options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
|---|---|---|---|---|---|
a ) 1000,3500 , b ) 1000,3000 , c ) 1000,2000 , d ) 1000,5000 , e ) 1000,2500 | b | divide(multiply(10000, const_1), const_3) | a and b invests rs . 10000 each , a investing for 4 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 4000 , find their shares ? | the ratio of their profits a : b = 4 : 12 = 1 : 3 share of a in the total profit = 1 / 4 * 4000 = rs . 1000 share of b in the total profit = 3 / 4 * 4000 = rs . 3000 answer : b | a = 10000 * 1
b = a / 3
|
a ) 1.8 , b ) 3 , c ) 6 , d ) 18 , e ) 60 | b | divide(divide(multiply(add(18, 2), add(divide(subtract(18, 2), const_2), const_1)), const_2), divide(multiply(add(divide(subtract(10, 2), const_2), const_1), add(2, 10)), const_2)) | for all even integers n , h ( n ) is defined to be the sum of the even integers between 2 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ? | "mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 2 + 18 ) / 2 ] * 9 = 90 h ( 10 ) = ( 2 + 10 ) / 2 ] * 5 = 30 h ( 18 ) / h ( 10 ) = ( 90 ) / ( 30 ) = 3 answer : b" | a = 18 + 2
b = 18 - 2
c = b / 2
d = c + 1
e = a * d
f = e / 2
g = 10 - 2
h = g / 2
i = h + 1
j = 2 + 10
k = i * j
l = k / 2
m = f / l
|
a ) 160 , b ) 320 , c ) 480 , d ) 600 , e ) 720 | c | multiply(subtract(power(const_2, 5), 2), multiply(4, 4)) | in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ? | there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 30 * 16 = 480 . the answer is c . | a = 2 ** 5
b = a - 2
c = 4 * 4
d = b * c
|
a ) 8 , b ) 3 , c ) 9 , d ) 4 , e ) 2 | d | multiply(subtract(power(add(divide(divide(10, const_2), const_100), const_1), const_2), add(divide(10, const_100), const_1)), 1600) | the difference between simple and compound interest on rs . 1600 for one year at 10 % per annum reckoned half - yearly is ? | "s . i . = ( 1600 * 10 * 1 ) / 100 = rs . 160 c . i . = [ 1600 * ( 1 + 5 / 100 ) 2 - 1600 ] = rs . 164 difference = ( 164 - 160 ) = rs . 4 . answer : d" | a = 10 / 2
b = a / 100
c = b + 1
d = c ** 2
e = 10 / 100
f = e + 1
g = d - f
h = g * 1600
|
a ) 2 km , b ) 4 km , c ) 7 km , d ) 9 km , e ) 5 km | b | multiply(multiply(divide(divide(47, const_60), add(add(divide(const_1, 4), divide(const_1, 5)), divide(const_1, 6))), const_3), const_1000) | a person travels equal distances with speeds of 4 km / hr , 5 km / hr and 6 km / hr and takes a total time of 47 minutes . the total distance is ? | "let the total distance be 3 x km . then , x / 4 + x / 5 + x / 6 = 47 / 60 37 x / 60 = 47 / 60 = > x = 1.27 total distance = 3 * 1.27 = 3.81 km . answer : b" | a = 47 / const_60
b = 1 / 4
c = 1 / 5
d = b + c
e = 1 / 6
f = d + e
g = a / f
h = g * 3
i = h * 1000
|
a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 4 | e | multiply(divide(subtract(10, 3), add(3, 4)), 4) | one hour after yolanda started walking from x to y , a distance of 10 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob Ρ ' s was 4 miles per hour , how many miles had bob walked when they met ? | "when b started walking y already has covered 3 miles out of 10 , hence the distance at that time between them was 10 - 3 = 7 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 7 / 7 = 1 hours . in 6 hours b walked 1 * 4 = 4 miles . answer : e ." | a = 10 - 3
b = 3 + 4
c = a / b
d = c * 4
|
a ) 167.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5 | b | divide(subtract(divide(multiply(multiply(5000, 7), 2), const_100), divide(multiply(multiply(5000, 4), 2), const_100)), 2) | a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 7 % p . a for 2 years . find his gain in the transaction per year . | "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 Γ 4 Γ 2 / 100 = 400 he also lends it at 7 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 Γ 7 Γ 2 / 100 = 700 his overall gain in 2 years = rs . 700 - rs . 400 = rs . 300 his overall gain in 1 year = 300 / 2 = rs . 150 answer : option b" | a = 5000 * 7
b = a * 2
c = b / 100
d = 5000 * 4
e = d * 2
f = e / 100
g = c - f
h = g / 2
|
a ) 168 , b ) 150 , c ) 180 , d ) 200 , e ) 250 | a | divide(multiply(divide(14, multiply(multiply(divide(const_1, const_4), divide(const_1, const_3)), divide(const_2, add(const_2, const_3)))), 40), const_100) | one fourth of one third of two fifth of a number is 14 . what will be 40 % of that number | "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 14 then x = 14 * 30 = 420 40 % of 420 = 168 answer : option a" | a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3
e = 2 / d
f = c * e
g = 14 / f
h = g * 40
i = h / 100
|
a ) 60 kmph , b ) 61 kmph , c ) 62 kmph , d ) 64 kmph , e ) 66 kmph | a | divide(540, multiply(divide(3, 2), 6)) | a vantakes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph a ) | a = 3 / 2
b = a * 6
c = 540 / b
|
a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | b | add(divide(subtract(7.30, multiply(0.80, const_2)), 0.70), const_2) | a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.30 , 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 $ 7.30 until we get a multiple of $ 0.70 . $ 7.30 , $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 3 apples . the answer is b ." | a = 0 * 80
b = 7 - 30
c = b / 0
d = c + 2
|
a ) 22 days , b ) 36 / 5 days , c ) 67 days , d ) 17 / 7 days , e ) 18 days | b | divide(multiply(4, 9), divide(subtract(multiply(4, 9), multiply(add(divide(multiply(4, 9), 4), divide(multiply(4, 9), 9)), 2)), 2)) | a can do a piece of work in 4 days . b can do it in 9 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ? | "c = 1 / 2 - 1 / 4 - 1 / 9 = 5 / 36 = > 36 / 5 days answer : b" | a = 4 * 9
b = 4 * 9
c = 4 * 9
d = c / 4
e = 4 * 9
f = e / 9
g = d + f
h = g * 2
i = b - h
j = i / 2
k = a / j
|
a ) 370 , b ) 365 , c ) 398 , d ) 456 , e ) 460 | c | subtract(multiply(255, const_2), 112) | a number when divided by a certain divisor left remainder 255 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ? | easy solution : n = dq 1 + 255 2 n = 2 dq 1 + 51 0 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 398 d * some integer = 398 checking all options only ( c ) syncs with it . answer c | a = 255 * 2
b = a - 112
|
a ) 42 , b ) 40 , c ) 26 , d ) 36 , e ) 66 | a | divide(divide(12.6, const_100), divide(30, const_100)) | if 30 % of a number is 12.6 , find the number ? | "a 40" | a = 12 / 6
b = 30 / 100
c = a / b
|
a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2 | a | multiply(divide(5, 3), const_100) | 5 + 3 | a | a = 5 / 3
b = a * 100
|
a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156 | a | multiply(divide(60, const_2), 5) | find the number , difference between number and its 3 / 5 is 60 . | "explanation : let the number = x , then , x - ( 3 / 5 ) x = 60 , = > ( 2 / 5 ) x = 60 = > 2 x = 60 * 5 , = > x = 150 answer : option a" | a = 60 / 2
b = a * 5
|
a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20 | e | multiply(16, inverse(subtract(const_1, divide(8, 40)))) | x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 16 days . how long will y take to complete the work ? | "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 16 days whole work will be done by y in 16 * 5 / 4 = 20 days answer is e" | a = 8 / 40
b = 1 - a
c = 1/(b)
d = 16 * c
|
a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2 | c | divide(3, 3) | a positive number x is multiplied by 3 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ? | "we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us β ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 β 2 x = 0 x ( 3 x β 2 ) = 0 x = 0 or 3 x β 2 = 0 3 x = 2 x = 4 / 3 because x is positive , x = 4 / 3 . the answer is c ." | a = 3 / 3
|
a ) 25 , b ) 20 , c ) 30 , d ) 10 , e ) 15 | a | divide(multiply(10, 10), 4) | 10 men do a work in 10 days . how many men are needed to finish the work in 4 days ? | "men required to finish the work in 4 days = 10 * 10 / 4 = 25 answer is a" | a = 10 * 10
b = a / 4
|
a ) 22 , b ) 75 , c ) 90 , d ) 78 , e ) 66 | e | subtract(divide(6900, 80), 20) | a trader sells 80 meters of cloth for rs . 6900 at the profit of rs . 20 per metre of cloth . what is the cost price of one metre of cloth ? | "sp of 1 m of cloth = 6900 / 80 = rs . 86 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 86 - rs . 20 = rs . 66 . answer : e" | a = 6900 / 80
b = a - 20
|
a ) 5 a , b ) 15 a , c ) 20 a , d ) 1 / 25 a , e ) 30 a | c | floor(divide(80, add(4, const_1))) | during a certain two - week period , 80 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ? | "movies : 80 % comedies . 20 % remaining genre . now in this 20 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 4 x . total 5 x . 5 x = 20 ; x = 4 action movies : 4 % drama movies : 16 % we can say that out of 100 z , : comedies : 80 z action : 4 z drama : 16 z now action movies werea this means : a = 4 z . z = ( a / 4 ) comedies : 80 z = 80 * ( a / 4 ) 20 a c is the answer ." | a = 4 + 1
b = 80 / a
c = math.floor(b)
|
a ) 880 , b ) 550 , c ) 1100 , d ) 1020 , e ) 600 | d | multiply(100, power(add(const_4, const_1), const_4)) | ( 100 x 60 ) + ( 138 x 400 ) = ? x 60 | "explanation : ? = ( 100 x 60 ) + ( 138 x 400 ) / 60 = 6000 + 55200 / 60 = 1020 answer : option d" | a = 4 + 1
b = a ** 4
c = 100 * b
|
a ) 8 hours , b ) 6 hours , c ) 4.2 hours , d ) 5 hours , e ) 6 hours | c | divide(42, subtract(12, subtract(divide(42, 3), 12))) | the speed of the boat in still water in 12 kmph . it can travel downstream through 42 kms in 3 hrs . in what time would it cover the same distance upstream ? | "still water = 12 km / hr downstream = 42 / 3 = 14 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 14 / 2 = 10 km / hr so time taken in upstream = 42 / 10 = 4.2 hrs answer : c" | a = 42 / 3
b = a - 12
c = 12 - b
d = 42 / c
|
a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7 | c | divide(divide(20, 3), 20) | tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bearsa number which is a multiple of 3 ? | "here , s = [ 1 , 2 , 3 , 4 , β¦ . , 19 , 20 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 ] p ( e ) = n ( e ) / n ( s ) = 6 / 20 = 3 / 10 c" | a = 20 / 3
b = a / 20
|
a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 8 , e ) 2 / 10 | d | multiply(divide(1, 4), divide(subtract(1, divide(2, 3)), divide(2, 3))) | two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 4 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ? | "suppose the water in each jug is l liters cx x ( 1 / 4 ) = l cx = 4 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 4 l = 1 / 8 answer will be d" | a = 1 / 4
b = 2 / 3
c = 1 - b
d = 2 / 3
e = c / d
f = a * e
|
a ) 1 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 3 / 5 , e ) 4 / 5 | e | divide(subtract(subtract(subtract(7, 2), 1), 1), 5) | harry started a 6 - mile hike with a full 7 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 5 miles of the hike ? | "a . no of cups leaked during the trip = 2 cups . no of cups harry drank = 4 cups . no of cups harry drank during the first 5 miles = 4 . drink / mile = 4 / 5 answer : e" | a = 7 - 2
b = a - 1
c = b - 1
d = c / 5
|
a ) 58.6 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs | a | divide(add(multiply(58.4, 20), subtract(60, 56)), 20) | the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 60 kg . what is the correct weight ? | actual total weight is ( 20 x 58.4 - 56 + 60 ) = 1172 kgs actual average weight is 1172 / 20 = 58.6 kgs a | a = 58 * 4
b = 60 - 56
c = a + b
d = c / 20
|
a ) 14.0 , b ) 13.0 , c ) 12.0 , d ) 11.0 , e ) 10.0 | c | add(06, add(divide(multiply(divide(subtract(divide(500, const_100), const_1), divide(800, 1,000)), subtract(divide(800, 1,000), divide(500, 700))), add(divide(500, 700), const_1)), divide(subtract(divide(500, const_100), const_1), divide(800, 700)))) | hillary and eddy are climbing to the summit of mt . everest from a base camp 4,700 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ? | "solution : h stopped 700 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . c" | a = 500 / 100
b = a - 1
c = 800 / 1
d = b / c
e = 800 / 1
f = 500 / 700
g = e - f
h = d * g
i = 500 / 700
j = i + 1
k = h / j
l = 500 / 100
m = l - 1
n = 800 / 700
o = m / n
p = k + o
q = 6 + p
|
a ) $ 3 , b ) $ 5 , c ) $ 7 , d ) $ 9 , e ) $ 11 | c | subtract(divide(420, divide(10, subtract(divide(const_3, const_2), const_1))), divide(420, add(divide(10, subtract(divide(const_3, const_2), const_1)), 10))) | p and q are the only two applicants qualified for a short - term research project that pays 420 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p β s hourly wage is how many dollars greater than candidate q β s hourly wage ? | let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 420 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 420 / 30 = $ 14 p ' s hourly wage is 420 / ( t - 10 ) = $ 21 which is $ 7 per hour more . the answer is c . | a = 3 / 2
b = a - 1
c = 10 / b
d = 420 / c
e = 3 / 2
f = e - 1
g = 10 / f
h = g + 10
i = 420 / h
j = d - i
|
a ) 0 , b ) 21 / 64 , c ) 1 , d ) 22 / 63 , e ) 23 / 65 | b | divide(add(const_1, divide(add(const_1, divide(1, 4)), 4)), 4) | log ( a ( a ( a ) ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 here base is a . | log ( a ( a ( a ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 1 + 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 16 ) ^ 1 / 4 = > log ( a ^ 1 + 5 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 64 ) = > 21 / 64 log ( a ) = > 21 / 64 answer : b | a = 1 / 4
b = 1 + a
c = b / 4
d = 1 + c
e = d / 4
|
a ) 12 , b ) 14 , c ) 10 , d ) 16 , e ) 18 | c | subtract(add(30, 20), multiply(20, const_2)) | rahul is 30 years older than his daughter mary . in 20 years rahul will be twice as old as mary . what is mary current age . | now : mary = x , rahul = x + 30 in 20 years mary = x + 20 , rahul = x + 30 + 20 or 2 ( x + 20 ) x + 30 + 20 = 2 ( x + 20 ) x + 50 = 2 x + 40 50 - 40 = 2 x - x x = 10 mary is 10 years old answer : c | a = 30 + 20
b = 20 * 2
c = a - b
|
a ) 95 , b ) 92 , c ) 88 , d ) 82 , e ) 80 | c | subtract(rectangle_perimeter(2020, divide(680680, 2020)), 2020) | a rectangular field has to be fenced on three sides leaving a side of 2020 feet uncovered . if the area of the field is 680680 sq . feet , how many feet of fencing will be required ? | "explanation : area of the field = 680 sq . feet . length of the adjacent sides are 20 feet and 680 / 20 = 34 feet . required length of the fencing = 20 + 34 + 34 = 88 feet answer : option c" | a = 680680 / 2020
b = rectangle_perimeter - (
|
a ) 320 , b ) 300 , c ) 310 , d ) 315 , e ) 330 | d | subtract(divide(multiply(multiply(3500, 13), 3), const_100), divide(multiply(multiply(3500, 10), 3), const_100)) | if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 13 % per annum then the gain of b in a period of 3 years is ? | "( 3500 * 3 * 3 ) / 100 = > 315 answer : d" | a = 3500 * 13
b = a * 3
c = b / 100
d = 3500 * 10
e = d * 3
f = e / 100
g = c - f
|
a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 11 | c | divide(11, divide(multiply(11, subtract(11, const_3)), const_2)) | what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11 - sided polygon ) ? | "from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 8 = 1 / 4 . the answer is c ." | a = 11 - 3
b = 11 * a
c = b / 2
d = 11 / c
|
a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 41 % | e | subtract(multiply(divide(subtract(const_100, 6), const_100), multiply(add(const_100, 20), divide(add(const_100, 25), const_100))), const_100) | a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 6 % . what was its profit on the items sold in february ? | "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.94 * 150 x = 141 x hence total profit = 41 % option e" | a = 100 - 6
b = a / 100
c = 100 + 20
d = 100 + 25
e = d / 100
f = c * e
g = b * f
h = g - 100
|
['a ) 22', 'b ) 28', 'c ) 99', 'd ) 77', 'e ) 16'] | b | divide(144, add(const_2, const_pi)) | the perimeter of a semi circle is 144 cm then the radius is ? | 36 / 7 r = 144 = > r = 28 answer : b | a = 2 + math.pi
b = 144 / a
|
['a ) 7.22 m ^ 2', 'b ) 3.86 m ^ 2', 'c ) 8.96 m ^ 2', 'd ) 2.68 m ^ 2', 'e ) 7.89 m ^ 2'] | a | multiply(divide(const_1, const_2), multiply(3.8, 3.8)) | find the area of the square , one of whose diagonals is 3.8 m long ? | area of the square = 1 / 2 ( diagonal ) ^ 2 = ( 1 / 2 * 3.8 * 3.8 ) m ^ 2 = 7.22 m ^ 2 answer ( a ) | a = 1 / 2
b = 3 * 8
c = a * b
|
a ) 30,000 , b ) 15,450 , c ) 45,000 , d ) 60,000 , e ) 15,000 | e | divide(1500, divide(10, const_100)) | in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 1500 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ? | "total # of votes cast = 100 x , out of these , let the # of votes won by the winner = w , and for the loser ( l ) = 100 x - w . given that w - ( 100 x - w ) = 10 % of total votes cast = 10 x thus , 2 w - 100 x = 10 x β β w = 55 x and l = 100 x - 55 x = 45 x . according to the new condition , if the loser had won 45 x + 1500 votes , then , ( 45 x + 1500 ) - ( 55 x - 1500 ) = 10 % of total votes cast = 10 x thus , 3000 = 20 x and 100 x = 15000 answer : e" | a = 10 / 100
b = 1500 / a
|
a ) 41 / 50 , b ) 1 / 216 , c ) 1 / 221 , d ) 1 / 84 , e ) 1 / 42 | b | divide(const_1, power(subtract(divide(22, const_3), const_1), const_2)) | in a certain game of dice , the player β s score is determined as a sum of three throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ? | "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and john will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : b ." | a = 22 / 3
b = a - 1
c = b ** 2
d = 1 / c
|
a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2 | d | divide(add(divide(subtract(8, 2), 2), 2), divide(add(2, 8), 2)) | line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 8 , - 2 ) . what is the slope of line m ? | "the midpoint of ( 2,8 ) and ( 8 , - 2 ) is ( 5,3 ) . the slope of a line through ( 0 , - 2 ) and ( 5,3 ) is ( 3 - ( - 2 ) ) / ( 5 - 0 ) = 5 / 5 = 1 the answer is d ." | a = 8 - 2
b = a / 2
c = b + 2
d = 2 + 8
e = d / 2
f = c / e
|
a ) 298 , b ) 231 , c ) 342 , d ) 876 , e ) 291 | b | subtract(subtract(340, divide(multiply(340, 20), const_100)), divide(multiply(subtract(340, divide(multiply(340, 20), const_100)), 15), const_100)) | the sale price sarees listed for rs . 340 after successive discount is 20 % and 15 % is ? | "340 * ( 80 / 100 ) * ( 85 / 100 ) = 231 answer : b" | a = 340 * 20
b = a / 100
c = 340 - b
d = 340 * 20
e = d / 100
f = 340 - e
g = f * 15
h = g / 100
i = c - h
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a ) 150 , b ) 88 , c ) 77 , d ) 62 , e ) 350 | e | subtract(multiply(250, divide(15, divide(15, const_3))), multiply(100, divide(20, divide(15, const_3)))) | a train crosses a platform of 100 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ? | "length of the train be Γ’ β¬ Λ x Γ’ β¬ β’ x + 100 / 15 = x + 250 / 20 4 x + 400 = 3 x + 750 x = 350 m answer : e" | a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 100 * e
g = c - f
|
a ) 1.12 , b ) 1.16 , c ) 1.2 , d ) 1.35 , e ) none of these | d | divide(multiply(0.75, 9), 5) | if 0.75 : x : : 5 : 9 , then x is equal to : | "explanation : ( x * 5 ) = ( 0.75 * 9 ) x = 6.75 / 5 = 1.35 answer : d" | a = 0 * 75
b = a / 5
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a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | c | add(add(2, const_2.0), 1) | in the xy - plane , the point ( 3 , 1 ) is the center of a circle . the point ( 3 , - 2 ) lies inside the circle and the point ( - 2 , 1 ) lies outside the circle . if the radius r of the circle is an integer , then r = | "an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 3 , 1 ) and the point inside the circle ( 3 , - 2 ) is 3 units ( both points are on x = 3 line so the distance will simply be 1 - ( - 2 ) = 3 ) so the radius must be more than 3 units . the distance between the center ( 3,1 ) and the point outside the circle ( - 2,1 ) is 5 units ( both points are on y = 1 line so the distance will simply be 3 - ( - 2 ) = 5 ) so the radius must be less than 5 units , which implies 3 < r < 5 , thus as r is an integer then r = 4 . answer : c ." | a = 2 + 2
b = a + 1
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a ) t = 350 , b ) t = 353 , c ) t = 354 , d ) t = 356 , e ) 357 | b | add(add(add(add(const_60, 4), 4), multiply(add(add(const_60, 4), 4), 4)), add(multiply(3, 1), multiply(multiply(3, 2), 2))) | s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits t are in s ( 99 ) ? | "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b" | a = const_60 + 4
b = a + 4
c = const_60 + 4
d = c + 4
e = d * 4
f = b + e
g = 3 * 1
h = 3 * 2
i = h * 2
j = g + i
k = f + j
|
a ) 198 , b ) 195 , c ) 196 , d ) 197 , e ) 200 | d | add(add(add(55, 45), 44), 41) | you have been given a physical balance and 7 weights of 57 , 55 , 45 , 44 , 43 , 41 and 85 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 199 kgs . | "85 + 55 + 57 = 197 answer : d" | a = 55 + 45
b = a + 44
c = b + 41
|
a ) 42 , b ) 40 , c ) 30 , d ) 18 , e ) 11 | a | divide(add(add(26, 30), multiply(7, 4)), const_2) | the average age of 7 men increases by 4 years when two women are included in place of two men of ages 26 and 30 years . find the average age of the women ? | "explanation : 26 + 30 + 7 * 4 = 84 / 2 = 42 answer : a" | a = 26 + 30
b = 7 * 4
c = a + b
d = c / 2
|
a ) 12980 , b ) 12532 , c ) 12610 , d ) 12430 , e ) 12560 | b | add(450.271, divide(multiply(369.422, 0.03), divide(108.612, 2.001))) | 450.271 + 369.422 Γ· 0.03 - 108.612 x 2.001 = ? | "explanation : ? = 450.271 + ( 369.422 Γ· 0.03 ) - ( 108.612 x 2.001 ) β 450 + 369 / 0.03 - ( 109 x 2 ) β 450 + 12300 - 218 β 12532 answer : option b" | a = 369 * 422
b = 108 / 612
c = a / b
d = 450 + 271
|
a ) 16 , b ) 80 , c ) 400 , d ) 180 , e ) 240 | c | add(multiply(const_100, 3), const_100) | how many 3 - digit numerals begin with a digit that represents a prime number ? | prime digits 2 , 35 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : c | a = 100 * 3
b = a + 100
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a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104 | b | divide(subtract(multiply(150, divide(add(const_100, 50), const_100)), 10), add(divide(add(const_100, 50), const_100), const_1)) | if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 150 pounds . what is leo ' s current weight ? | "l + k = 150 and so k = 150 - l l + 10 = 1.5 k = 1.5 ( 150 - l ) 2.5 l = 215 l = 86 the answer is b ." | a = 100 + 50
b = a / 100
c = 150 * b
d = c - 10
e = 100 + 50
f = e / 100
g = f + 1
h = d / g
|
a ) 15 , b ) 24 , c ) 30 , d ) 20 , e ) 10 | b | subtract(30, divide(multiply(25, 30), add(100, 25))) | a group of workers had agreed on a very strange payment schedule . each of them would get $ 100 for every day that they had worked , but for every day they did not work will have to return $ 25 . after 30 days they realised they did not earn any money . how many days the workers did not work ? | the workers earn 4 times more than they have to return per day for not working . so the number of days they did not work is 4 times the number of days they worked . that means 24 days of not working in 30 days . correct answer b | a = 25 * 30
b = 100 + 25
c = a / b
d = 30 - c
|
a ) 5 hrs , b ) 7 hrs , c ) 12 hrs , d ) 14 hrs , e ) none | d | divide(const_1, subtract(divide(const_1, 2), divide(const_1, add(2, divide(1, 3))))) | a pump can fill a tank with a water in 2 hours . because of a leak , it took 2 x 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in | "sol . work done by the leak in 1 hour = ( 1 / 2 - 3 / 7 ) = 1 / 14 . β΄ leak will empty the tank in 14 hrs . answer d" | a = 1 / 2
b = 1 / 3
c = 2 + b
d = 1 / c
e = a - d
f = 1 / e
|
a ) 3 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4 | a | divide(add(divide(subtract(multiply(7, 2), 5), subtract(multiply(2, 2), const_1)), subtract(7, multiply(2, divide(subtract(multiply(7, 2), 5), subtract(multiply(2, 2), const_1))))), 2) | if 2 x + y = 7 and x + 2 y = 5 , then ( 2 x + 2 y ) / 3 = | "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 2 * 3 + 2 * 1 ) / 3 = ( 6 + 3 ) / 3 = 9 / 3 = 3 a" | a = 7 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l
n = m / 2
|
a ) 2 miles , b ) 4 miles , c ) 6.6 miles , d ) 8 miles , e ) 10 miles | c | multiply(divide(const_1, add(divide(const_1, 5), divide(const_1, 25))), const_1_6) | johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 25 miles per hour . how far is it to the school ? | answer : c ) 6.6 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 25 / ( 5 + 25 ) = 6.6 m / hr the distance between schoolhome should be half of that . ie . 6.6 miles answer c | a = 1 / 5
b = 1 / 25
c = a + b
d = 1 / c
e = d * const_1_6
|
a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8 | a | divide(add(multiply(factorial(12), factorial(3)), multiply(factorial(12), factorial(4))), 12) | what is the units digit of ( 12 ^ 3 ) ( 15 ^ 4 ) ( 31 ^ 7 ) ? | "the units digit of 12 ^ 3 is the units digit of 2 ^ 3 which is 8 . the units digit of 15 ^ 4 is the units digit of 5 ^ 4 which is 5 . the units digit of 31 ^ 7 is the units digit of 1 ^ 7 which is 1 . the units digit of 8 * 5 * 1 is 0 . the answer is a ." | a = math.factorial(12)
b = math.factorial(3)
c = a * b
d = math.factorial(12)
e = math.factorial(4)
f = d * e
g = c + f
h = g / 12
|
a ) 37.5 % , b ) 37.6 % , c ) 38.5 % , d ) 17.5 % , e ) 37.2 % | a | multiply(subtract(divide(subtract(const_100, 12), 64), const_1), const_100) | the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % ? | "let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 88 gain % = 24 / 64 * 100 = 37.5 % . answer : a" | a = 100 - 12
b = a / 64
c = b - 1
d = c * 100
|
a ) 74 , b ) 75 , c ) 69 , d ) 78 , e ) 45 | d | subtract(subtract(multiply(25, 18), multiply(12, 17)), multiply(12, 14)) | the average of 25 results is 18 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ? | "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 18 or , x = 78 . answer : option d" | a = 25 * 18
b = 12 * 17
c = a - b
d = 12 * 14
e = c - d
|
a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60 | a | subtract(speed(speed(300, 15), const_0_2778), 20) | an woman sitting in a train which is travelling at 20 kmph observes that a goods train travelling in a opposite direction , takes 15 seconds to pass him . if the goods train is 300 m long , find its speed . | relative speed = ( 300 / 15 ) m / s = ( 300 / 15 ) * ( 18 / 5 ) = 72 kmph speed of goods train = 72 - 20 = 52 kmph answer is a | a = speed - (
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a ) 145 , b ) 185 , c ) 253 , d ) 370 , e ) none | c | add(add(multiply(const_100, subtract(divide(10, const_2), 3)), multiply(divide(10, const_2), 10)), 3) | a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is | solution let the number be x . then 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digit is smaller than the units digit . hence , required number = 253 . answer c | a = 10 / 2
b = a - 3
c = 100 * b
d = 10 / 2
e = d * 10
f = c + e
g = f + 3
|
a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9 | c | subtract(7538, multiply(floor(divide(7538, 14)), 14)) | what least number must be subtracted from 7538 so that remaining no . is divisible by 14 | "explanation : on dividing 7538 by 14 we get the remainder 6 , so 6 should be subtracted option c" | a = 7538 / 14
b = math.floor(a)
c = b * 14
d = 7538 - c
|
a ) 12 % , b ) 15 % , c ) 18 % , d ) 20 % , e ) 25 % | d | add(subtract(subtract(const_100, 60), multiply(divide(3, 4), subtract(const_100, 60))), subtract(60, multiply(divide(5, 6), 60))) | in a survey of parents , exactly 5 / 6 of the mothers and 3 / 4 of the fathers held full - time jobs . if 60 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ? | "fathers without full - time jobs are 1 / 4 * 2 / 5 = 2 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 6 * 3 / 5 = 1 / 10 of all the parents surveyed . the percent of parents without full - time jobs is 2 / 20 + 1 / 10 = 1 / 5 = 20 % the answer is d ." | a = 100 - 60
b = 3 / 4
c = 100 - 60
d = b * c
e = a - d
f = 5 / 6
g = f * 60
h = 60 - g
i = e + h
|
a ) 9 km , b ) 72.5 km , c ) 190.75 km , d ) 848 km , e ) none of these | d | multiply(divide(5.3, 0.4), 64) | on a scale of map , 0.4 cm represents 5.3 km . if the distance between the points on the map is 64 cm , the actual distance between these points is : | explanation : let the actual distance be x km . then , more distance on the map , more is the actual distance ( direct proportion ) = > 0.4 : 64 : : 5.3 : x = > 0.4 x = 64 x 5.3 = > x = 64 x 5.3 / 0.4 = > x = 848 answer : d | a = 5 / 3
b = a * 64
|
a ) 79 litres , b ) 78 litres , c ) 77 litres , d ) 152 liters , e ) 304 litres | c | add(76, const_1) | the ratio w , by volume of soap to alcohol to water in a 76 litre solution is 2 : 50 : 100 . the solution is then altered by adding more soap , alcohol and water . after this alteration the ratio , by volume of soap to water in the solution doubles whereas the ratio , by volume of soap to water remains the same as before . what could be the resulting volume . | i guess it should be the ratio w , by volume ofsoaptowaterin the solutiondoubleswhereas the ratio , by volume ofalocoholtowaterremains thesameas before 2 : 50 : 100 = > 1 : 25 : 50 . if we add all the parts , we get 76 liters so we have 1 liters of soap , 25 liters of alcohol and 50 liters of water . now as per the question , soap : water doubles but alcohol to water remains the same . so soap becomes 2 liters , alcohol remains 25 liters and water remains at 50 liters . hence 77 liters - option c ) | a = 76 + 1
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a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 50 | b | divide(multiply(98, lcm(3, 5)), add(multiply(8, 3), add(multiply(5, 2), multiply(5, 3)))) | the sum of the numbers is 98 . if the ratio between the first and the second be 2 : 3 and that between the second and third be 5 : 8 , then find the second number ? | given ratios 2 : 3 5 : 8 10 : 15 : 24 the second number = 98 / ( 10 + 15 + 24 ) * 15 = 30 answer is b | a = math.lcm(3, 5)
b = 98 * a
c = 8 * 3
d = 5 * 2
e = 5 * 3
f = d + e
g = c + f
h = b / g
|
a ) 5 , b ) 11 , c ) 17 , d ) 22 , e ) 30 | d | add(divide(lcm(35, 55), 35), const_10) | jaime earned enough money by selling seashells at 35 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ? | let ' s test answer d : 22 seashells . . . . with 22 seashells , jamie would have 22 ( 35 ) = 770 cents . this would allow him to buy 14 books for 770 cents total , with no money left over . this is an exact match for what we were told , so this must be the answer . final answer : [ reveal ] spoiler : d | a = math.lcm(35, 55)
b = a / 35
c = b + 10
|
a ) 5.4 , b ) 5.9 , c ) 6.3 , d ) 6.7 , e ) 7.5 | b | add(divide(multiply(divide(1, 5), subtract(17, 8)), divide(40, const_100)), multiply(subtract(15, 8), divide(1, 5))) | a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 40 % longer than the smallest size , how long , in inches , is the shoe in size 15 ? | let x be the length of the size 8 shoe . then 0.4 x = 9 / 5 x = 4.5 inches the size 15 shoe has a length of 4.5 + 7 / 5 = 5.9 inches the answer is b . | a = 1 / 5
b = 17 - 8
c = a * b
d = 40 / 100
e = c / d
f = 15 - 8
g = 1 / 5
h = f * g
i = e + h
|
a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26 | c | divide(subtract(multiply(7, 1000), multiply(7, 780)), subtract(850, 780)) | the average salary / head of allthe workers in a workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ? | "let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y β 7000 + 780 y - 5460 = 850 y β 70 y = 1540 β΄ y = 22 so total number of workers = 22 c" | a = 7 * 1000
b = 7 * 780
c = a - b
d = 850 - 780
e = c / d
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a ) 1410 , b ) 1420 , c ) 1430 , d ) 1440 , e ) 1280 | e | divide(multiply(subtract(const_100, 20), 1600), const_100) | a man buys a cycle for rs . 1600 and sells it at a loss of 20 % . what is the selling price of the cycle ? | "s . p . = 80 % of rs . 1600 = 80 / 100 x 1600 = rs . 1280 answer : e" | a = 100 - 20
b = a * 1600
c = b / 100
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a ) 1628.4 , b ) 1534 , c ) 780 , d ) 1496 , e ) none of these | c | multiply(divide(add(multiply(10, 50), multiply(subtract(15, 10), 4)), subtract(15, subtract(15, 10))), 15) | 15 people went to a hotel for combine dinner party 10 of them spent rs . 50 each on their dinner and rest spent 4 more than the average expenditure of all the 15 . what was the total money spent by them . | "solution : let average expenditure of 15 people be x . then , 15 x = 10 * 50 + 5 * ( x + 4 ) ; or , 15 x = 10 * 50 + 5 x + 20 ; or , x = 52 ; so , total money spent = 52 * 15 = rs . 780 . answer : option c" | a = 10 * 50
b = 15 - 10
c = b * 4
d = a + c
e = 15 - 10
f = 15 - e
g = d / f
h = g * 15
|
a ) 5 , b ) 10 , c ) 16 , d ) 20 , e ) 9 | e | divide(multiply(15, 15), multiply(5, 5)) | what is the maximum number of pieces of birthday cake of size 5 β by 5 β that can be cut from a cake 15 β by 15 β ? | "the prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 3 ' pieces ' each , we have ( 3 ) ( 3 ) = 9 total smaller squares ( at maximum ) . e" | a = 15 * 15
b = 5 * 5
c = a / b
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a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m | d | divide(sqrt(divide(450, divide(const_1, const_2))), const_2) | the width of a rectangular hall is Β½ of its length . if the area of the hall is 450 sq . m , what is the difference between its length and breadth ? | "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 450 = x * 1 x / 2 x Β² = 900 x = 30 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 30 / 2 = 15 m answer : d" | a = 1 / 2
b = 450 / a
c = math.sqrt(b)
d = c / 2
|
a ) 4 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3 | a | add(divide(1, 7), divide(subtract(2, divide(4, 5)), add(2, divide(4, 5)))) | if p / q = 4 / 5 , then the value of 1 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ? | "answer given exp . = 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 1 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 1 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 1 / 7 + 6 / 14 = 1 / 7 + 3 / 7 = 4 / 7 correct option : a" | a = 1 / 7
b = 4 / 5
c = 2 - b
d = 4 / 5
e = 2 + d
f = c / e
g = a + f
|
a ) 16 , b ) 14 , c ) 28 , d ) 11 , e ) 9 | c | add(multiply(add(add(const_4, const_3), add(const_1, const_2)), const_2), multiply(floor(divide(5060, 1020)), floor(divide(7080, 3040)))) | when a natural number n is successively divided by 1020 , 3040 . the remainders are 5060 , 7080 . what will be the sum of the remainders if the order of the division is reversed ? | 10 20 30 40 50 60 70 80 leave the top right - most number 8 start with bottom right - most number 5 80 * 30 + 70 = 2470 2470 * 20 + 60 = 49460 49460 * 10 + 50 = 494650 this is the number required now , do the successive division in the reverse order the sum of the remainders is 28 hence , the correct option is c | a = 4 + 3
b = 1 + 2
c = a + b
d = c * 2
e = 5060 / 1020
f = math.floor(e)
g = 7080 / 3040
h = math.floor(g)
i = f * h
j = d + i
|
a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 136 | e | add(add(const_1, 68), 68) | in the land of oz only one or two - letter words are used . the local language has 68 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ? | "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 68 letters is 68 ; the number of 2 letter words ( xx ) that can be made from 68 letters is 68 * 68 , since each x can take 68 values . total : 68 + 68 * 68 . similarly : the number of 1 letter words ( x ) that can be made from 67 letters is 67 ; the number of 2 letter words ( xx ) that can be made from 67 letters is 67 * 67 , since each x can take 67 values . total : 67 + 67 * 67 . the difference is ( 68 + 68 * 68 ) - ( 67 + 67 * 67 ) = 136 . answer : e ." | a = 1 + 68
b = a + 68
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a ) 146.69 , b ) 146.66 , c ) 146.62 , d ) 146.61 , e ) 146.6 | b | subtract(multiply(add(divide(add(4, divide(1, 4)), const_100), 1), divide(8000, add(divide(add(divide(1, 2), 1), const_100), 1))), 8000) | if the sales tax be reduced from 4 ( 1 / 3 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 8000 ? | "explanation : required difference = ( 4 ( 1 / 3 ) of rs . 8000 ) - ( 2 ( 1 / 2 ) of rs . 8000 ) = ( 13 / 3 β 5 / 2 ) % of rs . 8000 = ( 11 / 6 ) x ( 1 / 100 ) x 8000 = rs . 146.66 answer : b" | a = 1 / 4
b = 4 + a
c = b / 100
d = c + 1
e = 1 / 2
f = e + 1
g = f / 100
h = g + 1
i = 8000 / h
j = d * i
k = j - 8000
|
a ) 43 , b ) 45 , c ) 47 , d ) 50 , e ) 52 | a | subtract(floor(divide(const_1000, lcm(3, 7))), floor(divide(const_100, lcm(3, 7)))) | how many positive 3 - digit integers are divisible by both 3 and 7 ? | a number to be divisible by both 3 and 7 should be divisible by the least common multiple of 3 and 7 so by 21 . multiples of 21 between 100 and 999 , inclusive is ( last - first ) / multiple + 1 = ( 987 - 105 ) / 21 + 1 = 42 + 1 = 43 answer : a . | a = math.lcm(3, 7)
b = 1000 / a
c = math.floor(b)
d = math.lcm(3, 7)
e = 100 / d
f = math.floor(e)
g = c - f
|
a ) 22.3 , b ) 33.2 , c ) 22.2 , d ) 51.3 , e ) 62.5 | e | divide(subtract(multiply(50, 62), add(45, 55)), subtract(50, const_2)) | the average of 50 numbers id 62 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is : | "explanation : total of 50 numbers = ( 50 Γ 62 ) = 3100 total of 48 numbers = ( 3100 - ( 45 + 55 ) ] = 3000 required average = 3000 / 48 = 62.5 answer : e" | a = 50 * 62
b = 45 + 55
c = a - b
d = 50 - 2
e = c / d
|
a ) 8.5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds | d | divide(100, multiply(144, const_0_2778)) | in what time will a train 100 meters long cross an electric pole , if its speed is 144 km / hr | "first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 100 / 40 = 2.5 seconds answer : d" | a = 144 * const_0_2778
b = 100 / a
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a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | divide(multiply(factorial(6), factorial(6)), multiply(factorial(6), factorial(3))) | what is the unit digit of ( 6 ! * 6 ! / 6 ! * 3 ! ) ? | ( 6 ! * 6 ! / 6 ! * 3 ! ) = ( 6 ! / 3 ! ) = 720 / 6 = 120 units digit of the above product will be equal to 0 answer a | a = math.factorial(6)
b = math.factorial(6)
c = a * b
d = math.factorial(6)
e = math.factorial(3)
f = d * e
g = c / f
|
a ) 11 : 5 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4 | a | divide(add(multiply(5, divide(add(6, 2), add(5, 3))), 6), add(multiply(3, divide(add(6, 2), add(5, 3))), 2)) | two vessels contains equal number of mixtures milk and water in the ratio 5 : 3 and 6 : 2 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ? | "the ratio of milk and water in the new vessel is = ( 5 / 8 + 6 / 8 ) : ( 3 / 8 + 2 / 8 ) = 11 / 8 : 5 / 8 = 11 : 5 answer is a" | a = 6 + 2
b = 5 + 3
c = a / b
d = 5 * c
e = d + 6
f = 6 + 2
g = 5 + 3
h = f / g
i = 3 * h
j = i + 2
k = e / j
|
a ) 130 , b ) 80 , c ) 100 , d ) 120 , e ) 150 | a | add(multiply(39, 3), divide(39, 3)) | mona and donald fly to rome for the weekend . they take cash only in notes of $ 10 and notes of β¬ 10 . mona carries 3 times the amount of euros donald carries . she also carries as many dollars as donald carries . the number of β¬ 10 notes they take is double the number of $ 10 notes they take . if donald carries a total of 39 notes ( of either $ 10 or β¬ 10 , ) then what is the total number of notes ( of either $ 10 or β¬ 10 , ) they take ? | let e 10 = x no . d 10 = y no . donald is having x + y notes mona carries 3 x + y again x = 2 y or donald x + y = 39 or 3 y = 39 y = 13 ; x = 26 , total notes they carry = 104 + 26 = 130 a | a = 39 * 3
b = 39 / 3
c = a + b
|
a ) 33 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47 | a | subtract(34, const_1) | in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 34 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ? | "working backward from the day it ' s covered : day 34 : fully covered day 33 : half covered so 33 days answer : a" | a = 34 - 1
|
a ) h β 12 , b ) h β 56 , c ) h β 14 , d ) h + 14 , e ) h - 126 | e | multiply(14, divide(4, 5)) | the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 5 days ago , the water level was at h inches . what will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same ? | "drop = 14 inches / day 5 days ago = h , means now it ' s equal h - 70 and in 4 days = h - 70 - 56 = h - 126 answer e" | a = 4 / 5
b = 14 * a
|
a ) 28 , b ) 27 , c ) 55 , d ) 18 , e ) 67.7 | e | divide(add(165, 850), multiply(54, const_0_2778)) | how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 850 meters in length ? | "t = ( 850 + 165 ) / 54 * 18 / 5 t = 67.7 answer : e" | a = 165 + 850
b = 54 * const_0_2778
c = a / b
|
a ) 1800 , b ) 1900 , c ) 2100 , d ) 2000 , e ) 2200 | d | add(350, 250) | in the faculty of reverse - engineering , 350 second year students study numeric methods , 250 second year students study automatic control of airborne vehicles and 100 second year students study them both . how many students are there in the faculty if the second year students are approximately 25 % of the total ? | "total number of students studying both are 350 + 250 - 100 = 500 ( subtracting the 100 since they were included in the both the other numbers already ) . so 25 % of total is 500 , so 100 % is 2000 answer is d" | a = 350 + 250
|
a ) 5 , b ) 7 , c ) 4 , d ) 11 , e ) 12 | c | add(divide(subtract(multiply(floor(divide(79, 11)), 11), multiply(add(floor(divide(39, 11)), const_1), 11)), 11), const_1) | how many numbers from 39 to 79 are exactly divisible by 11 ? | 39 / 11 = 1 and 79 / 11 = 7 = = > 7 - 3 = 4 numbers answer : c | a = 79 / 11
b = math.floor(a)
c = b * 11
d = 39 / 11
e = math.floor(d)
f = e + 1
g = f * 11
h = c - g
i = h / 11
j = i + 1
|
a ) 4.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12 | c | multiply(multiply(12, 2), divide(1, 2)) | in the coordinate plane , points ( x , 1 ) and ( 12 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y = | "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 1 ) = ( 2 , 1 ) and ( 12 , y ) = ( 12,6 ) - - > x + y = 2 + 6 = 8 . answer : c ." | a = 12 * 2
b = 1 / 2
c = a * b
|
a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 4 | e | multiply(divide(8, 12), 6) | when a number is divided by 6 & then multiply by 12 the answer is 8 what is the no . ? | "if $ x $ is the number , x / 6 * 12 = 8 = > 2 x = 8 = > x = 4.0 e" | a = 8 / 12
b = a * 6
|
a ) 7787 , b ) 8000 , c ) 15000 , d ) 1277 , e ) 2081 | c | divide(divide(13650, subtract(const_1, divide(30, const_100))), add(const_1, divide(30, const_100))) | in one year , the population , of a village increased by 30 % and in the next year , it decreased by 30 % . if at the end of 2 nd year , the population was 13650 , what was it in the beginning ? | "x * 130 / 100 * 70 / 100 = 13650 x * 0.91 = 13650 x = 13650 / 0.91 = > 15000 answer : c" | a = 30 / 100
b = 1 - a
c = 13650 / b
d = 30 / 100
e = 1 + d
f = c / e
|
['a ) 22 square inches', 'b ) 20 square inches', 'c ) 24 square inches', 'd ) 28 square inches', 'e ) 30 square inches'] | a | divide(subtract(subtract(208, 24), multiply(175, divide(80, const_100))), const_2) | three table runners have a combined area of 208 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ? | total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 208 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 208 - 24 - 140 all three = 22 answer : a | a = 208 - 24
b = 80 / 100
c = 175 * b
d = a - c
e = d / 2
|
a ) 7,000 , b ) 4,000 , c ) 6,000 , d ) 5,000 , e ) 8,000 | d | divide(multiply(const_100, 460), 9) | calculate the amount that an investor needs to be invest to earn $ 460 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 9 % compounded semi - annually ? | "the approach is substitution , our interest requirement is 460 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields 460 in 12 months 5,000 yielded $ 460 using the formula a = p ( 1 + r / n ) nt hence answer is d" | a = 100 * 460
b = a / 9
|
a ) 11115 , b ) 15110 , c ) 15120 , d ) 15210 , e ) 12510 | b | multiply(38,50, const_10) | the least number , which when divided by 48,60 , 72,108 and 140 leaves 38,50 , 62,98 and 130 as remainder respectively , is : | "solution here ( 48 - 38 ) = 10 , ( 60 - 50 ) = 10 , ( 72 - 62 ) = 10 , ( 108 - 98 ) = 10 & ( 140 - 130 ) = 10 . so , required number = ( l . c . m . of 48 , 60,72 , 108,140 ) - 10 = 15120 - 10 = 15110 . answer b" | a = 38 * 50
|
a ) 10,000 , b ) 11.0 , c ) 12,000 , d ) 13,200 , e ) 14,000 | d | subtract(multiply(multiply(const_12, const_100), 25), add(multiply(400, 12), multiply(subtract(subtract(25, 12), const_1), 1,000))) | company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 12 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ? | "the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 12 of the products sell for less than $ 1,000 , then let ' s make these 12 items to be at $ 400 each ( min possible ) . now , the remaining 12 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 12 items is $ 1,000 . thus the minimum possible value of 24 products is 12 * 400 + 12 * 1,000 = $ 16,800 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 16,800 = $ 13,200 . answer : d ." | a = 12 * 100
b = a * 25
c = 400 * 12
d = 25 - 12
e = d - 1
f = e * 1
g = c + f
h = b - g
|
a ) 6400 , b ) 2000 , c ) 5500 , d ) 7400 , e ) 3000 | b | divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(80, 11.25), 6)) | how many bricks , each measuring 80 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ? | "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 80 x 11.25 x 6 ) = 2000 answer : b" | a = 8 * 100
b = 6 * 100
c = a * b
d = c * 22
e = 80 * 11
f = e * 6
g = d / f
|
a ) 0 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph | d | divide(subtract(13, 8), const_2) | a man goes downstream at 13 kmph , and upstream 8 kmph . the speed of the stream is | "speed of the stream = 1 / 2 ( 13 - 8 ) kmph = 2.5 kmph . correct option : d" | a = 13 - 8
b = a / 2
|
a ) 2 / 3 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 6 , e ) 7 / 8 | b | divide(add(multiply(divide(1, 2), const_12), multiply(divide(const_12, 2), divide(1, 2))), const_12) | drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 2 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ? | "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 2 ) y = ( 3 / 4 ) y the answer is b ." | a = 1 / 2
b = a * 12
c = 12 / 2
d = 1 / 2
e = c * d
f = b + e
g = f / 12
|
a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg | d | add(multiply(2.5, 8), 45) | the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ? | the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 45 + 20 ) kg = 65 kg the answer is d . | a = 2 * 5
b = a + 45
|
a ) a ) 65 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 88 | a | subtract(multiply(add(32, 3), add(10, const_1)), multiply(10, 32)) | average of 10 matches is 32 , how many runs one should should score to increase his average by 3 runs . | "explanation : average after 11 innings should be 35 so , required score = ( 11 * 35 ) - ( 10 * 32 ) = 385 - 320 = 65 answer : option a" | a = 32 + 3
b = 10 + 1
c = a * b
d = 10 * 32
e = c - d
|
a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10 | d | multiply(subtract(multiply(const_2, const_4), const_3), divide(multiply(const_2, const_4), const_2)) | how many internal diagonals does a hexagon ( six sided polygon ) have ? | "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 6 no . of diagonals = 6 ( 6 - 3 ) / 2 = 9 ans d" | a = 2 * 4
b = a - 3
c = 2 * 4
d = c / 2
e = b * d
|
a ) 4 , b ) 6 , c ) 18 , d ) 10 , e ) 12 | c | multiply(multiply(3, 2), 3) | running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 3 w widgets . | "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 18 days to doing 3 w widgets . answer : c" | a = 3 * 2
b = a * 3
|
a ) 25 , b ) 28 , c ) 58 , d ) 34 , e ) 36 | c | add(add(add(add(add(add(add(add(const_2, const_3), add(const_2, const_3)), add(add(const_2, const_3), const_2)), add(7, const_2)), add(add(7, const_2), const_2)), add(add(add(7, const_2), const_2), const_4)), add(add(add(add(7, const_2), const_2), const_4), const_2)), add(add(add(add(add(7, const_2), const_2), const_4), const_2), const_4)) | find a sum for 1 st 7 prime number ' s ? | "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 ) = 58 note : 1 is not a prime number option c" | a = 2 + 3
b = 2 + 3
c = a + b
d = 2 + 3
e = d + 2
f = c + e
g = 7 + 2
h = f + g
i = 7 + 2
j = i + 2
k = h + j
l = 7 + 2
m = l + 2
n = m + 4
o = k + n
p = 7 + 2
q = p + 2
r = q + 4
s = r + 2
t = o + s
u = 7 + 2
v = u + 2
w = v + 4
x = w + 2
y = x + 4
z = t + y
|
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