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 . 4... | 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 ... | 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 , ... | "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 acti... | 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 c... | 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 th... | "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 ... | "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 ar... | 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 ... | 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 - 1... | 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 ... | 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 player... | "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
|
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
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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 tha... | a = 2 + 2
b = a + 1
|
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 .... | 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 befo... | 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 que... | 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
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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
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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 ... | 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
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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
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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... | 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
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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 tota... | 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
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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 ... | 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 ... | 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)... | 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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