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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harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 5 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ? | "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 5 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 5 x = 11 x august tips as a fraction of total tips = 5 ... | a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 11 | e | divide(multiply(5, const_1), add(multiply(5, const_1), multiply(5, const_1))) | multiply(n0,const_1)|add(#0,#0)|divide(#0,#1)| | general |
a clock store sold a certain clock to a collector for 45 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 25 percent of what the collector had paid . the shop then sold the clock again at a profit of 55 percent on its... | "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 45 % profit . this means the clocks ' selling price was c ( 1.45 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , th... | a ) $ 149.55 , b ) $ 134.56 , c ) $ 175.43 , d ) $ 158.65 , e ) $ 255.45 | d | divide(multiply(180, divide(multiply(add(180, 55), divide(add(180, 45), const_2)), 180)), subtract(divide(add(180, 45), const_2), 45)) | add(n2,n3)|add(n0,n3)|divide(#1,const_2)|multiply(#0,#2)|subtract(#2,n0)|divide(#3,n3)|multiply(n3,#5)|divide(#6,#4)| | general |
in a hostel there were 100 students . to accommodate some more students the average budget is decreased by rupees 10 . but total expenditure increased by rs . 400 . if the total expenditure of the hostel now 5400 , find the number of student joined ? | let average is x 100 x + 400 = 5400 x = 50 let the number of student joined is y ( 100 + y ) * ( 50 - 10 ) = 5400 y = 35 answer : d | a ) 30 , b ) 20 , c ) 35 , d ) 32 , e ) 40 | d | subtract(subtract(divide(5400, subtract(divide(subtract(5400, 400), 100), 10)), 100), const_3) | subtract(n3,n2)|divide(#0,n0)|subtract(#1,n1)|divide(n3,#2)|subtract(#3,n0)|subtract(#4,const_3) | general |
54 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ? | "( 54 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 120 120 – 54 = 66 answer : b" | a ) 33 , b ) 66 , c ) 18 , d ) 100 , e ) 281 | b | subtract(divide(multiply(divide(multiply(54, 8), 30), 50), 6), 54) | multiply(n0,n1)|divide(#0,n2)|multiply(n3,#1)|divide(#2,n4)|subtract(#3,n0)| | physics |
what is the probability of getting sum 10 with the help of three dice ? | "( 1 , 3,6 ) 3 ! = 6 ( 2 , 2,6 ) = 3 ! / 2 = 3 ( 1 , 4,5 ) 3 ! = 6 ( 2 , 4,4 ) = 3 ( 2 , 3,5 ) 3 ! = 6 ( 3 , 3,4 ) = 3 prob . of getting sum 10 = ( 6 + 6 + 6 + 3 + 3 + 3 ) / 216 = 1 / 8 ans answer : b" | a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 24 , e ) 1 / 32 | b | divide(const_2, choose(add(const_3, const_3), const_3)) | add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1)| | probability |
a certain fraction has the same ratio to 1 / 18 , as 2 / 5 does to 7 / 9 . what is this certain fraction ? | "x / ( 1 / 18 ) = ( 2 / 5 ) / ( 7 / 9 ) x = 2 * 9 * 1 / 18 * 5 * 7 = 1 / 35 the answer is d ." | a ) 1 / 20 , b ) 1 / 25 , c ) 1 / 30 , d ) 1 / 35 , e ) 1 / 40 | d | divide(1, 18) | divide(n0,n1)| | other |
a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 4 . find his average after 17 th inning . | "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 4 ) . ∴ 16 ( x – 4 ) + 87 = 17 x or x = ( 87 – 64 ) = 23 . answer c" | a ) 36 , b ) 39 , c ) 23 , d ) 45 , e ) none of the above | c | add(subtract(87, multiply(17, 4)), 4) | multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)| | general |
. if the sides of two cubes are in the ratio 3 : 1 the ratio of their total surface area is ? | a 1 : a 2 = 3 : 1 6 a 12 : 6 a 22 = 9 : 1 answer : c | ['a ) 3 : 1', 'b ) 8 : 1', 'c ) 9 : 1', 'd ) 12 : 1', 'e ) 9 : 1'] | c | divide(surface_cube(3), surface_cube(1)) | surface_cube(n0)|surface_cube(n1)|divide(#0,#1) | geometry |
the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 16 positive perfect squares ? | "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 16 and c = 1 / 2 into the equation and simplify to get the answer 1496... | a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 1,496 | e | divide(divide(multiply(multiply(16, add(16, const_1)), add(multiply(16, 2), const_1)), 6), divide(multiply(multiply(16, add(16, const_1)), add(multiply(16, 2), const_1)), 6)) | add(n4,const_1)|multiply(n4,n2)|add(#1,const_1)|multiply(n4,#0)|multiply(#2,#3)|divide(#4,n3)|divide(#5,#5)| | general |
when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 6 x is divided by 9 ? | "i tried plugging in numbers x = 9 q + 5 x = 14 6 x = 84 6 x / 9 = 9 * 9 + 3 remainder is 3 . answer is c ." | a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6 | c | reminder(multiply(5, 6), 9) | multiply(n1,n2)|reminder(#0,n0)| | general |
set a : 3 , r , 8 , 10 set b : 4 , g , 9 , 11 the terms of each set above are given in ascending order . if the median of set a is equal to the median of set b , what is the value of g – r ? | so we have even no . of elements in the set so median is the average of middle two numbers ( r + 8 ) / 2 = ( g + 9 ) / 2 g - r = - 1 answer b | a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2 | b | subtract(divide(add(add(3, 8), 10), const_3), divide(add(add(4, 9), 11), 3)) | add(n0,n1)|add(n3,n4)|add(n2,#0)|add(n5,#1)|divide(#2,const_3)|divide(#3,n0)|subtract(#4,#5) | general |
how many integers from 40 to 200 , inclusive , are divisible by 3 but not divisible by 7 ? | "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 40 to 200 , inclusive is ( 189 - 42 ) / 21 + 1 = 8 ; 53 - 8 = 45 . answer : e ." | a ) 20 , b ) 31 , c ) 35 , d ) 40 , e ) 45 | e | divide(200, const_10) | divide(n1,const_10)| | general |
water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 45 ° c , what is the temperature of the pot of water in ° f ? | "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 45 ) / 5 + 32 = 113 ° f the answer is d ." | a ) 92 ° f , b ) 97 ° f , c ) 104 ° f , d ) 113 ° f , e ) 118 ° f | d | add(multiply(divide(subtract(212, 32), 100), 45), 32) | subtract(n0,n2)|divide(#0,n1)|multiply(n4,#1)|add(n2,#2)| | physics |
a sum of money at simple interest amounts to rs . 415 in 2 years and to rs . 514 in 4 years . the sum is ? | "explanation : s . i . for 2 years = ( 514 - 415 ) = rs . 99 s . i . for 1 year = 99 / 2 principal = ( 415 - 99 ) = rs . 316 . answer is a" | a ) rs . 316 , b ) rs . 251 , c ) rs . 154 , d ) rs . 294 , e ) rs . 200 | a | subtract(415, divide(multiply(subtract(514, 415), 2), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | gain |
a man can row his boat with the stream at 26 km / h and against the stream in 4 km / h . the man ' s rate is ? | "ds = 26 us = 4 s = ? s = ( 26 - 4 ) / 2 = 11 kmph answer : d" | a ) 1 kmph , b ) 7 kmph , c ) 98 kmph , d ) 11 kmph , e ) 4 kmph | d | divide(subtract(26, 4), const_2) | subtract(n0,n1)|divide(#0,const_2)| | gain |
a and b can complete a work in 30 days and 15 day . they started doing the work together but after 5 days b had to leave and a alone completed the remaining work . the whole work was completed in ? | a + b 1 day work = 1 / 30 + 1 / 15 = 1 / 10 work done by a and b in 10 days = 1 / 10 * 5 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 now 1 / 30 work is done by a in 1 day 1 / 2 work will be done by a in 30 * 1 / 2 = 15 days total time taken = 15 + 5 = 20 days answer is c | a ) 10 days , b ) 12 days , c ) 20 days , d ) 18 days , e ) 25 days | c | add(multiply(subtract(const_1, multiply(add(divide(const_1, 30), divide(const_1, 15)), 5)), 30), 5) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3)|multiply(n0,#4)|add(n2,#5) | physics |
karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many e miles will tom drive before karen wins the bet ? | let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance trave... | a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27 | d | subtract(divide(add(multiply(divide(45, const_60), 4), 4), subtract(divide(60, const_60), divide(45, const_60))), 4) | divide(n3,const_60)|divide(n2,const_60)|multiply(n0,#0)|subtract(#1,#0)|add(n0,#2)|divide(#4,#3)|subtract(#5,n0) | physics |
the sum of two numbers is 73 and their difference is 28 . find the difference between their squares . | "explanation : let x and y be the two given numbers ( x + y ) = 73 ; ( x – y ) = 28 ( x 2 – y 2 ) = ( x + y ) ( x – y ) = 73 * 28 = 2044 answer : c" | a ) 101 , b ) 45 , c ) 2044 , d ) 2048 , e ) 2064 | c | divide(subtract(28, power(73, const_2)), const_2) | power(n0,const_2)|subtract(n1,#0)|divide(#1,const_2)| | general |
a large tank can filled by a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tanker from empty state if b is used for half the time and a and b fill it together for the other half ? | part filled by a + b in 1 minute = 1 / 60 + 1 / 40 = 1 / 24 suppose the tank is filled in x minutes then , x / 2 ( 1 / 24 + 1 / 40 ) = 1 x / 2 * 1 / 15 = 1 x = 30 min answer is c | a ) 10 min , b ) 15 min , c ) 30 min , d ) 25 min , e ) 42 min | c | multiply(divide(const_1, add(add(divide(const_1, 60), divide(const_1, 40)), divide(const_1, 40))), const_2) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|add(#2,#1)|divide(const_1,#3)|multiply(#4,const_2) | physics |
in order to fence a square manish fixed 48 poles . if the distance between two poles , is 1 metres then what will be the area of the square so formed ? | "let the side of the square be x m . ∴ perimeter of the square = 48 × 1 = 4 x ∴ x = 12 m ∴ area = ( 12 ) 2 = 144 cm 2 answer a" | a ) 144 cm 2 , b ) 260 cm 2 , c ) 2500 cm 2 , d ) 302 cm 2 , e ) none of these | a | square_area(divide(48, 1)) | divide(n0,n1)|square_area(#0)| | physics |
the ratio , by volume , of bleach to detergent to water in a certain solution is 4 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will ... | b : d : w = 4 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 4 / 40 ) = ( 1 / 30 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be c | ['a ) 80', 'b ) 70', 'c ) 60', 'd ) 40', 'e ) 50'] | c | multiply(divide(300, 100), divide(40, const_2)) | divide(n3,n2)|divide(n1,const_2)|multiply(#0,#1) | other |
two vessels contains equal number of mixtures milk and water in the ratio 8 : 2 and 9 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ? | "the ratio of milk and water in the new vessel is = ( 8 / 10 + 9 / 10 ) : ( 2 / 10 + 1 / 10 ) = 17 / 10 : 3 / 10 = 17 : 3 answer is e" | a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 17 : 3 | e | divide(add(multiply(8, divide(add(9, 1), add(8, 2))), 9), add(multiply(2, divide(add(9, 1), add(8, 2))), 1)) | add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(n0,#2)|multiply(n1,#2)|add(n2,#3)|add(n3,#4)|divide(#5,#6)| | other |
for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers r are there between # 6 + 2 and # 6 + 6 , inclusive ? | "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a" | a ) none , b ) one , c ) two , d ) three , e ) four | a | add(1, 1) | add(n0,n0)| | general |
tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ? | s = { 1 , 23 , … . 20 } e = { 3 , 6 , 912 , 1518 } p ( e ) = 6 / 20 = 3 / 10 option a | a ) 3 / 10 , b ) 3 / 20 , c ) 2 / 5 , d ) 1 / 2 , e ) 1 / 3 | a | divide(3, const_10) | divide(n2,const_10) | general |
find the ratio between whole surfaces of a sphere and a hemisphere ? | 4 ï € r 2 : 3 ï € r 2 = > 4 : 3 answer a | ['a ) 4 : 3', 'b ) 3 : 4', 'c ) 3 : 2', 'd ) 5 : 2', 'e ) 4 : 6'] | a | divide(multiply(const_4, multiply(power(const_2, const_2), const_pi)), multiply(const_3, multiply(power(const_2, const_2), const_pi))) | power(const_2,const_2)|multiply(#0,const_pi)|multiply(#1,const_4)|multiply(#1,const_3)|divide(#2,#3) | other |
some of 10 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 15 % . what fraction of the original paint was replaced ? | "let total paint = 1 let amount replaced = x 10 ( 1 - x ) + 20 x = 15 x = 1 / 2 answer : c" | a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 5 | c | divide(subtract(divide(15, const_100), divide(10, const_100)), subtract(divide(20, const_100), divide(10, const_100))) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|subtract(#0,#1)|subtract(#2,#1)|divide(#3,#4)| | gain |
a person walks from one end to the other of a 100 - meter long moving walkway at a constant rate in 25 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 150 seconds because the person is traveling against the d... | "let v be the speed of the person and let x be the speed of the walkway . 25 ( v + x ) = 100 then 150 ( v + x ) = 600 150 ( v - x ) = 100 when we add the two equations : 300 v = 700 v = 7 / 3 time = 100 / ( 7 / 3 ) = ( 300 / 7 ) seconds which is about 43 seconds the answer is d ." | a ) 37 , b ) 39 , c ) 41 , d ) 43 , e ) 45 | d | divide(100, divide(add(divide(100, 25), divide(100, 150)), const_2)) | divide(n0,n1)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)|divide(n0,#3)| | physics |
a certain number of workers can do a work in 65 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ? | "number of workers = 10 * ( 65 - 10 ) / 10 = 55 answer is a" | a ) 55 , b ) 30 , c ) 28 , d ) 24 , e ) 32 | a | divide(multiply(subtract(65, 10), 10), subtract(65, subtract(65, 10))) | subtract(n0,n1)|multiply(n1,#0)|subtract(n0,#0)|divide(#1,#2)| | physics |
a bag contains 6 black and 9 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? | "let number of balls = ( 6 + 9 ) = 15 . number of white balls = 9 . p ( drawing a white ball ) = 9 / 15 = 3 / 5 hence answer is e" | a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 3 / 5 | e | divide(add(divide(divide(factorial(9), factorial(subtract(9, const_2))), factorial(const_2)), divide(divide(factorial(6), factorial(subtract(6, const_2))), factorial(const_2))), divide(divide(factorial(add(6, 9)), factorial(subtract(add(6, 9), const_2))), factorial(const_2))) | add(n0,n1)|factorial(n1)|factorial(const_2)|factorial(n0)|subtract(n1,const_2)|subtract(n0,const_2)|factorial(#4)|factorial(#5)|factorial(#0)|subtract(#0,const_2)|divide(#1,#6)|divide(#3,#7)|factorial(#9)|divide(#10,#2)|divide(#11,#2)|divide(#8,#12)|add(#13,#14)|divide(#15,#2)|divide(#16,#17)| | probability |
walking at the rate of 8 kmph a man cover certain distance in 4 hr 45 min . running at a speed of 19 kmph the man will cover the same distance in . | "distance = speed * time 8 * 19 / 4 = 38 km new speed = 19 kmph therefore time = d / s = 38 / 19 = 120 min answer : d ." | a ) 100 min , b ) 110 min , c ) 140 min , d ) 120 min , e ) 150 min | d | multiply(divide(multiply(8, add(4, divide(45, const_60))), 19), const_60) | divide(n2,const_60)|add(n1,#0)|multiply(n0,#1)|divide(#2,n3)|multiply(#3,const_60)| | physics |
a train 420 m long , running with a speed of 63 km / hr will pass a tree in ? | "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 420 * 2 / 35 = 24 sec answer : option e" | a ) 15 , b ) 16 , c ) 17 , d ) 20 , e ) 24 | e | multiply(divide(420, multiply(63, const_1000)), const_3600) | multiply(n1,const_1000)|divide(n0,#0)|multiply(#1,const_3600)| | physics |
every day daniel drives 100 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive b... | "let ' s test x = 4 . . . . on sunday , daniel drove 100 miles at 4 miles / hour . d = ( r ) ( t ) 100 = ( 4 ) ( t ) 100 / 4 = 25 = t it takes 25 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 68 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t )... | a ) 10 % , b ) 28 % , c ) 33 % , d ) 42 % , e ) 52 % | e | multiply(divide(subtract(add(divide(32, 2), multiply(subtract(100, 32), 2)), 100), 100), const_100) | divide(n1,n2)|subtract(n0,n1)|multiply(#1,n2)|add(#0,#2)|subtract(#3,n0)|divide(#4,n0)|multiply(#5,const_100)| | physics |
in what ratio must tea of rs . 42 per kg be mixed with tea of rs . 50 per kg so that cost of mixture is rs . 45 per kg ? | 50 - 45 : 45 - 42 = 5 : 3 answer : a | a ) 5 : 3 , b ) 3 : 5 , c ) 2 : 3 , d ) 3 : 4 , e ) 1 : 2 | a | divide(subtract(50, 45), subtract(45, 42)) | subtract(n1,n2)|subtract(n2,n0)|divide(#0,#1) | other |
in the biotechnology class of 2000 , there were x graduates . 32 of the graduates found a job , 45 continued on to their second degree and 13 did both . if only 9 people did n ' t do both , what is x equal to ? | graduates got job = 32 graduates continued to second degree = 45 graduates got job and continued to second degree = 13 graduates did n ' t get job and did n ' t continue to second degree = 9 job no job total second degree 13 32 45 no second degree 19 9 28 total 32 41 x therefore x = 73 answer c | a ) 69 . , b ) 71 , c ) 73 , d ) 75 , e ) 76 | c | add(subtract(add(32, 45), 13), 9) | add(n1,n2)|subtract(#0,n3)|add(n4,#1) | other |
the number 61 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? | "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 61 : 1 , 4 , 9 , 16 , 25 , 36 , 49 . now , 61 should be the sum of 3 of those 7 numbers . also to simplify a little bit trial and error , we can notice that as 61 is an odd numbers then either all... | a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13 | e | 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 |
the average weight of 6 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ? | "total weight increases = 6 × 1.5 = 9 kg so the weight of new person = 65 + 9 = 74 kg answer a" | a ) 74 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these | a | add(65, multiply(6, 1.5)) | multiply(n0,n1)|add(n2,#0)| | general |
a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 54 , what is the total amount ? | "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 54 39 - - - ? = > 234 answer : a" | a ) 234 , b ) 116 , c ) 117 , d ) 118 , e ) 119 | a | add(add(multiply(divide(const_100, 45), 54), multiply(divide(50, 45), 54)), 54) | divide(const_100,n0)|divide(n1,n0)|multiply(n2,#0)|multiply(n2,#1)|add(#2,#3)|add(n2,#4)| | general |
from the sale of sleeping bags , a retailer made a gross profit of 14 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ? | "cost price * 1.14 = selling price - - > cost price * 1.14 = $ 28 - - > cost price = $ 24.56 . answer : c ." | a ) 3.0 , b ) 3.36 , c ) 24.56 , d ) 25.0 , e ) 31.36 | c | divide(multiply(28, const_100), add(const_100, 14)) | add(n0,const_100)|multiply(n1,const_100)|divide(#1,#0)| | gain |
in 150 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by : | "distance covered by b in 9 sec . = 150 / 45 x 9 m = 30 m . a beats b by 30 metres . answer : option e" | a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) 30 m | e | multiply(divide(150, 45), subtract(45, 36)) | divide(n0,n2)|subtract(n2,n1)|multiply(#0,#1)| | physics |
the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.5 * 23.25 * 7.57 ) is close to | "( 34.31 * 0.473 * 1.567 ) / ( 0.5 * 23.25 * 7.57 ) = 25.4303 / 88.00125 = 0.29 answer : d" | a ) 2 , b ) 1.15 , c ) 2.05 , d ) 0.29 , e ) 2.35 | d | divide(divide(multiply(multiply(34.31, 0.473), 1.567), multiply(multiply(7.57, 23.25), 0.5)), const_10) | multiply(n0,n1)|multiply(n4,n5)|multiply(n2,#0)|multiply(n3,#1)|divide(#2,#3)|divide(#4,const_10)| | general |
if x is 12 percent greater than 70 , then x = | "12 % of 70 = ( 70 * 0.11 ) = 8.4 12 % greater than 70 = 70 + 8.4 = 78.4 answer is clearly a ." | a ) 78.4 , b ) 91.0 , c ) 88.0 , d ) 70.4 , e ) 71.2 | a | add(70, multiply(divide(12, const_100), 70)) | divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)| | general |
a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is | "solution let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . then â € ¹ = â € º ( x + 28 ) + 2 = 2 ( x + 2 ) â € ¹ = â € º x + 30 = 2 x + 4 x = 26 . answer a" | a ) 26 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none | a | divide(subtract(28, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general |
a and b invests rs . 3000 and rs . 10000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ? | "( 3 * 6 + 6 * 6 ) : ( 10 * 12 ) 54 : 120 = > 9 : 20 . answer : c" | a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 20 , d ) 9 : 9 , e ) 9 : 5 | c | divide(add(multiply(3000, 6), multiply(multiply(3000, const_2), 6)), multiply(10000, add(6, 6))) | add(n2,n2)|multiply(n0,n2)|multiply(n0,const_2)|multiply(n2,#2)|multiply(n1,#0)|add(#1,#3)|divide(#5,#4)| | gain |
what is the smallest integer that is multiple of 3 , 5,7 | "it is the lcm of 3 , 5 and 7 which is 105 . the answer is a ." | a ) a ) 105 , b ) b ) 35 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140 | a | add(const_3, const_4) | add(const_3,const_4)| | general |
a call center has two teams . each member of team a was able to process 7 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ? | "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 7 calls , so total calls for team a = 35 fraction for team b = 40 / ( 40 + 35 ) = 8 / 15 = answer = c" | a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 15 , d ) 1 / 2 , e ) 1 / 5 | c | divide(multiply(8, 5), add(multiply(8, 5), multiply(5, 7))) | multiply(n1,n3)|multiply(n0,n1)|add(#0,#1)|divide(#0,#2)| | general |
the speed at which a man can row a boat in still water is 10 kmph . if he rows downstream , where the speed of current is 2 kmph , what time will he take to cover 60 metres ? | "speed of the boat downstream = 10 + 2 = 12 kmph = 12 * 5 / 18 = 10 / 3 m / s hence time taken to cover 60 m = 60 * 3 / 10 = 18 seconds . answer : a" | a ) 18 seconds , b ) 34 seconds , c ) 14 seconds , d ) 12 seconds , e ) 15 seconds | a | divide(60, multiply(add(10, 2), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)| | physics |
what is the value of 4 ^ 5 + 4 ^ 4 ? | "4 ^ 5 + 4 ^ 4 = 4 ^ 4 ( 4 + 1 ) = 4 ^ 4 * 5 answer b" | a ) 4 ^ 12 , b ) 5 ( 4 ^ 4 ) , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 7 ( 4 ^ 5 ) | b | divide(multiply(add(add(const_100, const_60), const_1), 4), const_100) | add(const_100,const_60)|add(#0,const_1)|multiply(n0,#1)|divide(#2,const_100)| | general |
the positive numbers w , x , y , and z are such that x is 10 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ? | "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 16 - answer b" | a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 % | b | multiply(const_100, subtract(multiply(multiply(divide(add(10, const_100), const_100), divide(add(10, const_100), const_100)), divide(subtract(const_100, 10), const_100)), const_1)) | add(n0,const_100)|subtract(const_100,n0)|divide(#1,const_100)|divide(#0,const_100)|multiply(#3,#3)|multiply(#2,#4)|subtract(#5,const_1)|multiply(#6,const_100)| | general |
a man misses a bus by 40 minutes if he travels at 30 kmph . if he travels at 40 kmph , then also he misses the bus by 10 minutes . what is the minimum speed required to catch the bus on time ? | let the distance to be travelled to catch the bus be x km x / 30 - x / 40 = 30 / 60 = > ( 4 x - 3 x ) / 120 = 1 / 2 = > x = 60 km by traavelling 30 kmph time taken = 60 / 30 = 2 hours by taking 2 hours , he is late by 40 min . so , he has to cover 60 km in at most speed = 60 / ( 4 / 3 ) = 45 kmph . answer : b | a ) 22 , b ) 45 , c ) 66 , d ) 88 , e ) 12 | b | divide(multiply(multiply(40, const_3), divide(30, const_60)), subtract(divide(multiply(multiply(40, const_3), divide(30, const_60)), 30), divide(40, const_60))) | divide(n1,const_60)|divide(n0,const_60)|multiply(n0,const_3)|multiply(#0,#2)|divide(#3,n1)|subtract(#4,#1)|divide(#3,#5) | physics |
5 n + 2 > 12 and 7 n + 2 < 44 ; n must be between which numbers ? | "5 n + 2 > 12 5 n > 10 n > 2 7 n + 2 < 44 7 n < 42 n < 6 so n must be between 2 and 6 2 < n < 6 correct answer b" | a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 9 | b | add(multiply(2, const_10), divide(add(44, 2), 7)) | add(n4,n5)|multiply(const_10,n1)|divide(#0,n3)|add(#2,#1)| | general |
a committee is reviewing a total of 20 x black - and - white films and 4 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ? | "say x = y = 10 . in this case we would have : 20 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 2 black - and - white films and all 40 color films , thus total of 42 films were selected . color films thus compose 40 / 42 = 20 / 21 of the selec... | a ) 26 / 21 , b ) 28 / 21 , c ) 20 / 21 , d ) 40 / 21 , e ) 60 / 21 | c | divide(4, add(divide(20, const_100), 4)) | divide(n0,const_100)|add(n1,#0)|divide(n1,#1)| | general |
a jogger running at 9 kmph along side a railway track is 250 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? | "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 250 + 120 ) m = 370 m . ∴ time taken = ( 370 ⁄ 10 ) sec = 37 sec . answer b" | a ) 3.6 sec , b ) 37 sec , c ) 36 sec , d ) 72 sec , e ) none of these | b | multiply(multiply(divide(divide(add(250, 120), const_1000), subtract(45, 9)), const_60), const_60) | add(n1,n2)|subtract(n3,n0)|divide(#0,const_1000)|divide(#2,#1)|multiply(#3,const_60)|multiply(#4,const_60)| | physics |
in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 11 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ? | "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 11 = 63 answer e" | a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 63 | e | multiply(11, inverse(subtract(1, add(divide(1, 5), divide(2, 3))))) | divide(n0,n1)|divide(n2,n3)|add(#0,#1)|subtract(n0,#2)|inverse(#3)|multiply(n4,#4)| | physics |
a train traveling at 42 kms / hr passes a cyclist going in the same direction in 9 secs . if the cyclist had been going in the opposite direction , the train would have passed him in 5 secs . find the length of the train . | let the length of the train be x meter and the speed of the cyclist is y m / s now when the train and the cyclist are in the same direction , the relative speed is : ( 35 / 3 - y ) m / s [ converting 42 km / h to m / s - 35 / 3 m / s ] now distance / relative speed = 9 seconds substituting the values , we get x + 9 y .... | a ) 75 meters , b ) 60 meters , c ) 90 meters , d ) 80 meters , e ) 70 meters | a | multiply(subtract(divide(multiply(42, const_1000), const_3600), divide(subtract(multiply(divide(multiply(42, const_1000), const_3600), 9), multiply(divide(multiply(42, const_1000), const_3600), 5)), add(9, 5))), 9) | add(n1,n2)|multiply(n0,const_1000)|divide(#1,const_3600)|multiply(n1,#2)|multiply(n2,#2)|subtract(#3,#4)|divide(#5,#0)|subtract(#2,#6)|multiply(n1,#7) | physics |
the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 245 , then the mean profit for the last 15 days would be | "average would be : 350 = ( 245 + x ) / 2 on solving , x = 455 . answer : d" | a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 455 , e ) none of these | d | divide(subtract(multiply(30, 350), multiply(15, 245)), 15) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n3)| | gain |
in what ratio should a variety of rice costing rs . 5.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ? | "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5.5 ) = 5 / 8 answer : d" | a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 8 , e ) 7 / 6 | d | divide(divide(subtract(8.75, 7.50), subtract(8.75, 5.5)), subtract(const_1, divide(subtract(8.75, 7.50), subtract(8.75, 5.5)))) | subtract(n1,n2)|subtract(n1,n0)|divide(#0,#1)|subtract(const_1,#2)|divide(#2,#3)| | other |
john can complete a given task in 16 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 5 days before the work got over . in how many days did the work get over from the time john and jane started to wor... | "in such questions , you need to start from the end . last 5 days john works alone and completes 5 * ( 1 / 16 ) = 5 / 16 of the work . so 11 / 16 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 16 + 1 / 12 = 7 / 48 time taken to complete 11 / 16 o... | a ) 62 , b ) 64 , c ) 66 / 7 , d ) 10 , e ) 68 / 7 | e | add(5, divide(subtract(multiply(16, 12), multiply(12, 5)), add(12, 16))) | add(n0,n1)|multiply(n0,n1)|multiply(n1,n2)|subtract(#1,#2)|divide(#3,#0)|add(n2,#4)| | physics |
what is the least positive integer that is not a factor of 30 ! and is not a prime number ? | a ) 31 is prime and per the question stem we can not use this b ) 32 = 2 * 16 - within 30 ! we have a 2 and 16 so 32 will be a factor of 30 ! c ) 33 = 3 * 11 - again within 30 ! we have a 3 and an 11 so 33 will be a factor of 30 ! d ) 62 = 31 * 2 - bingo 31 is not included in 30 ! e ) 64 = 16 * 4 - both 16 and 4 are mu... | a ) 31 , b ) 32 , c ) 33 , d ) 62 , e ) 64 | d | multiply(add(30, const_1), const_2) | add(n0,const_1)|multiply(#0,const_2) | other |
if the true discount on a sum due 3 years hence at 14 % per annum be rs . 168 , the sum due is : | "sol . p . w . = 100 * t . d . / r * t = 100 * 168 / 14 * 2 = 600 . ∴ sum = ( p . w . + t . d . ) = rs . ( 600 + 168 ) = rs . 768 . answer b" | a ) 698 , b ) 768 , c ) 1430 , d ) 1980 , e ) none | b | add(divide(multiply(const_100, 168), multiply(14, const_2.0)), 168) | multiply(n2,const_100)|multiply(const_2.0,n1)|divide(#0,#1)|add(n2,#2)| | gain |
find the slope of the line perpendicular to the line y = ( 1 / 5 ) x - 7 | two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 5 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 5 ) = - 1 solve for m m = - 5 correct answer c ) - 5 | a ) 1 , b ) 2 , c ) - 5 , d ) 4 , e ) 5 | c | divide(1, 5) | divide(n0,n1) | general |
each child has 2 pencils and 13 skittles . if there are 9 children , how many pencils are there in total ? | 2 * 9 = 18 . answer is c . | a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08 | c | multiply(2, 9) | multiply(n0,n2)| | general |
a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 400 m long ? | "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1600 m t = d / s t = 1600 / 10 t = 160 sec answer : d" | a ) 176 sec , b ) 190 sec , c ) 178 sec , d ) 160 sec , e ) 276 sec | d | divide(add(1200, 400), divide(1200, 120)) | add(n0,n2)|divide(n0,n1)|divide(#0,#1)| | physics |
chris age after 14 years will be 5 times his age 5 years back . what is the present age of chris ? | "chris present age = x after 14 years = x + 14 5 years back = x - 5 x + 14 = 5 ( x - 5 ) x = 11 answer is e" | a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 11 | e | subtract(divide(add(multiply(5, 5), 14), subtract(5, const_1)), subtract(divide(add(multiply(5, 5), 14), subtract(5, const_1)), 5)) | multiply(n1,n1)|subtract(n1,const_1)|add(n0,#0)|divide(#2,#1)|subtract(#3,n1)|subtract(#3,#4)| | general |
the average of 13 numbers is 59 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ? | "sum of all the 13 numbers = 13 * 59 = 767 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 767 = 59 . answer : a" | a ) 59 , b ) 83 , c ) 45 , d ) 53 , e ) 64 | a | subtract(multiply(8, 61), subtract(multiply(13, 59), multiply(57, 7))) | multiply(n5,n6)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3)| | general |
x is a positive integer less than 400 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ? | the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at... | a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25 | c | subtract(add(multiply(reminder(7, 400), 3), reminder(3, 400)), reminder(1, 400)) | reminder(n1,n0)|reminder(n3,n0)|reminder(n2,n0)|multiply(n3,#0)|add(#3,#1)|subtract(#4,#2) | general |
a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 8 sec . what is the length of the platform ? | "speed = 300 / 8 = 75 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 75 / 2 = > x = 1162.5 m . answer : e" | a ) 287 m , b ) 350 m , c ) 1267 m , d ) 1287 m , e ) 1162.5 m | e | subtract(multiply(speed(300, 8), 39), 300) | speed(n0,n2)|multiply(n1,#0)|subtract(#1,n0)| | physics |
the rate of increase of the price of sugar is observed to be 3 percent more than the inflation rate expressed in percentage . the price of sugar , on january 1 , 1994 , is rs . 25 per kg . the inflation rate for the years 1994 and 1995 are expected to be 12 % each . the expected price of sugar on january 1 , 1996 would... | explanation : increase in the price of sugar = ( 12 + 3 ) = 15 % hence , price of the sugar on jan 1 , 1996 = > ( 25 * 115 * 115 ) / ( 100 * 100 ) = rs 33.06 . answer : a | a ) 33.06 , b ) 34.1 , c ) 34.2 , d ) 24.6 , e ) none of these | a | divide(multiply(multiply(25, add(add(12, 3), const_100)), add(add(12, 3), const_100)), multiply(const_100, const_100)) | add(n0,n6)|multiply(const_100,const_100)|add(#0,const_100)|multiply(n3,#2)|multiply(#2,#3)|divide(#4,#1) | general |
a metallic sheet is of rectangular shape with dimensions 30 m x 25 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 6 m , the volume of the box ( in m cube ) is : | "explanation : l = ( 30 - 12 ) m = 20 m , [ because 6 + 6 = 12 ] b = ( 25 - 12 ) m = 13 m , h = 6 m . volume of the box = ( 12 x 13 x 6 ) m cube = 936 m cube . option e" | a ) 920 m cube , b ) 840 m cube , c ) 1000 m cube , d ) 120 m cube , e ) none of these | e | volume_rectangular_prism(subtract(30, multiply(6, const_2)), subtract(25, multiply(6, const_2)), 6) | multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|volume_rectangular_prism(n2,#1,#2)| | geometry |
average weight of 10 people increased by 3 kg when one person of 45 kg is replaced by a new man . then weight of the new man is | explanation : total weight increased is 3 * 10 = 30 . so weight of new person is 45 + 30 = 75 answer : option e | a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 75 | e | add(45, multiply(3, 10)) | multiply(n0,n1)|add(n2,#0) | general |
find the average of all numbers between 4 and 41 which are divisible by 5 | "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 ) / 8 = 180 / 8 = 22.5 answer : option a" | a ) 22.5 , b ) 20 , c ) 25 , d ) 30 , e ) 35 | a | divide(add(add(add(multiply(5, const_3), add(5, multiply(5, const_2))), multiply(5, const_4)), multiply(add(const_4, const_1), 5)), 5) | add(const_1,const_4)|multiply(n2,const_2)|multiply(n2,const_3)|multiply(n2,const_4)|add(n2,#1)|multiply(n2,#0)|add(#4,#2)|add(#6,#3)|add(#7,#5)|divide(#8,n2)| | general |
the value of log 5 ( 1 / 125 ) is | "solution let log 5 ( 1 / 125 ) = n . then , 5 n = 1 / 125 ‹ = › 5 n = 5 - 3 n = - 3 . answer b" | a ) 3 , b ) - 3 , c ) 1 / 3 , d ) - 1 / 3 , e ) none | b | log(divide(log(subtract(1, multiply(add(const_4, const_1), const_1000))), log(add(const_4, const_1)))) | add(const_1,const_4)|log(#0)|multiply(#0,const_1000)|subtract(n1,#2)|log(#3)|divide(#4,#1)|log(#5)| | other |
a train 280 m long , running with a speed of 63 km / hr will pass a tree in ? | "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 280 * 2 / 35 = 16 sec answer : b" | a ) 65 sec , b ) 16 sec , c ) 18 sec , d ) 13 sec , e ) 76 sec | b | multiply(divide(280, multiply(63, const_1000)), const_3600) | multiply(n1,const_1000)|divide(n0,#0)|multiply(#1,const_3600)| | physics |
at a certain bowling alley , it costs $ 1 to rent bowling shoes for the day and $ 1.25 to bowl 1 game . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ? | "after renting bowling shoes the person is left with $ 12.80 - $ 1 = $ 11.80 , which is enough for 11.8 / 1.25 < 10 = ~ 9 . answer : e ." | a ) 7 , b ) 8 , c ) 5 , d ) 10 , e ) 9 | e | divide(subtract(12.80, 1), 1.25) | subtract(n3,n0)|divide(#0,n1)| | physics |
sales price is $ 54 , gross profit is 125 % of cost , what is the value of gross profit ? | "cost + profit = sales cost + ( 125 / 100 ) cost = 54 cost = 24 profit = 54 - 24 = 30 answer ( b )" | a ) 32 , b ) 30 , c ) 39 , d ) 40 , e ) 42 | b | subtract(54, divide(54, add(const_1, divide(125, const_100)))) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)| | gain |
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 22 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ? | "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 22 + 21 = 43 t = 12 d = 43 * 12 = 516 answer : b" | a ) 288 , b ) 516 , c ) 877 , d ) 278 , e ) 178 | b | add(multiply(divide(60, subtract(21, 22)), 22), multiply(divide(60, subtract(21, 22)), 21)) | subtract(n1,n0)|divide(n2,#0)|multiply(n0,#1)|multiply(n1,#1)|add(#2,#3)| | physics |
marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 10 % . what percent of the projected revenue was the actual revenue ? | "last year revenue = 100 ( assume ) ; this year revenue = 90 ; projected revenue = 120 . actual / projected * 100 = 90 / 120 * 100 = 75 % . answer : e ." | a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 % | e | multiply(divide(subtract(const_100, 10), add(20, const_100)), const_100) | add(n0,const_100)|subtract(const_100,n1)|divide(#1,#0)|multiply(#2,const_100)| | general |
if the l . c . m of two numbers is 750 and their product is 18750 , find the h . c . f of the numbers | "explanation : h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18750 / 750 = 25 . answer : d" | a ) 23 , b ) 28 , c ) 48 , d ) 25 , e ) 99 | d | divide(18750, 750) | divide(n1,n0)| | physics |
in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 12 . if the shop carries 375 dogs and bunnies total in stock , how many dogs are there ? | "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 12 x total dogs and bunnies = 15 x . and we are given that 15 x = 375 . hence x = 25 . dogs = 3 x = 3 * 25 = 75 ( option c )" | a ) 42 , b ) 66 , c ) 75 , d ) 112 , e ) 154 | c | multiply(divide(375, add(3, 12)), 3) | add(n0,n2)|divide(n3,#0)|multiply(n0,#1)| | other |
30 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ? | "30 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 30 ) * 100 = 120 square feet answer : option b" | a ) 14.4 , b ) 120 , c ) 50.4 , d ) 60 , e ) 90 | b | divide(multiply(4, 9), divide(30, const_100)) | divide(n0,const_100)|multiply(n1,n2)|divide(#1,#0)| | gain |
a sum of money at simple interest amounts to rs . 830 in 3 years and to rs . 854 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 854 - 830 ) = rs . 24 . s . i . for 3 years = rs . ( 24 x 3 ) = rs . 72 . principal = rs . ( 830 - 72 ) = rs . 758 . answer : c" | a ) 647 , b ) 698 , c ) 758 , d ) 847 , e ) 976 | c | subtract(830, divide(multiply(subtract(854, 830), 3), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | gain |
a person p takes 4 hrs time to complete a job and q takes 6 hrs to complete the same job if they work together how much time will they require to complete the job ? | explanation : p ’ s 1 hr work = 1 / 4 q ’ s 1 hr work = 1 / 6 ( p + q ) ’ s 1 hr work = 1 / 4 + 1 / 6 = 5 / 12 = > time = 12 / 5 = 2.4 hrs answer : option c | a ) 1.2 hrs , b ) 1.8 hrs , c ) 2.4 hrs , d ) 3.0 hrs , e ) none of these | c | inverse(add(divide(const_1, 4), divide(const_1, 6))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2) | physics |
a shopkeeper fixes the marked price of an item 35 % above its cost price . the percentage of discount allowed to gain 8 % is | solution let c . p = rs . 100 then , marked price = rs . 135 , s . p = rs . 108 . discount % = ( 27 / 135 × 100 ) % = 20 % answer a | a ) 20 % , b ) 27 % , c ) 31 % , d ) 43 % , e ) none | a | subtract(const_100, multiply(divide(add(8, const_100), add(35, const_100)), const_100)) | add(n1,const_100)|add(n0,const_100)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3) | gain |
if the cost price of 22 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ? | "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 22 articles = rs . 22 . selling price of 16 articles = rs . 22 therefore , selling price of 22 articles is : - = > 22 / 16 ã — 22 = > 30.25 . therefore , profit = selling price - cost price . = > 30.25 â ˆ ’ 22 = 8.25 hence , the percentag... | a ) 20 % loss , b ) 37.5 % profit , c ) 37.5 % loss , d ) 30.33 % loss , e ) none of these | b | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 16), 22)), divide(multiply(const_100, 16), 22))) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)|divide(#2,#1)|multiply(#3,const_100)| | gain |
six bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ? | "l . c . m . of 2 , 4 , 6 , 8 , 10 , 12 is 120 . so , the bells will toll together after every 120 seconds ( 2 minutes ) . in 30 minutes , they will toll together 30 / 2 + 1 = 16 times answer d" | a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) none | d | divide(10, divide(multiply(multiply(2, multiply(multiply(add(2, const_3), 2), const_3)), 2), 10)) | add(n0,const_3)|multiply(n0,#0)|multiply(#1,const_3)|multiply(n0,#2)|multiply(n0,#3)|divide(#4,n4)|divide(n4,#5)| | physics |
at what rate percent per annum will the simple interest on a sum of money be 4 / 5 of the amount in 10 years ? | "let sum = x . then , s . i . = 4 x / 5 , time = 10 years . rate = ( 100 * 4 x ) / ( x * 5 * 10 ) = 8 % answer : c" | a ) 4 % , b ) 7 % , c ) 8 % , d ) 3 % , e ) 1 % | c | divide(multiply(divide(4, 5), const_100), 10) | divide(n0,n1)|multiply(#0,const_100)|divide(#1,n2)| | gain |
the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length of this rectangle . | "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c" | a ) 40 , b ) 70 , c ) 20 , d ) 80 , e ) 60 | c | divide(subtract(divide(70, const_2), sqrt(subtract(multiply(divide(70, const_2), divide(70, const_2)), multiply(const_4, 300)))), const_2) | divide(n1,const_2)|multiply(n0,const_4)|multiply(#0,#0)|subtract(#2,#1)|sqrt(#3)|subtract(#0,#4)|divide(#5,const_2)| | geometry |
a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ? | speed of down stream = 5 + 1 = 6 kmph speed of upstream = 5 - 1 = 4 kmph let the required distance be xkm x / 6 + x / 4 = 1 2 x + 3 x = 12 x = 2.4 km answer is e | a ) 1 km , b ) 1.5 km , c ) 5 km , d ) 3.2 km , e ) 2.4 km | e | divide(multiply(subtract(5, 1), const_3), 5) | subtract(n0,n1)|multiply(#0,const_3)|divide(#1,n0) | physics |
a sum fetched a total simple interest of $ 4106.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ? | "e 8927 principal = $ 100 x 4106.25 / 9 x 5 = $ 410625 / 45 = $ 8927 ." | a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8927 | e | divide(divide(multiply(4106.25, const_100), 9), 5) | multiply(n0,const_100)|divide(#0,n1)|divide(#1,n2)| | gain |
find the perimeter and area of a square of side 13 cm . | we know that the perimeter of square = 4 ã — side side = 13 cm therefore , perimeter = 4 ã — 13 cm = 52 cm now , area of the square = ( side ã — side ) sq . units = 13 ã — 13 cm â ² = 169 cm â ² answer : c | ['a ) 121', 'b ) 144', 'c ) 169', 'd ) 196', 'e ) 225'] | c | square_area(13) | square_area(n0) | geometry |
a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 75 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ? | 300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 75 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 75 = 1733.33 c is the answer | a ) 1000 , b ) 1250 , c ) 1733.33 , d ) 1800 , e ) 2025 | c | divide(add(divide(multiply(300, const_100), 30), 300), divide(75, const_100)) | divide(n1,const_100)|multiply(n0,const_100)|divide(#1,n3)|add(n0,#2)|divide(#3,#0) | general |
the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 45 % profit ? | "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 145 % of $ 640 = $ 928 . c" | a ) $ 480 , b ) $ 450 , c ) $ 928 , d ) $ 870 , e ) $ 660 | c | add(divide(multiply(divide(add(832, 448), const_2), 45), const_100), divide(add(832, 448), const_2)) | add(n0,n1)|divide(#0,const_2)|multiply(n2,#1)|divide(#2,const_100)|add(#3,#1)| | gain |
find the area of a right - angled triangle whose base is 12 cm and hypotenuse is 13 cm . | sol . height of the triangle = [ ( 13 ) 2 - ( 12 ) 2 ] ( 1 / 2 ) cm = ( 25 ) ( 1 / 2 ) cm = 5 cm . its area = ( 1 / 2 ) * base * height = ( ( 1 / 2 ) * 12 * 5 ) cm ^ 2 = 30 cm ^ 2 . ans : b | ['a ) 15', 'b ) 30', 'c ) 18', 'd ) 12', 'e ) 25'] | b | triangle_area(12, sqrt(subtract(power(13, const_2), power(12, const_2)))) | power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|triangle_area(n0,#3) | geometry |
a motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr . his average speed for the whole journey in km / hr is ? | explanation : average speed = ( 2 xy ) / ( x + y ) km / hr = ( 2 * 50 * 30 ) / ( 50 + 30 ) km / hr . 37.5 km / hr . answer : c | a ) 37.9 , b ) 37.53 , c ) 37.5 , d ) 37.1 , e ) 37.4 | c | divide(multiply(const_2, multiply(50, 30)), add(50, 30)) | add(n1,n2)|multiply(n1,n2)|multiply(#1,const_2)|divide(#2,#0) | general |
4685 * 999 | "explanation : 4685 * ( 1000 - 1 ) = 4685000 - 4685 = 4680315 option c" | a ) 4680250 , b ) 4685850 , c ) 4680315 , d ) 4685975 , e ) none of these | c | multiply(divide(4685, 999), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 5 like all . how many people like apple ? | "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 5 40 + 10 + 5 - 7 = 48 like apple answer : a" | a ) 48 , b ) 46 , c ) 54 , d ) 58 , e ) 62 | a | add(add(subtract(40, const_3), 7), subtract(10, 7)) | subtract(n0,const_3)|subtract(n2,n1)|add(n1,#0)|add(#2,#1)| | general |
a textile manufacturing firm employees 56 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 56 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly sprea... | "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 55 / 56 ) â ˆ ’ 150... | a ) 13000 , b ) 6250 , c ) 10000 , d ) 5000 , e ) none of these | b | subtract(subtract(multiply(multiply(5, const_1000), const_100), add(multiply(75000, const_2), 75000)), subtract(subtract(multiply(divide(subtract(56, 1), 56), multiply(multiply(5, const_1000), const_100)), multiply(multiply(75000, const_2), divide(subtract(56, 1), 56))), 75000)) | multiply(n2,const_1000)|multiply(n6,const_2)|subtract(n0,n4)|add(n6,#1)|divide(#2,n0)|multiply(#0,const_100)|multiply(#4,#5)|multiply(#4,#1)|subtract(#5,#3)|subtract(#6,#7)|subtract(#9,n6)|subtract(#8,#10)| | general |
a factory produces 5505 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ? | to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 5505 / 5 = 1101 toys correct answer c | a ) 4436 toys , b ) 5487 toys , c ) 1101 toys , d ) 2354 toys , e ) 1375 toys | c | divide(5505, 5) | divide(n0,n1) | physics |
8 men , working 8 hours a day can complete a work in 24 days . how many hours a day must 12 men work to complete the same work in 16 days ? | "the number of hours required to complete the work is 8 * 8 * 24 = 1536 12 × 16 × ( x ) = 1536 x = 8 the answer is c ." | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | c | divide(multiply(multiply(8, 8), 24), multiply(12, 16)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)| | physics |
in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 9 , 1 ) , ( 1 , 1 ) , ( 1 , - 8 ) and ( - 9 , - 8 ) ? | "length of side 1 = 9 + 1 = 10 length of side 2 = 8 + 1 = 9 area of rectangle = 10 * 9 = 90 d is the answer" | a ) 72 , b ) 180 , c ) 70 , d ) 90 , e ) 140 | d | multiply(add(9, 1), add(1, 8)) | add(n0,n1)|add(n1,n5)|multiply(#0,#1)| | geometry |
company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 1 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last... | "# of basic stereos was 1 / 3 of total and # of deluxe stereos was 2 / 3 of total , let ' s assume total = 15 , then basic = 5 and deluxe = 10 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 5 * 1 = 5 and tot... | a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 14 / 19 , e ) 1 / 2 | d | divide(add(3, 1), const_10) | add(n0,n1)|divide(#0,const_10)| | general |
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