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 ) 7 min , b ) 6 min , c ) 9 min , d ) 8 min , e ) 11 min | d | multiply(const_60, divide(subtract(52, 45), 52)) | excluding stoppages , the speed of a bus is 52 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ? | "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( 7 / 52 ) x 60 = 8 min answer : d" | a = 52 - 45
b = a / 52
c = const_60 * b
|
a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 14 | a | add(const_3, const_4) | what is the smallest positive integer x , such that β 392 x is an integer ? | "for a perfect square , the powers of prime factors should be even . 392 can be broken up as 2 ^ 3 * 7 ^ 2 . you just need 2 to be multiplied to this number so that the number finally becomes 2 ^ 4 * 7 ^ 2 which is a perfect square . therefore x = 2 . answer : a" | a = 3 + 4
|
a ) 33 , b ) 12 , c ) 68 , d ) 36 , e ) 54 | e | divide(multiply(60, 10), const_100) | the cost of an article is decreased by 10 % . if the original cost is $ 60 , find the decrease cost . | "original cost = $ 60 decrease in it = 10 % of $ 60 = 10 / 100 Γ£ β 60 = 600 / 100 = $ 6 therefore , decrease cost = $ 60 - $ 6 = $ 54 answer : e" | a = 60 * 10
b = a / 100
|
a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 8 / 21 | e | multiply(multiply(multiply(divide(multiply(5, const_2), multiply(5, const_2)), divide(multiply(4, 4), subtract(multiply(5, const_2), const_1))), divide(subtract(multiply(4, 4), const_2), multiply(4, 4))), divide(subtract(subtract(multiply(4, 4), const_2), const_2), subtract(multiply(4, 4), const_1))) | if 4 people are selected from a group of 5 married couples , what is the probability that none of them would be married to each other ? | "if we are to select 4 people from 5 couples without any restriction , how many ways can we make the selection ? 10 ! / 4 ! 6 ! = 210 if we are to select 4 people from 5 couples with restriction that no married couple can both make it to the group , only a representative ? 5 ! / 4 ! 1 ! = 5 but we know that to select a... | a = 5 * 2
b = 5 * 2
c = a / b
d = 4 * 4
e = 5 * 2
f = e - 1
g = d / f
h = c * g
i = 4 * 4
j = i - 2
k = 4 * 4
l = j / k
m = h * l
n = 4 * 4
o = n - 2
p = o - 2
q = 4 * 4
r = q - 1
s = p / r
t = m * s
|
a ) 5729 , b ) 5760 , c ) 2889 , d ) 3600 , e ) 2799 | d | divide(multiply(2.5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1)) | a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 2.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ? | "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 2.5 = 3600 . answer : d" | a = 8 * const_60
b = 2 * 5
c = 8 * const_60
d = 6 * const_60
e = c / d
f = e - 1
g = b / f
|
a ) a ) 78 , b ) b ) 82 , c ) c ) 96 , d ) d ) 91 , e ) e ) 85 | c | divide(add(subtract(multiply(100, 10), 50), 10), 10) | the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ? | "correct avg marks = 100 + ( 10 - 50 ) / 10 avg = 100 - 4 = 96 answer is c" | a = 100 * 10
b = a - 50
c = b + 10
d = c / 10
|
a ) $ 250 , b ) $ 300 , c ) $ 750 , d ) $ 600 , e ) $ 1000 | c | multiply(2500, divide(3, const_100)) | find the simple interest on $ 2500 for 3 years at 10 % per annum ? | "si = ptr / 100 = 2500 * 3 * 10 / 100 = $ 750 answer is c" | a = 3 / 100
b = 2500 * a
|
a ) a ) 6.24 , b ) b ) 4.1 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24 | b | max(multiply(subtract(add(55, 10), const_1), subtract(divide(10, 40), divide(10, 55))), const_4) | due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 40 = 10 * 3 / 2 = 15 time difference = 4.1 ans : b" | a = 55 + 10
b = a - 1
c = 10 / 40
d = 10 / 55
e = c - d
f = b * e
g = max(f)
|
a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 25 days | e | add(16, divide(subtract(const_1, divide(16, 40)), add(inverse(40), inverse(24)))) | p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 16 days till the completion of the work . how long did the work last ? | "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 16 days = 16 Γ£ β ( 1 / 40 ) = 2 / 5 remaining work = 1 Γ’ β¬ β 2 / 5 = 3 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 3 / 5 ) / ( 1 / 15 ) = 9 t... | a = 16 / 40
b = 1 - a
c = 1/(40)
d = 1/(24)
e = c + d
f = b / e
g = 16 + f
|
a ) 750 , b ) 700 , c ) 900 , d ) 850 , e ) none of these | c | divide(multiply(const_100, 360), subtract(70, subtract(const_100, 70))) | in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 360 vote β s majority . what is the total number of votes polled ? | "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 360 ( 40 * 9 = 360 ) 100 % - - - - - > 900 ( 100 * 9 = 900 ) answer : option c" | a = 100 * 360
b = 100 - 70
c = 70 - b
d = a / c
|
a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 33.33 % , e ) none of these | b | multiply(subtract(const_1, divide(const_100, add(const_100, 25))), const_100) | if the price of petrol increases by 25 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ? | "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 25 ) i . e 125 . now , his consumption should be reduced to : - = 125 β 100125 β 100 . hence , the consumption should be reduced to 20 % . answer : b" | a = 100 + 25
b = 100 / a
c = 1 - b
d = c * 100
|
a ) 30.47 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 % | a | multiply(divide(multiply(divide(60, const_100), 640), multiply(const_100, power(const_4, const_2))), const_100) | an association of mathematics teachers has 1,260 members . only 640 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ? | "total number of members = 1260 number of members that cast votes = 640 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 640 = 384 percent of total membership that voted for winning candidate = ( 384 / 1260 ) * 100 = 30.47 % answer a" | a = 60 / 100
b = a * 640
c = 4 ** 2
d = 100 * c
e = b / d
f = e * 100
|
a ) 10 , b ) 30 , c ) 45 , d ) 60 , e ) 90 | c | divide(multiply(10, subtract(10, const_1)), const_2) | there are 10 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? | "10 players are there . two players play one game with one another . so 10 c 2 = 10 * 9 / 2 = 45 so option c is correct" | a = 10 - 1
b = 10 * a
c = b / 2
|
a ) 8 , b ) 9 , c ) 16 , d ) 6 , e ) 4 | c | multiply(divide(const_1, multiply(add(const_100, 20), divide(const_1, subtract(const_100, 20)))), 24) | by selling 24 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ? | "80 % - - - 24 120 % - - - ? 80 / 120 * 24 = 16 answer : c" | a = 100 + 20
b = 100 - 20
c = 1 / b
d = a * c
e = 1 / d
f = e * 24
|
a ) 34778 , b ) 26888 , c ) 2899 , d ) 18975 , e ) 12778 | d | divide(multiply(add(const_100, 10), add(divide(multiply(13500, const_100), subtract(const_100, 20)), add(125, 250))), const_100) | ramesh purchased a refrigerator for rs . 13500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ? | "price at which the tv set is bought = rs . 13,500 discount offered = 20 % marked price = 13500 * 100 / 80 = rs . 16875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no di... | a = 100 + 10
b = 13500 * 100
c = 100 - 20
d = b / c
e = 125 + 250
f = d + e
g = a * f
h = g / 100
|
a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) none of these | c | multiply(subtract(const_1, divide(9, 15)), 15) | suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 15 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ? | "the part of job that suresh completes in 9 hours = 9 Γ’ Β β 15 = 3 Γ’ Β β 5 remaining job = 1 - 3 Γ’ Β β 5 = 2 Γ’ Β β 5 remaining job can be done by ashutosh in 2 Γ’ Β β 5 Γ£ β 15 = 6 hours answer c" | a = 9 / 15
b = 1 - a
c = b * 15
|
a ) 0.5 , b ) 1.0 , c ) 1.5 , d ) 2.0 , e ) 2.5 | a | divide(multiply(10, 0.31), 4) | water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 4 meters . what is value of the radius ? | "10 * 0.31 = 3.1 m ^ 3 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 4 ) which is about 1 / 4 r = 1 / 2 the answer is a ." | a = 10 * 0
b = a / 4
|
a ) 4 , b ) 3 , c ) 10 , d ) 2 , e ) 9 | e | add(4, 2) | in a family 4 people eat only vegetarian , 3 people eat only non veg . , 2 people eat both veg and non veg . . how many people are in the family ? | "total number of people in family = veg + non veg + ( both veg and non veg ) total = 4 + 3 + 2 = 9 answer is e" | a = 4 + 2
|
a ) 0 , b ) 3 , c ) 4 , d ) 5 , e ) 1 | a | divide(72, 36) | how many of the positive factors of 36 are not factors of 72 | "factors of 36 - 1 , 2,3 , 4,6 , 9,12 , 18,36 , factors of 72 - 1,2 , 3,4 , 6,8 , 9,12 , 18,24 , 36,72 , comparing both , we have no factors of 36 which are not factors of 72 - 0 answer ( a )" | a = 72 / 36
|
a ) 34 , b ) 36 , c ) 31 , d ) 40 , e ) ( f ) 42 | c | add(add(add(const_10, add(1, 1)), add(2, 6)), add(7, 1)) | trapezoid jklm in the x - y plane has coordinates j = ( β 2 , β 1 ) , k = ( β 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , β 1 ) . what is its perimeter ? | "jk = 2 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 31 c" | a = 1 + 1
b = 10 + a
c = 2 + 6
d = b + c
e = 7 + 1
f = d + e
|
a ) 6.75 , b ) 7 , c ) 8 , d ) 12 , e ) 14 | d | divide(multiply(6, 4), subtract(multiply(const_2, 4), 6)) | noelle walks from point a to point b at an average speed of 4 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 6 kilometers per hour ? | "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 6 = 2 * 4 * x / 4 + x x = 12 d is the answer" | a = 6 * 4
b = 2 * 4
c = b - 6
d = a / c
|
a ) 1242 , b ) 1542 , c ) 1742 , d ) 1610 , e ) 1842 | a | multiply(divide(divide(subtract(multiply(4, add(const_10, const_1)), multiply(const_1, 4)), subtract(multiply(4, const_2), multiply(const_1, 4))), const_2), add(multiply(4, const_2), multiply(4, add(const_10, const_1)))) | the sum of all two digit numbers divisible by 4 is | "required numbers are 12 , 16,20 . . . . . 96 this is an a . p . in which a = 12 , d = 4 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 12 + ( n - 1 ) * 6 = 96 , 12 + 4 n - 4 = 96 4 + 4 n = 96 4 n = 96 - 4 n = 92 / 4 then n = 23 . required sum = n / 2 ( a + l ) = 23 / 2 ( 12 + 9... | a = 10 + 1
b = 4 * a
c = 1 * 4
d = b - c
e = 4 * 2
f = 1 * 4
g = e - f
h = d / g
i = h / 2
j = 4 * 2
k = 10 + 1
l = 4 * k
m = j + l
n = i * m
|
a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 % | d | multiply(const_100, subtract(multiply(add(const_1, divide(50, const_100)), multiply(add(const_1, divide(35, const_100)), subtract(const_1, divide(20, const_100)))), const_1)) | the profits of qrs company rose 35 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ? | assume 100 in march , then 135 in april as 35 % increase , then 108 in may as 20 % decrease from april , and then 162 in june which is 150 % of 108 . so overall increase is from 100 to 162 is 62 % answer d | a = 50 / 100
b = 1 + a
c = 35 / 100
d = 1 + c
e = 20 / 100
f = 1 - e
g = d * f
h = b * g
i = h - 1
j = 100 * i
|
a ) 760 , b ) 284 , c ) 288 , d ) 864 , e ) 820 | d | multiply(36, 24) | find the area of a parallelogram with base 36 cm and height 24 cm ? | "area of a parallelogram = base * height = 36 * 24 = 864 cm 2 answer : d" | a = 36 * 24
|
a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters | e | subtract(18, divide(multiply(18, 40), 60)) | what quantity of water should taken out to concentrate 18 liters of 40 % acidic liquid to 60 % acidic liquid ? | "required answer is = 18 ( 60 - 40 ) / 60 = 6 liters answer is e" | a = 18 * 40
b = a / 60
c = 18 - b
|
a ) 20 , b ) 10 , c ) 32 , d ) 40 , e ) 5 | c | subtract(multiply(26, const_2), multiply(10, const_2)) | if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 26 , what is the value of r - p ? | "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 52 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 32 hence , the correct answer is c" | a = 26 * 2
b = 10 * 2
c = a - b
|
a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,1200 , e ) 550,1450 | d | divide(multiply(6, 4), add(6, 4)) | a can do a work in 6 days . b can do the same work in 4 days . both a & b together will finish the work and they got $ 2000 from that work . find their shares ? | "ratio of their works a : b = 6 : 4 ratio of their wages a : b = 2 : 3 a ' s share = ( 2 / 5 ) 2000 = 800 b ' s share = ( 3 / 5 ) 2000 = 1200 correct option is d" | a = 6 * 4
b = 6 + 4
c = a / b
|
a ) 88 , b ) 108 , c ) 110 , d ) 75 , e ) 93 | d | subtract(subtract(subtract(182, 35), subtract(73, const_1)), const_4) | veena ranks 73 rd from the top in a class of 182 . what is her rank from the bottom if 35 students have failed the examination ? | "total student = 182 failed = 35 paasd student = 182 - 35 = 160 from bottom her rank is = 147 - 73 + 1 = 75 answer : d" | a = 182 - 35
b = 73 - 1
c = a - b
d = c - 4
|
a ) 30 , b ) 32 , c ) 34 , d ) 36 , e ) 38 | e | multiply(divide(20, 6), const_12) | the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 20 ? | "$ 20 = 3 * $ 6 + $ 2 the number of doughnuts is 3 * 12 + 2 = 38 the answer is e ." | a = 20 / 6
b = a * 12
|
a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | a | multiply(divide(70, const_100), divide(multiply(4, const_100), multiply(subtract(divide(70, const_100), divide(divide(const_100, const_2), const_100)), const_100))) | a bowl was half full of water . 4 cups of water were then added to the bowl , filling the bowl to 70 % of its capacity . how many cups of water are now in the bowl ? | lets say total volume of the container = v initial water content is half of total volume = v / 2 then 4 cups of water were added . current water content = ( v / 2 ) + 4 cups = ( 70 / 100 ) v = > v = 20 cups = > current water content is equivalent to = v / 2 + 4 cups = 20 / 2 + 4 = 14 cups ; answer : a | a = 70 / 100
b = 4 * 100
c = 70 / 100
d = 100 / 2
e = d / 100
f = c - e
g = f * 100
h = b / g
i = a * h
|
a ) 60,88 , b ) 60,86 , c ) 60,82 , d ) 60,84 , e ) 60,83 | d | multiply(5, 25) | two numbers are in the ratio of 5 : 7 . if 25 be subtracted from each , they are in the ratio of 35 : 59 . find the numbers ? | "( 5 x - 25 ) : ( 7 x - 25 ) = 35 : 59 x = 12 = > 60,84 answer : d" | a = 5 * 25
|
a ) 8 , b ) 15 , c ) 20 , d ) 27 , e ) 39 | c | multiply(floor(power(divide(189, const_2), divide(const_1, const_3))), power(subtract(189, power(floor(power(divide(189, const_2), divide(const_1, const_3))), const_3)), divide(const_1, const_3))) | the number 189 is equal to the sum of the cubes of two integers . what is the product of those integers ? | "4 ^ 3 + 5 ^ 3 = 189 the number is 4 * 5 = 20 c" | a = 189 / 2
b = 1 / 3
c = a ** b
d = math.floor(c)
e = 189 / 2
f = 1 / 3
g = e ** f
h = math.floor(g)
i = h ** 3
j = 189 - i
k = 1 / 3
l = j ** k
m = d * l
|
a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500 | a | divide(multiply(multiply(const_1000, const_100), 0.036), divide(36000, const_1000)) | in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 36000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ? | "0.037 * 10 ^ 5 can be written as 3600 74000 * 10 ^ ( - 3 ) can be written as 36 required = 3600 / 36 = 100 answer : a" | a = 1000 * 100
b = a * 0
c = 36000 / 1000
d = b / c
|
a ) 24 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) 12 m | a | multiply(divide(120, 45), subtract(45, 36)) | in 120 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by : | "distance covered by b in 9 sec . = 120 / 45 x 9 m = 24 m . a beats b by 24 metres . answer : option a" | a = 120 / 45
b = 45 - 36
c = a * b
|
a ) 20 , b ) 27 , c ) 42 , d ) 32 , e ) 60 | b | divide(450, multiply(subtract(63, 3), const_0_2778)) | how many seconds will a 450 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 450 * 3 / 50 = 27 sec . answer : option b" | a = 63 - 3
b = a * const_0_2778
c = 450 / b
|
a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 40 % | e | multiply(subtract(divide(22, const_100), divide(subtract(9, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(10, 3), multiply(18, 2)))), const_100) | fox jeans regularly sell for $ 10 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22... | "x discount on pony jeans , ( 0.22 - x ) discount on fox jeans . set the equation : 3 * 10 ( 0.22 - x ) + 2 * 18 x = 9 - - > x = 0.4 = 40 % answer : e ." | a = 22 / 100
b = 22 / 100
c = 18 * 2
d = b * c
e = 9 - d
f = 10 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
|
a ) 60 , b ) 72 , c ) 48 , d ) 36 , e ) 64 | a | divide(add(multiply(3, 30), multiply(3, 30)), subtract(add(3, 3), 3)) | a taxi leaves point a 3 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours . | let the speed of bus be v - 30 , speed of taxi be v the bus travelled a total of 6 hrs and taxi a total of 3 hrs . hence 6 * ( v - 30 ) = 3 v 6 v - 180 = 3 v 3 v = 180 v = 60 mph a | a = 3 * 30
b = 3 * 30
c = a + b
d = 3 + 3
e = d - 3
f = c / e
|
a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 180 kmph , e ) 59 kmph | d | subtract(multiply(7, multiply(const_60.0, const_0_2778)), 100) | a train 100 m long crosses a platform 250 m long in 7 sec ; find the speed of the train ? | "d = 100 + 250 = 350 t = 7 s = 350 / 7 * 18 / 5 = 180 kmph answer : d" | a = const_60 * 0
b = 7 * a
c = b - 100
|
a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30 | e | multiply(subtract(216, 10), 10) | what is the greatest positive integer x such that 6 ^ x is a factor of 216 ^ 10 ? | "216 ^ 10 = ( 6 ^ 3 ) ^ 10 = 6 ^ 30 answer : e" | a = 216 - 10
b = a * 10
|
a ) 4 % . , b ) 25 / 4 % . , c ) 5 % , d ) 6 % . , e ) 3 % . | c | divide(add(multiply(floor(sqrt(multiply(divide(1, 4), const_100))), const_10), 1), const_3) | simple interest on a certain sum at a certain annual rate of interest is 1 / 4 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is : | "explanation : let sum = x . then , s . i . = x / 4 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 4 ? r ^ 2 = 100 / 4 = 25 r = 5 hence , rate of interest = 5 % . answer : c" | a = 1 / 4
b = a * 100
c = math.sqrt(b)
d = math.floor(c)
e = d * 10
f = e + 1
g = f / 3
|
a ) 150 , b ) 135 , c ) 160 , d ) 200 , e ) 155 | d | divide(add(40, 40), divide(40, const_100)) | ravish has to secure 40 % marks to clear his board exam of class 10 th . he got 40 marks and failed by 40 marks . what is the maximum marks ? | d 200 to pass the exam ravish needs 40 + 40 = 80 marks . = > ( 80 / 40 ) * 100 = 200 | a = 40 + 40
b = 40 / 100
c = a / b
|
a ) 83 , b ) 85 , c ) 87 , d ) 79 , e ) 89 | d | subtract(add(floor(divide(172, const_3)), floor(divide(172, add(const_1, const_4)))), multiply(floor(divide(172, multiply(const_3, add(const_1, const_4)))), const_2)) | there are 172 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off ... | "editing my solution : number of switches = 172 number of switches turned on by a : 3 , 6 , . . . 171 = 57 number of switches turned on by b : 5 , 10 , . . . . 170 = 34 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a a... | a = 172 / 3
b = math.floor(a)
c = 1 + 4
d = 172 / c
e = math.floor(d)
f = b + e
g = 1 + 4
h = 3 * g
i = 172 / h
j = math.floor(i)
k = j * 2
l = f - k
|
a ) 140 , b ) 175 , c ) 210 , d ) 245 , e ) 280 | d | multiply(35, divide(multiply(divide(72, const_60), 35), subtract(41, 35))) | car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 41 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ? | "in 72 minutes , car x travels 42 miles . car y gains 6 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d ." | a = 72 / const_60
b = a * 35
c = 41 - 35
d = b / c
e = 35 * d
|
a ) 5 , b ) 24 , c ) 7 , d ) 42 , e ) 6 | c | divide(add(divide(48, 6), divide(36, 6)), const_2) | a man swims downstream 36 km and upstream 48 km taking 6 hours each time , what is the speed of the man in still water ? | "36 - - - 6 ds = 6 ? - - - - 1 48 - - - - 6 us = 8 ? - - - - 1 m = ? m = ( 6 + 8 ) / 2 = 7 answer : c" | a = 48 / 6
b = 36 / 6
c = a + b
d = c / 2
|
a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 27 / 100 , e ) 9 / 100 | d | divide(subtract(100, subtract(add(50, 40), 17)), 100) | a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 17 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neithe... | c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 17 - 2 cmb = 100 b - cb - mb - 2 cmb = 27 hence the... | a = 50 + 40
b = a - 17
c = 100 - b
d = c / 100
|
a ) $ 130 , b ) $ 136 , c ) $ 144 , d ) $ 150 , e ) $ 160 | c | subtract(add(150, divide(multiply(150, 20), const_100)), divide(multiply(add(150, divide(multiply(150, 20), const_100)), 20), const_100)) | the original price of a suit is $ 150 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ? | "0.8 * ( 1.2 * 150 ) = $ 144 the answer is c ." | a = 150 * 20
b = a / 100
c = 150 + b
d = 150 * 20
e = d / 100
f = 150 + e
g = f * 20
h = g / 100
i = c - h
|
a ) 812 cm , b ) 820 cm , c ) 850 cm , d ) 889 cm , e ) 854 cm | d | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 350), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | convert 350 inches into centimeter ? | "1 inch = 2.54 cm 350 inches = 100 * 2.54 = 889 cm answer is d" | a = 3 + 2
b = a * 2
c = 3 + 2
d = c * 2
e = b * d
f = e * 350
g = 3 + 2
h = g * 2
i = 3 + 2
j = i * 2
k = h * j
l = f / k
|
a ) 22.8 m . , b ) 21.6 m . , c ) 21.1 m . , d ) 20.6 m . , e ) 22.5 m . | b | multiply(sqrt(divide(divide(624, 4), const_3)), const_3) | the length of a rectangular floor is more than its breadth by 200 % . if rs . 624 is required to paint the floor at the rate of rs . 4 per sq m , then what would be the length of the floor ? | "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 624 / 4 = 156 sq m l b = 156 i . e . , l * l / 3 = 156 l 2 = 468 = > l = 21.6 m . answer : b" | a = 624 / 4
b = a / 3
c = math.sqrt(b)
d = c * 3
|
a ) 10 / 3 , b ) 8 , c ) 9 , d ) 7 / 3 , e ) 12 | a | inverse(add(divide(const_1, 10), multiply(divide(const_1, 10), const_2))) | a is twice as fast as b . if b alone can do a piece of work in 10 days , in what time can a and b together complete the work ? | "a can do the work in 10 / 2 i . e . , 5 days . a and b ' s one day ' s work = 1 / 5 + 1 / 10 = ( 2 + 1 ) / 10 = 10 / 3 so a and b together can do the work in 10 / 3 days . answer : a" | a = 1 / 10
b = 1 / 10
c = b * 2
d = a + c
e = 1/(d)
|
a ) 65 sec , b ) 36 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec | b | subtract(divide(multiply(1.10, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(0.4, const_1000), divide(multiply(90, const_1000), const_3600))) | two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ? | "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.4 = 1.5 km = 1500 m . required time = 1500 * 3 / 125 = 36 sec . answer : b" | a = 1 * 10
b = 60 * 1000
c = b / 3600
d = a / c
e = 0 * 4
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
|
a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 9 s , e ) 7.4 s | d | multiply(divide(divide(225, const_1000), 90), const_3600) | how much time does a train 225 metres long running at 90 km / hr take to pass a pole ? | "explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 225 / t t = 9 s answer : d" | a = 225 / 1000
b = a / 90
c = b * 3600
|
a ) 1000 , b ) 1200 , c ) 1400 , d ) 1600 , e ) 1800 | b | divide(divide(divide(120, subtract(const_1, divide(3, 5))), divide(3, 4)), divide(1, 3)) | of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many ... | "let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 3 ) x = 120 ( 6 / 60 ) x = 120 x = 1200 the answer is b ." | a = 3 / 5
b = 1 - a
c = 120 / b
d = 3 / 4
e = c / d
f = 1 / 3
g = e / f
|
a ) 11.73 , b ) 12.5 , c ) 13.8 , d ) 14 , e ) 15.87 | b | divide(divide(multiply(300, subtract(const_100, 20)), const_100), 20) | the price of lunch for 20 people was $ 300 including a 20 % gratuity for service . what was the average price per person , excluding the gratuity ? | "clearly b is the answer i used poe here lets consider option ( b ) 20 * 12.5 = 250 now 250 ( 120 / 100 ) = 300 = > possible answer imo b" | a = 100 - 20
b = 300 * a
c = b / 100
d = c / 20
|
['a ) 79.5', 'b ) 89.3', 'c ) 85.5', 'd ) 75.4', 'e ) 72.5'] | a | subtract(divide(power(28, const_2), const_2), divide(power(25, const_2), const_2)) | the size of a flat - screen television is given as the length of the screen β s diagonal . how many square inches greater is the screen of a square 28 - inch flat - screen television than a square 25 - inch flat - screen television ? | if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 28 - inch flat - screen television the diagonal ( hypotenuse ) = 28 so , we can apply the pythagorean theorem to get x Β² + x Β² = 28 Β² s... | a = 28 ** 2
b = a / 2
c = 25 ** 2
d = c / 2
e = b - d
|
a ) 60 cm , b ) 63.2 cm , c ) 70 cm , d ) 80 cm , e ) 90 cm | b | multiply(multiply(const_2, divide(multiply(subtract(14, const_3), const_2), add(const_4, const_3))), 14) | the sector of a circle has radius of 14 cm and central angle 144 o . find its perimeter ? | "perimeter of the sector = length of the arc + 2 ( radius ) = ( 144 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 35.2 + 28 = 63.2 cm answer : b" | a = 14 - 3
b = a * 2
c = 4 + 3
d = b / c
e = 2 * d
f = e * 14
|
a ) 73.5 , b ) 68 , c ) 60.5 , d ) none of these , e ) can not be determined | c | divide(subtract(5, multiply(const_3, 4)), multiply(const_3, const_2)) | a number is doubled and 4 is added . if the resultant is divided by 5 , it becomes 25 . what is that number ? | "solution let the number be x . then , ( 2 x + 4 ) / 5 βΉ = βΊ 25 βΉ = βΊ 2 x + 4 = 125 βΉ = βΊ 2 x = 121 x = 60.5 answer c" | a = 3 * 4
b = 5 - a
c = 3 * 2
d = b / c
|
a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7 | c | divide(4, add(multiply(4, 3), 4)) | chris mixed 4 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ? | "1 lbs of raisin = $ 1 4 lbs of raisin = $ 4 1 lbs of nuts = $ 3 4 lbs of nuts = $ 12 total value of mixture = 12 + 4 = 16 fraction of the value of raisin = 4 / 16 = 1 / 4 ans : c" | a = 4 * 3
b = a + 4
c = 4 / b
|
a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) 172 | b | add(subtract(subtract(const_1000, const_10), multiply(multiply(const_10, multiply(3, 3)), multiply(const_4, const_2))), const_10) | how many 3 digit numbers are divisible by 6 in all ? | "explanation : required numbers are 102 , 108 , 114 , . . . , 996 this is an a . p . in which a = 102 , d = 6 and l = 996 let the number of terms be n . then , a + ( n - 1 ) d = 996 102 + ( n - 1 ) x 6 = 996 6 x ( n - 1 ) = 894 ( n - 1 ) = 149 n = 150 . answer is b" | a = 1000 - 10
b = 3 * 3
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
|
a ) a ) 3623216 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3636649 , e ) e ) 3625216 | d | multiply(divide(1907, 1907), const_100) | 1907 x 1907 = ? | "1907 x 1907 = ( 1907 ) 2 = ( 1900 + 7 ) 2 = ( 1900 ) 2 + ( 7 ) 2 + ( 2 x 1900 x 7 ) = 3610000 + 49 + 26600 . = 3636649 . d )" | a = 1907 / 1907
b = a * 100
|
a ) 720 , b ) 360 , c ) 250 , d ) 280 , e ) 290 | a | multiply(divide(3120, add(add(2, 3), 4)), 4) | an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ? | "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 3120 = rs . 720 an... | a = 2 + 3
b = a + 4
c = 3120 / b
d = c * 4
|
a ) 5 % , b ) 18 % , c ) 32 % , d ) 35 % , e ) 38 % | c | multiply(subtract(multiply(add(divide(20, const_100), const_1), add(const_1, divide(10, const_100))), const_1), const_100) | a certain company β s profit in 1996 was 10 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company β s profit in 1997 was what percent greater than its profit in 1995 ? | profit in 1995 - 100 profit in 1996 - 110 % increae profit in 1997 in comparison to 1995 = 10 + 110 * 20 % = 32 correct option : c | a = 20 / 100
b = a + 1
c = 10 / 100
d = 1 + c
e = b * d
f = e - 1
g = f * 100
|
a ) 8 , b ) 5 , c ) 1 , d ) 3 , e ) 4 | c | divide(sqrt(multiply(add(6, 2), add(15, 3))), add(11, 1)) | if a * b * c = ( β ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 11 . | "6 * 15 * 11 = ( β ( 6 + 2 ) ( 15 + 3 ) ) / ( 11 + 1 ) = ( β 8 * 18 ) / 12 = ( β 144 ) / 12 = 12 / 124 = 1 . answer is c" | a = 6 + 2
b = 15 + 3
c = a * b
d = math.sqrt(c)
e = 11 + 1
f = d / e
|
a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700 | b | multiply(divide(1500, 5), subtract(8, 3)) | an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 8 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ? | "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 8 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2400 . hence , ( r - p ) = ( 2400 - 900 ) = 1500 answer : b" | a = 1500 / 5
b = 8 - 3
c = a * b
|
a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 20 | d | subtract(add(add(add(50, 45), 8), 224), add(add(multiply(const_2, 50), multiply(const_4, 45)), multiply(const_4, 8))) | in a caravan , in addition to 50 hens , there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads in the caravan , the number of keepers is | explanation : let number of keepers be x . then , total number of feet = 2 x 50 + 4 x 45 + 4 x 8 + 2 x = 2 x + 312 . total number of heads = 50 + 45 + 8 + x = 103 + x . therefore ( 2 x + 312 ) = ( 103 + x ) + 224 or x = 15 . answer : d | a = 50 + 45
b = a + 8
c = b + 224
d = 2 * 50
e = 4 * 45
f = d + e
g = 4 * 8
h = f + g
i = c - h
|
a ) 288 , b ) 160 , c ) 188 , d ) 188 , e ) 12 | b | divide(add(1500, 500), divide(1500, 120)) | a 1500 m long train crosses a tree in 120 sec , how much time will it take to pass a platform 500 m long ? | "l = s * t s = 1500 / 120 s = 12.5 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 12.5 t = 160 sec answer : b" | a = 1500 + 500
b = 1500 / 120
c = a / b
|
a ) 6 , b ) 5 , c ) 1 , d ) 3 , e ) 2 | c | divide(6, add(4, 2)) | n is a positive integer . when n + 1 is divided by 6 , the remainder is 4 . what is the remainder when n is divided by 2 ? | n + 1 = 6 a + 4 i . e . n + 1 = 10 , 16 , 22 , 28 , . . . etc . i . e . n = 9 , 15 , 21 , 27 , . . . etc . when n is divided by 2 remainder is always 1 answer : c | a = 4 + 2
b = 6 / a
|
a ) 2999 , b ) 1350 , c ) 2677 , d ) 2898 , e ) 2787 | b | multiply(subtract(rectangle_area(add(75, multiply(2.5, 2)), add(55, multiply(2.5, 2))), rectangle_area(75, 55)), 2) | a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ? | "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 2 = rs . 1350 answerb" | a = 2 * 5
b = 75 + a
c = 2 * 5
d = 55 + c
e = rectangle_area - (
f = e * rectangle_area
|
a ) 3 , b ) 1 , c ) 3 / 4 , d ) - 1 / 3 , e ) - 3 | c | divide(3, subtract(9, 5)) | if 9 / ( 5 + 3 / x ) = 1 , then x = | the expression 9 / ( 5 + 3 / x ) = 1 should have been equal to something . if 9 / ( 5 + 3 / x ) = 1 = > 9 x / ( 5 x + 3 ) = 1 = > 9 x = 5 x + 3 = > 4 x = 3 = > x = 3 / 4 correct option : c | a = 9 - 5
b = 3 / a
|
a ) 31 , b ) 32 , c ) 46 , d ) 47 , e ) 48 | a | multiply(subtract(multiply(divide(subtract(const_100, 25), const_100), divide(add(const_100, 75), const_100)), const_1), const_100) | if price of t . v set is reduced by 25 % , then its sale increases by 75 % , find net effect on sale value | "- a + b + ( ( - a ) ( b ) / 100 ) = - 25 + 75 + ( - 25 * 75 ) / 100 = - 25 + 75 - 19 = 31 answer : a" | a = 100 - 25
b = a / 100
c = 100 + 75
d = c / 100
e = b * d
f = e - 1
g = f * 100
|
a ) 400 , b ) 300 , c ) 425 , d ) 450 , e ) 325 | a | subtract(negate(175), multiply(subtract(50, 100), divide(subtract(50, 100), subtract(25, 50)))) | 25 , 50 , 100 , 175 , 275 , ( . . . . ) | "explanation : the pattern is 25 , 50 , 75 , 100 , etc . hence 125 = 400 answer : a" | a = negate - (
|
a ) 30 , b ) 20 , c ) 19 , d ) 29 , e ) 39 | b | divide(multiply(multiply(15, 21), 8), multiply(multiply(21, 9), divide(2, 3))) | 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 9 hrs . each would it take for 21 women if 3 women do as much work as 2 men ? | "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 9 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 9 * ( 2 / 3 ) ) days = > 20 days answer : b" | a = 15 * 21
b = a * 8
c = 21 * 9
d = 2 / 3
e = c * d
f = b / e
|
a ) 8 / 15 , b ) 4 / 3 , c ) 15 / 8 , d ) 24 / 7 , e ) 15 / 4 | d | multiply(divide(const_1, add(divide(const_1, 3), divide(const_1, 4))), const_2) | kathleen can paint a room in 3 hours , and anthony can paint an identical room in 4 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ? | "( 1 / 3 + 1 / 4 ) t = 2 t = 24 / 7 answer : d" | a = 1 / 3
b = 1 / 4
c = a + b
d = 1 / c
e = d * 2
|
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | d | floor(const_2) | how many prime numbers are between 25 / 8 and 213 / 6 ? | "25 / 8 = 4 - 213 / 6 = 36 - prime numbers between 4 and 36 are 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , and 31 - sign signifies that the number is marginally less . answer d" | a = math.floor(2)
|
a ) β 14 , b ) β 10 , c ) β 6 , d ) 10 , e ) 14 | a | subtract(negate(2), multiply(2, subtract(2, negate(2)))) | on the number line , the number p is twice as many units from - 2 as - 2 is from 4 . if p is less than β 2 , what is the value of p ? | "distance between - 2 and 4 = 6 since number p is twice as many units from - 2 as - 2 is from 4 , therefore p can be - 14 since , p is less than - 2 , the value of p = - 14 answer a" | a = negate - (
|
a ) 18 : 13 , b ) 16 : 13 , c ) 19 : 13 , d ) 14 : 11 , e ) 13 : 11 | c | power(1, 3) | two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 3 : 1 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel . | "vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 375 , water = 125 ; vessel a + b = 800 gallons - - > milk = 475 , water 325 . the ratio = 475 / 325 - - > 19 / 13 answer : c" | a = 1 ** 3
|
a ) 48 kmph , b ) 78 kmph , c ) 28 kmph , d ) 18 kmph , e ) 98 kmph | a | divide(add(40, 60), const_2) | a bus travels first half distance between two places with a speed of 40 kmph and the rest half distance with a speed of 60 kmph . the average speed of the bus is ? | explanation : we know that speed = distance traveled / time taken let the total distance traveled by the car is 2 x km . then time taken by it to cover first half is hour . and for second half is hour . then average speed = total distance travelled / total time taken . i . e . = > = 48 kmph . answer : a | a = 40 + 60
b = a / 2
|
a ) 54888 , b ) 2777 , c ) 5400 , d ) 1278 , e ) 2881 | c | multiply(subtract(divide(add(multiply(add(100, 20), 5), 400), 20), 5), add(100, 20)) | in a hostel there were 100 students . to accommodate 20 more students the average is decreased by rupees 5 . but total expenditure increased by rs . 400 . find the total expenditure of the hostel now ? | "100 x + 400 = 12 ( x β 5 ) x = 50 100 * 50 + 400 = 5400 answer : c" | a = 100 + 20
b = a * 5
c = b + 400
d = c / 20
e = d - 5
f = 100 + 20
g = e * f
|
a ) rs . 750 , b ) rs . 1000 , c ) rs . 850 , d ) rs . 1250 , e ) none of these | d | multiply(multiply(50, 1), divide(add(add(add(multiply(const_10, const_100), multiply(const_3, const_100)), multiply(const_2, const_10)), add(const_2, const_3)), add(multiply(1, 3), multiply(50, 1)))) | the ratio between the number of passengers travelling by i and ii class between the two railway stations is 1 : 50 , whereas the ratio of i and ii class fares between the same stations is 3 : 1 . if on a particular day rs . 1,325 were collected from the passengers travelling between these stations , then what was the a... | let x be the number of passengers and y be the fare taken from passengers . 3 xy + 50 xy = 1325 = > xy = 25 amount collected from ii class passengers = 25 Γ 50 = rs . 1250 . answer : d | a = 50 * 1
b = 10 * 100
c = 3 * 100
d = b + c
e = 2 * 10
f = d + e
g = 2 + 3
h = f + g
i = 1 * 3
j = 50 * 1
k = i + j
l = h / k
m = a * l
|
a ) 14700 , b ) 15960 , c ) 14900 , d ) 14300 , e ) 14000 | b | multiply(add(divide(subtract(multiply(5000, const_10), add(add(4000, 5000), 5000)), const_3), add(4000, 5000)), divide(multiply(multiply(const_3, const_12), const_1000), multiply(5000, const_10))) | a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 38,000 , what will be the amount a receives ? | "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 β 3 x + 14000 = 50000 β 3 x = 50000 β 14000 = 36000 β x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 inves... | a = 5000 * 10
b = 4000 + 5000
c = b + 5000
d = a - c
e = d / 3
f = 4000 + 5000
g = e + f
h = 3 * 12
i = h * 1000
j = 5000 * 10
k = i / j
l = g * k
|
a ) 1.07 , b ) 1.0 , c ) - 1.065 , d ) 1.71 , e ) 2.71 | c | divide(subtract(negate(multiply(1.9, 0.6)), multiply(2.6, 1.2)), 4.0) | ( ( - 1.9 ) ( 0.6 ) β ( 2.6 ) ( 1.2 ) ) / 4.0 = ? | "dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 1.065 answer c" | a = 1 * 9
b = negate - (
c = 2 * 6
d = b / c
|
a ) 178.5 , b ) 156.6 , c ) 160.4 , d ) 163.6 , e ) 164.1 | d | add(multiply(divide(30, 20), divide(120, 40)), 5) | if Γ’ β¬ Ε * Γ’ β¬ Β is called Γ’ β¬ Ε + Γ’ β¬ Β , Γ’ β¬ Ε / Γ’ β¬ Β is called Γ’ β¬ Ε * Γ’ β¬ Β , Γ’ β¬ Ε - Γ’ β¬ Β is called Γ’ β¬ Ε / Γ’ β¬ Β , Γ’ β¬ Ε + Γ’ β¬ Β is called Γ’ β¬ Ε - Γ’ β¬ Β . 120 / 40 Γ’ β¬ β 30 * 20 - 5 = ? | "explanation : given : 120 / 40 Γ’ β¬ β 30 * 20 - 5 = ? substituting the coded symbols for mathematical operations , we get , 120 * 40 / 30 + 20 / 5 = ? 120 * 1.33 + 4 = ? 159.6 + 4 = 163.6 answer : d" | a = 30 / 20
b = 120 / 40
c = a * b
d = c + 5
|
a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21 | a | add(divide(add(multiply(add(7, 2), 2), sqrt(subtract(power(multiply(add(7, 2), 2), const_2), multiply(subtract(power(7, const_2), power(2, const_2)), const_4)))), const_2), 2) | the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle . the shorter side of the triangle is 7 centimeters less than the longer side . find the length of the hypotenuse . | let a and b be the two sides of the triangle such that a is longer than b . the statement ` ` the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle ' ' may be fomulated by h = a + 2 or a = h - 2 the statement ` ` the shorter side of the triangle is 7 centimeters less than the lon... | a = 7 + 2
b = a * 2
c = 7 + 2
d = c * 2
e = d ** 2
f = 7 ** 2
g = 2 ** 2
h = f - g
i = h * 4
j = e - i
k = math.sqrt(j)
l = b + k
m = l / 2
n = m + 2
|
a ) 13.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 13.9 sec , e ) 47.98 sec | d | divide(add(120, 145), multiply(70, const_0_2778)) | how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 145 m length ? | "speed = 70 * 5 / 18 = 19 m / sec total distance covered = 120 + 145 = 265 m . required time = 265 / 19 = 13.9 sec . answer : d" | a = 120 + 145
b = 70 * const_0_2778
c = a / b
|
a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | d | divide(divide(divide(divide(650, const_2), const_3), const_4), divide(const_10, const_2)) | if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 650 , what is the least possible value of n ? | "650 = 2 * 5 * 5 * 13 so the least value forncan be 13 . d" | a = 650 / 2
b = a / 3
c = b / 4
d = 10 / 2
e = c / d
|
a ) 70 feet , b ) 52 feet , c ) 32 feet , d ) 12 feet , e ) 55 feet | a | add(multiply(divide(600, 30), const_2), 30) | a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ? | "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 30 * breadth = 600 = > breadth = 20 feet area to be fenced = 2 b + l = 2 * 20 + 30 = 70 feet answer : option a" | a = 600 / 30
b = a * 2
c = b + 30
|
a ) s . 254 , b ) s . 284 , c ) s . 290 , d ) s . 304 , e ) s . 380 | a | divide(multiply(560, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | two employees x and y are paid a total of rs . 560 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ? | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 560 but x = 120 % of y = 120 y / 100 = 12 y / 10 β΄ 12 y / 10 + y = 560 β y [ 12 / 10 + 1 ] = 560 β 22 y / 10 = 560 β 22 y = 5600 β y = 5600 / 22 = rs . 254 ( approx ) a )" | a = 1 + 4
b = a * 2
c = 560 * b
d = 1 + 4
e = d * 2
f = e + 1
g = f * 2
h = c / g
|
a ) 426 , b ) 406 , c ) 401 , d ) 409 , e ) 405 | b | multiply(add(28, const_1), divide(28, const_2)) | calculate the sum of first 28 natural numbers . | "solution we know that ( 1 + 2 + 3 + . . . . . + 28 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 28 ) = ( 28 Γ 29 / 2 ) = 406 . answer b" | a = 28 + 1
b = 28 / 2
c = a * b
|
a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 2 , e ) 1 / 32 | a | divide(const_1, power(const_2, 4)) | when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land on the same side each time ? | "must be either 4 tails or 4 heads 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 1 / 16 + 1 / 16 = 1 / 8 answer : a" | a = 2 ** 4
b = 1 / a
|
a ) 32 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42 | a | add(add(add(const_10, add(1, 3)), add(2, 6)), add(7, 3)) | trapezoid jklm in the x - y plane has coordinates j = ( β 2 , β 3 ) , k = ( β 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , β 3 ) . what is its perimeter ? | "jk = 4 lm = 10 kl = using distance formula 10 jm = using distance formula 8 sum of all is 32 a" | a = 1 + 3
b = 10 + a
c = 2 + 6
d = b + c
e = 7 + 3
f = d + e
|
a ) 60 % , b ) 50 % , c ) 70 % , d ) 90 % , e ) 55 % | b | multiply(subtract(const_1, divide(8, 16)), const_100) | the c . p of 8 books is equal to the s . p of 16 books . find his gain % or loss % ? | "explanation : 8 cp = 16 sp 16 - - - 8 cp loss 100 - - - ? = > 50 % loss answer : b" | a = 8 / 16
b = 1 - a
c = b * 100
|
a ) 28000 , b ) 30000 , c ) 32000 , d ) 35000 , e ) none of these | d | divide(5000, divide(multiply(const_1, const_1), add(multiply(const_3, const_2), multiply(const_1, const_1)))) | a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 5000 as profit , what is their total profit ? | "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 5000 = > total profit = 5000 * 7 = 35000 . answer : option d" | a = 1 * 1
b = 3 * 2
c = 1 * 1
d = b + c
e = a / d
f = 5000 / e
|
a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7 | b | add(divide(1, 6), divide(1, 8)) | a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 1 day . for how many number of days should a and c should work together to complete the remaining work ? | b work 1 / 8 * 1 = 1 / 8 remaining work = 1 - 1 / 8 = 7 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocal 7 / 8 * remaining work = 8 / 7 * 1 / 4 = 2 / 7 answer : b | a = 1 / 6
b = 1 / 8
c = a + b
|
a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9 | e | multiply(3, divide(negate(multiply(add(add(7, 4), 3), 6)), subtract(multiply(add(add(7, 4), 3), const_2), multiply(add(add(7, 4), 3), 4)))) | the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 6 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ? | "the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 6 pounds of clothes doubles the ratio of books to clothes , then 6 pounds represents half the weight of the clothes . 2 k = 6 pounds and then k = 3 pounds . the electronics weigh 3 ( 3 ) = 9 pounds . the answer is e ." | a = 7 + 4
b = a + 3
c = b * 6
d = negate / (
e = 7 + 4
f = e + 3
g = f * 2
h = 7 + 4
i = h + 3
j = i * 4
k = g - j
l = 3 * d
|
a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 9 / 10 | e | divide(add(subtract(50, add(5, 9)), 9), 50) | a bag consists of 50 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? | "bag consists of 50 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 50 - 5 - 9 = 36 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 50 + 36 / 50 = ... | a = 5 + 9
b = 50 - a
c = b + 9
d = c / 50
|
a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54 | e | subtract(200, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2)) | how many integers between 100 and 200 , inclusive , can not be evenly divided by 3 nor 5 ? | "the total numbers between 100 and 200 , inclusive , is 101 . 3 * 34 = 102 and 3 * 66 = 198 so the number of multiples of 3 is 33 . 5 * 20 = 100 and 5 * 40 = 200 so the number of multiples of 5 is 21 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 13 = 195 so the number of multiples of 1... | a = 2 * 100
b = 3 + 4
c = b * 10
d = a + c
e = d + 2
f = 200 - e
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 7 | d | subtract(divide(add(add(add(2, 4), 7), 22), add(const_4, const_1)), 4) | for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 22 , the mean is how much greater than the median ? | mean = ( x + x + 2 + x + 4 + x + 7 + x + 22 ) / 5 = ( 5 x + 35 ) / 5 = x + 7 median = x + 4 thus mean - median = x + 7 - ( x + 4 ) = 3 answer = d | a = 2 + 4
b = a + 7
c = b + 22
d = 4 + 1
e = c / d
f = e - 4
|
a ) 398 km , b ) 892 km , c ) 387 km , d ) 300 km , e ) 230 km | d | multiply(inverse(add(inverse(multiply(const_2, 30)), inverse(multiply(25, const_2)))), 11) | pavan travelled for 11 hours . he covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph . find the distance travelled by pavan ? | "let the distance travelled be x km . total time = ( x / 2 ) / 30 + ( x / 2 ) / 25 = 11 = > x / 60 + x / 50 = 11 = > ( 5 x + 6 x ) / 300 = 11 = > x = 300 km answer : d" | a = 2 * 30
b = 1/(a)
c = 25 * 2
d = 1/(c)
e = b + d
f = 1/(e)
g = f * 11
|
a ) 392 , b ) 229 , c ) 765 , d ) 493 , e ) 540 | c | multiply(multiply(multiply(divide(3, 4), divide(1, 2)), divide(2, 5)), 5100) | 3 / 4 of 1 / 2 of 2 / 5 of 5100 = ? | "c 765 ? = 5100 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 765" | a = 3 / 4
b = 1 / 2
c = a * b
d = 2 / 5
e = c * d
f = e * 5100
|
a ) rs . 6000 , b ) rs . 4590 , c ) rs . 4560 , d ) rs . 4500 , e ) rs . 4570 | b | multiply(divide(102, 20), 900) | in order to obtain an income of rs . 900 from 20 % stock at rs . 102 , one must make an investment of | "explanation : market value = rs . 102 . required income = rs . 900 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 20 ( ie , 20 % of the face value 100 ) , investment = rs . 102 to obtain rs . 900 , investment = 102 / 20 Γ£ β 900 = rs . 4590 answer : option... | a = 102 / 20
b = a * 900
|
a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 11 / 9 , e ) 8 / 7 | d | divide(multiply(add(add(const_100, const_60), const_1), 10), const_100) | what is the value of ( p + q ) / ( p - q ) if p / q is 10 ? | "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 10 + 1 ) / ( 10 - 1 ) = 11 / 9 = 11 / 9 answer : d" | a = 100 + const_60
b = a + 1
c = b * 10
d = c / 100
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.