Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 200 m , in what time will they cross other travelling in opposite direction ? | "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 200 + 200 ) / 20 = 20 sec . answer : e" | a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 20 sec | e | divide(multiply(200, const_2), add(speed(200, 15), speed(200, 10))) | multiply(n2,const_2)|speed(n2,n1)|speed(n2,n0)|add(#1,#2)|divide(#0,#3)| | physics |
if 20 men can build a wall 66 metres long in 8 days , what length of a similar can be built by 86 men in 8 days ? | "if 20 men can build a wall 66 metres long in 8 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 8 * 20 ) = 283.8 mtrs answer : a" | a ) 283.8 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs | a | multiply(66, divide(multiply(86, 8), multiply(20, 8))) | multiply(n3,n4)|multiply(n0,n2)|divide(#0,#1)|multiply(n1,#2)| | physics |
how many odd numbers between 10 and 1,300 are the squares of integers ? | "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 17 numbers . answer : ... | a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 17 | e | add(10, const_4) | add(n0,const_4)| | geometry |
the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 770 the other is | "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 770 = 90 answer is b ." | a ) 330 , b ) 90 , c ) 270 , d ) 250 , e ) 350 | b | divide(multiply(30, 2310), 770) | multiply(n0,n1)|divide(#0,n2)| | physics |
a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.20 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer wil... | "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.68 or 2 ) 25 + 25 + 25 = $ 96.60 c" | a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.68 , d ) $ 102.07 , e ) $ 105.3 | c | add(add(multiply(const_2, 32.20), multiply(const_1, 20.43)), multiply(const_1, 13.85)) | multiply(n5,const_2)|multiply(n3,const_1)|multiply(n1,const_1)|add(#0,#1)|add(#3,#2)| | general |
the distance between west - town to east - town is 15 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 2 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in ... | "time taken by the birds to meet = 15 / ( 2 + 1 ) = 5 mins distance traveled by the bird traveling from west - town = 2 * 5 = 10 answer : c" | a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 . , e ) 15 . | c | multiply(2, 2) | multiply(n1,n1)| | physics |
a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 10 : 00 , how many seconds elap... | "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 10 strikes , there would be 9 intervals . according to the question , the time spent... | a ) 42 , b ) 36 , c ) 46 , d ) 38 , e ) 40 | d | multiply(add(subtract(10, const_1), 10), divide(22, add(subtract(6, const_1), 6))) | subtract(n3,const_1)|subtract(n0,const_1)|add(n3,#0)|add(n0,#1)|divide(n2,#3)|multiply(#2,#4)| | general |
two trains , each 100 m long , moving in opposite directions , cross other in 20 sec . if one is moving twice as fast the other , then the speed of the faster train is ? | "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 20 = 3 x = > x = 10 / 3 . so , speed of the faster train = 20 / 3 = 20 / 3 * 18 / 5 = 24 km / hr . answer : e" | a ) 22 , b ) 98 , c ) 60 , d ) 88 , e ) 24 | e | divide(multiply(multiply(divide(add(100, 100), multiply(20, add(const_1, const_2))), const_2), const_3600), const_1000) | add(n0,n0)|add(const_1,const_2)|multiply(n1,#1)|divide(#0,#2)|multiply(#3,const_2)|multiply(#4,const_3600)|divide(#5,const_1000)| | physics |
if a and b get profits of rs . 6,000 and rs . 4,000 respectively at the end of year then ratio of their investments are | "suppose a and b is ratio of investment . so a : b = 6000 + 4000 a : b = 10000 a / ( a + b ) * 10000 = 6000 2 a = 3 b a / b = 3 / 2 i . e 3 : 2 answer : c" | a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5 | c | divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), multiply(add(const_2, const_3), const_2))) | add(const_2,const_3)|multiply(const_2,const_3)|multiply(#1,const_100)|multiply(#0,const_2)|multiply(#2,const_100)|divide(#4,#3)|divide(#4,#5)| | gain |
on dividing 171 by a number , the quotient is 8 and the remainder is 3 . find the divisor . | "d = ( d - r ) / q = ( 171 - 3 ) / 8 = 168 / 8 = 21 d" | a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22 | d | floor(divide(171, 8)) | divide(n0,n1)|floor(#0)| | general |
40 men shake hands with each other . maximum no of handshakes without cyclic handshakes . | "or , if there are n persons then no . of shakehands = nc 2 = 40 c 2 = 780 answer : a" | a ) 780 , b ) 200 , c ) 210 , d ) 220 , e ) 230 | a | multiply(subtract(40, const_1), divide(40, const_2)) | divide(n0,const_2)|subtract(n0,const_1)|multiply(#0,#1)| | general |
a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 21000 . a ' s share is ? | "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 21000 = 7000 answer : c" | a ) 2999 , b ) 2778 , c ) 7000 , d ) 2889 , e ) 6612 | c | multiply(multiply(const_1, const_12), divide(21000, add(add(multiply(const_1, const_12), multiply(subtract(const_12, 6), const_2)), multiply(subtract(const_12, 8), const_3)))) | multiply(const_1,const_12)|subtract(const_12,n0)|subtract(const_12,n1)|multiply(#1,const_2)|multiply(#2,const_3)|add(#0,#3)|add(#5,#4)|divide(n2,#6)|multiply(#7,#0)| | gain |
a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 15 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ? | "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 15 more blue balls than white balls . . . equation # 2 : y = 15 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equ... | a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | a | divide(subtract(100, multiply(15, const_3)), const_4) | multiply(n1,const_3)|subtract(n0,#0)|divide(#1,const_4)| | general |
how long does a train 150 m long traveling at 36 kmph takes to cross a signal post ? | d = 150 m s = 36 * 5 / 18 = 10 t = 150 * 1 / 10 = 15 sec answer : b | a ) 8 sec , b ) 15 sec , c ) 20 sec , d ) 10 sec , e ) 22 sec | b | divide(150, multiply(36, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0) | physics |
a car dealership has 40 cars on the lot , 20 % of which are silver . if the dealership receives a new shipment of 80 cars , 50 % of which are not silver , what percentage of total number of cars are silver ? | "the number of silver cars is 0.2 * 40 + 0.5 * 80 = 48 the percentage of cars which are silver is 48 / 120 = 40 % the answer is c ." | a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 % | c | multiply(divide(add(multiply(40, divide(20, const_100)), multiply(80, divide(50, const_100))), add(40, 80)), const_100) | add(n0,n2)|divide(n1,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n2,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)| | gain |
the two lines y = x and x = - 7 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ? | "the point of intersection is ( - 7 , - 7 ) . the triangle has a base of length 7 and a height of 7 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 7 * 7 = 24.5 the answer is c ." | a ) 18.5 , b ) 21.5 , c ) 24.5 , d ) 27.5 , e ) 30.5 | c | divide(multiply(7, 7), const_2) | multiply(n0,n0)|divide(#0,const_2)| | general |
a train 125 m long passes a man , running at 3 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ? | "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 3 ) km / hr . x - 3 = 45 = > x = 48 km / hr . answer : option e" | a ) 40 , b ) 50 , c ) 60 , d ) 79 , e ) 48 | e | divide(divide(subtract(125, multiply(multiply(3, const_0_2778), 3)), 10), const_0_2778) | multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n2)|divide(#3,const_0_2778)| | physics |
if 16 ^ y = 4 ^ 14 , what is y ? | 16 ^ y = 4 ^ 2 y = 4 ^ 14 2 y = 14 y = 7 the answer is e . | a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7 | e | divide(14, const_2) | divide(n2,const_2) | general |
if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 105 games will be played during the tournament . find the number of participants . | "let p be the number of participants . pc 2 = 105 ( p ) ( p - 1 ) = 210 = 15 * 14 p = 15 the answer is a ." | a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19 | a | divide(add(sqrt(add(multiply(multiply(105, const_2), const_4), const_1)), const_1), const_2) | multiply(n0,const_2)|multiply(#0,const_4)|add(#1,const_1)|sqrt(#2)|add(#3,const_1)|divide(#4,const_2)| | general |
a train running at the speed of 90 km / hr crosses a pole in 6 seconds . find the length of the train . | "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time ( 25 ) * 6 = 150 meter answer : a" | a ) 150 meter , b ) 100 meter , c ) 105 meter , d ) 120 meter , e ) 130 meter | a | multiply(divide(multiply(90, const_1000), const_3600), 6) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
jen has a jar of jam , and she ate 1 / 3 of the jam for lunch . if jen ate 1 / 7 of the remaining jam for dinner , what fraction of the jam was left after dinner ? | let x be the amount of jam at the beginning . after lunch , the remaining jam was ( 2 / 3 ) x . after dinner , the remaining jam was ( 6 / 7 ) ( 2 / 3 ) x = ( 4 / 7 ) x . the answer is c . | a ) 2 / 7 , b ) 3 / 7 , c ) 4 / 7 , d ) 9 / 14 , e ) 11 / 14 | c | divide(subtract(7, 3), 7) | subtract(n3,n1)|divide(#0,n3) | general |
a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.42 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer wil... | "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.77 or 2 ) 25 + 25 + 25 = $ 96.75 d" | a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.78 , d ) $ 98.77 , e ) $ 105.3 | d | add(add(multiply(const_2, 32.25), multiply(const_1, 20.42)), multiply(const_1, 13.85)) | multiply(n5,const_2)|multiply(n3,const_1)|multiply(n1,const_1)|add(#0,#1)|add(#3,#2)| | general |
the radius of the two circular fields is in the ratio 3 : 7 the area of the first field is what percent less than the area of the second ? | "r = 3 Γ― β¬ r 2 = 9 r = 7 Γ― β¬ r 2 = 49 49 Γ― β¬ Γ’ β¬ β 40 Γ― β¬ 100 - - - - ? = > 81.6 % . answer : e" | a ) 82.9 % , b ) 84.2 % , c ) 81.0 % , d ) 80.6 % , e ) 81.6 % | e | subtract(power(7, const_2), power(3, const_2)) | power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)| | geometry |
the distance between west - town to east - town is 20 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in ... | time taken by the birds to meet = 20 / ( 4 + 1 ) = 4 mins distance traveled by the bird traveling from west - town = 4 * 4 = 16 answer : d | a ) 3 . , b ) 7 . , c ) 10 . , d ) 16 . , e ) 15 . | d | multiply(4, const_4) | multiply(n1,const_4) | physics |
angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 6,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of m... | "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo β s and isabella β s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal bas... | a ) 3,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500 | a | floor(divide(divide(subtract(550, multiply(6,000, divide(8, const_100))), subtract(divide(10, const_100), divide(8, const_100))), 6,000)) | divide(n1,const_100)|divide(n3,const_100)|multiply(#0,n2)|subtract(#1,#0)|subtract(n0,#2)|divide(#4,#3)|divide(#5,n2)|floor(#6)| | general |
if p ^ 2 β 13 p + 40 = s , and p is a positive integer between 1 and 10 , inclusive , what is the probability that s < 0 ? | p 2 β 13 p + 40 = s so ( p β 8 ) ( p β 5 ) = s for q to be negative , the expressions ( p β 8 ) and ( p β 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p β 8 ) and ( p β 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included becau... | a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10 | b | divide(subtract(subtract(divide(add(13, sqrt(subtract(power(13, const_2), multiply(const_4, 40)))), const_2), subtract(13, divide(add(13, sqrt(subtract(power(13, const_2), multiply(const_4, 40)))), const_2))), const_1), 10) | multiply(n2,const_4)|power(n1,const_2)|subtract(#1,#0)|sqrt(#2)|add(n1,#3)|divide(#4,const_2)|subtract(n1,#5)|subtract(#5,#6)|subtract(#7,const_1)|divide(#8,n4) | general |
a and b complete a work in 6 days . a alone can do it in 10 days . if both together can do the work in how many days ? | "1 / 6 + 1 / 10 = 8 / 30 = 4 / 15 15 / 4 = 3.75 days answer : a" | a ) 3.75 days , b ) 3.78 days , c ) 3.25 days , d ) 3.15 days , e ) 2.75 days | a | inverse(add(inverse(6), inverse(10))) | inverse(n0)|inverse(n1)|add(#0,#1)|inverse(#2)| | physics |
5 * 2 is a 3 digit number with * is a missing digit . if the number is divisible by 6 , the missing digit is | sol . let the number be 5 x 2 . clearly , it is divisible by 2 . now , 5 + x + 2 = ( 7 + x ) must be divisible by 3 . so , x = 2 . answer b | a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9 | b | divide(subtract(add(add(add(multiply(5, const_100), 2), multiply(const_1, const_10)), multiply(const_1, const_10)), add(multiply(5, const_100), 2)), multiply(const_1, const_10)) | multiply(n0,const_100)|multiply(const_1,const_10)|add(n1,#0)|add(#2,#1)|add(#3,#1)|subtract(#4,#2)|divide(#5,#1) | general |
how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 38 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ? | selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 38 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1... | a ) 2 , b ) 5 , c ) 8 , d ) 15 , e ) 25 | c | divide(subtract(multiply(48, 40), multiply(divide(add(const_100, 20), const_100), multiply(38, 40))), subtract(multiply(50, divide(add(const_100, 20), const_100)), 48)) | add(n3,const_100)|multiply(n1,n4)|multiply(n1,n2)|divide(#0,const_100)|multiply(#3,#2)|multiply(n0,#3)|subtract(#1,#4)|subtract(#5,n4)|divide(#6,#7) | gain |
in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 600 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? | "number of newborns that can die in first month = 1 / 10 * 600 = 60 survived = 540 number of newborns that can die in second month = 1 / 10 * 540 = 54 survived = 486 number of newborns that can die in third month = 1 / 10 * 486 = 48 survived = 438 answer : a" | a ) 438 , b ) 446 , c ) 452 , d ) 462 , e ) 470 | a | multiply(multiply(multiply(600, subtract(1, divide(1, 10))), subtract(1, divide(1, 10))), subtract(1, divide(1, 10))) | divide(n1,n2)|subtract(n1,#0)|multiply(n3,#1)|multiply(#2,#1)|multiply(#3,#1)| | probability |
three interviewers , a , b , and c are interviewing 40 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer b admitted 15 applicants , a admitted 17 applicants , and c admitted 20 applicants , at least how many applicants get the admission ? | if b admitted 15 are overlapping with a admission of 17 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : d | ['a ) 8', 'b ) 2', 'c ) 6', 'd ) 0', 'e ) 12'] | d | subtract(add(add(15, 17), 20), 40) | add(n1,n2)|add(n3,#0)|subtract(#1,n0) | geometry |
0 , 1 , 5 , 14 , 30 , ____ | "0 , 1,5 , 14 , 30 , . . . . . 0 + 1 * 1 = 1 1 + 2 * 2 = 5 5 + 3 * 3 = 14 14 + 4 * 4 = 30 so 30 + 5 * 5 = 55 answer : e" | a ) 25 , b ) 35 , c ) 45 , d ) 65 , e ) 55 | e | subtract(negate(14), multiply(subtract(1, 5), divide(subtract(1, 5), subtract(0, 1)))) | negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)| | general |
the security gate at a storage facility requires a 4 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be odd , how many lock codes are possible ? | x - x - x - x - x - - > there are 4 odd digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 4 - x - x - 3 . other x ' s can take following values : 4 - 5 - 4 - 3 - - > 4 * 5 * 4 * 3 = 240 . answer : b . | a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440 | b | multiply(multiply(4, const_3), divide(factorial(add(4, const_1)), factorial(const_3))) | add(n0,const_1)|factorial(const_3)|multiply(n0,const_3)|factorial(#0)|divide(#3,#1)|multiply(#4,#2) | general |
if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 4 ] ] ? | "[ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 4 ] ] = 4 ^ 2 + 2 * 4 + 4 = 28 . option e" | a ) 3 , b ) 9 , c ) 15 , d ) 19 , e ) 28 | e | add(add(power(4, const_2.0), multiply(2, 2)), 4) | multiply(n3,n3)|power(n0,n0)|add(#0,#1)|add(n2,#2)| | general |
in a forest 110 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged d... | "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 110 * 10 = 1,100 . answer : d ." | a ) 150 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500 | d | multiply(50, 5) | multiply(n1,n3)| | general |
the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 4240 , what is the length of the plot in metres ? | "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 4240 [ 4 l - 40 ] = 4240 / 26.50 = 160 4 l = 200 l = 200 / 4 = 50 meters . answer : c" | a ) 20 , b ) 200 , c ) 50 , d ) 400 , e ) 140 | c | subtract(divide(divide(4240, 26.50), const_2), multiply(const_2, 20)) | divide(n2,n1)|multiply(n0,const_2)|divide(#0,const_2)|subtract(#2,#1)| | physics |
in the new budget the price of milk rose by 20 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ? | reduce in consumption = r / ( 100 + r ) * 100 % = 20 / 120 * 100 = 16.67 % answer is d | a ) 7.5 % , b ) 9.1 % , c ) 10.9 % , d ) 16.67 % , e ) 15 % | d | multiply(divide(20, add(20, const_100)), const_100) | add(n0,const_100)|divide(n0,#0)|multiply(#1,const_100) | general |
evaluate 64 / . 08 | "explanation : 64 / . 08 = 6400 / 8 = 800 option a" | a ) 800 , b ) 500 , c ) 505 , d ) none of these , e ) 506 | a | divide(const_100.0, divide(08, 64)) | divide(n1,const_100)|divide(n0,#0)| | general |
two airplanes take off from one airfield at noon . one flies due east at 206 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ? | "a in two hours : the plane flying east will be 412 miles away from airport . the other plane will be 566 miles away from airport . 566 / 412 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 412 miles apart . a" | a ) 412 , b ) 332 , c ) 400 , d ) 483 , e ) 566 | a | sqrt(subtract(power(multiply(283, 2), 2), power(multiply(206, 2), 2))) | multiply(n1,n2)|multiply(n0,n2)|power(#0,n2)|power(#1,n2)|subtract(#2,#3)|sqrt(#4)| | physics |
96 % of 5 / 8 = | "should be simple . 0.96 * 5 / 8 = 4.8 / 8 = 0.6 correct option : c" | a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0 | c | divide(multiply(divide(multiply(8, 5), const_100), 96), const_100) | multiply(n1,n2)|divide(#0,const_100)|multiply(n0,#1)|divide(#2,const_100)| | general |
a man goes downstream at 14 kmph , and upstream 8 kmph . the speed of the stream is | speed of the stream = 1 / 2 ( 14 - 8 ) kmph = 3 kmph . correct option : e | a ) 0 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 3 kmph | e | divide(subtract(14, 8), const_2) | subtract(n0,n1)|divide(#0,const_2) | physics |
the ratio of radius of a circle and the side of a square is 2 : 11 . find the ratio of their areas : | "radius / side = 2 / 11 β area of circle / area of square = 4 / 121 answer : d" | a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 121 , e ) none | d | power(divide(2, 11), 2) | divide(n0,n1)|power(#0,n0)| | geometry |
a train overtakes two person who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . the length of the train is : | let actual speed of train = s m / sec and length of train = l m . then , s - 2 Γ 5 / 18 = l 9 β 9 s = l + 5 . . . β¦ ( i ) and s - 4 Γ 5 β 18 = l β 10 β 90 s = 9 l + 100 . . . . . ( ii ) by ( i ) & ( ii ) , we get l = 50 m . answer b | a ) 45 m , b ) 50 m , c ) 54 m , d ) 72 m , e ) none of these | b | multiply(9, subtract(subtract(multiply(multiply(4, const_0_2778), 10), multiply(9, multiply(2, const_0_2778))), multiply(2, const_0_2778))) | multiply(n1,const_0_2778)|multiply(n0,const_0_2778)|multiply(n3,#0)|multiply(n2,#1)|subtract(#2,#3)|subtract(#4,#1)|multiply(n2,#5) | physics |
a is twice as good a workman as b and together they finish a piece in 18 days . in how many days will a alone finish the work ? | "sol . ( a β s 1 day β s work ) : ) ( b β s 1 days work ) = 2 : 1 . ( a + b ) ' s 1 day ' s work = 1 / 18 divide 1 / 18 in the ratio 2 : 1 . : . a β s 1 day ' s work = ( 1 / 18 * 2 / 3 ) = 1 / 27 hence , a alone can finish the work in 27 days . ans : e" | a ) 25 days , b ) 26 days , c ) 23 days , d ) 45 days , e ) 27 days | e | multiply(add(const_1, const_2), 18) | add(const_1,const_2)|multiply(n0,#0)| | physics |
on dividing a number by 56 , we get 26 as remainder . on dividing the same number by 8 , what will be the remainder ? | "number = 56 x + 26 ( β΅ since the number gives 26 as remainder on dividing by 56 ) = ( 7 Γ 8 Γ x ) + ( 3 Γ 8 ) + 2 hence , if the number is divided by 8 , we will get 2 as remainder . answer : a" | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | a | multiply(subtract(divide(power(26, const_2), 56), floor(divide(power(26, const_2), 56))), 56) | power(n1,const_2)|divide(#0,n0)|floor(#1)|subtract(#1,#2)|multiply(n0,#3)| | general |
if the wheel is 12 cm then the number of revolutions to cover a distance of 1240 cm is ? | "2 * 22 / 7 * 12 * x = 1240 = > x = 16 answer : c" | a ) 11 , b ) 14 , c ) 16 , d ) 12 , e ) 19 | c | divide(1240, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 12)) | 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 |
( ab ) x β 2 = ( ba ) x β 7 . what is the value of x ? | explanation : ( a / b ) x β 2 = ( b / a ) x β 7 β ( a / b ) x β 2 = ( a / b ) β ( x β 7 ) β x β 2 = β ( x β 7 ) β x β 2 = β x + 7 β x β 2 = β x + 7 β 2 x = 9 β x = 92 = 4.5 option b | a ) 1.5 , b ) 4.5 , c ) 7.5 , d ) 9.5 , e ) 8.7 | b | divide(add(2, 7), 2) | add(n0,n1)|divide(#0,n0) | general |
a and b together can do a piece of work in 6 days and a alone can do it in 10 days . in how many days can b alone can do it ? | "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 10 work in 1 day b alone can do ( 1 / 6 - 1 / 10 ) = 1 / 15 work in 1 day = > complete work can be done in 15 days by b answer : option c" | a ) 12 days , b ) 18 days , c ) 15 days , d ) 21 days , e ) 22 days | c | inverse(subtract(inverse(6), inverse(10))) | inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)| | physics |
jerry β s average ( arithmetic mean ) score on the first 3 of 4 tests is 94 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ? | total score on 3 tests = 94 * 3 = 282 jerry wants the average to be = 96 hence total score on 4 tests should be = 96 * 4 = 384 score required on the fourth test = 384 - 282 = 102 option e | a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 102 | e | subtract(multiply(4, add(94, 2)), multiply(94, 3)) | add(n2,n3)|multiply(n0,n2)|multiply(n1,#0)|subtract(#2,#1) | general |
in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 18000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ? | "0.036 * 10 ^ 5 can be written as 3600 18000 * 10 ^ ( - 3 ) can be written as 18 required = 3600 / 18 = 200 answer : b" | a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500 | b | divide(multiply(multiply(const_1000, const_100), 0.036), divide(18000, const_1000)) | divide(n3,const_1000)|multiply(const_100,const_1000)|multiply(n0,#1)|divide(#2,#0)| | general |
an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4400 , what will be the difference between q and r ' s share ? | 4 - - - 4400 5 - - - ? = > 5500 answer : b | a ) 2788 , b ) 5500 , c ) 7282 , d ) 2782 , e ) 2729 | b | multiply(subtract(12, 7), divide(4400, subtract(7, 3))) | subtract(n1,n0)|subtract(n2,n1)|divide(n3,#0)|multiply(#2,#1) | general |
it takes avery 3 hours to build a brick wall while tom can do it in 2.5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ? | "avery ' s efficiency is 100 / 3 = 33 % tom ' s = 100 / 2.5 = 40 % they worked together for 1 hour and finished 73 % of the job remaining = 27 % tom will complete 40 % in 60 minutes , 20 % in 30 minutes and , 7 % in 60 * 7 / 40 minutes = 10.5 minutes time taken by tom to finish the remaining on his own = 30 + 10.5 = 40... | a ) 25 minutes . , b ) 30 minutes . , c ) 40 minutes . , d ) 55 minutes , e ) 1 hour and 20 minutes | c | multiply(divide(subtract(const_1, add(divide(const_1, 3), divide(const_1, 2.5))), divide(const_1, 2.5)), const_60) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|subtract(const_1,#2)|divide(#3,#1)|multiply(#4,const_60)| | physics |
if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is ? | "let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c" | a ) 127 , b ) 688 , c ) 200 , d ) 121 , e ) 123 | c | divide(subtract(350, 340), divide(5, const_100)) | divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)| | gain |
the current of a stream runs at the rate of 3 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ? | "s = 3 m = x ds = x + 3 us = x - 3 6 / ( x + 3 ) + 6 / ( x - 3 ) = 2 x = 7.24 answer : a" | a ) a ) 7.24 , b ) b ) 2 , c ) c ) 8.5 , d ) d ) 6.67 , e ) e ) 3 | a | divide(power(3, 2), 2) | power(n0,n2)|divide(#0,n2)| | physics |
an article with cost price of 180 is sold at 15 % profit . what is the selling price ? | "sp = 1.15 * 180 = 207 answer : d" | a ) 198 , b ) 200 , c ) 204 , d ) 207 , e ) 210 | d | add(180, multiply(180, divide(15, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | gain |
the average monthly salary of 15 employees in an organisation is rs . 1800 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ? | "manager ' s monthly salary = rs . ( 1950 * 16 - 1800 * 15 ) = rs . 4200 answer : c" | a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4200 , d ) rs . 3619 , e ) rs . 3610 | c | subtract(multiply(add(1800, 150), add(15, const_1)), multiply(1800, 15)) | add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
8 machines , each working at the same constant rate , together can complete a certain job in 24 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 16 days ? | "another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 24 to 16 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 8 = 12 so we need 12 - 8 = 4 more machines . answer : c" | a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8 | c | subtract(divide(multiply(8, add(const_4, const_1)), 24), add(const_4, const_1)) | add(const_1,const_4)|multiply(n0,#0)|divide(#1,n1)|subtract(#2,#0)| | physics |
a group of boy scouts and girls scouts is going on a rafting trip . 52 % of the scouts arrived with signed permission slips . if 40 % of the scouts were boy scouts and 62.5 % of the boy scouts arrived with signed permission slips , then what percentage of the children were girl scouts who arrived with signed permission... | "we do n ' t know how many scouts went on the trip , so let ' s assume 100 scouts went on the trip ( since we only are concerned with percents in the answer ) 40 % were boy scouts so 40 % of 100 = 40 were boy scouts 62.5 % of the boy scouts brought their permission slips signed , so . 625 * 40 = 25 boy scouts had signe... | a ) 27 , b ) 28 , c ) 29 , d ) 30 , e ) 31 | a | multiply(divide(subtract(52, divide(multiply(40, 62.5), const_100)), subtract(const_100, 40)), const_100) | multiply(n1,n2)|subtract(const_100,n1)|divide(#0,const_100)|subtract(n0,#2)|divide(#3,#1)|multiply(#4,const_100)| | gain |
seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ? | "assuming the weight of the mixture to be 100 g * * , then the weight of ryegrass in the mixture would be 30 g . also , assume the weight mixture x used in the mixture is xg , then the weight of mixture y used in the mixture would be ( 100 - x ) g . so we can now equate the parts of the ryegrass in the mixture as : 0.4... | a ) 10 % , b ) 33 1 / 3 % , c ) 40 % , d ) 50 % , e ) 66 2 / 3 % | b | divide(subtract(30, 25), subtract(divide(40, const_100), divide(25, const_100))) | divide(n0,const_100)|divide(n2,const_100)|subtract(n4,n2)|subtract(#0,#1)|divide(#2,#3)| | gain |
a , b and c invests rs . 4000 , rs . 3000 and rs . 2000 in a business . after one year b removed his money ; a and c continued the business for one more year . if the net profit after 2 years be rs . 2400 , then b ' s share in the profit is ? | "4 * 24 : 3 * 12 : 2 * 24 8 : 3 : 4 3 / 15 * 2400 = 480 answer : c" | a ) 276 , b ) 289 , c ) 480 , d ) 400 , e ) 278 | c | multiply(divide(4000, add(4000, add(multiply(3000, 2), multiply(2000, 2)))), 4000) | multiply(n1,n3)|multiply(n2,n3)|add(#0,#1)|add(n0,#2)|divide(n0,#3)|multiply(n0,#4)| | gain |
a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 3 hours to fill the tank . the leak can drain all the water in ? | "work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 leak will empty the tank in 14 hrs answer is b" | a ) 10 hr , b ) 14 hr , c ) 12 hr , d ) 9 hr , e ) 15 hr | b | inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 3), 1), 3)))) | divide(n2,n0)|multiply(n0,n3)|add(n2,#1)|divide(#2,n3)|inverse(#3)|subtract(#0,#4)|inverse(#5)| | physics |
the cost of 16 pens and 8 pencils is rs . 352 and the cost of 4 pens and 4 pencils is rs . 96 . find the cost of each pen ? | "let the cost of each pen and pencil be ' p ' and ' q ' respectively . 16 p + 8 q = 352 - - - ( 1 ) 4 p + 4 q = 96 8 p + 8 q = 192 - - - ( 2 ) ( 1 ) - ( 2 ) = > 8 p = 160 = > p = 20 answer : e" | a ) rs . 32 , b ) rs . 28 , c ) rs . 36 , d ) rs . 25 , e ) none of these | e | multiply(multiply(16, const_4), divide(352, add(16, 4))) | add(n0,n4)|multiply(n0,const_4)|divide(n2,#0)|multiply(#2,#1)| | general |
if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 55 minutes ? | "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 55 minutes the population increases by 55 x 4 = 220 people . answer . e ." | a ) 80 , b ) 100 , c ) 150 , d ) 180 , e ) 220 | e | multiply(divide(const_60, 15), 55) | divide(const_60,n0)|multiply(n1,#0)| | physics |
five 6 faced dice are thrown together . the probability that all the three show the same number on them is ? | the three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways . hence the probability is 6 / 7776 = 1 / 1296 answer : b | a ) 1 / 32 , b ) 1 / 1296 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34 | b | multiply(multiply(multiply(divide(const_1, 6), divide(const_1, 6)), divide(const_1, 6)), divide(const_1, 6)) | divide(const_1,n0)|multiply(#0,#0)|multiply(#0,#1)|multiply(#0,#2) | probability |
in the junior basketball league there are 21 teams , 1 / 3 of them are bad and Β½ are rich . what ca n ' t be the number of teams that are rich and bad ? | "total teams = 21 bad teams = ( 1 / 3 ) * 21 = 7 rich teams = 10 so maximum value that the both rich and bad can take will be 10 . so e = 11 can not be that value . ans e ." | a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 11 . | e | add(multiply(21, divide(const_1, 1)), const_1) | divide(const_1,n1)|multiply(n0,#0)|add(#1,const_1)| | general |
a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a . | "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a β s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 Β» ) = rs . 150 . answer is b" | a ) 500 , b ) 600 , c ) 750 , d ) 800 , e ) none of them | b | multiply(divide(const_1, add(add(const_4, 3), const_1)), 1200) | add(n3,const_4)|add(#0,const_1)|divide(const_1,#1)|multiply(n0,#2)| | physics |
a can do a half of certain work in 60 days and b one third of the same in 35 days . they together will do the whole work in . | "a = 120 days b = 105 days 1 / 120 + 1 / 105 = 45 / 2520 = 1 / 56 = > 56 days answer : a" | a ) 56 days , b ) 420 days , c ) 46 days , d ) 560 days , e ) 96 days | a | add(inverse(multiply(60, const_2)), inverse(multiply(35, const_3))) | multiply(n0,const_2)|multiply(n1,const_3)|inverse(#0)|inverse(#1)|add(#2,#3)| | physics |
if p is a prime number greater than 3 , find the remainder when p ^ 2 + 15 is divided by 12 . | "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 15 = 36 n ^ 2 + 12 n + 1 + 15 = 36 n ^ 2 + 12 n + 12 + 4 if p = 6 n - 1 , then p ^ 2 + 15 = 36 n ^ 2 - 12 n + 1 + 15 = 36 n ^ 2 - 12 n + 12 + 4 when divided by 12 , it must leave a remainder of 4 . the answer is b ." | a ) 6 , b ) 4 , c ) 0 , d ) 8 , e ) 7 | b | subtract(add(15, power(add(const_1, const_4), 2)), multiply(12, 3)) | add(const_1,const_4)|multiply(n0,n3)|power(#0,n1)|add(n2,#2)|subtract(#3,#1)| | general |
a merchant marks his goods up by 40 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ? | "let the price be 100 . the price becomes 140 after a 40 % markup . now a discount of 10 % on 126 . profit = 126 - 100 26 % answer c" | a ) 8 % , b ) 14 % , c ) 26 % , d ) 15 % , e ) 17 % | c | subtract(subtract(add(40, const_100), divide(multiply(add(40, const_100), 10), const_100)), const_100) | add(n0,const_100)|multiply(n1,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(#3,const_100)| | gain |
if a and b are positive numbers , and a ^ 3 + b ^ 3 = 100 , then the greatest possible value of a is between : | "if a = 4.5 and b is a bit more than 2 , then a ^ 3 + b ^ 3 can equal 100 . if a > 5 , then a ^ 3 + b ^ 3 > 100 . the answer is c ." | a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9 | c | add(multiply(floor(power(100, inverse(3))), const_10), add(floor(power(100, inverse(3))), const_1)) | inverse(n0)|power(n2,#0)|floor(#1)|add(#2,const_1)|multiply(#2,const_10)|add(#3,#4)| | general |
the average age of 18 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ? | age of the 15 th student = 18 * 15 - ( 14 * 5 + 16 * 9 ) = 270 - 214 = 56 years answer is c | a ) 9 , b ) 31 , c ) 56 , d ) 72 , e ) 90 | c | subtract(subtract(multiply(18, 15), multiply(5, 14)), multiply(9, 16)) | multiply(n0,n1)|multiply(n2,n3)|multiply(n4,n5)|subtract(#0,#1)|subtract(#3,#2) | general |
money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 1800 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ? | "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1800 triples to $ 5400 , in 28 years , it will again triple to $ 5400 * 3 = $ 16,200 answer a" | a ) $ 16,200 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500 | a | multiply(1800, power(const_3, divide(28, divide(112, 8)))) | divide(n0,n2)|divide(n3,#0)|power(const_3,#1)|multiply(n1,#2)| | gain |
a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ? | "a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 420 - 280 = 140 answer : b" | a ) s . 240 , b ) s . 140 , c ) s . 340 , d ) s . 50 , e ) s . 90 | b | subtract(divide(divide(700, add(divide(1, 2), divide(1, 3))), 2), divide(divide(700, add(divide(1, 2), divide(1, 3))), 3)) | divide(n1,n2)|divide(n1,n4)|add(#0,#1)|divide(n0,#2)|divide(#3,n2)|divide(#3,n4)|subtract(#4,#5)| | general |
a shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount had been offered ? | "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 Γ ( 100 + 23.5 ) / ( 100 β 5 ) = 100 Γ 247 / 190 = 130 hence , required % profit = 130 β 100 = 30 % answer c" | a ) 28.5 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) none of these | c | subtract(divide(multiply(add(const_100, 23.5), const_100), subtract(const_100, 5)), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,const_100)|divide(#2,#1)|subtract(#3,const_100)| | gain |
p and q started a business investing rs 10000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively . | "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 10000 : 15000 = 10 : 15 = 2 : 3 option d" | a ) 2 : 7 , b ) 2 : 6 , c ) 17 : 6 , d ) 2 : 3 , e ) 7 : 8 | d | divide(10000, 15000) | divide(n0,n1)| | gain |
0.99999 + 0.11112 = ? | "0.99999 + 0.11112 = 0.99999 + 0.11111 + 0.00001 = ( 0.99999 + 0.00001 ) + 0.11111 = 1 + 0.11111 = 1.11111 e" | a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.11111 | e | multiply(divide(0.99999, 0.11112), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
the perimeter of one square is 40 cm and that of another is 20 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ? | "4 a = 40 4 a = 20 a = 10 a = 5 a 2 = 100 a 2 = 25 combined area = a 2 = 125 = > a = 11.2 d = 11.2 β 2 answer : a" | a ) 11.2 β 2 , b ) 13 β 2 , c ) 23 β 2 , d ) 12 β 4 , e ) 13 β 9 | a | sqrt(multiply(add(power(divide(40, const_4), const_2), power(divide(20, 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 |
a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 860 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 860 - 815 ) = rs . 45 . s . i . for 3 years = rs . ( 45 x 3 ) = rs . 135 . principal = rs . ( 815 - 135 ) = rs . 680 . answer : option c" | a ) s . 650 , b ) s . 690 , c ) s . 680 , d ) s . 700 , e ) s . 720 | c | subtract(815, divide(multiply(subtract(860, 815), 3), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | gain |
a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 874 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 874 - 815 ) = rs . 59 . s . i . for 3 years = rs . ( 59 x 3 ) = rs . 177 . principal = rs . ( 815 - 177 ) = rs . 638 . answer : option b" | a ) s . 650 , b ) s . 638 , c ) s . 698 , d ) s . 700 , e ) s . 760 | b | subtract(815, divide(multiply(subtract(874, 815), 3), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | gain |
the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 3 / 8 is given by ? | 2 / 3 * 6 / 7 * 1 / 3 * 3 / 8 = 36 / 504 = 3 / 42 answer : e | a ) 7 / 98 , b ) 1 / 48 , c ) 1 / 98 , d ) 1 / 96 , e ) 3 / 42 | e | inverse(multiply(2, 7)) | multiply(n0,n3)|inverse(#0) | other |
find the quantities of two types of rice to be mixed , first variety is of rs . 12 per kg and second variety is of rs . 20 per kg . to get 12 kg of rice mixture worth rs . 15 per kg ? ( in kg ) | from allegation & mixture ratio = c - m / m - d = 20 - 15 / 15 - 12 = 5 / 3 . from the option c r = 7.5 / 4.5 = 5 / 3 answer : c | a ) 3.5 , 8.5 , b ) 7 , 5 , c ) 7.5 , 4.5 , d ) 8 , 4 , e ) 8 , 5 | c | floor(subtract(12, divide(subtract(multiply(12, 15), multiply(12, 12)), subtract(20, 12)))) | multiply(n0,n3)|multiply(n0,n0)|subtract(n1,n0)|subtract(#0,#1)|divide(#3,#2)|subtract(n0,#4)|floor(#5) | physics |
there are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . | "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 3 and for second = 2 so total methods = 3 * 2 = 6 answer : d" | a ) 5 , b ) 1 , c ) 3 , d ) 6 , e ) 7 | d | add(choose(3, 2), choose(3, 2)) | choose(n0,n1)|add(#0,#0)| | probability |
a boy is traveling from his house to school at 10 km / hr and reached school 2 hours late . next day he traveled 20 km / hr and reached 1 hour early . then find the distance between house and school ? | let distance be x s 1 = 10 km / hr s 2 = 20 km / hr t 1 = x / 10 hr t 2 = x / 20 hr difference in time = 2 + 1 = 3 hr ( x / 10 ) - ( x / 20 ) = 3 x = 60 km answer is d | a ) 50 km , b ) 45 km , c ) 33 km , d ) 60 km , e ) 54 km | d | multiply(add(divide(add(multiply(2, 10), 20), subtract(20, 10)), 2), 10) | multiply(n0,n1)|subtract(n2,n0)|add(n2,#0)|divide(#2,#1)|add(n1,#3)|multiply(n0,#4) | physics |
the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 285 , then the mean profit for the last 15 days would be | "average would be : 350 = ( 285 + x ) / 2 on solving , x = 415 . answer : d" | a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 415 , e ) none of these | d | divide(subtract(multiply(30, 350), multiply(15, 285)), 15) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n3)| | gain |
a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.20 , what total number of apples and bananas did the customer purchase ? | "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 7.20 until we get a multiple of $ 0.50 . $ 7.20 , $ 6.40 , $ 5.60 , $ 4.80 , $ 4.00 = 8 * $ 0.50 the customer purchased 8 bananas and 4 apples . the answer is c ." | a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | c | add(divide(subtract(7.20, multiply(0.80, const_2)), 0.50), const_2) | multiply(n0,const_2)|subtract(n2,#0)|divide(#1,n1)|add(#2,const_2)| | other |
in the first 7 overs of a cricket game , the run rate was only 4.2 . what should be the rate in the remaining 30 overs to reach the target of 282 runs ? | "required run rate = [ 282 - ( 4.2 * 7 ) ] / 30 = 252.60 / 40 = 8.42 answer : b" | a ) 6.25 , b ) 8.42 , c ) 8.3 , d ) 8.1 , e ) 6.21 | b | divide(subtract(282, multiply(7, 4.2)), 30) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | gain |
an empty tank be filled with an inlet pipe β a β in 42 minutes . after 12 minutes an outlet pipe β b β is opened which can empty the tank in 30 minutes . after 6 minutes another inlet pipe β c β opened into the same tank , which can fill the tank in 35 minutes and the tank is filled . find the time taken to fill the ta... | assume total tank capacity = 210 liters now capacity of pipe a = 210 / 42 = 5 liters capacity of b = 210 / 30 = - 7 liters capacity of c = 210 / 35 = 6 min assume tank gets filled in x min after the third pipe got opened . so x Γ 5 + 6 Γ ( β 2 ) + 4 x = 210 x Γ 5 + 6 Γ ( β 2 ) + 4 x = 210 β 48 + 4 x = 210 β 4 x = 162 β... | a ) 51.6 , b ) 51.5 , c ) 51.7 , d ) 51.1 , e ) 51.0 | b | divide(subtract(add(add(30, 35), 42), const_2), const_2) | add(n2,n4)|add(n0,#0)|subtract(#1,const_2)|divide(#2,const_2) | physics |
in a group of 50 people , 25 have visited iceland and 23 have visited norway . if 21 people have visited both iceland and norway , how many people have visited neither country ? | "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 50 = 25 + 23 - 21 + ( # in neither group ) = 23 the prompt gives you all of t... | a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | d | subtract(50, subtract(add(25, 23), 21)) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)| | other |
a container holds 4 quarts of alcohol and 4 quarts of water . how many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume ? | let the number of quarts that should be added to get the required ratio = x so total quarts of water = ( x + 4 ) but the original number of quarts of alcohol remains the same , so we have : 4 / ( x + 4 ) = 3 / 5 cross - multiply : now we have 20 = 3 x + 12 = > 3 x = 20 - 12 = > x = 8 / 3 answer - d | a ) 4 / 3 , b ) 5 / 3 , c ) 7 / 3 , d ) 8 / 3 , e ) 10 / 3 | d | subtract(divide(4, divide(3, 5)), 4) | divide(n2,n3)|divide(n0,#0)|subtract(#1,n0) | general |
set a of 8 positive integers may have the same element and have 37 . and set b of 8 positive integers must have different elements and have 37 . when m and n are the greatest possible differences between 37 and other elements β sums in set a and set b , respectively , m - n = ? | this is maximum - minimum . hence , 37 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 30 and 37 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 9 . so , 30 - 9 = 21 . the correct answer is b . | a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 26 | b | subtract(37, add(add(8, const_2), 8)) | add(n0,const_2)|add(n0,#0)|subtract(n1,#1)| | general |
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 |
an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how m... | "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m = q , leaving 1 m of empty space . thus , i believe the answer is b ) 1" | a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3 | b | subtract(15, add(multiply(const_4, 2), multiply(const_4, 1.5))) | multiply(n1,const_4)|multiply(n2,const_4)|add(#0,#1)|subtract(n0,#2)| | general |
if the average of 8 x and 8 y is greater than 120 , and x is twice y , what is the least integer value of x ? | "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 ... | a ) 20 , b ) 25 , c ) 30 , d ) 32 , e ) 42 | a | multiply(8, const_2) | multiply(n0,const_2)| | general |
when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 39 , what is the remainder when k is divided by 7 ? | cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 39 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible va... | a ) 4 , b ) 5 , c ) 6 , d ) 3 , e ) 7 | d | reminder(add(const_12, 5), 7) | add(n0,const_12)|reminder(#0,n5) | general |
in may , the grounds keeper at spring lake golf club built a circular green with an area of 81 Ο square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ? | "area of circle 81 pi sq feet = pi r ^ 2 therefore r = 9 now green radi doubled i . e r = 18 area = 324 pi e" | a ) 100 pi , b ) 144 pi , c ) 196 pi , d ) 256 pi , e ) 324 pi | e | circle_area(multiply(sqrt(81), const_2)) | sqrt(n0)|multiply(#0,const_2)|circle_area(#1)| | geometry |
the batting average of a particular batsman is 61 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score . | "explanation : total runs scored by the batsman = 61 * 46 = 2806 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2806 β 2552 = 254 runs . let the highest score be x , hence the lowest score = x β 150 x + ( x - 150 ) = 254 2 x = 404 x = 202 runs answer ... | a ) 179 , b ) 202 , c ) 210 , d ) 223 , e ) 229 | b | divide(add(150, subtract(multiply(61, 46), multiply(58, subtract(46, const_2)))), const_2) | multiply(n0,n1)|subtract(n1,const_2)|multiply(n3,#1)|subtract(#0,#2)|add(n2,#3)|divide(#4,const_2)| | general |
the product of two numbers is 4107 . if the h . c . f of these numbers is 37 , then the greater number is ? | "let the numbers be 37 a and 37 b . then , 37 a * 37 b = 4107 = > ab = 3 now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 * 1 , 37 * 3 ) i . e . , ( 1 , 111 ) . greater number = 111 . answer : c" | a ) 377 , b ) 126 , c ) 111 , d ) 727 , e ) 121 | c | sqrt(add(power(sqrt(subtract(37, multiply(const_2, 4107))), const_2), multiply(const_4, 4107))) | multiply(n0,const_4)|multiply(n0,const_2)|subtract(n1,#1)|sqrt(#2)|power(#3,const_2)|add(#0,#4)|sqrt(#5)| | general |
the surface area of a sphere is 4 Ο r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area t of that hemisphere ? | "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total sur... | a ) 6 / Ο , b ) 9 / Ο , c ) 6 , d ) 9 , e ) 12 | d | add(divide(multiply(multiply(4, const_pi), divide(3, const_pi)), 2), multiply(const_pi, divide(3, const_pi))) | divide(n2,const_pi)|multiply(n0,const_pi)|multiply(#0,#1)|multiply(#0,const_pi)|divide(#2,n1)|add(#4,#3)| | geometry |
there are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed . | "explanation : hcf ( 408 , 216 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 216 / 24 = 17 + 9 = 26 answer : a" | a ) 26 , b ) 32 , c ) 35 , d ) 30 , e ) 45 | a | divide(add(408, 216), multiply(multiply(multiply(const_2, const_2), const_2), const_3)) | add(n0,n1)|multiply(const_2,const_2)|multiply(#1,const_2)|multiply(#2,const_3)|divide(#0,#3)| | general |
the number 250 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ? | sum of the squares of 3 different positive integers = 250 15 ^ 2 + 3 ^ 2 + 4 ^ 2 = 250 now , sum of these 3 different integers = 15 + 3 + 4 = 22 ans - b | ['a ) 18', 'b ) 22', 'c ) 21', 'd ) 20', 'e ) 19'] | b | multiply(const_2, sqrt(divide(250, const_2))) | divide(n0,const_2)|sqrt(#0)|multiply(#1,const_2) | geometry |
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