 3 : 2 answer b" | a ) 2 : 3 , b ) 3 : 2 , c ) 1 : 3 , d ) 2 : 1 , e ) none of these | b | divide(subtract(15, 9), subtract(19, 15)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | general |
in triangle pqr , the angle q = 90 degree , pq = 7 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz | look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 7 = 8 : 10 - - > qy = 5.6 . answer : a . | ['a ) 5.6 cm', 'b ) 2.4 cm', 'c ) 4.8 cm', 'd ) 2.16 cm', 'e ) 3.2 cm'] | a | divide(multiply(7, 8), const_10) | multiply(n1,n2)|divide(#0,const_10) | geometry |
in a family 15 people eat only vegetarian , 8 people eat only non veg . , 11 people eat both veg and non veg . . how many people eat veg in the family ? | "total people eat veg = only veg + both veg and non veg total = 15 + 11 = 26 answer = d" | a ) 20 , b ) 11 , c ) 23 , d ) 26 , e ) 21 | d | add(15, 11) | add(n0,n2)| | other |
two trains a and b are 125 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b . | "detailed solution speed of a = 54 β 1000 / 60 β 60 = 15 m / s speed of b = 36 β 1000 / 60 β 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross... | a ) 10 s , b ) 11 s , c ) 4 s , d ) 8 s , e ) 12 s | b | divide(add(125, 150), add(divide(multiply(54, const_1000), const_3600), divide(multiply(36, const_1000), const_3600))) | add(n0,n1)|multiply(n2,const_1000)|multiply(n3,const_1000)|divide(#1,const_3600)|divide(#2,const_3600)|add(#3,#4)|divide(#0,#5)| | physics |
together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours t would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( ass... | "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above :... | a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above . | c | divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15)) | divide(const_1,n2)|divide(const_1,n5)|add(#0,#1)|divide(#2,n0)|divide(const_1,#3)| | physics |
a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 320 m long platform ? | "a 44 min let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 320 ) / 36 * 5 / 18 = 44 min ." | a ) 44 min , b ) 55 min , c ) 47 min , d ) 67 min , e ) 45 min | a | divide(add(320, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36)) | multiply(n0,const_0_2778)|multiply(n1,#0)|add(n2,#1)|divide(#2,#0)| | physics |
the price of a book is increased from $ 300 to $ 450 . what is the % of increase in its price ? | "explanation : change in the price = rs 450 Γ’ β¬ β rs 300 = rs 150 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 150 300 ) * 100 = 50 % d" | a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 % | d | multiply(divide(subtract(450, 300), 300), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a man can row downstream at 26 kmph and upstream at 22 kmph . find the speed of the man in still water and the speed of stream respectively ? | "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 22 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 48 = > x = 24 , y = 2 . answer : option a" | a ) 24 , 2 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) none of these | a | divide(divide(add(26, 22), const_2), const_2) | add(n0,n1)|divide(#0,const_2)|divide(#1,const_2)| | physics |
a train is walking at 6 / 7 of its usual speed , the train is 20 minutes too late . find its usual time to cover the journey . | new speed = 6 / 7 of the usual speed new time taken = 7 / 6 of the usual time taken so , ( 7 / 6 of the usual time ) - ( usual time ) = 20 min 1 / 6 of the usual time = 20 min usual time = 20 * 6 = 120 min = 2 hours correct option is e | a ) 1 hour , b ) 30 min , c ) 3 hours 20 min , d ) 2 hours 30 min , e ) 2 hours | e | divide(divide(multiply(divide(6, 7), 20), subtract(const_1, divide(6, 7))), const_60) | divide(n0,n1)|multiply(n2,#0)|subtract(const_1,#0)|divide(#1,#2)|divide(#3,const_60) | physics |
what is the sum of all remainders obtained when the first 110 natural numbers are divided by 9 ? | "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such bloc... | a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 399 | c | add(const_3, multiply(divide(subtract(110, reminder(110, 9)), 9), add(add(add(const_1, const_2), const_3), add(add(const_1, const_4), add(const_4, add(add(const_1, const_2), const_3)))))) | add(const_1,const_2)|add(const_1,const_4)|reminder(n0,n1)|add(#0,const_3)|subtract(n0,#2)|add(#3,const_4)|divide(#4,n1)|add(#1,#5)|add(#3,#7)|multiply(#8,#6)|add(#9,const_3)| | general |
by how much is 30 % of 80 greater than 4 / 5 th of 25 ? | "answer it is ( 30 x 80 ) / 100 - ( 4 x 25 ) / 5 = 24 - 20 = 4 correct option : b" | a ) 2 , b ) 4 , c ) 10 , d ) 15 , e ) 17 | b | subtract(multiply(80, divide(30, const_100)), multiply(divide(4, const_100), 5)) | divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n3,#1)|subtract(#2,#3)| | general |
there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 77 . ... | "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 77 ) = 308 x = 73 and the fourth person has a height of 73 + 10 = 83 inches the answer is c ." | a ) 79 , b ) 81 , c ) 83 , d ) 85 , e ) 87 | c | add(divide(subtract(multiply(77, 4), add(6, add(4, 6))), 4), add(4, 6)) | add(n0,n2)|multiply(n0,n3)|add(n2,#0)|subtract(#1,#2)|divide(#3,n0)|add(#0,#4)| | general |
t = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set t and one integer from set b . what is the probability that the sum of the two integers will equal 9 ? | the total number of pairs t , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b . | a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33 | b | divide(add(add(5, 6), 9), const_100) | add(n3,n6)|add(n9,#0)|divide(#1,const_100) | general |
a man whose speed is 7 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ? | "m = 7.0 s = 1.5 ds = 8.5 us = 5.5 as = ( 2 * 8.5 * 5.5 ) / 14 = 6.7 answer : a" | a ) 6.7 , b ) 4 , c ) 6 , d ) 9 , e ) 3 | a | divide(add(7, subtract(7, 1.5)), const_2) | subtract(n0,n1)|add(n0,#0)|divide(#1,const_2)| | general |
a sum was put at simple interest at a certain rate for 3 years . had it been put at 2 % higher rate , it would have fetched rs . 360 more . find the sum . | "let sum = p and original rate = r . then , [ ( p * ( r + 2 ) * 3 ) / 100 ] β [ ( p * r * 3 ) / 100 ] = 360 . = 3 pr + 6 p - 3 pr = 36000 ο 6 p = 36000 ο p = 6000 hence , sum = rs . 6000 . answer is b ." | a ) 3000 , b ) 6000 , c ) 2000 , d ) 4000 , e ) none of them | b | divide(360, multiply(divide(2, const_100), 3)) | divide(n1,const_100)|multiply(n0,#0)|divide(n2,#1)| | gain |
30 ^ 10 / 210 ^ 5 = ? | "30 ^ 10 / 210 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . ( 30 / 7 ) ^ 5 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 210 ^ 5 = ( 30 ^ 10 ) / ( 7 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 7 ^ 5 ) = ( 30 / 7 ) ^ 5 . thus , c is the answer ." | a ) 6 ^ 5 , b ) 5 ^ 6 , c ) ( 30 / 7 ) ^ 5 , d ) 6 ^ 3 , e ) 15 ^ 3 | c | divide(power(30, 10), power(30, 5)) | power(n0,n1)|power(n0,n3)|divide(#0,#1)| | general |
the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 420 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office . | "let no . of non - officers be x 15 * 420 + x * 110 = ( x + 15 ) 120 x = 450 d" | a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 510 | d | divide(subtract(multiply(15, 420), multiply(15, 120)), subtract(120, 110)) | multiply(n1,n3)|multiply(n0,n3)|subtract(n0,n2)|subtract(#0,#1)|divide(#3,#2)| | general |
if ( a - b - c + d = 13 ) and ( a + b - c - d = 9 ) , what is the value of ( b - d ) ^ 2 ? | "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 9 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 9 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 4 ( 2 ) simplify - b + d = 2 b - d = - 2 ( b - d ) ^ 2 = ( - 2 ) ^ 2 = 4 my answer : a" | a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 . | a | power(subtract(9, divide(add(13, 9), 2)), 2) | add(n0,n1)|divide(#0,n2)|subtract(n1,#1)|power(#2,n2)| | general |
in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 70 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , b... | since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 60 : 40 represents the number ratio of republicans : democrats . ... | a ) 2 % , b ) 4 % , c ) 8 % , d ) 10 % , e ) 15 % | b | multiply(divide(subtract(add(multiply(divide(25, const_100), 2), multiply(divide(70, const_100), 3)), add(subtract(3, multiply(divide(70, const_100), 3)), subtract(2, multiply(divide(25, const_100), 2)))), add(3, 2)), const_100) | add(n0,n1)|divide(n3,const_100)|divide(n2,const_100)|multiply(n1,#1)|multiply(n0,#2)|add(#3,#4)|subtract(n0,#4)|subtract(n1,#3)|add(#6,#7)|subtract(#5,#8)|divide(#9,#0)|multiply(#10,const_100) | other |
a family pays $ 800 per year for an insurance plan that pays 85 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total . | "upfront payment for insurance plan = 800 $ family needs to pay 15 % of first 1000 $ in expense = 150 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 150 = 950 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount pai... | a ) $ 1,100 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200 | a | subtract(1,000, 800) | subtract(n2,n0)| | general |
a vendor bought toffees at 6 for a dollar . how many for a dollar must he sell to gain 20 % ? | "c 5 c . p . of 6 toffees = $ 1 s . p . of 6 toffees = 120 % of $ 1 = $ 6 / 5 for $ 6 / 5 , toffees sold = 6 . for $ 1 . toffees sold = 6 * 5 / 6 = 5" | a ) 7 , b ) 6 , c ) 5 , d ) 9 , e ) 8 | c | multiply(6, add(const_1, divide(20, const_100))) | divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)| | gain |
if each year the population of the country grows by 100 % , how many years will elapse before the population of the country doubles ? | "till year 2010 , population is 100 . year 2001 : population becomes 200 . . . . . . . . . . . . . 1 year elapsed answer : a" | a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | a | add(const_4, const_4) | add(const_4,const_4)| | gain |
positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 50 . what is the value of x ? | "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 50 y / 100 * 4 y = 50 y = 35 and x = 140 answer - d" | a ) 50 , b ) 100 , c ) 200 , d ) 140 , e ) 2,000 | d | multiply(multiply(divide(50, 50), divide(50, 50)), const_1000) | divide(n0,n2)|divide(n1,n2)|multiply(#0,#1)|multiply(#2,const_1000)| | general |
the number 149 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? | "2 ^ 2 + 8 ^ 2 + 9 ^ 2 = 149 - - > 2 + 9 + 8 = 19 . a" | a ) 19 , b ) 16 , c ) 15 , d ) 14 , e ) 13 | a | add(add(add(const_4, 3), add(3, const_2)), 3) | add(n1,const_4)|add(const_2,n1)|add(#0,#1)|add(n1,#2)| | geometry |
a cube of side 8 meter length is cut into small cubes of side 16 cm each . how many such small cubes can be obtained ? | "along one edge , the number of small cubes that can be cut = 800 / 16 = 50 along each edge 50 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 50 * 50 * 50 = 125000 answer : c" | a ) 10780 , b ) 127600 , c ) 125000 , d ) 152000 , e ) 10000 | c | divide(power(power(8, const_2), const_3), power(8, const_3)) | power(n0,const_2)|power(n0,const_3)|power(#0,const_3)|divide(#2,#1)| | physics |
in a group of 28 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ? | "a 7 seven students are not taking a language . add 7 + 10 + 4 to get 21 . then subtract 21 from the total students : 28 - 21 = 7 ." | a ) 7 , b ) 6 , c ) 8 , d ) 4 , e ) 3 | a | subtract(28, add(7, 10)) | add(n1,n2)|subtract(n0,#0)| | other |
on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is | "( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : e" | a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60 | e | divide(720, subtract(17, 5)) | subtract(n0,n2)|divide(n1,#0)| | gain |
the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 384 square centimeters , what is the length of the rectangle in centimeters ? | "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 384 2 l ^ 2 / 3 = 384 l ^ 2 = 576 l = 24 cm the answer is e ." | a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | e | divide(384, const_10) | divide(n2,const_10)| | geometry |
a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.0 . if the company β s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ? | "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 5 $ then total value is 300 * 5.0 = 1500 . imo option b is correct answer . ." | a ) $ 960 , b ) $ 1,500 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250 | b | divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 5.0), const_1000) | multiply(const_100,const_3)|multiply(n0,n1)|multiply(n0,n1)|add(#0,#1)|multiply(n2,#2)|add(#3,const_4)|multiply(#5,const_1000)|divide(#6,#4)|multiply(n3,#7)|divide(#8,const_1000)| | general |
ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ? | "explanation : price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of... | a ) 12880 , b ) 12789 , c ) 27108 , d ) 17600 , e ) 18291 | d | divide(multiply(add(const_100, 10), add(divide(multiply(12500, const_100), subtract(const_100, 20)), add(125, 250))), const_100) | add(n4,const_100)|add(n2,n3)|multiply(n0,const_100)|subtract(const_100,n1)|divide(#2,#3)|add(#1,#4)|multiply(#0,#5)|divide(#6,const_100)| | gain |
9873 + x = 13200 , then x is ? | "answer x = 13200 - 9873 = 3327 option : a" | a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these | a | subtract(13200, 9873) | subtract(n1,n0)| | general |
a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 5 days starting with sunday is | "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 Γ 5 + 240 Γ 25 / 30 ) = ( 8550 / 5 ) = 1710 answer : option d" | a ) 1215 , b ) 1314 , c ) 2900 , d ) 1710 , e ) 2750 | d | divide(add(multiply(add(floor(divide(5, add(const_3, const_4))), const_1), 510), multiply(subtract(5, add(floor(divide(5, add(const_3, const_4))), const_1)), 240)), 5) | add(const_3,const_4)|divide(n2,#0)|floor(#1)|add(#2,const_1)|multiply(n0,#3)|subtract(n2,#3)|multiply(n1,#5)|add(#4,#6)|divide(#7,n2)| | general |
in an election , candidate a got 70 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ? | total number of invalid votes = 15 % of 560000 = 15 / 100 Γ 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 β 84000 = 476000 percentage of votes polled in favour of candidate a = 70 % therefore , the number of valid votes polled in favour of candidate a = 70 % of 476000 = 70 / 100 Γ 476000 = 33320000 ... | a ) 355600 , b ) 355800 , c ) 356500 , d ) 356800 , e ) 333200 | e | multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(70, const_100)) | divide(n0,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(n2,#2)|multiply(#0,#3) | gain |
a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be odd , how many different codes can be created ? | "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 555 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 26 = 1 ... | a ) 20 , b ) 22 , c ) 24 , d ) 1 , e ) 30 | d | subtract(power(3, 3), const_1) | power(n0,n0)|subtract(#0,const_1)| | general |
if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 30 * 24 ) ) = ? | "the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 30 and 24 is 6 . hence 30 * 24 = 6 . hence ( ( 12 * 16 ) * ( 30 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ." | a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2 | e | divide(divide(30, const_3), const_3) | divide(n2,const_3)|divide(#0,const_3)| | general |
a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 60 , how many horses are there ? | "legs 12 * 4 = 48 now half on their horses so remaining on the walk so 6 men 6 men has 12 legs so , 12 + 48 = 60 legs walking answer : b" | a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | b | divide(60, add(const_4, divide(const_2, const_2))) | divide(const_2,const_2)|add(#0,const_4)|divide(n0,#1)| | general |
in a certain parking lot , 2 % of the cars are towed for parking illegally . however 90 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ? | "let x be the number of cars and let y be the number of cars parked illegally . 2 % * x = 10 % * y y / x = 1 / 5 = 20 % the answer is e ." | a ) 10 % , b ) 12 % , c ) 16 % , d ) 18 % , e ) 20 % | e | divide(subtract(const_1, divide(90, const_100)), divide(2, const_100)) | divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|divide(#2,#1)| | gain |
a certain sky blue paint contains 10 percent blue pigment and 90 percent red pigment by weight . a certain green paint contains 70 percent blue pigment and 30 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 g... | 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 9 = 4.5 grams of red pigment | a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5 | d | multiply(divide(90, multiply(const_100, const_2)), 10) | multiply(const_100,const_2)|divide(n1,#0)|multiply(n0,#1) | gain |
alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 985 . find the cost of each ice - cream cup ? | explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 985 96 + 225 + 490 + 6 x = 985 6 x = 174 = > x = 29 . answer : c | a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20 | c | divide(subtract(subtract(subtract(985, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6) | multiply(n0,n3)|multiply(n1,n5)|multiply(n2,n6)|subtract(n7,#0)|subtract(#3,#1)|subtract(#4,#2)|divide(#5,n3) | general |
excluding stoppages , the speed of a bus is 65 kmph and including stoppages , it is 48 kmph . for how many minutes does the bus stop per hour ? | "d 15.6 min due to stoppages , it covers 17 km less . time taken to cover 17 km = ( 17 / 65 x 60 ) min = 15.6 min" | a ) 70 min , b ) 15 min , c ) 20.4 min , d ) 15.6 min , e ) 40 min | d | multiply(const_60, divide(subtract(65, 48), 65)) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_60)| | physics |
a and b β s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b β s salary ? | "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 answer b" | a ) 777 , b ) 500 , c ) 789 , d ) 776 , e ) 881 | b | divide(multiply(multiply(multiply(const_2, multiply(const_4, add(const_2, const_3))), const_100), subtract(const_1, divide(85, const_100))), add(subtract(const_1, divide(95, const_100)), subtract(const_1, divide(85, const_100)))) | add(const_2,const_3)|divide(n2,const_100)|divide(n1,const_100)|multiply(#0,const_4)|subtract(const_1,#1)|subtract(const_1,#2)|add(#5,#4)|multiply(#3,const_2)|multiply(#7,const_100)|multiply(#8,#4)|divide(#9,#6)| | gain |
the inner circumference of a circular race track , 14 m wide is 440 m . find the radius of the outer circle . | "explanation : let inner radius be r meters . { \ color { black } then , 2 \ pi r = 440 \ rightarrow r = 440 \ times \ frac { 7 } { 22 } \ times \ frac { 1 } { 2 } = 70 m } radius of outer circle = 70 + 14 = 84 m answer : a ) 84 m" | a ) 84 , b ) 12 , c ) 67 , d ) 28 , e ) 21 | a | add(14, divide(divide(440, const_pi), const_2)) | divide(n1,const_pi)|divide(#0,const_2)|add(n0,#1)| | physics |
the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ? | "explanation : a / 8 = 8 * 8 = > a = 8 * 8 * 8 x * 2 x = 8 * 8 * 8 x = 16 = > 2 x = 32 answer : option b" | a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 42 | b | sqrt(divide(multiply(square_area(8), 8), inverse(const_2))) | inverse(const_2)|square_area(n0)|multiply(n2,#1)|divide(#2,#0)|sqrt(#3)| | geometry |
two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one . | "explanation : relative speed = = ( 45 + 30 ) km / hr = 75 x 5 / 18 m / sec = 125 / 6 m / sec we have to find the time taken by the slower train to pass the driver of the faster train and not the complete train . so , distance covered = length of the slower train . therefore , distance covered = 500 m . required time =... | a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) 65 sec | b | multiply(divide(500, divide(multiply(const_1000, add(45, 30)), const_3600)), const_2) | add(n1,n2)|multiply(#0,const_1000)|divide(#1,const_3600)|divide(n0,#2)|multiply(#3,const_2)| | physics |
the age of somu is one - third his father ' s . 5 years back he was one - fifth of his father ' s age . what is his persent age ? | "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 5 = 3 x - 5 / 5 = x = 10 answer : option e" | a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10 | e | divide(subtract(multiply(add(const_4, const_1), 5), 5), subtract(add(const_4, const_1), const_3)) | add(const_1,const_4)|multiply(n0,#0)|subtract(#0,const_3)|subtract(#1,n0)|divide(#3,#2)| | general |
a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number w of tickets sold by the male members of the association | "given that , total average w sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ." | a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66 | c | subtract(multiply(66, add(1, 2)), multiply(70, 2)) | add(n2,n3)|multiply(n1,n3)|multiply(n0,#0)|subtract(#2,#1)| | general |
amit and ananthu can do a work in 15 days and 90 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ? | "amit β s one day β s work = 1 / 15 amit β s 3 day β s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu β s one day β s work = 1 / 90 ananthu can do work in = 4 / 5 * 90 = 72 days so total days = 72 + 3 = 75 days answer : d" | a ) 68 days , b ) 70 days , c ) 73 days , d ) 75 days , e ) 77 days | d | add(divide(subtract(const_1, multiply(inverse(15), 3)), inverse(90)), 3) | inverse(n0)|inverse(n1)|multiply(#0,n2)|subtract(const_1,#2)|divide(#3,#1)|add(#4,n2)| | physics |
city x has a population 6 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ? | "x = 6 y , y = 2 * z x : y , y : z 6 : 1 , 2 : 1 12 : 2 , 2 : 1 so , x : z = 12 : 1 ( e )" | a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 12 : 1 | e | multiply(6, const_2) | multiply(n0,const_2)| | general |
a and b can do a work in 2 days , b and c in 4 days and c and a in 6 days . in how many days will the work be completed , if all three of them work together ? | one day work of a and b = 1 / 2 one day work of b and c = 1 / 4 one day work of c and a = 1 / 6 2 ( a + b + c ) = 1 / 2 + 1 / 4 + 1 / 6 . 2 ( a + b + c ) = 11 / 12 ( a + b + c ) = 11 / 24 number of days required = 24 / 11 days . answer : c | a ) 10 / 12 , b ) 16 / 28 , c ) 24 / 11 , d ) 42 / 16 , e ) 18 / 12 | c | divide(const_1, divide(add(add(inverse(2), inverse(4)), inverse(6)), const_2)) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|divide(const_1,#5) | physics |
what is the sum of all the multiples of 7 between 30 and 100 ? | "you first have to know all the multiples of 7 between 30 and 100 . they are 35 , 42 , 49 , 56 , 63 , 70 , 77 , 84 , 91 , and 98 . if you add all these numbers together , you get 665 . final answer : e" | a ) 692 , b ) 700 , c ) 677 , d ) 654 , e ) 665 | e | add(add(add(add(add(add(const_12, const_2), const_1), add(add(const_12, const_2), add(add(add(add(add(const_2, const_4), const_4), subtract(const_10, const_1)), add(add(const_2, const_4), const_4)), add(const_10, const_2)))), add(add(add(const_12, const_2), const_1), const_1)), 7), add(const_2, const_4)) | add(const_12,const_2)|add(const_2,const_4)|add(const_10,const_2)|subtract(const_10,const_1)|add(#0,const_1)|add(#1,const_4)|add(#5,#3)|add(#4,const_1)|add(#6,#5)|add(#8,#2)|add(#0,#9)|add(#4,#10)|add(#11,#7)|add(n0,#12)|add(#13,#1)| | general |
if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 20 } + { 24 } ? | "soln : { 24 } + { 20 } = 24 * { 20 } + { 20 } = 25 * { 20 } answer : b" | a ) 23 , b ) 25 , c ) 11 , d ) 5 , e ) 2 | b | add(divide(add(20, 24), const_2), multiply(1, const_2)) | add(n1,n2)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1)| | general |
the maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ? | "number of pens = 1001 number of pencils = 910 required number of students = h . c . f . of 1001 and 910 = 91 answer is b" | a ) 87 , b ) 91 , c ) 100 , d ) 96 , e ) 101 | b | gcd(1001, 910) | gcd(n0,n1)| | general |
how many even integers n , such that 20 < = n < = 250 are of the form 3 k + 4 , where k is any natural number ? | "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 250 = 16 + 6 ( 39 ) there are 39 numbers in the list . the answer is c ." | a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45 | c | add(divide(subtract(subtract(250, const_2), add(20, const_2)), add(const_2, 4)), const_1) | add(n0,const_2)|add(const_2,n3)|subtract(n1,const_2)|subtract(#2,#0)|divide(#3,#1)|add(#4,const_1)| | general |
a trader sells 85 meters of cloth for $ 8925 at the profit of $ 15 per metre of cloth . what is the cost price of one metre of cloth ? | c $ 90 sp of 1 m of cloth = 8925 / 85 = $ 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = $ 105 - $ 15 = $ 90 . | a ) $ 69 , b ) $ 78 , c ) $ 90 , d ) $ 86 , e ) $ 77 | c | subtract(divide(8925, 85), 15) | divide(n1,n0)|subtract(#0,n2) | physics |
a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 12 : 8 : 7 , respectively , by weight . if 54 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ? | "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 12 x : 8 x : 7 x we are given that 54 pounds of the mixture is prepared... | a ) 15 , b ) 10 , c ) 9 , d ) 6 , e ) 4 | b | subtract(multiply(12, const_2), multiply(7, const_2)) | multiply(n0,const_2)|multiply(n2,const_2)|subtract(#0,#1)| | general |
of the six - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? | "of the six - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7... | a ) 2443200 , b ) 3643200 , c ) 5443200 , d ) 1443200 , e ) 2163200 | c | multiply(multiply(subtract(const_10, const_1), subtract(const_10, const_2)), const_1) | subtract(const_10,const_1)|subtract(const_10,const_2)|multiply(#0,#1)|multiply(#2,const_1)| | general |
two employees x and y are paid a total of rs . 330 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ? | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 330 but x = 120 % of y = 120 y / 100 = 12 y / 10 Γ’ Λ Β΄ 12 y / 10 + y = 330 Γ’ β‘ β y [ 12 / 10 + 1 ] = 330 Γ’ β‘ β 22 y / 10 = 330 Γ’ β‘ β 22 y = 3300 Γ’ β‘ β y = 3300 / 22 = 300 / 2 = rs . 150 a )" | a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400 | a | divide(multiply(330, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | add(const_1,const_4)|multiply(#0,const_2)|add(#1,const_1)|multiply(n0,#1)|multiply(#2,const_2)|divide(#3,#4)| | general |
if the price of a certain computer increased 30 percent from d dollars to 338 dollars , then 2 d = | "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 338 ( given ) i . e . d = 338 / 1.3 = $ 260 i . e . 2 d = 2 * 260 = 520 answer : option b" | a ) 540 , b ) 520 , c ) 619 , d ) 649 , e ) 700 | b | multiply(divide(338, divide(add(const_100, 30), const_100)), 2) | add(n0,const_100)|divide(#0,const_100)|divide(n1,#1)|multiply(n2,#2)| | general |
simple interest on a certain sum of money for 2 years at 16 % per annum is one fourth the compound interest on rs . 4000 for 2 years at 8 % per annum . the sum placed on simple interest is | "solution c . i . = rs [ 4000 x ( 1 + 8 / 100 ) Γ’ Β² - 4000 ] rs . ( 4000 x 108 / 100 x 108 / 100 - 4000 ) = rs . 665.6 . sum = rs . [ 166.4 x 100 / 2 x 16 ] = rs . 520 . answer c" | a ) rs . 4000 , b ) rs . 665.6 , c ) rs . 520 , d ) rs . 166.4 , e ) none | c | divide(multiply(divide(divide(add(divide(multiply(4000, 8), const_100), divide(multiply(add(4000, divide(multiply(4000, 8), const_100)), 8), const_100)), 2), 2), const_100), 16) | multiply(n2,n4)|divide(#0,const_100)|add(n2,#1)|multiply(n4,#2)|divide(#3,const_100)|add(#1,#4)|divide(#5,n3)|divide(#6,n0)|multiply(#7,const_100)|divide(#8,n1)| | gain |
each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 1 and the 5 can not be adjacent digits in the integer , how many 5 - digit integers are possible ? | "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 1 and 5 are adjacent - consider 1 and 5 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 1 and 5 can be arranged as 15 or 51 . number of arrangements in... | a ) 48 , b ) 66 , c ) 76 , d ) 78 , e ) none of these | e | subtract(multiply(multiply(multiply(5, 5), 1), const_2), multiply(multiply(multiply(5, 1), const_2), const_2)) | multiply(n1,n4)|multiply(n3,n4)|multiply(n3,#0)|multiply(#1,const_2)|multiply(#2,const_2)|multiply(#3,const_2)|subtract(#4,#5)| | general |
a pupil ' s marks were wrongly entered as 79 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is : | "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 79 - 45 ) = > x / 2 = 34 = > x = 68 . answer : d" | a ) 30 , b ) 80 , c ) 20 , d ) 68 , e ) 26 | d | multiply(subtract(79, 45), const_2) | subtract(n0,n1)|multiply(#0,const_2)| | general |
in a can , there is a mixture of milk and water in the ratio 2 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 5 . find the capacity of the can ? | "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 2 / 7 ( t - 8 ) after adding milk , quantity of milk in the mixture = 4 / 9 t . 4 t / 9 - 8 = 2 / 7 ( t - 8 ) 2 t = 72 - 56 = > t = 8 . answer : e" | a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 8 | e | add(add(multiply(5, divide(8, subtract(multiply(divide(4, 5), 5), 2))), divide(8, subtract(multiply(divide(4, 5), 5), 2))), 8) | divide(n3,n4)|multiply(n1,#0)|subtract(#1,n0)|divide(n2,#2)|multiply(n1,#3)|add(#3,#4)|add(n2,#5)| | general |
90 % of the population of a village is 45000 . the total population of the village is ? | "x * ( 90 / 100 ) = 45000 x = 500 * 100 x = 50000 answer : c" | a ) 26799 , b ) 24000 , c ) 50000 , d ) 29973 , e ) 12312 | c | multiply(divide(const_100, 90), 45000) | divide(const_100,n0)|multiply(n1,#0)| | general |
total 52 matches are conducted in knockout match type . how many players will be participated in that tournament ? | "51 players answer : b" | a ) 60 , b ) 51 , c ) 53 , d ) 56 , e ) 50 | b | add(52, const_1) | add(n0,const_1)| | general |
the ratio between the number of sheep and the number of horses at the stewart farm is 1 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ? | "let the number of sheeps and horses be 1 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 1 x = 1 * 8 = 8 . hence e" | a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 8 | e | multiply(divide(divide(add(add(multiply(multiply(const_4, const_2), const_10), multiply(multiply(const_4, const_2), const_100)), multiply(const_12, const_1000)), 230), 7), 1) | multiply(const_2,const_4)|multiply(const_1000,const_12)|multiply(#0,const_10)|multiply(#0,const_100)|add(#2,#3)|add(#4,#1)|divide(#5,n2)|divide(#6,n1)|multiply(n0,#7)| | other |
there are 12 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ? | 12 c 2 = 66 the answer is c . | a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74 | c | divide(factorial(12), multiply(factorial(subtract(12, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4) | general |
the length of a rectangle is increased by 45 % and its breadth is decreased by 20 % . what is the effect on its area ? | "100 * 100 = 10000 145 * 80 = 11600 answer : e" | a ) 1288 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 11600 | e | multiply(add(45, const_100), subtract(const_100, 20)) | add(n0,const_100)|subtract(const_100,n1)|multiply(#0,#1)| | geometry |
michael cashed a check for $ 1270 and received only $ 10 and $ 50 bills in return . during the course of a day , he used 15 bills and then lost the rest of the money . if the number of $ 10 bills used was either one more or one less than the number of $ 50 bills used , what is the minimum possible amount of money that ... | 1 . 15 bills spent 2 . number of $ 10 bills is one more or one less than number of $ 50 bills . so , 2 choices 1 . 7 * 10 + 8 * 50 = $ 470 2 . 8 * 10 + 7 * 50 = $ 430 least money lost implies most money spent . i . e $ 470 therefore , lost money = 1270 - 470 = 800 . answer b | a ) $ 830 , b ) $ 800 , c ) $ 770 , d ) $ 730 , e ) $ 700 | b | subtract(1270, add(multiply(50, subtract(15, floor(divide(15, const_2)))), multiply(floor(divide(15, const_2)), 10))) | divide(n3,const_2)|floor(#0)|multiply(n1,#1)|subtract(n3,#1)|multiply(n2,#3)|add(#4,#2)|subtract(n0,#5) | general |
a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 180 , how many hours overtime did he work ? | "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 180 - $ 120 = $ 60 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 60 / $ 6 = 10 ans is e" | a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 10 | e | divide(subtract(180, multiply(3, 40)), multiply(3, const_2)) | multiply(n0,n1)|multiply(n0,const_2)|subtract(n2,#0)|divide(#2,#1)| | physics |
if a farmer sells 5 of his goats , his stock of feed will last for 4 more days than planned , but if he buys 10 more goats , he will run out of feed 3 days earlier than planned . if no goats are sold or bought , the farmer will be exactly on schedule . how many goats does the farmer have ? | say farmer has n goat and he is good for d days . : - we have 3 equations given in question : - ( n - 5 ) * d + 4 = ( n + 10 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 10 d - 3 n = 30 4 n - 5 d = 20 = > n = 20 ans b it is ! | a ) 12 , b ) 20 , c ) 48 , d ) 55 , e ) 60 | b | multiply(subtract(multiply(3, 4), 10), 10) | multiply(n1,n3)|subtract(#0,n2)|multiply(n2,#1) | general |
cole drove from home to work at an average speed of 30 kmh . he then returned home at an average speed of 90 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ? | "let the distance one way be x time from home to work = x / 30 time from work to home = x / 90 total time = 2 hrs ( x / 30 ) + ( x / 90 ) = 2 solving for x , we get x = 45 time from home to work in minutes = ( 45 ) * 60 / 30 = 90 minutes ans = e" | a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 90 | e | multiply(divide(multiply(90, 2), add(30, 90)), const_60) | add(n0,n1)|multiply(n1,n2)|divide(#1,#0)|multiply(#2,const_60)| | physics |
when tom works alone he chops 3 lb . salad in 2 minutes , and when tammy works alone she chops 2 lb . salad in 3 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent lesser than the quantifying chopped by to... | "tom chops 4 lbs in 6 minutes tammy chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , an... | a ) 44 % , b ) 100 % , c ) 15 % , d ) 125 % , e ) 400 % | d | multiply(divide(subtract(divide(2, 3), divide(const_2.0, 2)), divide(3, 2)), const_100) | divide(const_3.0,const_2.0)|divide(const_2.0,n1)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)| | physics |
what is the smallest integer y for which 27 ^ y > 3 ^ 24 ? | "27 ^ y > 3 ^ 24 converting into the same bases : 27 ^ y > 27 ^ 8 therefore for the equation to hold true , y > 8 or y = 9 option c" | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12 | c | add(floor(divide(24, const_3)), const_1) | divide(n2,const_3)|floor(#0)|add(#1,const_1)| | general |
a and b together can do a piece of work in 4 days . if a alone can do the same work in 20 days , then b alone can do the same work in ? | "b = 1 / 4 β 1 / 20 = 0.2 days answer : e" | a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.2 days | e | inverse(subtract(inverse(4), inverse(20))) | inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)| | physics |
a bell curve ( normal distribution ) has a mean of β 1 and a standard deviation of 1 / 8 . how many integer values z are within 3 standard deviations of the mean ? | got the question correctly - - the second item - - [ highlight ] bthe list of elements in the set is required . [ / highlight ] is not required . with the new information , there is only one integer value ( - 1 ) that is between ( - 1.375 , - 0.625 ) i . e . , falls within the three 3 sd range . b | a ) 0 , b ) 1 , c ) 3 , d ) 6 , e ) 7 | b | subtract(1, 1) | subtract(n0,n0) | general |
a man ' s speed with the current is 15 km / hr and the speed of the current is 2.8 km / hr . the man ' s speed against the current is ? | "man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 2.8 km / hr hence , speed of the man = 15 - 2.8 = 12.2 km / hr man ' s speed against the current = speed of the man - speed of the current = 12.2 - 2.8 = 9.4 km / hr answer is a ." | a ) 9.4 , b ) 20 , c ) 50 , d ) 30 , e ) 40 | a | subtract(subtract(15, 2.8), 2.8) | subtract(n0,n1)|subtract(#0,n1)| | gain |
1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 2 / 15 = | "we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let β s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 β 5 / 6 = 0 looking a... | a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6 | b | divide(2, 15) | divide(n12,n13)| | general |
a river 2 m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is ? | "( 3000 * 2 * 5 ) / 60 = 4500 m 3 answer : a" | a ) 4500 , b ) 2678 , c ) 2689 , d ) 2761 , e ) 2882 | a | divide(multiply(multiply(2, 45), multiply(3, const_1000)), multiply(const_1, const_60)) | multiply(n0,n1)|multiply(n2,const_1000)|multiply(const_1,const_60)|multiply(#0,#1)|divide(#3,#2)| | physics |
in a coconut grove , ( x + 2 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x β 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x . | "( x + 2 ) Γ 60 + x Γ 120 + ( x β 2 ) Γ 180 / ( x + 2 ) + x + ( x β 2 ) = 100 β 360 x β 240 / 3 x = 100 β 60 x = 240 β x = 4 answer e" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | e | divide(subtract(multiply(180, 2), multiply(60, 2)), subtract(add(add(60, 120), 180), multiply(100, const_3))) | add(n1,n2)|multiply(n0,n4)|multiply(n0,n1)|multiply(n5,const_3)|add(n4,#0)|subtract(#1,#2)|subtract(#4,#3)|divide(#5,#6)| | general |
tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 70 ? | "you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 12 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is c" | a ) 4 , b ) 12 , c ) 15 , d ) 20 , e ) 24 | c | divide(subtract(multiply(70, 30), 1800), subtract(70, 50)) | multiply(n0,n5)|subtract(n5,n1)|subtract(#0,n3)|divide(#2,#1)| | general |
in a graduating class , 40 percent of the students are male . in this class , 50 percent of the male students and 40 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ? | "let x be the total number of students . the number students who are younger than 25 is 0.5 * 0.4 x + 0.6 * 0.6 x = 0.56 x the answer is c ." | a ) 0.44 , b ) 0.5 , c ) 0.56 , d ) 0.62 , e ) 0.68 | c | subtract(const_1, add(multiply(divide(40, const_100), divide(50, const_100)), multiply(divide(40, const_100), subtract(const_1, divide(40, const_100))))) | divide(n0,const_100)|divide(n1,const_100)|divide(n2,const_100)|multiply(#0,#1)|subtract(const_1,#0)|multiply(#2,#4)|add(#3,#5)|subtract(const_1,#6)| | general |
what is the remainder when 14,451 Γ 15,654 Γ 16,783 is divided by 5 ? | "only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 1 * 4 * 3 = will give units digit as 2 so , whatever be the number , if it ends in 2 , the remainder after dividing with 5 will be 2 . option c" | a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5 | c | reminder(multiply(15,654, 14,451), 16,783) | multiply(n0,n1)|reminder(#0,n2)| | general |
up to 20 , how many no . are odd and prime both ? | we have to calculate it manually . odd 1,3 , 5,7 , 9,11 , 13,15 , 17,19 prime 2,3 , 5,7 , 11,13 , 17,19 common 3 , 5,7 , 11,13 , 17,19 total no . 7 answer d | a ) 9 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | d | add(divide(20, const_4), const_2) | divide(n0,const_4)|add(#0,const_2) | other |
the area of sector of a circle whose radius is 15 metro and whose angle at the center is 42 Γ’ Β° is ? | "42 / 360 * 22 / 7 * 15 * 15 = 82.5 m 2 answer : e" | a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 52.1 , e ) 82.5 | e | multiply(multiply(power(15, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(42, divide(const_3600, const_10))) | add(const_3,const_4)|divide(const_3600,const_10)|multiply(const_10,const_2)|power(n0,const_2)|add(#2,const_2)|divide(n1,#1)|divide(#4,#0)|multiply(#6,#3)|multiply(#5,#7)| | geometry |
9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 42 miles per hour faster than the first runner ' s rate . how far apart , to the neare... | "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 10 m / h - - > 5 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 5 ^ 2 d ^ 2 = 41 = ~ 6 answer option a" | a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14 | a | sqrt(add(power(multiply(8, divide(1, 42)), 42), power(multiply(subtract(8, 42), divide(1, 42)), 42))) | divide(n3,n2)|subtract(n1,n2)|multiply(n1,#0)|multiply(#0,#1)|power(#2,n2)|power(#3,n2)|add(#4,#5)|sqrt(#6)| | physics |
if x , y , and z are positive integers and 2 x = 4 y = 5 z , then the least possible value of x + y + z is | "given 2 x = 4 y = 5 z x + y + z in terms of x = x + ( 2 x / 4 ) + ( 2 x / 5 ) = 38 x / 20 = 19 x / 10 now checking with each of the answers and see which value gives a minimum integer value . a x = 10 / 19 * 40 , not an integer b , c , e can be ruled out similarly . d is minimum value as x = 19 * 10 / 19 = 10 answer i... | a ) 40 , b ) 50 , c ) 55 , d ) 60 , e ) 19 | e | add(subtract(divide(multiply(multiply(2, 4), 5), 2), divide(multiply(multiply(2, 4), 5), 4)), divide(multiply(multiply(2, 4), 5), 5)) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n2)|divide(#1,n0)|divide(#1,n1)|subtract(#3,#4)|add(#2,#5)| | general |
a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 68 km downstream . | "speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 68 km downstream = 68 / 17 = 4 hrs ans - b" | a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 3 | b | divide(68, add(13, 4)) | add(n0,n1)|divide(n2,#0)| | physics |
the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 5 times the probability that both events a and b occur . what is the probabili... | let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 5 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 5 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 5 * 2 b * b 3 b ... | a ) 1 / 45 , b ) 1 / 2 , c ) 1 / 8 , d ) 2 / 3 , e ) 2 / 11 | b | multiply(divide(add(const_2, const_1), add(multiply(5, const_2), const_2)), const_2) | add(const_1,const_2)|multiply(n1,const_2)|add(#1,const_2)|divide(#0,#2)|multiply(#3,const_2) | general |
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