Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 164 | correct stringclasses 5 values | annotated_formula stringlengths 7 1.65k | linear_formula stringlengths 8 925 | category stringclasses 6 values | answer stringclasses 5 values |
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find a two digit number , given that the sum of the digits is 12 and the difference of the digits is 2 . ? | "using elimination method find which of the options fit the description of the number . . . from the option only 75 meets this description sum of digits - - - 7 + 5 = 12 difference of digits - - - 7 - 5 = 2 answer c ." | a ) 66 , b ) 87 , c ) 75 , d ) 88 , e ) 90 | c | multiply(multiply(2, 2), add(2, const_4)) | add(n1,const_4)|multiply(n1,n1)|multiply(#0,#1)| | general | C |
if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 160 , what is the value of a β c ? | "( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 220 - 320 = = = > a + b - b - c = - 100 = = = > a - c = - 100 answer : b" | a ) β 220 , b ) β 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given | b | subtract(multiply(const_60.0, const_2), multiply(110, const_2)) | multiply(const_60.0,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | general | B |
a train covers a distance of 12 km in 5 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the train = 40 * 6 = 240 m . answer : c" | a ) 120 m , b ) 180 m , c ) 240 m , d ) 220 m , e ) 280 m | c | divide(12, subtract(divide(12, 5), 6)) | divide(n0,n1)|subtract(#0,n2)|divide(n0,#1)| | physics | C |
the average age of 30 students in a class is 10 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ? | "total age of 50 students = 30 * 10 = 300 total age of 51 persons = 31 * 11 = 341 age of teacher = 341 - 300 = 41 years answer is d" | a ) 59 , b ) 55 , c ) 61 , d ) 41 , e ) 36 | d | subtract(add(add(multiply(30, 10), 1), 30), multiply(30, 10)) | multiply(n0,n1)|add(n2,#0)|add(n0,#1)|subtract(#2,#0)| | general | D |
the wages earned by robin is 50 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ? | "let wage of erica = 10 wage of robin = 1.5 * 10 = 15 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 15 ) / 15 * 100 % = 1 / 15 * 100 % = 7 % answer e" | a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 50 % , e ) 7 % | e | multiply(divide(subtract(add(const_100, 60), add(const_100, 50)), add(const_100, 50)), const_100) | add(n1,const_100)|add(n0,const_100)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)| | general | E |
if ( n + 2 ) ! / n ! = 156 , n = ? | "( n + 2 ) ! / n ! = 156 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 156 from here , we might just test the answer choices . since ( 13 ) ( 12 ) = 156 , we can see that n = 11 d" | a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | d | subtract(add(const_4, const_4), const_1) | add(const_4,const_4)|subtract(#0,const_1)| | general | D |
a number increased by 10 % gives 660 . the number is ? | "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 10 % = 110 % 110 % - - - - - - - > 660 ( 110 Γ£ β 6 = 660 ) 100 % - - - - - - - > 600 ( 100 Γ£ β 6 = 600 ) option ' d '" | a ) 200 , b ) 300 , c ) 500 , d ) 600 , e ) 400 | d | divide(660, add(const_1, divide(10, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | gain | D |
a military camp has a food reserve for 250 personnel for 40 days . if after 15 days 50 more personnel are added to the camp , find the number of days the reserve will last for ? | explanation : as the camp has a reserve for 250 personnel that can last for 40 days , after 10 days the reserve left for 250 personnel is for 30 days . now 50 more personnel are added in the camp . hence , the food reserve for 300 personnel will last for : 250 : 300 : : x : 30 β¦ β¦ . . ( it is an indirect proportion as less men means more days ) x = ( 250 * 30 ) / 300 x = 25 days answer : a | a ) 25 , b ) 67 , c ) 26 , d ) 29 , e ) 18 | a | add(divide(multiply(250, subtract(40, 15)), add(250, 50)), const_3) | add(n0,n3)|subtract(n1,n2)|multiply(n0,#1)|divide(#2,#0)|add(#3,const_3) | general | A |
in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 12 to the thrice of the remainder . the dividend is | "divisor = ( 6 * 3 ) + 12 = 30 5 * quotient = 30 quotient = 6 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 6 ) + 6 = 126 . d )" | a ) 74 , b ) 78 , c ) 86 , d ) 126 , e ) 98 | d | add(multiply(add(multiply(6, const_3), 12), divide(add(multiply(6, const_3), 12), 5)), 6) | multiply(n0,const_3)|add(n2,#0)|divide(#1,n1)|multiply(#1,#2)|add(n0,#3)| | general | D |
if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 6 have ? | ", p ^ 2 , p ^ 3 and q , q ^ 1 , q ^ 2 . . . . q ^ 6 together essentially there are 18 different combinations you can make ( 3 x 6 ) also you have to include the different combinations the p and q exponents can be a divisor . there are 3 different p exponents and 6 different q exponents : p , p ^ 2 , p ^ 3 , q , q ^ 2 , q ^ 3 . . . q ^ 6 also add 1 since ` ` 1 ' ' can also be a divisor . 18 + 3 + 6 + 1 = 28 , answer : d" | a ) 9 , b ) 12 , c ) 18 , d ) 28 , e ) 363 | d | multiply(add(3, const_1), add(6, const_1)) | add(n0,const_1)|add(n1,const_1)|multiply(#0,#1)| | general | D |
if the sum of two numbers is 30 and the sum of their squares is 840 , then the product of the numbers is | sol . let the numbers be x and y . then , ( x + y ) = 30 and x 2 + y 2 = 840 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 30 ) 2 - 840 = 900 - 840 = 60 xy = 30 . answer e | a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 30 | e | divide(subtract(power(30, const_2), 840), const_2) | power(n0,const_2)|subtract(#0,n1)|divide(#1,const_2) | general | E |
the first year , two cows produced 8100 litres of milk . the second year their production increased by 15 % and 10 % respectively , and the total amount of milk increased to 9100 litres a year . how many litres were milked from each cow each year ? | let x be the amount of milk the first cow produced during the first year . then the second cow produced ( 8100 β x ) ( 8100 β x ) litres of milk that year . the second year , each cow produced the same amount of milk as they did the first year plus the increase of 15 % 15 % or 10 % 10 % . so 8100 + 15100 β
x + 10100 β
( 8100 β x ) = 91008100 + 15100 β
x + 10100 β
( 8100 β x ) = 9100 therefore 8100 + 320 x + 110 ( 8100 β x ) = 91008100 + 320 x + 110 ( 8100 β x ) = 9100 120 x = 190120 x = 190 x = 3800 x = 3800 therefore , the cows produced 3800 and 4300 litres of milk the first year , and 4370 and 4730 litres of milk the second year , respectively . answer : c | a ) 3472 , b ) 8222 , c ) 4370 , d ) 26777 , e ) 8222 | c | subtract(8100, divide(subtract(9100, multiply(add(const_1, divide(10, const_100)), 8100)), subtract(add(const_1, divide(15, const_100)), add(const_1, divide(10, const_100))))) | divide(n2,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(n0,#2)|subtract(#3,#2)|subtract(n3,#4)|divide(#6,#5)|subtract(n0,#7) | general | C |
the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ? | "a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 7 / 4 ) * 4 = 1 / 7 the answer is a ." | a ) 1 / 7 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2 | a | multiply(divide(subtract(const_100, 80), add(const_100, 75)), divide(5, 4)) | add(n2,const_100)|divide(n1,n0)|subtract(const_100,n3)|divide(#2,#0)|multiply(#3,#1)| | general | A |
how many seconds will a train 110 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ? | "d = 110 + 150 = 260 s = 36 * 5 / 18 = 10 mps t = 260 / 10 = 26 sec e" | a ) 28 sec , b ) 23 sec , c ) 24 sec , d ) 25 sec , e ) 26 sec | e | divide(add(150, 110), multiply(36, const_0_2778)) | add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1)| | physics | E |
in traveling from a dormitory to a certain city , a student went 1 / 2 of the way by foot , 1 / 4 of the way by bus , and the remaining 6 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ? | "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 1 / 4 x + 6 x - 1 / 2 x - 1 / 4 x = 6 x = 24 km option : d" | a ) 35 , b ) 24 , c ) 14 , d ) 24 , e ) 12 | d | multiply(6, inverse(subtract(1, add(divide(1, 2), divide(1, 4))))) | divide(n0,n1)|divide(n2,n3)|add(#0,#1)|subtract(n0,#2)|inverse(#3)|multiply(n4,#4)| | physics | D |
the average ( arithmetic mean ) of 4 different integers is 74 . if the largest integer is 90 , what is the least possible value of the smallest integer ? | "total of integers = 74 * 4 = 296 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 296 - ( 90 + 89 + 88 ) = 296 - 267 = 29 answer : c" | a ) 1 , b ) 19 , c ) 29 , d ) 30 , e ) 33 | c | subtract(subtract(subtract(multiply(74, 4), 90), subtract(90, const_1)), subtract(90, const_2)) | multiply(n0,n1)|subtract(n2,const_1)|subtract(n2,const_2)|subtract(#0,n2)|subtract(#3,#1)|subtract(#4,#2)| | general | C |
the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.4 kg . the weight of the new student is | "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.4 weight of the new student = ( 30 * 27.4 β 29 * 28 ) = 822 - 812 = 10 answer : d" | a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 10 kg , e ) none of these | d | subtract(multiply(add(29, const_1), 27.4), multiply(29, 28)) | add(n0,const_1)|multiply(n0,n1)|multiply(n2,#0)|subtract(#2,#1)| | general | D |
there were two candidates in an election . winner candidate received 62 % of votes and won the election by 324 votes . find the number of votes casted to the winning candidate ? | "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 324 62 % - - - - - - - - ? = > 837 answer : b" | a ) 456 , b ) 837 , c ) 912 , d ) 1200 , e ) 1400 | b | divide(multiply(divide(324, divide(subtract(62, subtract(const_100, 62)), const_100)), 62), const_100) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)| | gain | B |
you buy a piece of land with an area of β 900 , how long is one side of the land plot ? | try filling the numbers into the answer y x y = find the closest to 900 . answer c | ['a ) 28', 'b ) 29', 'c ) 30', 'd ) 31', 'e ) 32'] | c | sqrt(900) | sqrt(n0) | geometry | C |
having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.96 at the candy store . what is john β s weekly allowance ? | "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 96 4 x / 15 = 96 x = $ 3.60 = $ 3.60 the answer is d ." | a ) $ 3.00 , b ) $ 3.20 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 3.80 | d | divide(0.96, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5)))))) | divide(n0,n1)|divide(const_1,n0)|subtract(const_1,#0)|multiply(#1,#2)|add(#0,#3)|subtract(const_1,#4)|divide(n2,#5)| | general | D |
the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 294 . what is the rate of interest per annum ? | "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 294 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 294 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 294 r 2 = ( 294 * 2 ) / 3 = 196 = > r = 14 rate = 14 % answer : option d" | a ) 18 , b ) 12 , c ) 9 , d ) 14 , e ) 16 | d | sqrt(294) | sqrt(n2)| | gain | D |
the difference between simple interest and compound interest on rs . 1200 for one year at 10 % per annum reckoned half - yearly is : | s . i = ( 1000 * 10 * 4 ) / 100 = rs . 400 c . i = 1200 * 1 + 5 / 100 ) 2 β 1200 = 123 . difference = rs . ( 123 - 120 ) = rs . 3 answer : b | a ) rs . 2.50 , b ) rs . 3 , c ) rs . 3.75 , d ) rs . 4 , e ) rs . 5 | b | subtract(subtract(multiply(power(add(divide(divide(10, const_2), const_100), const_1), const_2), 1200), 1200), divide(multiply(1200, 10), const_100)) | divide(n1,const_2)|multiply(n0,n1)|divide(#0,const_100)|divide(#1,const_100)|add(#2,const_1)|power(#4,const_2)|multiply(n0,#5)|subtract(#6,n0)|subtract(#7,#3) | gain | B |
find the area of a parallelogram with base 30 cm and height 12 cm ? | "area of a parallelogram = base * height = 30 * 12 = 360 cm 2 answer : b" | a ) 290 cm 2 , b ) 360 cm 2 , c ) 270 cm 2 , d ) 280 cm 2 , e ) 260 cm 2 | b | multiply(30, 12) | multiply(n0,n1)| | geometry | B |
a sum of rs . 1530 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b β s share is : | "explanation let c β s share = rs . x then , b β s share = rs . x / 4 , a β s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1530 = > 17 x / 12 = 1530 = > 1530 x 12 / 17 = rs . 1080 hence , b β s share = rs . ( 1080 / 4 ) = rs . 270 . answer c" | a ) rs . 120 , b ) rs . 160 , c ) rs . 270 , d ) rs . 300 , e ) none | c | subtract(subtract(multiply(divide(1530, const_10), const_2), const_12), const_12) | divide(n0,const_10)|multiply(#0,const_2)|subtract(#1,const_12)|subtract(#2,const_12)| | general | C |
the denominator of a fraction is 15 greater than the numerator . if the numerator and the denominator are increased by 3 , the resulting fraction is equal to 3 Γ’ Β β 4 . what is the value of the original fraction ? | "let the numerator be x . then the denominator is x + 15 . x + 3 / x + 18 = 3 / 4 . 4 x + 12 = 3 x + 54 . x = 42 . the original fraction is 42 / 57 . the answer is e ." | a ) 23 / 38 , b ) 29 / 44 , c ) 33 / 48 , d ) 38 / 53 , e ) 42 / 57 | e | divide(divide(subtract(multiply(3, add(3, 15)), 4), subtract(4, 3)), add(divide(subtract(multiply(3, add(3, 15)), 4), subtract(4, 3)), 15)) | add(n0,n1)|subtract(n3,n2)|multiply(n2,#0)|subtract(#2,n3)|divide(#3,#1)|add(n0,#4)|divide(#4,#5)| | general | E |
rice weighing 29 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces ) | "29 / 4 Γ· 4 = 29 / 16 pounds in each container 29 / 16 pounds * 16 ounces / pound = 29 ounces in each container the answer is c ." | a ) 21 , b ) 25 , c ) 29 , d ) 33 , e ) 37 | c | divide(multiply(divide(29, 4), 16), 4) | divide(n0,n1)|multiply(n4,#0)|divide(#1,n2)| | general | C |
a sum is divided among b , c and d in such a way that for each rupee b gets , c gets 150 paisa and d gets 50 paisa . if the share of c is rs . 40 , what is the total amount ? | b : c : d = 100 : 150 : 100 20 : 30 : 10 30 - - - 40 60 - - - ? = > 80 answer : c | a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 90 | c | multiply(divide(add(divide(50, 50), add(divide(const_100, 50), divide(150, 50))), divide(150, 50)), 40) | divide(const_100,n1)|divide(n0,n1)|divide(n1,n1)|add(#0,#1)|add(#3,#2)|divide(#4,#1)|multiply(n2,#5) | general | C |
the ratio of the volumes of two cubes is 729 : 1331 . what is the ratio of their total surface areas ? | "ratio of the sides = Β³ β 729 : Β³ β 1331 = 9 : 11 ratio of surface areas = 92 : 112 = 81 : 121 answer : a" | a ) 81 : 121 , b ) 81 : 126 , c ) 81 : 189 , d ) 81 : 176 , e ) 81 : 117 | a | power(divide(729, 1331), divide(const_1, const_3)) | divide(n0,n1)|divide(const_1,const_3)|power(#0,#1)| | geometry | A |
the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre . | "solution area of the floor = ( 5.5 x 3.75 ) m Β² = 20.635 m Β² cost of paying = rs . ( 600 x 20.625 ) = rs . 12,375 . answer c" | a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 12,375 , d ) rs . 16,500 , e ) none | c | multiply(600, multiply(5.5, 3.75)) | multiply(n0,n1)|multiply(n2,#0)| | physics | C |
a man travelled for 13 hours . he covered the first half of the distance at 20 kmph and remaining half of the distance at 25 kmph . find the distance travelled by the man ? | let the distance travelled be x km . total time = ( x / 2 ) / 20 + ( x / 2 ) / 25 = 13 = > x / 40 + x / 50 = 13 = > ( 5 x + 4 x ) / 200 = 13 = > x = 200 km answer : c | a ) 168 km , b ) 864 km , c ) 200 km , d ) 240 km , e ) 460 km | c | add(multiply(divide(13, const_3), 20), multiply(divide(13, const_3), 25)) | divide(n0,const_3)|multiply(n1,#0)|multiply(n2,#0)|add(#1,#2) | physics | C |
2 + 2 + 2 ^ 2 + 2 ^ 3 + 2 ^ 4 + 2 ^ 5 + 2 ^ 6 + 2 ^ 7 + 2 ^ 8 = | let ' s see that : 2 + 2 is 2 ^ 2 , then : 2 ^ 2 + 2 ^ 2 becomes 2 x 2 ^ 2 that is 2 ^ 3 . you follow with the next : 2 ^ 3 + 2 ^ 3 is equal to 2 x 2 ^ 3 that is 2 ^ 4 . then is assumed right before 2 ^ 8 : 2 ^ 8 x 2 ^ 8 becomes 2 x 2 ^ 8 that is 2 ^ 9 . option a , 2 ^ 9 . | a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 12 , d ) 2 ^ 16 , e ) 2 ^ 20 | a | add(add(add(power(2, 6), add(power(2, 5), add(power(2, 4), add(power(2, 3), add(power(const_2, const_2), add(2, 2)))))), power(2, 7)), power(2, 8)) | add(n0,n0)|power(const_2,const_2)|power(n0,n5)|power(n0,n7)|power(n0,n9)|power(n0,n11)|power(n0,n13)|power(n0,n15)|add(#0,#1)|add(#8,#2)|add(#9,#3)|add(#10,#4)|add(#11,#5)|add(#12,#6)|add(#13,#7) | general | A |
how many positive integers less than 60 have a reminder 01 when divided by 4 ? | "1 also gives the remainder of 1 when divided by 4 . so , there are total of 15 numbers . answer : c ." | a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | c | divide(factorial(subtract(add(const_4, 01), const_1)), multiply(factorial(01), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | general | C |
how much is 80 % of 40 is greater than 4 / 5 of 25 ? | ( 80 / 100 ) * 40 β ( 4 / 5 ) * 25 32 - 20 = 12 answer : d | a ) 22 , b ) 77 , c ) 15 , d ) 12 , e ) 88 | d | subtract(multiply(40, divide(80, const_100)), multiply(divide(4, 5), 25)) | divide(n0,const_100)|divide(n2,n3)|multiply(n1,#0)|multiply(n4,#1)|subtract(#2,#3) | general | D |
a train 280 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 280 * 3 / 55 = 15 sec . answer : a" | a ) 15 , b ) 6 , c ) 7 , d ) 9 , e ) 5 | a | divide(280, multiply(add(60, 6), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics | A |
a cistern normally takes 6 hours to be filled by a tap but because of a leak , 2 hours more . in how many hours will the leak empty a full cistern ? | β΅ cistern fill in 6 hours . β΄ in 1 hour , filled part = 1 β 6 th now , due to leakage , filled part in 1 hour = 1 β 8 th part of the cistern emptied , due to leakage in 1 hour = 1 β 6 - 1 β 8 = 1 β 24 th β΄ the leakage will empty the full cistern in 24 hrs . answer b | a ) 20 hours , b ) 24 hours , c ) 26 hours , d ) 18 hours , e ) none of these | b | inverse(subtract(inverse(6), inverse(add(2, 6)))) | add(n0,n1)|inverse(n0)|inverse(#0)|subtract(#1,#2)|inverse(#3) | physics | B |
a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 6 inches wide on each side , the total area would have been ( m + 200 ) square inches . what is the perimeter of the photograph , in inches ? | "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 12 ) ( y + 12 ) = m and so ( 2 ) xy + 12 x + 12 y + 144 = m + 200 let ' s subtract equation ( 1 ) from equation ( 2 ) . 10 x + 10 y + 140 = 200 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ." | a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24 | b | divide(subtract(200, subtract(power(multiply(6, const_2), const_2), power(multiply(1, const_2), const_2))), const_2) | multiply(n1,const_2)|multiply(n0,const_2)|power(#0,const_2)|power(#1,const_2)|subtract(#2,#3)|subtract(n2,#4)|divide(#5,const_2)| | geometry | B |
lionel left his house and walked towards walt ' s house , 48 miles away . four hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ? | "in the first 4 hours lionel at the rate of 2 miles per hour covered distance = rate * time = 4 * 2 = 8 miles . so , the distance between him and walt was 48 - 8 = 40 miles when walt left his house . now , their combined rate to cover this distance was 2 + 6 = 8 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 40 / 8 = 5 hours . total time that lionel was walking is 4 + 5 = 9 hours , which means that he covered in that time interval distance = rate * time = 2 * 9 = 18 miles . answer : b ." | a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 28 | b | multiply(2, add(divide(subtract(48, multiply(2, 2)), add(6, 2)), 2)) | add(n1,n2)|multiply(n1,n1)|subtract(n0,#1)|divide(#2,#0)|add(#3,n1)|multiply(n1,#4)| | physics | B |
when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 5 . what is the value of 7 y β x ? | "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 5 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y + 1 = x 7 y - x = - 1 the answer is d ." | a ) 2 , b ) 1 , c ) 0 , d ) - 1 , e ) - 2 | d | subtract(multiply(7, divide(subtract(multiply(2, 4), 5), subtract(multiply(6, 3), multiply(2, 11)))), add(multiply(11, divide(subtract(multiply(2, 4), 5), subtract(multiply(6, 3), multiply(2, 11)))), 4)) | multiply(n1,n2)|multiply(n3,n4)|multiply(n0,n2)|subtract(#0,n5)|subtract(#1,#2)|divide(#3,#4)|multiply(n6,#5)|multiply(n0,#5)|add(n1,#7)|subtract(#6,#8)| | general | D |
tom traveled the entire 80 miles trip . if he did the first 30 miles of at a constant rate 30 miles per hour and the remaining trip of at a constant rate 50 miles per hour , what is the his average speed , in miles per hour ? | "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 30 + 50 ) / ( ( 30 / 30 ) + ( 50 / 50 ) ) = 80 / 2 = 40 mph c" | a ) 55 mph , b ) 50 mph , c ) 40 mph , d ) 60 mph , e ) 70 mph | c | divide(80, add(divide(50, subtract(80, 30)), divide(30, 30))) | divide(n1,n2)|subtract(n0,n1)|divide(n3,#1)|add(#2,#0)|divide(n0,#3)| | physics | C |
what is the square root of 81 ? | "9 x 9 = 81 answer d" | a ) 2 , b ) 8 , c ) 12 , d ) 9 , e ) 16 | d | circle_area(divide(81, multiply(const_2, const_pi))) | multiply(const_2,const_pi)|divide(n0,#0)|circle_area(#1)| | other | D |
in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7500 , the number of valid votes that the other candidate got , was | solution number of valid votes = 80 % of 7500 = 6000 . valid votes polled by other candidates = 45 % of 6000 ( 45 / 100 Γ 6000 ) = 2700 . answer b | a ) 2500 , b ) 2700 , c ) 3000 , d ) 3100 , e ) nobe | b | multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 7500) | divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(n2,#4) | gain | B |
in an intercollegiate competition that lasted for 3 days , 157 students took part on day 1 , 111 on day 2 and 98 on day 3 . if 89 took part on day 1 and day 2 and 56 took part on day 2 and day 3 and 32 took part on all three days , how many students took part only on day 1 ? | "day 1 & 2 = 89 ; only day 1 & 2 ( 89 - 32 ) = 57 , day 2 & 3 = 56 ; only day 2 & 3 ( 56 - 32 ) = 24 , only day 1 = 157 - ( 57 + 24 + 32 ) = 44 answer : b" | a ) 40 , b ) 44 , c ) 35 , d ) 49 , e ) 38 | b | subtract(157, add(add(32, 89), divide(add(32, subtract(111, add(add(89, 56), 32))), 2))) | add(n7,n13)|add(n7,n10)|add(n13,#1)|subtract(n3,#2)|add(n13,#3)|divide(#4,n4)|add(#0,#5)|subtract(n1,#6)| | physics | B |
a 250 meter long train crosses a platform in 40 seconds while it crosses a signal pole in 20 seconds . what is the length of the platform ? | "speed = [ 250 / 20 ] m / sec = 25 / 2 m / sec . let the length of the platform be x meters . then , x + 250 / 40 = 25 / 2 2 ( x + 250 ) = 1000 Γ¨ x = 250 m . answer : d" | a ) 500 , b ) 1000 , c ) 350 , d ) 250 , e ) 20 | d | subtract(multiply(divide(250, 20), 40), 250) | divide(n0,n2)|multiply(n1,#0)|subtract(#1,n0)| | physics | D |
for how many integers pair ( x , y ) satisfies the result ( 1 / x ) + ( ( 1 / y ) = 1 / 16 | it seems that the accepted answer is wrong , according to wolframalpha . the answer should be 31 , which is n ' t even listed as a selectable answer . e | a ) a ) 12 , b ) b ) 6 , c ) c ) 10 , d ) d ) 16 , e ) e ) 19 | e | add(add(add(16, 1), 1), 1) | add(n0,n3)|add(n0,#0)|add(n0,#1) | general | E |
a question paper has 2 parts , a & b , each containing 5 questions . if a student has to choose 3 from part a & 4 from part b , in how many ways can he choose the questions ? | "there 3 questions in part a out of which 4 question can be chosen as = 5 c 3 . similarly , 5 questions can be chosen from 10 questions of part b as = 5 c 4 . hence , total number of ways , = 5 c 3 * 5 c 4 = [ 5 ! / ( 2 ! 3 ! ) ] * [ 5 ! / ( 4 ! * 1 ) ] = { 10 } * { 5 * 4 ! / ( 4 ! ) } = 10 * 5 = 50 . a" | a ) 50 , b ) 100 , c ) 152 , d ) 150 , e ) 55 | a | divide(multiply(choose(5, 3), choose(5, 4)), 5) | choose(n1,n2)|choose(n1,n3)|multiply(#0,#1)|divide(#2,n1)| | probability | A |
a man can swim in still water at 5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ? | m = 5 s = x ds = 5 + x us = 5 - x 5 + x = ( 5 - x ) 2 5 + x = 10 - 2 x 3 x = 5 x = 1.667 answer : b | a ) 1.78 , b ) 1.667 , c ) 1.15 , d ) 1.5 , e ) 1.2 | b | divide(5, const_3) | divide(n0,const_3) | general | B |
what is the tens digit of 7 ^ 1415 ? | "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1415 = 4 * 353 + 3 the ten ' s digit will be 4 . answer e" | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | floor(divide(reminder(power(7, reminder(1415, add(const_4, const_1))), const_100), const_10)) | add(const_1,const_4)|reminder(n1,#0)|power(n0,#1)|reminder(#2,const_100)|divide(#3,const_10)|floor(#4)| | general | E |
a palindrome is a number that reads the same forward and backward , such as 121 . how many odd , 4 - digit numbers are palindromes ? | first recognize you only need to consider the first two digits ( because the second two are just the first two flipped ) there are 90 possibilities for the first two digits of a 4 digit number , 10 - 99 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 90 = 50 answer : c | a ) 40 , b ) 45 , c ) 50 , d ) 90 , e ) 2500 | c | divide(power(const_10, divide(4, const_2)), const_2) | divide(n1,const_2)|power(const_10,#0)|divide(#1,const_2) | general | C |
a train 220 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 220 * 3 / 55 = 12 sec . answer : option a" | a ) 12 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | a | divide(220, multiply(add(60, 6), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics | A |
ratio of two numbers x and y is 3 : 7 . if x is increased by 50 % and y is increased by 2 then the new ratio becomes 1 : 2 . what is the ratio 2 y : ( 2 x + 6 ) | "let : x = 3 n y = 7 n 4.5 n / ( 7 n + 5 ) = 1 / 2 9 n = 7 n + 2 n = 1 so , x = 3 ; y = 7 2 y / ( 2 x + 6 ) = 14 / 12 = 7 : 6 answer = c" | a ) 16 : 15 , b ) 4 : 5 , c ) 7 : 12 , d ) 4 : 9 , e ) 6 : 5 | c | divide(multiply(2, multiply(divide(2, subtract(multiply(divide(add(const_100, 50), const_100), 2), divide(7, 3))), divide(7, 3))), add(divide(2, subtract(multiply(divide(add(const_100, 50), const_100), 2), divide(7, 3))), 2)) | add(n2,const_100)|divide(n1,n0)|divide(#0,const_100)|multiply(n5,#2)|subtract(#3,#1)|divide(n3,#4)|add(n7,#5)|multiply(#5,#1)|multiply(#7,n6)|divide(#8,#6)| | general | C |
the average of 6 number is 3.95 . the average of two of them is 3.8 , while the average of the other two is 3.85 . what is the average of the remaining two number ? | solution : sum of the remaining two numbers = ( 3.95 Γ 6 ) - [ ( 3.8 Γ 2 ) + ( 3.85 Γ 2 ) ] = 23.70 - ( 7.6 + 7.7 ) = 23.70 - 15.3 = 8.4 . β΄ required average = 8.4 / 2 = 4.2 answer b | a ) 4.5 , b ) 4.2 , c ) 4.7 , d ) 4.8 , e ) none of these | b | divide(subtract(multiply(3.95, 6), add(multiply(3.8, const_2), multiply(3.85, const_2))), const_2) | multiply(n0,n1)|multiply(n2,const_2)|multiply(n3,const_2)|add(#1,#2)|subtract(#0,#3)|divide(#4,const_2) | general | B |
pumps a , b , and c operate at their respective constant rates . pumps a and b , operating simultaneously , can fill a certain tank in 2 hours ; pumps a and c , operating simultaneously , can fill the tank in 3 / 2 hours ; and pumps b and c , operating simultaneously , can fill the tank in 2 hours . how many hours does it take pumps a , b , and c , operating simultaneously , to fill the tank . | a + b = 2 ; a + c = 3 / 2 , b + c = 2 ; add then 2 * ( a + b + c ) = 4 + 3 / 2 = 11 / 2 a + b + c = 11 / 4 hrs c | a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 , e ) 5 / 6 | c | divide(subtract(add(3, 3), add(divide(3, 2), add(2, 2))), 2) | add(n1,n1)|add(n0,n0)|divide(n1,n0)|add(#1,#2)|subtract(#0,#3)|divide(#4,n0) | physics | C |
a train 700 m long can cross an electric pole in 20 sec and then find the speed of the train ? | "length = speed * time speed = l / t s = 700 / 20 s = 35 m / sec speed = 35 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 126 kmph answer : c" | a ) 117 kmph , b ) 178 kmph , c ) 126 kmph , d ) 118 kmph , e ) 119 kmph | c | divide(divide(700, const_1000), divide(20, const_3600)) | divide(n0,const_1000)|divide(n1,const_3600)|divide(#0,#1)| | physics | C |
a cube of side 8 meter length is cut into small cubes of side 16 cm each . how many such small cubes can be obtained ? | "along one edge , the number of small cubes that can be cut = 800 / 16 = 50 along each edge 50 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 50 * 50 * 50 = 125000 answer : c" | a ) 10780 , b ) 127600 , c ) 125000 , d ) 152000 , e ) 10000 | c | divide(power(power(8, const_2), const_3), power(8, const_3)) | power(n0,const_2)|power(n0,const_3)|power(#0,const_3)|divide(#2,#1)| | physics | C |
if 6 and 8 are factors of 60 n , what is the minimum value of n ? | "60 n / 6 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 3 * 2 * 2 * 2 = 5 * n / 4 must be an integer for this to be true n must multiple of 4 , thus min of n = 4 hence b" | a ) 2 , b ) 4 , c ) 7 , d ) 14 , e ) 56 | b | lcm(6, 8) | lcm(n0,n1)| | other | B |
total dinning bill of 3 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared . | "dinner bill of 3 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 3 = $ 50.96 answer : b" | a ) 21.84 , b ) 50.96 , c ) 53.84 , d ) 24.84 , e ) 50.26 | b | divide(multiply(139.00, add(divide(const_1, 10), const_1)), 3) | divide(const_1,n2)|add(#0,const_1)|multiply(n1,#1)|divide(#2,n0)| | general | B |
the radius of a cylinder is 12 m , height 21 m . the lateral surface area of the cylinder is : | lateral surface area = 2 Ο rh = 2 Γ 22 / 7 Γ 12 Γ 21 = 44 Γ 36 = 1584 m ( power 2 ) answer is a . | ['a ) 1584', 'b ) 1854', 'c ) 1458', 'd ) 1485', 'e ) none of them'] | a | multiply(circumface(12), 21) | circumface(n0)|multiply(n1,#0) | geometry | A |
the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 88 and rs . 80 respectively . the sum is : | "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 88 * 80 / ( 88 - 80 ) = rs . 880 . answer a" | a ) 880 , b ) 1450 , c ) 1600 , d ) 1800 , e ) none | a | divide(multiply(88, 80), subtract(88, 80)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | gain | A |
a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 12 seconds to pass him . if the goods train is 300 m long , find its speed | "explanation : relative speed = 300 / 12 m / sec = ( ( 300 / 12 ) Γ ( 18 / 5 ) ) kmph = 90 kmph . speed of goods train = ( 90 - 60 ) kmph = 30 kmph answer : option d" | a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 30 kmph , e ) 34 kmph | d | subtract(multiply(divide(300, 12), const_3_6), 60) | divide(n2,n1)|multiply(#0,const_3_6)|subtract(#1,n0)| | physics | D |
sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 4 of the days were hot , then what was the price of 1 cup on a hot day ? | "6 regular days - - > sales = 6 * 32 * x = 192 x ; 4 hot days - - > sales = 4 * 32 * ( 1.25 x ) = 160 x ; total sales = 192 x + 160 x = 352 x . total cost = 10 * 32 * 0.75 = 240 . profit = 352 x - 240 = 350 - - > x = 1.676 . 1.25 x = ~ 2.09 . answer : c ." | a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.09 , d ) $ 2.50 , e ) $ 3.25 | c | multiply(divide(add(multiply(multiply(32, divide(75, const_100)), multiply(add(const_4, 1), const_2)), 350), add(multiply(subtract(multiply(add(const_4, 1), const_2), 4), 32), multiply(multiply(divide(add(const_100, 25), const_100), 4), 32))), divide(add(const_100, 25), const_100)) | add(n5,const_4)|add(n1,const_100)|divide(n2,const_100)|divide(#1,const_100)|multiply(n3,#2)|multiply(#0,const_2)|multiply(#4,#5)|multiply(n4,#3)|subtract(#5,n4)|add(n0,#6)|multiply(n3,#8)|multiply(n3,#7)|add(#10,#11)|divide(#9,#12)|multiply(#13,#3)| | gain | C |
the distance from city a to city b is 220 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ? | "the time it takes bob to drive to city b is 220 / 40 = 5.5 hours . alice needs to take less than 5 hours for the trip . alice needs to exceed a constant speed of 220 / 5 = 44 miles per hour . the answer is a ." | a ) 44 , b ) 48 , c ) 50 , d ) 52 , e ) 54 | a | divide(220, subtract(divide(220, 40), divide(30, const_60))) | divide(n0,n1)|divide(n2,const_60)|subtract(#0,#1)|divide(n0,#2)| | physics | A |
if ( 20 ) Β² is subtracted from the square of a number , the answer so obtained is 4321 . what is the number ? | x ^ 2 = 4321 + 400 = 4721 4761 = 69 * 69 x = 69 answer : b | ['a ) 68', 'b ) 69', 'c ) 70', 'd ) 71', 'e ) 72'] | b | sqrt(add(4321, power(multiply(const_2, const_10), const_2))) | multiply(const_10,const_2)|power(#0,const_2)|add(n1,#1)|sqrt(#2) | geometry | B |
a train , 140 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is | "explanation : assume the length of the bridge = x meter total distance covered = 140 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 140 + x ) / 30 m / s = > 45 Γ£ β ( 10 / 36 ) = ( 140 + x ) / 30 = > 45 Γ£ β 10 Γ£ β 30 / 36 = 140 + x = > 45 Γ£ β 10 Γ£ β 10 / 12 = 140 + x = > 15 Γ£ β 10 Γ£ β 10 / 4 = 140 + x = > 15 Γ£ β 25 = 140 + x = 375 = > x = 375 - 140 = 235 answer : option c" | a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m | c | subtract(multiply(multiply(45, const_0_2778), 30), 140) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | physics | C |
in what time will a train 100 meters long cross an electric pole , if its speed is 180 km / hr | "explanation : first convert speed into m / sec speed = 180 * ( 5 / 18 ) = 50 m / sec time = distance / speed = 100 / 50 = 2 seconds answer : d" | a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2 seconds , e ) none of these | d | divide(100, multiply(180, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics | D |
what is the sum of all even numbers from 1 to 601 ? | "explanation : 600 / 2 = 300 300 * 301 = 90300 answer : c" | a ) 122821 , b ) 281228 , c ) 90300 , d ) 122850 , e ) 128111 | c | divide(multiply(1, 601), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general | C |
how many of the positive factors of 42 are not factors of 56 ? | "factors of 42 - 1 , 2,3 , 6,7 , 14,42 factors of 56 - 1,2 , 4,7 , 8,14 , 28,56 comparing both , we have three factors of 42 which are not factors of 56 - 3 , 6,42 . the answer is 3 . pls check your options again - d $ e are same . answer : c" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | divide(56, 42) | divide(n1,n0)| | other | C |
today joelle opened an interest - bearing savings account and deposited $ 5,000 . if the annual interest rate is 4 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ? | "interest for 1 st year = 5000 * 4 / 100 = 200 interest for 2 nd year = 5200 * 4 / 100 = 208 total = 5000 + 200 + 208 = 5408 answer : b" | a ) $ 5200 , b ) $ 5408 , c ) $ 5208 , d ) $ 5608 , e ) $ 5808 | b | add(add(multiply(multiply(multiply(const_3, 2), const_100), const_10), divide(multiply(multiply(multiply(multiply(const_3, 2), const_100), const_10), 4), const_100)), divide(multiply(add(multiply(multiply(multiply(const_3, 2), const_100), const_10), divide(multiply(multiply(multiply(multiply(const_3, 2), const_100), const_10), 4), const_100)), 4), const_100)) | multiply(n2,const_3)|multiply(#0,const_100)|multiply(#1,const_10)|multiply(n1,#2)|divide(#3,const_100)|add(#4,#2)|multiply(n1,#5)|divide(#6,const_100)|add(#5,#7)| | gain | B |
the population of a bacteria colony doubles every day . if it was started 6 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ? | "2 ^ 6 ( 2 ) = 2 ^ 7 = 128 the answer is e ." | a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 128 | e | subtract(power(2, add(6, const_1)), const_1) | add(n0,const_1)|power(n1,#0)|subtract(#1,const_1)| | physics | E |
a man can do a job in 20 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ? | "1 day work of the three persons = ( 1 / 20 + 1 / 20 + 1 / 25 ) = 7 / 50 so , all three together will complete the work in 300 / 47 = 7.1 days . answer : c" | a ) 6.3 , b ) 6.9 , c ) 7.1 , d ) 6.1 , e ) 6.2 | c | divide(const_1, add(divide(const_1, 25), add(divide(const_1, 20), divide(const_1, 20)))) | divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|add(#3,#2)|divide(const_1,#4)| | physics | C |
two trains 110 meters and 180 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? | "t = ( 110 + 180 ) / ( 80 + 65 ) * 18 / 5 t = 7.20 answer : a" | a ) 7.2 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.15 | a | divide(add(110, 180), multiply(add(80, 65), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | physics | A |
a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds . its length is ? | "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m . answer : e" | a ) 128 , b ) 177 , c ) 199 , d ) 178 , e ) 150 | e | multiply(100, subtract(const_2, const_1)) | subtract(const_2,const_1)|multiply(n1,#0)| | physics | E |
in an election a candidate who gets 60 % of the votes is elected by a majority of 1040 votes . what is the total number of votes polled ? | "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1040 20 x / 100 = 1040 x = 1040 * 100 / 20 = 5200 answer is b" | a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000 | b | divide(1040, divide(subtract(60, subtract(const_100, 60)), const_100)) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)| | gain | B |
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 22 , then 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 = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : d" | a ) 17 years , b ) 19 years , c ) 29 years , d ) 8 years , e ) 12 years | d | divide(multiply(subtract(22, 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 | D |
a train running at the speed of 90 km / hr crosses a pole in 15 seconds . what is the length of the train ? | "speed = ( 90 x ( 5 / 18 ) m / sec = ( 25 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 25 ) x 15 ) m = 375 m c" | a ) 325 , b ) 350 , c ) 375 , d ) 400 , e ) 425 | c | multiply(divide(multiply(90, const_1000), const_3600), 15) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics | C |
the cost price of a radio is rs . 4500 and it was sold for rs . 3200 , find the loss % ? | "4500 - - - - 1300 100 - - - - ? = > 28.9 % answer : a" | a ) 28.9 % , b ) 22 % , c ) 28 % , d ) 45 % , e ) 32 % | a | multiply(divide(subtract(4500, 3200), 4500), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | gain | A |
the product of 3 consecutive numbers is 210 . then the sum of the smallest two numbers is ? | product of three numbers = 210 210 = 2 * 3 * 5 * 7 = 5 * 6 * 7 . so , the three numbers are 5 , 6 and 7 . and sum of smallest of these two = 5 + 6 = 11 . answer : option a | a ) 11 , b ) 15 , c ) 20 , d ) 38 , e ) 56 | a | add(add(floor(power(210, const_0_33)), const_1), floor(power(210, const_0_33))) | power(n1,const_0_33)|floor(#0)|add(#1,const_1)|add(#2,#1) | general | A |
salesperson a ' s compensation for any week is $ 210 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ? | "210 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 150 x = $ 7,500 the answer is c ." | a ) $ 3500 , b ) $ 5500 , c ) $ 7500 , d ) $ 9500 , e ) $ 11,500 | c | divide(add(divide(subtract(210, multiply(divide(6, const_100), 1,000)), subtract(divide(8, const_100), divide(6, const_100))), divide(subtract(210, multiply(divide(6, const_100), 1,000)), subtract(divide(8, const_100), divide(6, const_100)))), 1,000) | divide(n1,const_100)|divide(n3,const_100)|multiply(#0,n2)|subtract(#1,#0)|subtract(n0,#2)|divide(#4,#3)|add(#5,#5)|divide(#6,n2)| | general | C |
jacob is 10 years old . he is 5 times as old as his brother . how old will jacob be when he is twice as old ? | "j = 10 ; j = 5 b ; b = 10 / 5 = 2 ; twice as old so b = 2 ( now ) + ( 2 ) = 4 ; jacob is 10 + 4 = 14 answer : b" | a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | b | multiply(10, 5) | multiply(n0,n1)| | general | B |
the perimeter of one face a of cube is 20 cm . its volume must be | solution edge of the cube = ( 20 / 4 ) cm βΉ = βΊ 5 cm . volume = ( 5 Γ 5 Γ 5 ) cm 3 βΉ = βΊ 125 cm 3 . answer a | ['a ) 125 cm 3', 'b ) 400 cm 3', 'c ) 1000 cm 3', 'd ) 8000 cm 3', 'e ) none'] | a | volume_cube(square_edge_by_perimeter(20)) | square_edge_by_perimeter(n0)|volume_cube(#0) | geometry | A |
every digit of a number written in binary is either 0 or 1 . to translate a number from binary , multiply the nth digit ( reading from right to left ) by 2 ^ ( n - 1 ) what is the largest prime number ( written in binary ) that is a factor of both 10010000 and 100100000 ? | binary divison can provide a quick answer if you are comfortable with it . as option e is the biggest binary number we try with it first : 100010000 / 1001 = 10000 1000100000 / 1001 = 100000 so answer is option is c | a ) 10 , b ) 11 , c ) 1001 , d ) 1011 , e ) 10001 | c | add(divide(100100000, 10010000), const_1000) | divide(n5,n4)|add(#0,const_1000) | general | C |
the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ? | "let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c" | a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27 | c | divide(subtract(add(add(26, 3), 26), subtract(11, 2)), subtract(11, subtract(11, 2))) | add(n1,n2)|subtract(n0,n3)|add(n1,#0)|subtract(n0,#1)|subtract(#2,#1)|divide(#4,#3)| | general | C |
[ ( 3.242 x 14 ) / 100 ] = ? | "answer multiplying 3.242 x 14 = 4.5388 now divide 4.5388 by 100 so , 4.5388 Γ· 100 = 0.045388 β΄ shift the decimal two places to the left as 100 correct option : a" | a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) none of these | a | divide(divide(multiply(3.242, 14), 100), const_10) | multiply(n0,n1)|divide(#0,n2)|divide(#1,const_10)| | general | A |
when 1 / 20 % of 4,000 is subtracted from 1 / 10 of 4,000 , the difference is | "( 1 / 10 ) * 4000 - ( 1 / 20 * 100 ) * 4000 = 400 - 2 = 398 answer d" | a ) 50 , b ) 200 , c ) 380 , d ) 398 , e ) 400 | d | multiply(inverse(10), multiply(multiply(const_100, 10), add(const_4, const_4))) | add(const_4,const_4)|inverse(n4)|multiply(n4,const_100)|multiply(#0,#2)|multiply(#1,#3)| | general | D |
a worker earns $ 24 on the first day and spends $ 18 on the second day . the worker earns $ 24 on the third day and spends $ 18 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 48 ? | every two days , the net total is $ 6 . after 8 days , the worker will have $ 24 . on day 9 , the worker will receive $ 24 for a net total of $ 48 . the answer is c . | a ) 6 , b ) 7 , c ) 9 , d ) 12 , e ) 16 | c | add(multiply(divide(24, subtract(24, 18)), const_2), const_1) | subtract(n0,n1)|divide(n0,#0)|multiply(#1,const_2)|add(#2,const_1) | physics | C |
calculate the standard deviation of each data set { 10 , 1010 , 1010 } | standard deviation data set a = β [ ( ( 9 - 10 ) 2 + ( 10 - 10 ) 2 + ( 11 - 10 ) 2 + ( 7 - 10 ) 2 + ( 13 - 10 ) 2 ) / 5 ] = 2 standard deviation data set b = β [ ( ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 ) / 5 ] = 0 standard deviation data set c = β [ ( ( 1 - 10 ) 2 + ( 1 - 10 ) 2 + ( 10 - 10 ) 2 + ( 19 - 10 ) 2 + ( 19 - 10 ) 2 ) / 5 ] = 8.05 option a | a ) 8.05 , b ) 9 , c ) 10 , d ) 15 , e ) 15.5 | a | divide(sqrt(divide(add(add(power(subtract(divide(add(add(10, 1010), 1010), const_3), 1010), const_2), power(subtract(divide(add(add(10, 1010), 1010), const_3), 1010), const_2)), power(subtract(divide(add(add(10, 1010), 1010), const_3), 10), const_2)), subtract(const_3, const_1))), multiply(add(const_4, const_3), 10)) | add(n0,n1)|add(const_3,const_4)|subtract(const_3,const_1)|add(n1,#0)|multiply(n0,#1)|divide(#3,const_3)|subtract(#5,n1)|subtract(#5,n0)|power(#6,const_2)|power(#7,const_2)|add(#8,#8)|add(#10,#9)|divide(#11,#2)|sqrt(#12)|divide(#13,#4) | general | A |
a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 146 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ? | "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 146 / 25 = 5 . . . . so the max is 5 146 / 20 = 7 . . . so the max is 7 146 - 145 = 1 ( 6 small box + 1 big box ) answer : d" | a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5 | d | subtract(25, 20) | subtract(n0,n1)| | general | D |
company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.3 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 month was what fraction of the total number of hours it took to produce all the stereos ? | "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.3 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 26 hours . total hours = 66 . then the fraction would be 26 / 66 = 13 / 33 . therefore answer b b ." | a ) 7 / 17 , b ) 13 / 33 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2 | b | divide(add(3, 2), const_10) | add(n0,n1)|divide(#0,const_10)| | general | B |
a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 4 . the ratio of economy cars to sport utility vehicles is 3 : 2 . what is the ratio of luxury cars to sport utility vehicles ? | "the ratio of economy to luxury cars is 5 : 4 - - > e : l = 5 : 4 = 15 : 12 . the ratio of economy cars to sport utility vehicles is 3 : 2 - - > e : s = 3 : 2 = 15 : 10 . thus , l : s = 12 : 10 = 6 : 5 . answer : c ." | a ) 9 : 8 , b ) 8 : 9 , c ) 6 : 5 , d ) 2 : 3 , e ) 1 : 2 | c | divide(divide(multiply(const_4, 2), multiply(2, 2)), divide(multiply(2, const_4), multiply(4, const_4))) | multiply(n3,const_4)|multiply(n3,n3)|multiply(n1,const_4)|divide(#0,#1)|divide(#0,#2)|divide(#3,#4)| | other | C |
if 20 % of a number is equal to three - fifth of another number , what is the ratio of first number to the second number ? | "let 20 % of a = 3 / 5 b . then , 20 a / 100 = 3 b / 5 = > 1 a / 5 = 3 b / 5 a / b = ( 3 / 5 * 5 / 1 ) = 3 / 1 a : b = 3 : 1 . answer : a" | a ) 3 : 1 , b ) 2 : 1 , c ) 1 : 3 , d ) 1 : 2 , e ) 2 : 3 | a | divide(divide(const_1, const_4), divide(20, const_100)) | divide(const_1,const_4)|divide(n0,const_100)|divide(#0,#1)| | general | A |
if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 23 , 30 , 22 , 26 , 19 , 33 and 35 ? | "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 23 , 30 , 22 , 26 , 19 , 33 and 35 19 , 22 , 23 , 26 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 22 , 23 , 26 . . the median of these numbers = center of 22 and 23 = 22.5 c" | a ) 33 , b ) 28 , c ) 22.5 , d ) 24 , e ) 23 | c | divide(add(23, 26), const_2) | add(n1,n4)|divide(#0,const_2)| | general | C |
worker a takes 10 hours to do a job . worker b takes 12 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ? | "a ' s one hour work = 1 / 10 . b ' s one hour work = 1 / 12 . ( a + b ) ' s one hour work = 1 / 10 + 1 / 12 = 11 / 60 . both a & b can finish the work in 60 / 11 days c" | a ) 40 days , b ) 40 / 9 days , c ) 60 / 11 days , d ) 30 / 9 days , e ) 60 / 9 days | c | divide(const_1, add(divide(const_1, 10), divide(const_1, 12))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)| | physics | C |
a pipe can empty 3 / 4 th of a cistern in 12 mins . in 8 mins , what part of the cistern will be empty ? | 3 / 4 - - - - 12 ? - - - - - 8 = = > 1 / 2 a | a ) 1 / 2 , b ) 3 / 7 , c ) 4 / 9 , d ) 3 / 8 , e ) 4 / 7 | a | divide(multiply(divide(3, 4), 8), 12) | divide(n0,n1)|multiply(n3,#0)|divide(#1,n2) | physics | A |
if there are 4 peanuts in a box and mary puts 8 more peanuts inside , how many peanuts are in the box ? | "8 + 4 = 12 correct answer is e ) 12" | a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | e | add(4, 8) | add(n0,n1)| | general | E |
a train 240 m in length crosses a telegraph post in 16 seconds . the speed of the train is ? | "s = 240 / 16 * 18 / 5 = 54 kmph answer : c" | a ) 77 kmph , b ) 55 kmph , c ) 54 kmph , d ) 58 kmph , e ) 76 kmph | c | multiply(const_3_6, divide(240, 16)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics | C |
each child has 5 crayons and 14 apples . if there are 10 children , how many crayons are there in total ? | 5 * 10 = 50 . answer is e . | a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 50 | e | multiply(10, 5) | multiply(n0,n2)| | general | E |
find the least positive integer divisible by each of the integers between 5 through 10 ( including 10 ) . | the integer should be divisible by : 5 , 6 , 7 , 89 , and 10 . the least common multiple of these integers is lcm = 420 . answer : 5 * 3 ^ 2 * 7 * 2 ^ 3 the answer is e ) | a ) 560 , b ) 380 , c ) 900 , d ) 2560 , e ) 2520 | e | multiply(multiply(multiply(power(const_2, const_3), power(const_3, const_2)), 5), add(const_3, const_4)) | add(const_3,const_4)|power(const_2,const_3)|power(const_3,const_2)|multiply(#1,#2)|multiply(n0,#3)|multiply(#0,#4) | general | E |
a man walks at a rate of 10 mph . after every ten miles , he rests for 5 minutes . how much time does he take to walk 50 miles ? | to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 5 = 20 minutes . total time = 300 + 20 = 320 minutes . answer : c . | a ) 300 , b ) 318 , c ) 320 , d ) 324 , e ) 330 | c | add(multiply(5, const_4), multiply(divide(50, 10), const_60)) | divide(n2,n0)|multiply(n1,const_4)|multiply(#0,const_60)|add(#1,#2) | physics | C |
average age of 7 members of a family is 29 years . if present age of the youngest member is 5 year , find average age of the remaining members at the time of birth of the youngest member . | average age ( present ) of 7 members = 29 years 5 years ago , average age of 7 members was 29 - 5 = 24 years . since , the youngest member was not born 5 years ago . therefore , average age of remaining 6 members is increased by 246246 = 4 years . therefore , 5 years ago , average age of 6 members was 24 + 4 = 28 years . answer : a | a ) 28 , b ) 37 , c ) 29 , d ) 237 , e ) 212 | a | divide(subtract(multiply(7, 29), multiply(7, 5)), subtract(7, const_1)) | multiply(n0,n1)|multiply(n0,n2)|subtract(n0,const_1)|subtract(#0,#1)|divide(#3,#2) | general | A |
a man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time . find the speed of the stream ? | explanation : speed of the boat downstream = speed of the boat upstream \ small \ therefore the speed of the stream = answer : a | a ) 5 kmph , b ) 6 kmph , c ) 8 kmph , d ) 1 kmph , e ) 2 kmph | a | divide(subtract(divide(60, 3), divide(30, 3)), const_2) | divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2) | physics | A |
if the operation β¬ is defined for all x and y by the equation x β¬ y = 2 * x * y , then 6 β¬ ( 4 β¬ 5 ) = | working inside out , ( 4 β¬ 5 ) = 2 * 4 * 5 = 40 6 β¬ 40 = 2 * 6 * 40 = 480 hence , answer is a | a ) 480 , b ) 120 , c ) 160 , d ) 240 , e ) 360 | a | multiply(multiply(2, 6), multiply(multiply(2, 4), 5)) | multiply(n0,n1)|multiply(n0,n2)|multiply(n3,#1)|multiply(#0,#2) | general | A |
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