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
values |
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653 Γ£ β 1001 = ? | "653 Γ£ β ( 1000 + 1 ) 653000 + 1 653001 answer d" | a ) 649011 , b ) 540041 , c ) 654321 , d ) 653001 , e ) 643001 | d | multiply(divide(653, 1001), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed x ? | "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this x we get x = 8 . b ." | a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16 | b | divide(add(divide(96, 16), sqrt(add(multiply(multiply(divide(divide(96, 16), add(const_1, divide(50, const_100))), 4), 4), power(divide(96, 16), const_2)))), const_2) | divide(n0,n2)|divide(n3,const_100)|add(#1,const_1)|power(#0,const_2)|divide(#0,#2)|multiply(n1,#4)|multiply(#5,n1)|add(#6,#3)|sqrt(#7)|add(#0,#8)|divide(#9,const_2)| | physics |
at a certain college , 50 percent of the total number of students are freshmen . if 40 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 20 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal ar... | "let ' s say there is a total of 100 students at this college . 50 percent of the total number of students are freshmen . # of freshmen = 50 % of 100 = 50 40 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 40 % of 50 = 20 . . . and , of these , 20 percent ar... | a ) 14 % , b ) 4 % , c ) 15 % , d ) 5 % , e ) 25 % | b | divide(multiply(divide(multiply(50, 40), const_100), 20), const_100) | multiply(n0,n1)|divide(#0,const_100)|multiply(n2,#1)|divide(#2,const_100)| | general |
what will be the difference between simple and compound interest at 10 % per annum on a sum of rs . 1000 after 4 years ? | "s . i . = ( 1000 * 10 * 4 ) / 100 = rs . 400 c . i . = [ 1000 * ( 1 + 10 / 100 ) 4 - 1000 ] = rs . 464.10 difference = ( 464.10 - 400 ) = rs . 64.10 answer : d" | a ) rs . 31 , b ) rs . 32.10 , c ) rs . 40.40 , d ) rs . 64.10 , e ) rs . 74.10 | d | subtract(subtract(multiply(1000, power(add(divide(10, const_100), const_1), 4)), 1000), multiply(multiply(1000, divide(10, const_100)), 4)) | divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|multiply(n2,#2)|power(#1,n2)|multiply(n1,#4)|subtract(#5,n1)|subtract(#6,#3)| | gain |
60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 50 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell... | lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters... | a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44 | a | multiply(divide(20, const_100), multiply(divide(20, const_100), 300)) | divide(n2,const_100)|multiply(n3,#0)|multiply(#0,#1) | general |
a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ? | "speed of the train relative to man = ( 200 / 10 ) m / sec = ( 20 ) m / sec . [ ( 20 ) * ( 18 / 5 ) ] km / hr = 72 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 72 = = > x = 77 km / hr . answer : c" | a ) 28 , b ) 50 , c ) 77 , d ) 22 , e ) 12 | c | divide(divide(subtract(200, multiply(multiply(5, const_0_2778), 5)), 5), const_0_2778) | multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)| | physics |
if there are 156 laborers in a crew , and on a certain day , 70 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) . | "70 / 156 * 100 = 44.87 44.9 % correct answer e" | a ) 45.9 % , b ) 43.9 % , c ) 42.9 % , d ) 41.9 % , e ) 44.9 % | e | divide(multiply(70, const_100), 156) | multiply(n1,const_100)|divide(#0,n0)| | physics |
a work can be finished in 16 days by 30 women . the same work can be finished in 10 days by sixteen men . the ratio between the capacity of a man and a woman is | "work done by 30 women in 1 day = 1 / 16 work done by 1 woman in 1 day = 1 / ( 16 Γ 30 ) work done by 16 men in 1 day = 1 / 10 work done by 1 man in 1 day = 1 / ( 10 Γ 16 ) ratio of the capacity of a man and woman = 1 / ( 10 Γ 16 ) : 1 / ( 16 Γ 30 ) = 1 / 10 : 1 / 30 = 1 / 1 : 1 / 3 = 3 : 1 option a" | a ) 3 : 1 , b ) 4 : 3 , c ) 2 : 3 , d ) 2 : 1 , e ) 2 : 4 | a | divide(divide(const_1, multiply(add(16, const_2), const_10)), divide(const_1, multiply(16, const_10))) | add(n0,const_2)|multiply(n0,const_10)|divide(const_1,#1)|multiply(#0,const_10)|divide(const_1,#3)|divide(#4,#2)| | physics |
the ratio of numbers is 4 : 5 and their h . c . f is 4 . their l . c . m is : | "let the numbers be 4 x and 5 x . then their h . c . f = x . so , x = 4 . so , the numbers are 16 and 20 . l . c . m of 16 and 20 = 80 . answer : a" | a ) 80 , b ) 16 , c ) 24 , d ) 48 , e ) 98 | a | lcm(multiply(4, 4), multiply(5, 4)) | multiply(n0,n2)|multiply(n1,n2)|lcm(#0,#1)| | other |
length of a rectangular plot is 12 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ? | let breadth = x metres . then , length = ( x + 12 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 12 ) + x ] = 200 2 x + 12 = 100 2 x = 88 x = 44 hence , length = x + 12 = 56 m a | ['a ) 56 m', 'b ) 60 m', 'c ) 80 m', 'd ) 82 m', 'e ) 84 m'] | a | divide(add(divide(5300, 26.5), multiply(const_2, 12)), const_4) | divide(n2,n1)|multiply(n0,const_2)|add(#0,#1)|divide(#2,const_4) | physics |
two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 65 km more than the other . what is the distance between the two stations ? | "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 65 km more than the other , 25 x Γ’ β¬ β 20 x = 65 5 x = 65 x = 13 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45... | a ) 585 km , b ) 767 km , c ) 276 km , d ) 178 km , e ) 176 km | a | multiply(add(20, 25), divide(65, subtract(25, 20))) | add(n0,n1)|subtract(n1,n0)|divide(n2,#1)|multiply(#0,#2)| | general |
what is the length of a bridge ( in meters ) , which a train 140 meters long and travelling at 45 km / h can cross in 30 seconds ? | "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 140 = 235 meters the answer is c ." | a ) 205 , b ) 220 , c ) 235 , d ) 250 , e ) 265 | c | subtract(multiply(multiply(45, const_0_2778), 30), 140) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | physics |
a train crosses a platform of 140 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ? | length of the train be Γ’ β¬ Λ x Γ’ β¬ β’ x + 140 / 15 = x + 250 / 20 4 x + 560 = 3 x + 750 x = 190 m answer : a | a ) 190 , b ) 88 , c ) 77 , d ) 62 , e ) 52 | a | subtract(multiply(250, divide(15, divide(15, const_3))), multiply(140, divide(20, divide(15, const_3)))) | divide(n1,const_3)|divide(n1,#0)|divide(n3,#0)|multiply(n2,#1)|multiply(n0,#2)|subtract(#3,#4) | physics |
what is the sum of the integers from - 170 to 171 , inclusive ? | "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 171 , a = - 170 , d = 1 hence , 171 = - 170 + ( n - 1 ) or n = 342 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 342 * ( - 170 + 171 ) / 2 sn = 342 * 1 / 2 sn = 171 ... | a ) 181 , b ) 171 , c ) 191 , d ) 201 , e ) 202 | b | divide(multiply(170, 171), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general |
if 7 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes | "n ( n - 1 ) / 2 = 7 * 6 / 2 = 21 answer : a" | a ) 21 , b ) 42 , c ) 43 , d ) 44 , e ) 45 | a | divide(factorial(7), multiply(factorial(subtract(7, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | general |
a sum was put a simple interest at a certain rate for 3 years . had it been put at 3 % higher rate , it would have fetched rs . 90 more . the sum is : | "explanation : let the sub be rs . x and the initial rate be r % . then x Γ£ β ( r + 3 ) Γ£ β 3 / 100 Γ’ Λ β x Γ£ β r Γ£ β 3 / 100 = 90 Γ’ β‘ β x Γ£ β 3 Γ£ β 3 / 100 = 90 Γ’ β‘ β x Γ£ β 3 / 100 = 30 Γ’ β‘ β 3 x = 3000 Γ’ β‘ β x = 1000 answer : option c" | a ) s . 750 , b ) s . 900 , c ) s . 1000 , d ) s . 1200 , e ) s . 1500 | c | multiply(divide(divide(90, 3), 3), const_100) | divide(n2,n0)|divide(#0,n1)|multiply(#1,const_100)| | gain |
at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 8.50 + 0.25 ( s β 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1... | oa is definitely wrong . the answer should be a . | a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75 | a | add(multiply(0.25, subtract(5, 1)), 0.25) | subtract(n1,n0)|multiply(n3,#0)|add(n3,#1)| | general |
find the ratio in which rice at rs . 7.00 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg | "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 70 = 6 : 7 answer : a" | a ) 6 : 7 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8 | a | divide(subtract(6.30, 5.70), subtract(7.00, 6.30)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | other |
if the lcm and hcf of 4 and another number is 36 and 2 respectively . find the other number ? | hcf x lcm = product of numbers 2 x 36 = 4 x the other number other number = ( 2 x 36 ) / 4 other number = 18 answer : a | a ) 18 , b ) 16 , c ) 14 , d ) 13 , e ) 15 | a | divide(multiply(36, 2), const_4) | multiply(n1,n2)|divide(#0,const_4) | physics |
a certain car uses one gallon of gasoline every 40 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ? | "4 miles on the highway = 4 / 40 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 40 + 4 / 20 = 3 / 10 gallons . 8 miles on the highway = 8 / 40 gallons . the % change = ( 3 / 10 - 8 / 40 ) / ( 8 / 40 ) = 1 / 2 = 0.50 . answer : e ." | a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 50 % | e | multiply(divide(subtract(add(multiply(divide(const_1, 20), 4), multiply(4, divide(const_1, 40))), multiply(8, divide(const_1, 40))), multiply(8, divide(const_1, 40))), const_100) | divide(const_1,n1)|divide(const_1,n0)|multiply(n2,#0)|multiply(n2,#1)|multiply(n4,#1)|add(#2,#3)|subtract(#5,#4)|divide(#6,#4)|multiply(#7,const_100)| | general |
a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 864 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 864 - 815 ) = rs . 49 . s . i . for 3 years = rs . ( 49 x 3 ) = rs . 147 . principal = rs . ( 815 - 147 ) = rs . 668 . answer : option c" | a ) s . 650 , b ) s . 690 , c ) s . 668 , d ) s . 700 , e ) s . 760 | c | subtract(815, divide(multiply(subtract(864, 815), 3), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | gain |
the breadth of a rectangular hall is two - thirds of its length . if the area of the hall is 2400 sq metres , what is the length in metres ? | let the length of the rectangular hall be β x β m , then the breadth of the rectangular hall = 2 x β 3 m . area of hall = 2 x β 3 Γ x = 2 x 2 β 3 or , 2 x 2 β 3 = 2400 or x = 60 m answer c | ['a ) 120', 'b ) 80', 'c ) 60', 'd ) 40', 'e ) none of these'] | c | sqrt(divide(2400, divide(const_2, const_3))) | divide(const_2,const_3)|divide(n0,#0)|sqrt(#1) | geometry |
if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 166 m , what is its area ? | "length = breadth + 23 . therefore , 4 Γ breadth + 2 Γ 23 = 166 m β breadth = 30 m length = 30 + 23 = 53 m area = 53 Γ 30 = 1590 m 2 answer is a ." | a ) 1590 , b ) 2535 , c ) 2530 , d ) 2515 , e ) 2520 | a | rectangle_area(add(divide(subtract(166, multiply(const_2, 23)), const_4), 23), divide(subtract(166, multiply(const_2, 23)), const_4)) | multiply(n0,const_2)|subtract(n1,#0)|divide(#1,const_4)|add(n0,#2)|rectangle_area(#3,#2)| | geometry |
a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.50 . 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 5.5 $ then total value is 300 * 5.5 = 1650 . imo option c is correct answer . ." | a ) $ 960 , b ) $ 1,350 , c ) $ 1,650 , d ) $ 2,050 , e ) $ 2,250 | c | divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 5.50), 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 |
find β ? / 18 = 4 ? | "answer let β n / 18 = 4 then β n = 18 x 4 = 72 β΄ n = 72 x 72 = 5184 . correct option : d" | a ) 76 , b ) 5776 , c ) 304 , d ) 5184 , e ) none | d | power(multiply(4, 18), const_2) | multiply(n0,n1)|power(#0,const_2)| | general |
the population of a city increases by 6 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ? | actual increase in population = 5 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 5 / 100 ) ^ 3 = 115.7625 β΄ required percentage = 15.7625 % answer : d | a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 15.76 % , e ) none of these | d | add(divide(multiply(add(const_100, add(divide(multiply(add(const_100, subtract(6, 1)), subtract(6, 1)), const_100), subtract(6, 1))), subtract(6, 1)), const_100), add(divide(multiply(add(const_100, subtract(6, 1)), subtract(6, 1)), const_100), subtract(6, 1))) | subtract(n0,n1)|add(#0,const_100)|multiply(#1,#0)|divide(#2,const_100)|add(#3,#0)|add(#4,const_100)|multiply(#5,#0)|divide(#6,const_100)|add(#4,#7) | general |
find the average of all the numbers between 6 and 34 which are divisible by 6 . | "solution average = ( ( 12 + 18 + 24 + 30 ) / 5 ) = 84 / 4 = 21 . answer e" | a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 21 | e | divide(add(add(6, const_4), subtract(34, const_4)), const_2) | add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)| | general |
a can do a piece of work in 3 hours ; b and c together can do it in 2 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ? | "a ' s 1 hour work = 1 / 3 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 3 + 1 / 2 ) = 5 / 6 b ' s 1 hour work = ( 5 / 6 - 1 / 2 ) = 1 / 3 b alone will take 3 hours to do the work . answer : b" | a ) 6 hours , b ) 3 hours , c ) 2 hours , d ) 5 hours , e ) 4 hours | b | divide(const_1, subtract(divide(const_1, 2), subtract(divide(const_1, 2), divide(const_1, 3)))) | divide(const_1,n1)|divide(const_1,n2)|divide(const_1,n0)|subtract(#1,#2)|subtract(#0,#3)|divide(const_1,#4)| | physics |
two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is ? | "answer : option b let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = Γ’ Λ Ε‘ b : Γ’ Λ Ε‘ a = Γ’ Λ Ε‘ 16 : Γ’ Λ Ε‘ 9 = 4 : 3" | a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) 5 : 2 | b | divide(sqrt(16), sqrt(9)) | sqrt(n1)|sqrt(n0)|divide(#0,#1)| | physics |
at what rate percent on simple interest will rs . 650 amount to rs . 950 in 5 years ? | "300 = ( 650 * 5 * r ) / 100 r = 9.23 % answer : e" | a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 9.23 % | e | multiply(divide(divide(subtract(950, 650), 650), 5), const_100) | subtract(n1,n0)|divide(#0,n0)|divide(#1,n2)|multiply(#2,const_100)| | gain |
a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and the other digits are correct , then the correct answer would be : | "explanation : 987 = 3 * 7 * 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 = > ( sum of digits = 28 , not divisible by 3 ) 555181 = > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by each one of 3 , 7 , 47 . answer : c ) 555681" | a ) 288889 , b ) 556677 , c ) 555681 , d ) 267788 , e ) 268811 | c | multiply(subtract(subtract(divide(559981, 987), const_4), const_0_33), 987) | divide(n1,n0)|subtract(#0,const_4)|subtract(#1,const_0_33)|multiply(n0,#2)| | other |
when leo imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that leo paid was $ 87.50 , what was the total value of the item ? | let the value of the item be $ x , then 0.07 ( x β 1000 ) = 87.5 - - > x β 1000 = 1250 x β 1000 = 1250 - - > x = 2250 . answer : c . | a ) $ 1600 , b ) $ 1850 , c ) $ 2250 , d ) $ 2400 , e ) $ 2750 | c | add(divide(87.5, divide(7, const_100)), 1000) | divide(n0,const_100)|divide(n2,#0)|add(n1,#1) | general |
the annual interest rate earned by an investment increased by 6 percent from last year to this year . if the annual interest rate earned by the investment this year was 15.90 percent , what was the annual interest rate last year ? | "let i = interest rate i ( this year ) = i ( last year ) + 0.06 i ( last year ) = 1.06 i ( last year ) 15.90 = 1.06 x i ( last year ) i ( last year ) = 15.90 / 1.06 = 1590 / 106 = 15 % answer : e" | a ) 20 % , b ) 18 % , c ) 16 % , d ) 25 % , e ) 15 % | e | divide(multiply(15.90, const_100), add(15.90, const_100)) | add(n1,const_100)|multiply(n1,const_100)|divide(#1,#0)| | gain |
john and steve are speed walkers in a race . john is 12 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john β s final push ? | let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 12 + 2 - - - > 0.5 t = 14 - - - > t = 28 seconds . e is the correct answer . | a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 34 seconds , e ) 28 seconds | e | divide(add(divide(multiply(3.7, add(12, 2)), subtract(4.2, 3.7)), add(12, 2)), 4.2) | add(n0,n3)|subtract(n1,n2)|multiply(n2,#0)|divide(#2,#1)|add(#0,#3)|divide(#4,n1) | physics |
i chose a number and divide it by 6 . then i subtracted 189 from the result and got 3 . what was the number i chose ? | "let x be the number i chose , then x / 6 β 189 = 3 x / 6 = 192 x = 1152 answer is b ." | a ) 1200 , b ) 1152 , c ) 1189 , d ) 1190 , e ) 100 | b | multiply(add(189, 3), 6) | add(n1,n2)|multiply(n0,#0)| | general |
a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 400 more . what was the sum ? | "at 5 % more rate , the increase in s . i for 10 years = rs . 400 ( given ) so , at 5 % more rate , the increase in si for 1 year = 400 / 10 = rs . 40 / - i . e . rs . 40 is 5 % of the invested sum so , 1 % of the invested sum = 40 / 5 therefore , the invested sum = 40 Γ 100 / 5 = rs . 800 answer : b" | a ) s . 1200 , b ) s . 800 , c ) s . 1400 , d ) s . 1000 , e ) s . 920 | b | divide(400, multiply(divide(5, const_100), 10)) | divide(n1,const_100)|multiply(n0,#0)|divide(n2,#1)| | gain |
a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 26 m * 2 m * 0.75 m ? | "26 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 26 = 1 / 1000 * x = > x = 26000 answer : d" | a ) 29798 , b ) 27908 , c ) 78902 , d ) 26000 , e ) 27991 | d | divide(divide(divide(multiply(multiply(multiply(26, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5) | multiply(n3,const_100)|multiply(n4,const_100)|multiply(n5,const_100)|multiply(#0,#1)|multiply(#3,#2)|divide(#4,n0)|divide(#5,n1)|divide(#6,n2)| | physics |
the product of two successive numbers is 462 . which is the smaller of the two numbers ? | a 21 from the given alternatives , 21 Γ 22 = 462 β΄ smaller number = 21 | a ) 21 , b ) 23 , c ) 26 , d ) 27 , e ) 29 | a | sqrt(462) | sqrt(n0) | general |
in a group of ducks and cows , the total number of legs are 30 more than twice the number of heads . find the total number of cows . | "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 30 + 2 ( c + d ) = > d + 2 c = 15 + c + d = > 2 c = 15 + c = > c = 15 i . e . , total... | a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20 | b | divide(30, const_2) | divide(n0,const_2)| | general |
two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is ? | "explanation : let the length of each train is x meter distance will be x + x = 2 x relative speed = 46 - 36 = 10 km / hr = 10 * ( 5 / 18 ) = 25 / 9 m / sec distance = speed * time 2 x = 25 / 9 β 36 2 x = 100 = > x = 50 so length of both the trains are 50 meters option c" | a ) 40 meter , b ) 45 meter , c ) 50 meter , d ) 55 meter , e ) none of these | c | divide(multiply(divide(multiply(subtract(46, 36), const_1000), const_3600), 36), const_2) | subtract(n0,n1)|multiply(#0,const_1000)|divide(#1,const_3600)|multiply(n2,#2)|divide(#3,const_2)| | general |
if a ' s height is 25 % less than that of b , how much percent b ' s height is more than that of a ? | "excess of b ' s height over a ' s = [ ( 25 / ( 100 - 25 ) ] x 100 % = 33.33 % answer : d )" | a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 33.33 % , e ) 66.65 % | d | multiply(divide(25, subtract(const_100, 25)), const_100) | subtract(const_100,n0)|divide(n0,#0)|multiply(#1,const_100)| | general |
the tax on a commodity is diminished by 24 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ? | "100 * 100 = 10000 76 * 112 = 8512 10000 - - - - - - - 1488 100 - - - - - - - ? = 15 % answer : c" | a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 % | c | subtract(const_100, divide(multiply(add(const_100, 12), subtract(const_100, 24)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | general |
a and b can do a piece of work in 6 2 / 3 days and 5 days respectively . they work together for 2 days and then a leaves . in how many days after that b will complete the work alone . | "explanation : 3 / 20 * 2 + ( 2 + x ) / 5 = 1 x = 1 Γ’ Β½ days answer : b" | a ) 6 Γ’ Β½ days , b ) 1 Γ’ Β½ days , c ) 8 Γ’ Β½ days , d ) 5 Γ’ Β½ days , e ) 2 Γ’ Β½ days | b | multiply(5, subtract(2, add(inverse(5), inverse(add(6, divide(2, 3)))))) | divide(n1,n2)|inverse(n3)|add(#0,n0)|inverse(#2)|add(#1,#3)|subtract(n4,#4)|multiply(n3,#5)| | physics |
convert the 13 / 48 m / s into kilometers per hour ? | "13 / 48 m / s = 13 / 48 * 18 / 5 = 49 / 50 = 0.98 kmph . answer : e" | a ) 1.5 kmph . , b ) 0.91 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 0.98 kmph . | e | multiply(const_3_6, divide(13, 48)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics |
the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ? | "let bresdth x cm length = 2 x cm new l = ( 2 x - 5 ) cm new breadth = ( x + 5 ) new area = ( 2 x - 5 ) sq cm = ( 2 x - 5 ) ( x + 5 ) = 2 x 2 + 75 x = 20 cm l = 2 x - 2 = 2 * 20 = 40 cm answer c" | a ) 18 cm , b ) 16 cm , c ) 40 cm , d ) 20 cm , e ) 50 cm | c | divide(const_100, const_3) | divide(const_100,const_3)| | geometry |
there is a total of 90 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 6 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ? | "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 30 / 30 - 5 / 30 - 6 / 30 = 19 / 30 the answer is d ." | a ) 3 / 5 , b ) 7 / 15 , c ) 11 / 15 , d ) 19 / 30 , e ) 23 / 30 | d | subtract(1, add(divide(1, 6), divide(1, 5))) | divide(n1,n2)|divide(n3,n4)|add(#0,#1)|subtract(n1,#2)| | general |
what is the average of first 21 multiples of 7 ? | "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 7 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 77 c" | a ) 67 , b ) 69 , c ) 77 , d ) 79 , e ) 81 | c | multiply(divide(divide(multiply(21, add(21, const_1)), const_2), 21), 7) | add(n0,const_1)|multiply(n0,#0)|divide(#1,const_2)|divide(#2,n0)|multiply(n1,#3)| | general |
uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 14 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ? | "answer is d . x / x + 36 = 1 / 5 x = 9 14 - 9 = 5" | a ) 3 , b ) 6 , c ) 7.2 , d ) 5 , e ) 9 | d | multiply(divide(20, const_100), 20) | divide(n2,const_100)|multiply(n2,#0)| | gain |
at 6 β² o a clock ticks 6 times . the time between first and last ticks is 25 seconds . how long does it tick at 12 β² o clock | "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 25 / 5 = 5 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 Γ 5 = 55 secs . answer : b" | a ) 47 , b ) 55 , c ) 28 , d ) 66 , e ) 11 | b | multiply(divide(25, subtract(6, const_1)), subtract(12, const_1)) | subtract(n0,const_1)|subtract(n3,const_1)|divide(n2,#0)|multiply(#2,#1)| | physics |
a number is said to be prime saturated if the product of all the different positive prime factors of q is less than the square root of q . what is the greatest two digit prime saturated integer ? | "q 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ." | a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95 | d | add(multiply(const_2, const_3), subtract(const_100, const_10)) | multiply(const_2,const_3)|subtract(const_100,const_10)|add(#0,#1)| | other |
two men a and b start from place x walking at 4 Β½ kmph and 5 ΒΎ kmph respectively . how many km apart they are at the end of 2 Β½ hours if they are walking in the same direction ? | "rs = 5 ΒΎ - 4 Β½ = 1 ΒΌ t = 2 Β½ h . d = 5 / 4 * 5 / 2 = 25 / 8 = 3 1 / 8 km answer : c" | a ) 7 km , b ) 6 km , c ) 3 1 / 8 km , d ) 9 km , e ) 5 km | c | add(multiply(add(2, divide(const_1, const_2)), subtract(add(5, divide(const_3, 4)), add(4, divide(const_1, const_2)))), const_2) | divide(const_1,const_2)|divide(const_3,n0)|add(n2,#0)|add(n1,#1)|add(n0,#0)|subtract(#3,#4)|multiply(#2,#5)|add(#6,const_2)| | physics |
if an object travels at 85 feet per second , how many feet does it travel in 30 minutes ? | "if an object travels at 85 feet per second it covers 85 x 60 feet in one minute , and 5 x 60 x 30 feet in 30 minutes . answer = 9000 answer : d" | a ) 3000 , b ) 1500 , c ) 1800 , d ) 9000 , e ) 2500 | d | multiply(multiply(const_3, const_60), const_60) | multiply(const_3,const_60)|multiply(#0,const_60)| | physics |
if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is : | "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a" | a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km | a | multiply(10, divide(20, subtract(14, 10))) | subtract(n0,n1)|divide(n2,#0)|multiply(n1,#1)| | general |
in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the compet... | "53900 = 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 7 times . the answer is a ." | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | a | floor(sqrt(divide(53900, multiply(multiply(multiply(11, 7), 5), 2)))) | multiply(n0,n1)|multiply(n2,#0)|multiply(n3,#1)|divide(n4,#2)|sqrt(#3)|floor(#4)| | general |
300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 15 % of the customers t... | "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 15 % = 27 responded as satisfied , so remaining satisfied are 120 - 27 = 93 so 93 is what percentage of 300 - 31 % so the answer should be a" | a ) 31 , b ) 25 , c ) 35 , d ) 45 , e ) 75 | a | multiply(divide(subtract(multiply(divide(40, 100), 300), multiply(divide(15, 100), multiply(300, divide(60, 100)))), 300), 100) | divide(n3,n2)|divide(n4,n2)|divide(n1,n2)|multiply(n0,#0)|multiply(n0,#2)|multiply(#1,#4)|subtract(#3,#5)|divide(#6,n0)|multiply(#7,n2)| | general |
the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 62 kg . what is the correct weight ? | "actual total weight is ( 20 x 58.4 - 56 + 62 ) = 1174 kgs actual average weight is 1174 / 20 = 58.7 kgs c" | a ) 58 kgs , b ) 58.85 kgs , c ) 58.7 kgs , d ) 59 kgs , e ) 59.85 kgs | c | divide(add(multiply(58.4, 20), subtract(62, 56)), 20) | multiply(n0,n1)|subtract(n3,n2)|add(#0,#1)|divide(#2,n0)| | general |
34 men can complete a piece of work in 18 days . in how many days will 17 men complete the same work ? | "explanation : let the required number of days be a . then , less men , more days ( indirect proportion ) 17 : 34 : : 18 : a 17 x a = 34 x 18 a = ( 34 x 18 ) / 17 a = 36 answer : a" | a ) 36 , b ) 26 , c ) 97 , d ) 26 , e ) 19 | a | divide(multiply(18, 34), 17) | multiply(n0,n1)|divide(#0,n2)| | physics |
the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ? | "b 80 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg ." | a ) 56 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these | b | add(multiply(8, 2.5), 60) | multiply(n0,n1)|add(n2,#0)| | general |
the perimeter of one square is 48 cm and that of another is 24 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ? | "4 a = 48 4 a = 24 a = 12 a = 6 a 2 = 144 a 2 = 36 combined area = a 2 = 180 = > a = 13.4 d = 13.4 β 2 answer : c" | a ) 13 β 4 , b ) 13 β 2 , c ) 13.4 β 2 , d ) 12 β 4 , e ) 13 β 9 | c | sqrt(multiply(add(power(divide(48, const_4), const_2), power(divide(24, const_4), const_2)), const_2)) | divide(n0,const_4)|divide(n1,const_4)|power(#0,const_2)|power(#1,const_2)|add(#2,#3)|multiply(#4,const_2)|sqrt(#5)| | geometry |
if a certain number when divided by the numbers 5 , 32 one after other successively , leaves a remainder 0 , 21 then what will be the remainders if it is divided by the numbers 2 , 35 | the number is 35 , when divided by 5 , 32 leaves remainder 0 , 21 respectively . so if 35 is divided by 2 , 35 leaves remainder 1 , 20 respectively . answer : a | a ) 1 , 20 , b ) 1 , 21 , c ) 1 , 22 , d ) 1 , 23 , e ) 1 , 24 | a | reminder(multiply(5, 21), 2) | multiply(n0,n3)|reminder(#0,n4) | general |
p and q invested in a business . the profit earned was divided in the ratio 2 : 3 . if p invested rs 30000 , the amount invested by q is | "let the amount invested by q = q 30000 : q = 2 : 3 β 30000 Γ 3 = 2 q β q = ( 30000 Γ 3 ) / 2 = 45000 answer is c ." | a ) 30000 , b ) 50000 , c ) 45000 , d ) 20000 , e ) 60000 | c | multiply(divide(30000, 2), 3) | divide(n2,n0)|multiply(n1,#0)| | gain |
the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number q ? | ( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = q answer : b | a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160 | b | divide(30, subtract(add(const_1, divide(12.5, const_100)), subtract(const_1, divide(25, const_100)))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|subtract(#2,#3)|divide(n2,#4) | general |
a man is 30 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ? | "let present age of the son = x years then , present age the man = ( x + 30 ) years given that , in 2 years , man ' s age will be twice the age of his son Γ’ β‘ β ( x + 30 ) + 2 = 2 ( x + 2 ) Γ’ β‘ β x = 28 answer : b" | a ) 23 years , b ) 28 years , c ) 21 years , d ) 20 years , e ) 19 years | b | divide(subtract(30, 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 |
what is the value of ( 4 ) ^ - 6 ? | "4 ^ - 6 = 1 / ( 4 ) ^ 6 = 1 / 4096 answer : e" | a ) 1 / 1008 , b ) 1 / 6400 , c ) 1 / 6550 , d ) 1 / 6660 , e ) 1 / 4096 | e | 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 |
machine x takes 60 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce | machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to s... | a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 3 | e | divide(1080, multiply(divide(60, const_10), 60)) | divide(n0,const_10)|multiply(n0,#0)|divide(n1,#1) | general |
the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam . | "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 10 x = > x = 35 . answer : b" | a ) 22 , b ) 35 , c ) 25 , d ) 99 , e ) 21 | b | divide(subtract(multiply(90, 5), multiply(5, 20)), subtract(90, 80)) | multiply(n1,n3)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)| | general |
a train running at the speed of 52 km / hr crosses a pole in 9 seconds . find the length of the train ? | "speed = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec length of train ( distance ) = speed * time ( 130 / 9 ) * 9 = 130 meter answer : a" | a ) 130 , b ) 272 , c ) 278 , d ) 277 , e ) 112 | a | multiply(divide(multiply(52, const_1000), const_3600), 9) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
what is the remainder when 1234 * 6789 * 1111 is divided by 19 | "12345 / 19 = = > remainder = 14 678910 / 19 = = > remainder = 2 111111 / 19 = = > remainder = 18 = 14 * 2 * 18 = 504 / 19 = = > remainder = 10 answer : d" | a ) 15 , b ) 23 , c ) 7 , d ) 10 , e ) 43 | d | reminder(multiply(6789, 1234), 1111) | multiply(n0,n1)|reminder(#0,n2)| | general |
how many 1 / 4 s are there in 37 1 / 2 ? | "required number = ( 75 / 2 ) / ( 1 / 4 ) = ( 75 / 2 x 4 / 1 ) = 150 . answer : a" | a ) 150 , b ) 450 , c ) 500 , d ) 650 , e ) 700 | a | divide(add(37, divide(1, 2)), divide(1, 4)) | divide(n0,n4)|divide(n0,n1)|add(n2,#0)|divide(#2,#1)| | general |
if x : y = 2 : 9 , find the value of ( 2 x + 2 y ) : ( 5 x β y ) | "explanation : given : x / y = 2 / 9 ( 2 x + 2 y ) : ( 5 x β y ) = ( 2 * 2 + 2 * 9 ) : ( 5 * 2 β 9 ) = 22 : 1 answer : a" | a ) 22 : 1 , b ) 22 : 3 , c ) 7 : 1 , d ) 5 : 3 , e ) 8 : 1 | a | divide(add(power(2, const_2.0), 2), add(add(2, 9), 2)) | add(const_4.0,n1)|power(n2,n3)|add(n3,#1)|add(n3,#0)|divide(#2,#3)| | general |
for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 8 , what are the odds of it burning out during ... | "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 8 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 8 = 7 / 8 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 7 / 8 = 4 / 9 - - - > p ( of burning ... | a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3 | c | multiply(subtract(1, divide(1, 8)), subtract(1, divide(subtract(1, divide(const_2.0, 8)), 1))) | divide(n3,n4)|subtract(n6,#0)|divide(#1,const_2.0)|subtract(n6,#2)|multiply(#1,#3)| | general |
a train 360 m long is running at a speed of 90 km / hr . in what time will it pass a bridge 140 m long ? | "speed = 90 * 5 / 18 = 25 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 25 = 20 sec answer : d" | a ) 40 sec , b ) 29 sec , c ) 26 sec , d ) 20 sec , e ) 34 sec | d | divide(360, multiply(subtract(90, 140), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
the sale price sarees listed for rs . 200 after successive discount is 20 % and 5 % is ? | "200 * ( 80 / 100 ) * ( 95 / 100 ) = 152 answer : c" | a ) 187 , b ) 169 , c ) 152 , d ) 178 , e ) 175 | c | subtract(subtract(200, divide(multiply(200, 20), const_100)), divide(multiply(subtract(200, divide(multiply(200, 20), const_100)), 5), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | gain |
the radius of the base of cone is 3 cm and height is 4 cm . find the volume of the cone ? | 1 / 3 * Ο * 3 * 3 * 4 = 12 Ο answer : a | ['a ) 12', 'b ) 75', 'c ) 97', 'd ) 15', 'e ) 91'] | a | rectangle_area(3, 4) | rectangle_area(n0,n1) | geometry |
bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy β s average speed . how many minutes does ben spend on his round trip ? | bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy β s average speed . how many minutes does ben spend on his round trip ? average speed = total distance / total time we know the t... | a ) 40 , b ) 80 , c ) 120 , d ) 160 , e ) 180 | d | multiply(divide(subtract(15, 5), divide(divide(15, const_2), const_2)), const_60) | divide(n1,const_2)|subtract(n1,n0)|divide(#0,const_2)|divide(#1,#2)|multiply(#3,const_60) | physics |
the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ? | "x - y = 1365 divide larger number by the smaller , we get 6 as quotient and the 15 as remainder x / y = 6 quotient and 15 reminder convert this as x = 6 y + 15 apply this x in above eqn therefore , 6 y + 15 - y = 1365 5 y + 15 = 1365 y + 3 = 273 y = 270 answer : b" | a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 260 | b | divide(add(1365, 15), subtract(6, const_1)) | add(n0,n2)|subtract(n1,const_1)|divide(#0,#1)| | general |
running at the same constant rate , 4 identical machines can produce a total of 16 bottles per minute . at this rate , how many bottles could 8 such machines produce in 3 minutes ? | "let ' s take the approach that uses the answer choices to eliminate wasted time . 16 / 4 = 4 . 8 machines = 32 per minute . 3 minutes worth = 96 bottles . looking at the answers it is clear . . . we can only choose ( c ) the correct answer is c ." | a ) 11 , b ) 92 , c ) 96 , d ) 174 , e ) 115 | c | multiply(multiply(divide(16, 4), 3), 8) | divide(n1,n0)|multiply(n3,#0)|multiply(n2,#1)| | gain |
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 12 , the how old is b ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 12 5 x = 10 x = 2 . hence , b ' s age = 2 x = 4 years . b )" | a ) 10 years , b ) 4 years , c ) 6 years , d ) 15 years , e ) 16 years | b | divide(multiply(subtract(12, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | general |
how many digits are required to number a book containing 300 pages ? | "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 300 - ( 90 + 9 ) = 201 pages will require 201 * 3 = 603 digits . the total number of digits is 9 + 180 + 603 = 792 . the answer is a ." | a ) 792 , b ) 684 , c ) 492 , d ) 372 , e ) 340 | a | add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(300, const_100), const_1), const_3)) | subtract(const_10,const_1)|subtract(n0,const_100)|add(#1,const_1)|multiply(#0,const_10)|multiply(#3,const_2)|multiply(#2,const_3)|add(#4,#0)|add(#6,#5)| | general |
natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 4 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ? | "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 4 km / hour x / 3 = 4 x = 12 km the average speed while climbing = distance / time... | a ) 2 , b ) 2.5 , c ) 3 , d ) 3.25 , e ) 3.5 | c | divide(divide(multiply(add(4, 2), 4), 2), 4) | add(n0,n1)|multiply(n2,#0)|divide(#1,n1)|divide(#2,n0)| | physics |
there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 36 , then find the smaller number ? | "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 36 3 x = 36 = > x = 12 = > smaller number = 5 x = 60 . answer : d" | a ) 25 , b ) 66 , c ) 77 , d ) 60 , e ) 44 | d | divide(multiply(36, 5), const_4) | multiply(n0,n2)|divide(#0,const_4)| | other |
if x = 1 - q and y = 2 q + 1 , then for what value of q , x is equal to y ? | explanation : x = y < = > 1 - q = 2 q + 1 < = > 3 q = 0 < = > q = 0 . answer : a | a ) 0 , b ) 1 , c ) - 1 , d ) - 2 , e ) 3 | a | add(1, subtract(1, 1)) | subtract(n0,n0)|add(n0,#0) | general |
if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 2 / 3 : 3 / 4 , then the third part is ? | given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 8 : 9 1 st part = 782 * 9 / 23 = rs . 306 . answer : b | a ) a ) 426 , b ) b ) 306 , c ) c ) 207 , d ) d ) 204 , e ) e ) 297 | b | add(add(const_100, 2), multiply(divide(multiply(const_2, const_3), add(add(add(multiply(const_2, const_3), 3), add(multiply(const_2, const_3), 2)), multiply(const_2, const_3))), 782)) | add(n3,const_100)|multiply(const_2,const_3)|add(n1,#1)|add(n3,#1)|add(#2,#3)|add(#4,#1)|divide(#1,#5)|multiply(n0,#6)|add(#0,#7) | general |
at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.65 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ? | "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ ... | a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,124 , e ) 2,628 | e | multiply(divide(250, 22.95), 250) | divide(n6,n5)|multiply(n4,#0)| | general |
a start walking from a place at a uniform speed of 5 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b . | "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 5 + 5 / 9 = 5.55 answer b" | a ) 4.7 kmph , b ) 5.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph | b | add(divide(1, divide(add(const_60, 48), const_60)), 5) | add(n2,const_60)|divide(#0,const_60)|divide(n1,#1)|add(n0,#2)| | physics |
the length of the bridge , which a train 110 m long and traveling at 45 km / hr can cross in 30 sec is ? | "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 110 + x ) / 30 = 25 / 2 x = 265 m . answer : e" | a ) 377 , b ) 367 , c ) 237 , d ) 245 , e ) 265 | e | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 110) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | physics |
a jar contains only red , yellow , and orange marbles . if there are 3 red , 7 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? | "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 5 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so... | a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22 | e | divide(multiply(choose(7, 2), choose(3, 1)), choose(add(add(7, 4), 3), 3)) | add(n1,n2)|choose(n1,n4)|choose(n0,n5)|add(n0,#0)|multiply(#1,#2)|choose(#3,n0)|divide(#4,#5)| | probability |
if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 49 ) which of these integers could be the value of z ? | "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( β which of these integers β¦ β ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 49 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 50 incorrect c . 2 / 2 = 2 / 3 + 2 / 51 incorrect d . 2 / 3 ... | a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 7 | e | divide(49, add(add(2, 2), 1)) | add(n0,n0)|add(n2,#0)|divide(n4,#1)| | general |
a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 35,000 , what will be the amount a receives ? | "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 β 3 x + 14000 = 50000 β 3 x = 50000 β 14000 = 36000 β x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 inves... | a ) 14700 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000 | a | multiply(add(divide(subtract(multiply(5000, const_10), add(add(4000, 5000), 5000)), const_3), add(4000, 5000)), divide(multiply(multiply(const_3, const_12), const_1000), multiply(5000, const_10))) | add(n1,n2)|multiply(n2,const_10)|multiply(const_12,const_3)|add(n2,#0)|multiply(#2,const_1000)|divide(#4,#1)|subtract(#1,#3)|divide(#6,const_3)|add(#0,#7)|multiply(#8,#5)| | general |
if t = 5 / 9 * ( k - 32 ) , and if t = 75 , then what is the value of k ? | k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 75 ) / 5 + 32 = 167 the answer is d . | a ) 158 , b ) 161 , c ) 164 , d ) 167 , e ) 170 | d | add(divide(multiply(75, 9), 5), 32) | multiply(n1,n3)|divide(#0,n0)|add(n2,#1) | general |
( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = | "( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 450 / 5 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : c" | a ) 99 , b ) 9.9 , c ) 990 , d ) 0.99 , e ) 0.099 | c | divide(multiply(0.0077, 4.5), multiply(multiply(0.05, 0.1), 0.007)) | multiply(n0,n1)|multiply(n2,n3)|multiply(n4,#1)|divide(#0,#2)| | general |
if the wheel is 14 cm then the number of revolutions to cover a distance of 2904 cm is ? | "2 * 22 / 7 * 14 * x = 2904 = > x = 33 answer : b" | a ) 22 , b ) 33 , c ) 17 , d ) 12 , e ) 88 | b | divide(2904, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14)) | multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)| | physics |
jerry went to a shop and bought things worth rs . 25 , out of which 30 $ went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ? | "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 $ is given as tax = > total tax incurred = 30 $ = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % β΄ ( 25 β 30 / 100 β x ) 6 / 100 = 30 / 100 β 6 ( 25 β 0.3 β x ) = 30 β ( 25 β 0.3 β x ) = 5 β x = 25 β 0.3 ... | a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 21.7 | b | subtract(25, add(multiply(divide(30, const_100), divide(const_100, 6)), divide(30, const_100))) | divide(n1,const_100)|divide(const_100,n2)|multiply(#0,#1)|add(#0,#2)|subtract(n0,#3)| | gain |
the average age of a class of 25 students is 19 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ? | "if age of the teacher was 19 , average would not have changed . since average increased by 2 , age of the teacher = 25 + 22 Γ 1 = 47 answer : c" | a ) 40 years , b ) 41 years , c ) 47 years , d ) 43 years , e ) 44 years | c | subtract(multiply(add(25, 2), add(19, 2)), multiply(25, 19)) | add(n0,n2)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
two spherical balls lie on the ground touching . if one of the balls has a radius of 6 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ? | "a straight line will join the two centers and the point of contact , thus making similar triangles . 4 / 6 = ( r - 10 ) / r 4 r = 6 r - 60 r = 30 the answer is e ." | a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 30 | e | add(add(6, 10), 6) | add(n0,n1)|add(#0,n0)| | physics |
of 70 players on a football team , 40 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? | "total = 70 thrower = 40 rest = 70 - 40 = 30 left handed = 30 / 3 = 10 right handed = 20 if all throwe 0 r are right handed then total right handed is 40 + 20 = 60 so c . 60 is the right answer" | a ) 54 , b ) 59 , c ) 60 , d ) 71 , e ) 92 | c | add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 40)), 40) | divide(const_1,const_3)|subtract(n0,n1)|subtract(const_1,#0)|multiply(#2,#1)|add(n1,#3)| | general |
of the 13 employees in a certain department , 1 has an annual salary of 38000 , 2 have an annual salary of 45700 each , 2 have an annual salary of 42500 each , 3 have an annual salary of 40000 each and 5 have an annual salary of 48500 each . what is the median annual salary for the 13 employees ? | median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.7 so , answer is d . | a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,700 , e ) 48,500 | d | multiply(42500, const_1) | multiply(n6,const_1) | general |
average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ? | "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 650 x 3 rs . = 990 rs . correct option : c" | a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none | c | subtract(multiply(735, 4), multiply(650, subtract(4, const_1))) | multiply(n0,n1)|subtract(n0,const_1)|multiply(n2,#1)|subtract(#0,#2)| | general |
a car travels a certain distance taking 7 hrs in forward journey , during the return journey increased speed 12 km / hr takes the times 5 hrs . what is the distance traveled | if x is the distance , then difference in speeds = x / 5 - x / 7 = 12 2 x / 35 = 12 x = 12 * 35 / 2 = 210 kms . answer : a | a ) 210 kms , b ) 30 kms , c ) 20 kms , d ) 40 kms , e ) none of these | a | multiply(divide(multiply(12, 5), subtract(7, 5)), 7) | multiply(n1,n2)|subtract(n0,n2)|divide(#0,#1)|multiply(n0,#2) | general |
a searchlight on top of the watch - tower makes 1 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 20 seconds ? | "1 revolutions per minute = 1 revolution every 60 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 60 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 20 seconds ) = 1 - p ( man in dark for max of 20 seconds ) = ... | a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4 | b | subtract(const_1, divide(20, divide(multiply(const_60, const_1), 1))) | multiply(const_1,const_60)|divide(#0,n0)|divide(n1,#1)|subtract(const_1,#2)| | physics |
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