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 ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1 | a | multiply(const_4, 1) | how many prime numbers between 1 and 100 are factors of 10010 ? | "factor of 10010 = 2 * 5 * 7 * 11 * 13 - - - 5 prime numbers a" | a = 4 * 1
|
a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 3 / 4 | a | divide(const_1, 2) | one lady has 2 children , one of her child is boy , what is the probability of having both are boys | n ( s ) = one of her child is boy out of 2 children = bb , bg = 2 n ( e ) = both are boys = bb = 1 so p = n ( e ) / n ( s ) = 1 / 2 answer : a | a = 1 / 2
|
a ) 28 % , b ) 41 % , c ) 60 % , d ) 72 % , e ) 78 % | c | multiply(divide(multiply(divide(70, const_100), divide(subtract(10, 7), 10)), add(multiply(divide(subtract(const_100, 80), const_100), divide(7, 10)), multiply(divide(70, const_100), divide(subtract(10, 7), 10)))), const_100) | 7 / 10 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is | "total population = 100 ( assume ) . 7 / 10 * 100 = 70 people from montague . 3 / 10 * 100 = 30 people from capulet . 0.2 * 70 = 14 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 14 + 21 ) = ~ 60 . answer : c" | a = 70 / 100
b = 10 - 7
c = b / 10
d = a * c
e = 100 - 80
f = e / 100
g = 7 / 10
h = f * g
i = 70 / 100
j = 10 - 7
k = j / 10
l = i * k
m = h + l
n = d / m
o = n * 100
|
a ) 11 : 6 , b ) 12 : 7 , c ) 29 : 18 , d ) 15 : 6 , e ) 13 : 6 | c | divide(multiply(58, 8), multiply(70, 4)) | car a runs at the speed of 58 km / hr & reaches its destination in 8 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ? | "sol . distance travelled by car a = 58 ã — 8 = 464 km distance travelled by car b = 70 ã — 4 = 280 km ratio = 464 / 280 = 29 : 18 c" | a = 58 * 8
b = 70 * 4
c = a / b
|
a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150 | b | add(divide(subtract(subtract(301, 1), add(99, 1)), 2), 1) | for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum y of all the even integers between 99 and 301 ? | "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum y = average * total count = 200 * 101 = 20,200 answer is b" | a = 301 - 1
b = 99 + 1
c = a - b
d = c / 2
e = d + 1
|
a ) 1 : 3 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 4 , e ) 3 : 5 | a | add(subtract(add(1, 3), add(4, 2)), const_1) | in what ratio p : q should the mixture p of milk and water in the ratio of 4 : 1 be mixed with another mixture q of milk and water in the ratio 2 : 3 so that the resultant mixture contains equal quantities of milk and water ? | "( 4 / 5 ) * p + ( 2 / 5 ) * q = ( 1 / 5 ) * p + ( 3 / 5 ) * q 3 p = q p / q = 1 / 3 the answer is a ." | a = 1 + 3
b = 4 + 2
c = a - b
d = c + 1
|
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | d | floor(sqrt(divide(12100, 101))) | if n is an integer and 101 n ^ 2 is less than or equal to 12100 , what is the greatest possible value of n ? | "101 * n ^ 2 < = 12100 n ^ 2 < = 12100 / 101 which will be less than 121 since 12100 / 100 = 121 which is the square of 9 next closest value of n where n ^ 2 < = 121 is 10 ans d" | a = 12100 / 101
b = math.sqrt(a)
c = math.floor(b)
|
a ) 40 , b ) 39 , c ) 42 , d ) 55 , e ) 29 | a | divide(subtract(subtract(multiply(12, const_60), multiply(9, const_60)), 20), add(3, const_1)) | how many minutes is it before 12 noon if 20 minutes ago it was 3 times as many minutes after 9 am ? | a 40 minutes , or 11.20 am | a = 12 * const_60
b = 9 * const_60
c = a - b
d = c - 20
e = 3 + 1
f = d / e
|
a ) 1 / 10 , b ) 1 / 6 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 4 | b | divide(choose(const_2.0, const_2.0), choose(add(4, 5), 4)) | a bag holds 4 red marbles and 5 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ? | "probability of selecting first red marble = 4 / 9 probability of selecting second red marble without replacement = 3 / 8 final probability = 4 / 9 * 3 / 8 = 1 / 6 the correct answer is b ." | a = math.comb(2, 0)
b = 4 + 5
c = math.comb(b, 4)
d = a / c
|
a ) 32 , b ) 88 , c ) 70 , d ) 123 , e ) 12 | a | add(add(power(add(add(divide(subtract(subtract(140, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(140, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(140, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(140, const_10), const_2), const_4), const_2), const_2))) | the sum of four consecutive even numbers is 140 . what would be the smallest number ? | "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x - 2 ) = 32 answer : a" | a = 140 - 10
b = a - 2
c = b / 4
d = c + 2
e = d + 2
f = e ** 2
g = 140 - 10
h = g - 2
i = h / 4
j = i + 2
k = j + 2
l = k + 2
m = l ** 2
n = f + m
o = 140 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 140 - 10
t = s - 2
u = t / 4
v = u + 2
w = v ** 2
x = r + w
y = n + x
|
a ) 5 , b ) 10 , c ) 8 , d ) none of these , e ) can not be determined | d | divide(subtract(5, multiply(const_3, 15)), multiply(const_3, const_2)) | a number is doubled and 15 is added . if the resultant is multiplied by 5 , it becomes 125 . what is that number ? | "solution let the number be x . then , 5 ( 2 x + 15 ) ‹ = › 125 ‹ = › 2 x + 15 = 25 ‹ = › 2 x = 10 x = 5 . answer d" | a = 3 * 15
b = 5 - a
c = 3 * 2
d = b / c
|
a ) 87 , b ) 69 , c ) 40 , d ) 72 , e ) 24 | e | divide(add(360, 140), divide(multiply(75, const_1000), const_3600)) | a train is 360 meter long is running at a speed of 75 km / hour . in what time will it pass a bridge of 140 meter length ? | "speed = 75 km / hr = 75 * ( 5 / 18 ) m / sec = 125 / 6 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 6 / 125 ) = 24 seconds answer : e" | a = 360 + 140
b = 75 * 1000
c = b / 3600
d = a / c
|
a ) 15 , b ) 30 , c ) 60 , d ) 90 , e ) 120 | b | divide(divide(120, const_2), const_2) | if k ^ 3 is divisible by 120 , what is the least possible value of integer k ? | "k ^ 3 = 120 * x = 2 ^ 3 * 3 * 5 * x the factors of k must at minimum include 2 * 3 * 5 = 30 . the answer is b ." | a = 120 / 2
b = a / 2
|
a ) 1131000 , b ) 979923 , c ) 980241 , d ) 2356677 , e ) 1083875 | a | multiply(1000000, multiply(multiply(add(const_1, divide(20, const_100)), subtract(const_1, divide(35, const_100))), add(const_1, divide(35, const_100)))) | population of a city in 20004 was 1000000 . if in 2005 there isan increment of 20 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007 | "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 20 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1131000 a" | a = 20 / 100
b = 1 + a
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f
h = e * g
i = 1000000 * h
|
a ) 12 , b ) 16 , c ) 34 , d ) 38 , e ) 8 | e | divide(40, add(4, const_1)) | sony and johnny caught 40 fishes . sony caught 4 times as many as johnny . how many fishes did johnny catch ? | s + j = 40 s = 4 * j j = 8 answer : e | a = 4 + 1
b = 40 / a
|
a ) 34 , b ) 50 , c ) 32 , d ) 28 , e ) 45 | e | add(add(20, 20), subtract(9, const_4)) | two digits in brother ' s age are the same as the digit in the sister ' s age , but in reverse order . in 20 9 years brother will be twice as old as sister will be then . what is the difference in their current age ? | brother ' s age = 10 x + y so sister ' s age = 10 y + x . . after 29 years , 10 x + y + 29 = 2 * ( 10 y + x + 29 ) . . . . so 29 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 6 . . . so ages are 61 and 16 and ans as found correctly by u is e . . 45 | a = 20 + 20
b = 9 - 4
c = a + b
|
a ) 40000 , b ) 60000 , c ) 10000 , d ) 25000 , e ) 50000 | c | divide(2000, multiply(divide(1, 3), divide(3, 5))) | a man owns 1 / 3 of market reserch beauro buzness , and sells 3 / 5 of his shares for 2000 rs , what is the value of buzness ? | "if value of business = x total sell ( 1 x / 3 ) ( 3 / 5 ) = 2000 - > x = 10000 answer : c" | a = 1 / 3
b = 3 / 5
c = a * b
d = 2000 / c
|
a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000 | c | multiply(const_1000, divide(1, 100)) | a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 100 that a person who randomly guesses the answer to each question will be a winner ? | "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 100 n = 50 satisfies this . c" | a = 1 / 100
b = 1000 * a
|
a ) 14 , b ) 18 , c ) 24 , d ) 28 , e ) none of these | b | divide(divide(1600, 20), divide(1400, multiply(15, 21))) | 15 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ? | "binders books days 15 1400 21 x 1600 20 x / 15 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 18 answer : b" | a = 1600 / 20
b = 15 * 21
c = 1400 / b
d = a / c
|
a ) 5307 , b ) 5647 , c ) 5927 , d ) 6297 , e ) 6557 | d | add(lcm(lcm(18, 70), lcm(100, 84)), 3) | what is the smallest number which when increased by 3 is divisible by 18 , 70 , 100 and 84 ? | "when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d ." | a = math.lcm(18, 70)
b = math.lcm(100, 84)
c = math.lcm(a, b)
d = c + 3
|
a ) 1 : 10 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 3 : 2 | a | multiply(divide(1, 2), multiply(divide(1, 2), divide(1, 2))) | find the compound ratio of ( 1 : 2 ) , ( 1 : 3 ) and ( 3 : 5 ) is | "required ratio = 1 / 2 * 1 / 3 * 3 / 5 = 1 / 10 = 1 : 10 answer is a" | a = 1 / 2
b = 1 / 2
c = 1 / 2
d = b * c
e = a * d
|
a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 13.5 | e | subtract(16.5, multiply(2, 1.5)) | the arithmetic mean and standard deviation of a certain normal distribution are 16.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ? | "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 16.5 - 2 * 1.5 = 13.5 . answer : e ." | a = 2 * 1
b = 16 - 5
|
a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 16 | a | divide(add(120, 1), 11) | find the value of 3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) … … … … . ( 1 + 1 / 120 ) ] is ? | "3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) . . . . . . . ( 1 + 1 / 120 ) ] 3 / 11 × [ 4 / 3 + 5 / 4 × . . . . . . . . 121 / 120 ] 3 / 11 × 4 / 3 × 5 / 4 × . . . . 121 / 120 121 / 11 = 11 . a )" | a = 120 + 1
b = a / 11
|
a ) 2.5 . , b ) 3 . , c ) 3.5 , d ) 4 . , e ) 4.5 . | d | divide(855, add(120, subtract(120, multiply(divide(120, const_100), 28)))) | two cars are driving towards one another . the first car is traveling at a speed of 120 km / h , which is 28 % faster than the second car . if the distance between the cars is 855 km , how long will it takes the cars to meet ( in hours ) ? | let s be the speed of the slower car . then the speed of the faster is 1.28 s 1.28 s = 120 s = 120 / 1.28 cumulative speed / rate = s + 1.28 s = 2.28 s time taken to meet = 855 / 2.28 s = 855 / 213.75 = 4 hrs answer : d | a = 120 / 100
b = a * 28
c = 120 - b
d = 120 + c
e = 855 / d
|
a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600 | b | add(150, multiply(3, const_10)) | according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 10 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ? | "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? b" | a = 3 * 10
b = 150 + a
|
a ) 7 / 24 , b ) 11 / 24 , c ) 13 / 24 , d ) 17 / 24 , e ) 19 / 24 | c | divide(add(3, const_10), 24) | which fraction should be added to : 1 / ( 2 ã — 3 ) + 1 / ( 3 ã — 4 ) + 1 / ( 4 ã — 5 ) + . . . . . . . + 1 / ( 23 ã — 24 ) so that the result is equal to 1 ? | the given expression = 1 / ( 2 ã — 3 ) + 1 / ( 3 ã — 4 ) + 1 / ( 4 ã — 5 ) + . . . . . . + 1 / ( 23 ã — 24 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . + ( 1 / 23 - 1 / 24 ) = 1 / 2 - 1 / 24 = 11 / 24 thus , the fraction we should add = 1 - 11 / 24 = 13 / 24 the answer is c . | a = 3 + 10
b = a / 24
|
a ) 850 , b ) 950 , c ) 1025 , d ) 975 , e ) 1000 | e | divide(90, multiply(divide(subtract(subtract(const_100, 80), 10), const_100), divide(90, const_100))) | of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 80 percent was planted with barley and 10 percent of the cleared land was planted with potato . if the remaining 90 acres of cleared land was planted with tomato , how many acres did the farmer own ? | 80 % of 90 % = 72 % , 10 % 0 f 90 % = 9 % so the remaining 90 - 72 - 9 = 9 % = 90 acres or 10 % of 90 % = 9 % - - > 90 / 9 * 100 = 1000 acres answer ( e ) | a = 100 - 80
b = a - 10
c = b / 100
d = 90 / 100
e = c * d
f = 90 / e
|
a ) 9 . , b ) 30 . , c ) 15 . , d ) 16 . , e ) 18 . | b | add(4, multiply(12, 2)) | if 4 xz + yw = 6 and xw + yz = 12 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ? | "( 2 x + y ) * ( 2 z + w ) = 6 + 2 ( 12 ) = 30 answer : b" | a = 12 * 2
b = 4 + a
|
a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1 | a | add(divide(add(power(3, const_3), sqrt(add(power(power(3, const_3), const_2), power(subtract(63, power(3, const_3)), const_2)))), multiply(power(3, const_2), const_2)), subtract(divide(add(power(3, const_3), sqrt(add(power(power(3, const_3), const_2), power(subtract(63, power(3, const_3)), const_2)))), multiply(power(3, const_2), const_2)), 3)) | if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 63 , what is their sum ? | 1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 the two numbers are 1 and 4 . the answer is a . | a = 3 ** 3
b = 3 ** 3
c = b ** 2
d = 3 ** 3
e = 63 - d
f = e ** 2
g = c + f
h = math.sqrt(g)
i = a + h
j = 3 ** 2
k = j * 2
l = i / k
m = 3 ** 3
n = 3 ** 3
o = n ** 2
p = 3 ** 3
q = 63 - p
r = q ** 2
s = o + r
t = math.sqrt(s)
u = m + t
v = 3 ** 2
w = v * 2
x = u / w
y = x - 3
z = l + y
|
a ) 50 , b ) 54 , c ) 52 , d ) 60 , e ) 63 | c | add(divide(const_100, const_2), 0.5) | in a recent election , geoff received 0.5 percent of the 5,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 2,571 more votes to win the election , what is the value of x ? | "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 25 votes he needs 2571 more votes so : 25 + 2571 = 2596 now what ' s the problem wants ? ? a x % . . . . . . . . 2596 is what % of total votes 5000 . . . . . . . . translating : 2596 = x / 100 * 5000 - - - x = 52 % . . . . . . . . . . c" | a = 100 / 2
b = a + 0
|
a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55 | b | divide(subtract(sqrt(add(multiply(multiply(360, 5), const_4), power(5, const_2))), 5), const_2) | a bus trip of 360 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ? | "the time is the distance / speed . the time difference is 1 hour . 360 / v - 360 / ( v + 5 ) = 1 360 ( v + 5 ) - 360 v = ( v ) ( v + 5 ) 1800 = ( v ) ( v + 5 ) 40 * 45 = ( v ) ( v + 5 ) v = 40 mph the answer is b ." | a = 360 * 5
b = a * 4
c = 5 ** 2
d = b + c
e = math.sqrt(d)
f = e - 5
g = f / 2
|
a ) 49 m 2 , b ) 50 m 2 , c ) 51.5 m 2 , d ) 53 m 2 , e ) 59 m 2 | c | multiply(multiply(power(12, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(41, divide(const_3600, const_10))) | the area of sector of a circle whose radius is 12 metro and whose angle at the center is 41 ° is ? | "41 / 360 * 22 / 7 * 12 * 12 = 51.5 m 2 answer : c" | a = 12 ** 2
b = 2 * 10
c = b + 2
d = 4 + 3
e = c / d
f = a * e
g = 3600 / 10
h = 41 / g
i = f * h
|
a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 60 | a | multiply(divide(10, 40), const_100) | 10 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ? | "i came up with ( a ) 25 think of 100 people total : from the first fact , 10 of these are women with fair hair . from the second fact , these 10 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 10 equals the number of fair haired men , which is 15 men with fair hair . add this 15 to the 10 women and get 25 fair haired men and women out of 100 total men and women . 25 % a" | a = 10 / 40
b = a * 100
|
['a ) rs . 3919', 'b ) rs . 3910', 'c ) rs . 3997', 'd ) rs . 3900', 'e ) rs . 3902'] | d | multiply(multiply(subtract(add(80, 60), 10), 10), 3) | a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ? | area = ( l + b – d ) d ( 80 + 60 – 10 ) 10 = > 1300 m 2 1300 * 3 = rs . 3900 answer : d | a = 80 + 60
b = a - 10
c = b * 10
d = c * 3
|
a ) 10 hr , b ) 12 hr , c ) 12 hr 24 min , d ) 12 hr , 40 min , e ) 13 hr , 20 min | a | add(divide(50, 8), divide(500,000, 40)) | it takes 50 identical printing machines 8 hours to print 500,000 posters . how long would it take 40 of these machines to print the same total ? | "50 machines finish the job in 8 hours . we do not have to take care of the 500 ' 000 posters , it does not matter . 40 machines means , 20 % less of capacity and therefore 20 % longer to work for a certain job . 8 * 1.2 = 9 hr , 36 min answer a . . hi reto , since you are looking time for 40 machines it is 25 % less so will take 25 % more . . ans 8 * 1.25 = 10 hrs . . a )" | a = 50 / 8
b = 500 / 0
c = a + b
|
a ) 13.64 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 % | a | divide(multiply(multiply(40, 60), divide(1212, const_100)), multiply(40, subtract(60, 5))) | a man bought 40 shares of rs . 60 at 5 discount , the rate of dividend being 1212 % the rate of interest obtained is | explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 5 = rs . 55 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 55 ) interest obtained = 40 × 7.5 × 100 / 40 × 55 = 13.64 % answer : option a | a = 40 * 60
b = 1212 / 100
c = a * b
d = 60 - 5
e = 40 * d
f = c / e
|
a ) 0.54202 , b ) 0.54204 , c ) 0.542022 , d ) 0.542025 , e ) none | d | divide(add(multiply(0.54204, 0.54203), multiply(0.54204, 0.54202)), 0.54204) | the average of numbers 0.54204 , 0.54203 , 0.54202 and 0.54201 is ? | "answer average = ( 0.54204 + 0.54203 + 0.54202 + 0.54201 ) / 4 = 2.1681 / 4 = 0.542025 correct option : d" | a = 0 * 54204
b = 0 * 54204
c = a + b
d = c / 0
|
a ) 0.00315 , b ) 0.0315 , c ) 0.315 , d ) 0.0351 , e ) none of them | a | multiply(divide(0.007, 0.45), const_100) | 0.007 x 0.45 = ? | "7 x 45 = 315 sum of decimal places = 5 therefore , 0.007 x 0.45 = 0.00315 answer is a ." | a = 0 / 7
b = a * 100
|
a ) 140 , b ) 150 , c ) 180 , d ) 200 , e ) 220 | c | divide(multiply(divide(15, 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 15 . what will be 40 % of that number | "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 15 then x = 15 * 30 = 450 40 % of 450 = 180 answer : option c" | a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3
e = 2 / d
f = c * e
g = 15 / f
h = g * 40
i = h / 100
|
a ) 20 , b ) 30 , c ) 34 , d ) 35 , e ) 33.33 | e | subtract(multiply(divide(const_1, subtract(const_1, divide(25, const_100))), const_100), const_100) | a certain candy manufacturer reduced the weight of candy bar m by 25 percent buy left the price unchanged . what was the resulting percent increase in the price per ounce of candy bar m ? | "assume 1 oz candy cost $ 1 before . now price remain same $ 1 but weight of candy reduces to 0.75 oz new price of candy = 1 / 0.75 = 1.3333 price increase 33.33 % e" | a = 25 / 100
b = 1 - a
c = 1 / b
d = c * 100
e = d - 100
|
a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 3.62 , e ) 3.61 | d | multiply(divide(subtract(11.67, multiply(subtract(33, 30), divide(subtract(12.48, 11.67), subtract(36, 33)))), 30), 10) | apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 11.67 and for 36 kgs of apples is 12.48 then the cost of first 10 kgs of apples is | "ans : by framing equations we get 30 l + 3 q = 11.67 30 l + 6 q = 12.48 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 0.362 cost of 10 kgs of apples = 0.362 x 10 = 3.62 answer : d" | a = 33 - 30
b = 12 - 48
c = 36 - 33
d = b / c
e = a * d
f = 11 - 67
g = f / 30
h = g * 10
|
a ) 81000 , b ) 97200 , c ) 27772 , d ) 29889 , e ) 22312 | b | add(add(76800, multiply(divide(1, 8), 76800)), multiply(divide(1, 8), add(76800, multiply(divide(1, 8), 76800)))) | every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 76800 ? | 76800 * 9 / 8 * 9 / 8 = 97200 . answer : b | a = 1 / 8
b = a * 76800
c = 76800 + b
d = 1 / 8
e = 1 / 8
f = e * 76800
g = 76800 + f
h = d * g
i = c + h
|
a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2400 km , e ) 3600 km | d | multiply(30, 48) | a walks at 30 kmph and 30 hours after his start , b cycles after him at 48 kmph . how far from the start does b catch up with a ? | "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 48 = 30 x = 2400 km answer is d" | a = 30 * 48
|
a ) 65 , b ) 69 , c ) 72 , d ) 79 , e ) none | d | divide(add(add(add(add(96, 65), 82), 67), 85), add(const_1, const_4)) | kamal obtained 96 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ? | "sol . average = 96 + 65 + 82 + 67 + 85 / 5 ) = ( 395 / 5 ) = 79 . answer d" | a = 96 + 65
b = a + 82
c = b + 67
d = c + 85
e = 1 + 4
f = d / e
|
a ) 17 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years | e | divide(multiply(subtract(32, const_2), const_2), add(const_4, const_1)) | a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e" | a = 32 - 2
b = a * 2
c = 4 + 1
d = b / c
|
a ) 7447.14775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775 | a | subtract(6702.5, multiply(multiply(670.25, 67.025), 6.7025)) | evaluate : 6702.5 + 670.25 + 67.025 + 6.7025 + 0.67025 | "6702.5 670.25 67.025 6.7025 + 0.67025 - - - - - - - - - - - - - - - 7447.14775 answer is a ." | a = 670 * 25
b = a * 6
c = 6702 - 5
|
a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi | d | multiply(multiply(4, 24), multiply(const_2, const_pi)) | a cylindrical can has a radius of 4 centimeters and a height of 24 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ? | "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 4 * 24 = 192 pi answer is d ." | a = 4 * 24
b = 2 * math.pi
c = a * b
|
a ) 10 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 20 min . | e | divide(multiply(12, divide(3, add(2, 3))), multiply(divide(3, add(2, 3)), divide(3, add(2, 3)))) | it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 12 minutes , how much time will she spend doing yoga ? ( rounded to minutes ) | the ratio is 2 : 3 = gym : ride , so ( 12 ) ( 3 / 2 ) = 18 minutes at the gym , and 18 + 12 = 30 minutes exercise , so ( 2 / 3 ) ( 30 ) = 20 minutes yoga . answer : e | a = 2 + 3
b = 3 / a
c = 12 * b
d = 2 + 3
e = 3 / d
f = 2 + 3
g = 3 / f
h = e * g
i = c / h
|
a ) 1 / 2 , b ) 1 , c ) 1 / 7 , d ) 3 / 4 , e ) 2 | c | multiply(subtract(3, divide(3, 4)), subtract(3, divide(3, 7))) | the probability that a man will be alive for 10 more yrs is 3 / 4 & the probability that his wife will alive for 10 more yrs is 3 / 7 . the probability that none of them will be alive for 10 more yrs , is | "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 7 ans . ( c )" | a = 3 / 4
b = 3 - a
c = 3 / 7
d = 3 - c
e = b * d
|
a ) 20 , b ) 21 . , c ) 22 , d ) 23 , e ) 24 | e | divide(subtract(sqrt(add(multiply(multiply(264, 2), const_4), power(2, 2))), 2), 2) | a jar of 264 marbles is divided equally among a group of marble - players . if 2 people join the group , each one would receive 1 marble less . how many people are there in the group today ? | "only 22 and 24 divide 264 perfectly , assume initially , there are 22 people , , each will get 12 marbles two people join , then 24 will get 11 marble each . hence answer e = 24" | a = 264 * 2
b = a * 4
c = 2 ** 2
d = b + c
e = math.sqrt(d)
f = e - 2
g = f / 2
|
a ) 27 and 36 . , b ) 25 and 30 . , c ) 23 and 44 . , d ) 63 and 12 . , e ) 12 and 36 . | a | add(multiply(multiply(3, 63), const_100), multiply(4, 63)) | two numbers are in the ratio 3 : 4 . if the sum of numbers is 63 , find the numbers . | "sum of the terms of the ratio = 3 + 4 = 7 sum of numbers = 63 therefore , first number = 3 / 7 × 63 = 27 second number = 4 / 7 × 63 = 36 therefore , the two numbers are 27 and 36 . answer is a" | a = 3 * 63
b = a * 100
c = 4 * 63
d = b + c
|
a ) 3200 , b ) 3400 , c ) 3600 , d ) 3800 , e ) 4000 | b | add(multiply(divide(1400, subtract(1, add(add(divide(2, 5), divide(3, 10)), divide(1, 8)))), divide(3, 10)), multiply(divide(1400, subtract(1, add(add(divide(2, 5), divide(3, 10)), divide(1, 8)))), divide(1, 8))) | a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food , and 1 / 8 of his salary on conveyance . if he has rs 1400 left with him , find his expenditure on food and conveyance | "if his salary is x , then x - x * ( 2 / 5 + 3 / 10 + 1 / 8 ) = 1400 x ( 1 - 33 / 40 ) = 1400 x = 1400 * 40 / 7 = rs 8000 expenditure on food and conveyance = 8000 * 3 / 10 + 8000 * 1 / 8 = 2400 + 1000 = 3400 answer : b" | a = 2 / 5
b = 3 / 10
c = a + b
d = 1 / 8
e = c + d
f = 1 - e
g = 1400 / f
h = 3 / 10
i = g * h
j = 2 / 5
k = 3 / 10
l = j + k
m = 1 / 8
n = l + m
o = 1 - n
p = 1400 / o
q = 1 / 8
r = p * q
s = i + r
|
a ) 54 , b ) 51 , c ) 59 , d ) 55 , e ) 52 | c | add(40, divide(subtract(976, multiply(14, 40)), divide(multiply(14, add(const_100, 75)), const_100))) | a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ? | "for 40 hrs = 40 * 14 = 560 excess = 976 - 560 = 416 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 416 / 24.5 = 18.82 = 19 approx . total hrs = 40 + 19 = 59 answer c 59" | a = 14 * 40
b = 976 - a
c = 100 + 75
d = 14 * c
e = d / 100
f = b / e
g = 40 + f
|
a ) 360 , b ) 487 , c ) 481 , d ) 729 , e ) 268 | a | multiply(24, 20) | a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 3 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ? | "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 3 = 360 answer : a" | a = 24 * 20
|
a ) $ 1000 , b ) $ 1500 , c ) $ 1200 , d ) $ 900 , e ) $ 1100 | a | multiply(divide(2, 2), 500) | the ratio of the incomes of a and b is 2 : 3 and the ratio of their expenditure is 1 : 2 . if at the end of the year , each saves $ 500 then the income of a is ? | "let the income of a and b be $ 2 x and $ 3 x let their expenditures be $ y and $ 2 y 2 x - y = 500 - - - - - - - 1 ) 3 x - 2 y = 500 - - - - - - - 2 ) from 1 ) and 2 ) x = 500 a ' s income = 2 x = 2 * 500 = $ 1000 answer is a" | a = 2 / 2
b = a * 500
|
a ) rs . 17037 , b ) rs . 17000 , c ) rs . 17276 , d ) rs . 170287 , e ) rs . 171881 | b | divide(multiply(const_100, 10200), multiply(divide(multiply(subtract(11730, 10200), const_100), divide(10200, const_2)), const_2)) | the compound and the simple interests on a certain sum at the same rate of interest for two years are rs . 11730 and rs . 10200 respectively . find the sum | explanation : the simple interest for the first year is 10200 / 2 is rs . 5100 and compound interest for first year also is rs . 5100 . the compound interest for second year on rs . 5100 for one year so rate of the interest = ( 100 * 1530 ) / ( 5100 * 1 ) = 30 % p . a . so p = ( 100 * 10200 ) / ( 30 * 2 ) = rs . 17000 answer : b | a = 100 * 10200
b = 11730 - 10200
c = b * 100
d = 10200 / 2
e = c / d
f = e * 2
g = a / f
|
a ) 25 , b ) 24 , c ) 23 , d ) 21 , e ) 28 | e | divide(subtract(120, power(8, const_2)), const_2) | the sum of two numbers is 8 and the sum of their squares is 120 . find the product of the two numbers . | let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 8 a ^ 2 + b ^ 2 = 120 so , 8 ^ 2 = 120 + 2 ab 2 ab = 120 - 64 2 ab = 56 ab = 28 ans e | a = 8 ** 2
b = 120 - a
c = b / 2
|
a ) 56.14 % , b ) 57.44 % , c ) 57.14 % , d ) 56.34 % , e ) 57.87 % | c | divide(const_100, divide(77, subtract(121, 77))) | if the cost price of 121 chocolates is equal to the selling price of 77 chocolates , the gain percent is : | "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 77 chocolates = rs . 77 ; s . p . of 77 chocolates = rs . 121 . . ' . gain % = 44 * 100 / 77 = 57.14 % answer : c" | a = 121 - 77
b = 77 / a
c = 100 / b
|
a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 550 | b | divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 500), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 140)), 30) | a library has an average of 500 visitors on sundays and 140 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is : | "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 500 * 5 + 140 * 25 ) / 30 = 6000 / 30 = 200 answer : b ) 200" | a = 3 + 4
b = 30 / a
c = math.floor(b)
d = c + 1
e = d * 500
f = 3 + 4
g = 30 / f
h = math.floor(g)
i = h + 1
j = 30 - i
k = j * 140
l = e + k
m = l / 30
|
a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7 | a | divide(subtract(6, 4), const_2) | a man can row his boat with the stream at 6 km / h and against the stream in 4 km / h . the man ' s rate is ? | "ds = 6 us = 4 s = ? s = ( 6 - 4 ) / 2 = 1 kmph answer : a" | a = 6 - 4
b = a / 2
|
a ) 81 , b ) 75 , c ) 72.63 , d ) 73 , e ) 76 | c | divide(add(multiply(100, subtract(const_100, 25)), multiply(90, subtract(const_100, 30))), add(100, 90)) | a man buys 100 lts of liquid which contains 25 % of the liquid and the rest is water . he then mixes it with 90 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ? | 25 % in 100 lts is 25 . so water = 100 - 25 = 75 lts . 30 % of 90 lts = 27 . so water in 2 nd mixture = 90 - 27 = 63 lts . now total quantity = 100 + 90 = 190 lts . total water in it will be 75 + 63 = 138 lts . % of water = ( 100 * 138 ) / 190 = 72.63 answer : c | a = 100 - 25
b = 100 * a
c = 100 - 30
d = 90 * c
e = b + d
f = 100 + 90
g = e / f
|
a ) 150 meter , b ) 170 meter , c ) 156 meter , d ) 168 meter , e ) 50 meter | e | multiply(divide(multiply(60, const_1000), const_3600), 3) | a train running at the speed of 60 km / hr crosses a pole in 3 seconds . find the length of the train ? | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 3 = 50 meter answer : e" | a = 60 * 1000
b = a / 3600
c = b * 3
|
a ) 227 , b ) 570 , c ) 342 , d ) 680 , e ) 230 | b | subtract(subtract(750, divide(multiply(750, 20), const_100)), divide(multiply(subtract(750, divide(multiply(750, 20), const_100)), 15), const_100)) | the sale price sarees listed for rs . 750 after successive discount is 20 % and 15 % is ? | "750 * ( 80 / 100 ) * ( 85 / 100 ) = 570 answer : b" | a = 750 * 20
b = a / 100
c = 750 - b
d = 750 * 20
e = d / 100
f = 750 - e
g = f * 15
h = g / 100
i = c - h
|
a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 % | a | divide(add(10, add(10, const_3)), const_2) | operation # is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ? | "any multiple of 10 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ." | a = 10 + 3
b = 10 + a
c = b / 2
|
a ) 73850 , b ) 73805 , c ) 844 , d ) 350 , e ) 2 | a | divide(multiply(add(multiply(8, const_100), 44), add(multiply(3, const_100), 50)), power(divide(add(multiply(8, const_100), 44), power(const_2, const_4)), const_2)) | a room of 8 m 44 cm long and 3 m 50 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor . | "explanation : area of the room = 844 * 350 sq cm size of largest square tile = h . c . f of 844 cm and 350 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 844 * 350 ) / ( 2 * 2 ) = 73850 answer : a ) 73850" | a = 8 * 100
b = a + 44
c = 3 * 100
d = c + 50
e = b * d
f = 8 * 100
g = f + 44
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
|
a ) 287 , b ) 279 , c ) 270 , d ) 278 , e ) 379 | c | multiply(divide(multiply(40, const_1), subtract(45, 40)), 45) | a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 45 kmph . when and at what distance from mumbai do the two trains meet ? | "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 45 - 40 ) = 8 hours so , the two trains meet at 6 p . m . the two trains meet 6 * 45 = 270 km away from mumbai . answer : c" | a = 40 * 1
b = 45 - 40
c = a / b
d = c * 45
|
a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 90 kg | e | add(multiply(3.5, 8), 62) | he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg . what might be the weight of the new person ? | "explanation : total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 62 + 28 ) kg = 90 kg . answer : e" | a = 3 * 5
b = a + 62
|
a ) 32.5 , b ) 35 , c ) 48.1 , d ) 65 , e ) 66.67 | e | multiply(const_100, divide(subtract(const_100, subtract(subtract(const_100, 20), multiply(subtract(const_100, 20), divide(25, const_100)))), subtract(subtract(const_100, 20), multiply(subtract(const_100, 20), divide(25, const_100))))) | the price of a jacket is reduced by 20 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ? | "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 20 % , therefore bringing down the price to $ 80 . 3 ) again it is further discounted by 25 % , therefore bringing down the price to $ 60 . 4 ) now 60 has to be added byx % in order to equal the original price . 60 + ( x % ) 60 = 100 . solving this eq for x , we get x = 66.67 ans is e ." | a = 100 - 20
b = 100 - 20
c = 25 / 100
d = b * c
e = a - d
f = 100 - e
g = 100 - 20
h = 100 - 20
i = 25 / 100
j = h * i
k = g - j
l = f / k
m = 100 * l
|
a ) 16 pi , b ) 72 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi | b | multiply(multiply(3, 12), multiply(const_2, const_pi)) | a cylindrical can has a radius of 3 centimeters and a height of 12 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ? | "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 3 * 12 = 72 pi answer is b ." | a = 3 * 12
b = 2 * math.pi
c = a * b
|
a ) 40 , b ) 60 , c ) 90 , d ) 120 , e ) 108 | e | divide(9.00, subtract(divide(1.00, 4), divide(0.50, 3))) | a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 9.00 ? | "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 9 ( 1 / 12 ) * x = 9 x = 108 answer : e" | a = 1 / 0
b = 0 / 50
c = a - b
d = 9 / 0
|
a ) rs . 16363.64 , b ) rs . 10 , 000.64 , c ) rs . 15 , 000,64 , d ) rs . 21 , 353.64 , e ) none | a | divide(divide(multiply(5400, const_100), multiply(3, 11)), multiply(divide(const_60, const_4), const_100)) | a man took a loan from a bank at the rate of 11 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was : | "solution principal = rs . ( 100 x 5400 / 11 x 3 ) = rs . 16363.64 . answer a" | a = 5400 * 100
b = 3 * 11
c = a / b
d = const_60 / 4
e = d * 100
f = c / e
|
a ) 32 , b ) 48 , c ) 45 , d ) 72 , e ) 18 | a | subtract(multiply(multiply(5, 5), divide(98, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))), multiply(multiply(3, 3), divide(98, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5))))) | the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 98 , what is the difference between the ages of patrick and monica ? | "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 98 x = 2 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 2 = 32 answer a" | a = 5 * 5
b = 3 * 3
c = 3 * 5
d = b + c
e = 5 * 5
f = d + e
g = 98 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k
m = 5 * 5
n = l + m
o = 98 / n
p = i * o
q = h - p
|
a ) 5 / 12 , b ) 4 / 13 , c ) 5 / 17 , d ) 3 / 12 , e ) 8 / 9 | a | multiply(multiply(multiply(divide(const_1, 6), divide(const_1, 6)), divide(const_1, 6)), divide(const_1, 6)) | three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is - . | "using question number 11 and 12 , we get the probability as 1 - ( 1 / 36 + 5 / 9 ) = 5 / 12 answer a" | a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
|
['a ) 18', 'b ) 17', 'c ) 16', 'd ) 15', 'e ) 14'] | a | subtract(divide(factorial(6), multiply(factorial(const_3), factorial(const_3))), const_2) | six dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 6 dots that do not form an equilateral triangle ? | the total number of ways we can choose three dots is 6 c 3 = 20 . we can form two equilateral triangles from these six dots . there are 20 - 2 = 18 combinations which do not form an equilateral triangle . the answer is a . | a = math.factorial(6)
b = math.factorial(3)
c = math.factorial(3)
d = b * c
e = a / d
f = e - 2
|
a ) 270 cm 2 , b ) 275 cm 2 , c ) 280 cm 2 , d ) 285 cm 2 , e ) 290 cm 2 | a | divide(multiply(15, add(20, 16)), const_2) | nd the area of trapezium whose parallel sides are 20 cm and 16 cm long , and the distance between them is 15 cm ? | "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 16 ) * ( 15 ) = 270 cm 2 answer : a" | a = 20 + 16
b = 15 * a
c = b / 2
|
a ) 44 , b ) 33 , c ) 50 , d ) 35 , e ) 14 | c | divide(1, 2) | how many positive integer solutions does the equation 2 x + 1 y = 100 have ? | "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 1 ) = 50 answer : c" | a = 1 / 2
|
a ) 330 , b ) 360 , c ) 380 , d ) 400 , e ) 420 | a | add(multiply(multiply(subtract(9, 6), const_10), const_10), multiply(subtract(9, 6), const_10)) | if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by how much ? | "unit place increased by 3 . so 6 , 16,26 , . . . . 96 . total 10 * 3 = 30 increased . ten ' s place increased by 30 . so 60,61 , . . . 69 . total 10 * 30 = 300 increased . so total varies = 300 + 30 = 330 . answer : a" | a = 9 - 6
b = a * 10
c = b * 10
d = 9 - 6
e = d * 10
f = c + e
|
a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 73 kmph | e | subtract(divide(130, multiply(6, const_0_2778)), 5) | a train 130 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train . | "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 130 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2340 < = > x = 73 speed of the train is 73 kmph . answer : option e" | a = 6 * const_0_2778
b = 130 / a
c = b - 5
|
a ) 4966 , b ) 6191 , c ) 2877 , d ) 2676 , e ) 1881 | b | multiply(subtract(divide(add(add(add(add(6835, 9927), 6855), 7230), 6562), 5), 6700), 5) | sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6700 ? | "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6700 x 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 answer : b" | a = 6835 + 9927
b = a + 6855
c = b + 7230
d = c + 6562
e = d / 5
f = e - 6700
g = f * 5
|
a ) 15.6 , b ) 22.5 , c ) 18.6 , d ) 32.2 , e ) 26.9 | b | divide(add(add(add(10, const_1), add(add(10, const_1), const_2)), add(subtract(40, 10), subtract(40, const_2))), 10) | find the average of all prime numbers between 10 and 40 | "prime numbers between 10 and 40 are 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 required average = ( 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 ) / 8 = 180 / 8 = 22.5 answer is b" | a = 10 + 1
b = 10 + 1
c = b + 2
d = a + c
e = 40 - 10
f = 40 - 2
g = e + f
h = d + g
i = h / 10
|
a ) 20 , b ) 25 , c ) 33 1 / 3 , d ) 44 4 / 9 , e ) 80 | d | multiply(divide(80, add(80, const_100)), const_100) | if y is 80 % greater than x , than x is what % less than y ? | "let x = 100 so y = 180 we want percentage change . so , ( 100 - 180 ) / 180 = - 44.44 % = 44 4 / 9 % lesser than y . hence option ( d ) ." | a = 80 + 100
b = 80 / a
c = b * 100
|
a ) 91.5 miles , b ) 92.75 miles , c ) 93.75 miles , d ) 94.5 miles , e ) 95.75 miles | c | divide(volume_cube(const_10), volume_cube(150)) | how many miles is 150 km ? | "93.75 miles 150 / 1.6 answer : c" | a = volume_cube / (
|
a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40 | c | multiply(divide(108, add(add(3, 7), 8)), subtract(8, 3)) | every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 108 , how many more green disks than blue disks are in the bag ? | "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 108 - - > x = 6 . g - b = 8 x - 3 x = 5 x = 30 . the answer is c ." | a = 3 + 7
b = a + 8
c = 108 / b
d = 8 - 3
e = c * d
|
a ) 10 , b ) 15 , c ) 17 , d ) 19 , e ) 21 | b | divide(multiply(add(multiply(7, const_100), 20), add(multiply(4, const_100), 32)), multiply(gcd(add(multiply(7, const_100), 20), add(multiply(4, const_100), 32)), gcd(add(multiply(7, const_100), 20), add(multiply(4, const_100), 32)))) | a room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room . | "let us calculate both the length and width of the room in centimeters . length = 7 meters and 20 centimeters = 720 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 720 and 432 = 144 thus , the number of square tiles required = ( 720 x 432 ) / ( 144 x 144 ) = 5 x 3 = 15 answer : b" | a = 7 * 100
b = a + 20
c = 4 * 100
d = c + 32
e = b * d
f = 7 * 100
g = f + 20
h = 4 * 100
i = h + 32
j = math.gcd(g, i)
k = 7 * 100
l = k + 20
m = 4 * 100
n = m + 32
o = math.gcd(l, n)
p = j * o
q = e / p
|
a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9 | b | subtract(8, const_1) | a number is greater than 3 but less than 8 . also the number is greater than 6 but less than 10 . what is the number ? | b 7 | a = 8 - 1
|
a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11 | e | add(sqrt(divide(subtract(power(13, const_2), power(const_2, const_2)), const_2)), const_2) | efrida and frazer who live 13 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ? | "it ' s a simple geometry problem . look at the diagram below : answer : e ." | a = 13 ** 2
b = 2 ** 2
c = a - b
d = c / 2
e = math.sqrt(d)
f = e + 2
|
a ) 133 , b ) 143 , c ) 153 , d ) 163 , e ) 173 | c | divide(1, subtract(divide(1, add(8, divide(1, 2))), divide(1, const_4))) | a cistern is filled by a tap in 8 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ? | "filling rate - leak rate = net rate 1 / 8.5 - leak rate = 1 / 9 leak rate = 2 / 17 - 1 / 9 = 1 / 153 the answer is c ." | a = 1 / 2
b = 8 + a
c = 1 / b
d = 1 / 4
e = c - d
f = 1 / e
|
a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 27 seconds , e ) 45 seconds | d | divide(54, subtract(5, 3)) | nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 54 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ? | "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 54 for cristina = c = 5 * t @ t = 27 , n = 135 c = 135 right answer ans : d" | a = 5 - 3
b = 54 / a
|
a ) 15 , b ) 20 , c ) 25 , d ) 65 , e ) 75 | e | add(multiply(divide(30, 10), 5), multiply(10, divide(30, 5))) | susan can type 10 pages in 5 minutes . mary can type 5 pages in 10 minutes . working together , how many pages can they type in 30 minutes ? | susan can type 2 pages in 1 min mary can type 0.5 pages in 1 min so , both of them work together they type 2.5 pages in 1 min so , in 30 min they type ( 30 * 2.5 ) = 75 pages answer : e | a = 30 / 10
b = a * 5
c = 30 / 5
d = 10 * c
e = b + d
|
a ) 125 , b ) 175 , c ) 225 , d ) 375 , e ) 524 | d | divide(multiply(divide(178, const_100), 1265), 5.96) | ( 178 % of 1265 ) ÷ 5.96 = ? | explanation : ? = ( 178 x 1265 / 100 ) ÷ 6 = 2250 / 600 = 375 answer : option d | a = 178 / 100
b = a * 1265
c = b / 5
|
a ) 430 , b ) 434 , c ) 438 , d ) 444 , e ) 446 | b | add(subtract(312, divide(112, const_2)), subtract(234, divide(112, const_2))) | at the faculty of aerospace engineering , 312 students study random - processing methods , 234 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ? | "312 + 234 - 112 ( since 112 is counted twice ) = 434 b is the answer" | a = 112 / 2
b = 312 - a
c = 112 / 2
d = 234 - c
e = b + d
|
a ) 152 , b ) 209 , c ) 57 , d ) 231 , e ) 181 | d | multiply(multiply(8, subtract(11, 8)), 11) | there are 399 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ? | "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 399 = 231 answer : d" | a = 11 - 8
b = 8 * a
c = b * 11
|
a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 2400 | e | subtract(divide(multiply(add(add(add(add(add(5000, 1500), 4500), 2500), 2000), 6100), const_100), subtract(const_100, 10)), add(add(add(add(add(5000, 1500), 4500), 2500), 2000), 6100)) | after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 6100 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ? | "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 6100 = 21600 exp in % = 100 - 10 = 90 % , 21600 = 90 % saving = 10 % = 21600 x 10 / 90 = rs . 2400 answer : e" | a = 5000 + 1500
b = a + 4500
c = b + 2500
d = c + 2000
e = d + 6100
f = e * 100
g = 100 - 10
h = f / g
i = 5000 + 1500
j = i + 4500
k = j + 2500
l = k + 2000
m = l + 6100
n = h - m
|
a ) 33 , b ) 27 , c ) 27 , d ) 50 , e ) 81 | d | divide(divide(subtract(825, multiply(multiply(5, const_0_2778), 5)), 5), const_0_2778) | a train 825 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 90 seconds . the speed of the train is : | "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = = > x = 50 km / hr . answer : d" | a = 5 * const_0_2778
b = a * 5
c = 825 - b
d = c / 5
e = d / const_0_2778
|
a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 7.4 % | e | multiply(subtract(const_1, divide(multiply(const_100, const_100), multiply(subtract(const_100, 10), add(const_100, 20)))), const_100) | in a hostel , the number of students decreased by 10 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ? | "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.9 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.9 * 1.2 ) = > f ( new ) = 0.9259 f therefore the new cost of food must be 92.59 % of the old cost , or the cost of food must decrease by 7.4 % ( option e )" | a = 100 * 100
b = 100 - 10
c = 100 + 20
d = b * c
e = a / d
f = 1 - e
g = f * 100
|
a ) 15 , b ) 19 , c ) 14 , d ) 21 , e ) 16 | d | subtract(63, divide(multiply(63, const_2), const_3)) | the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 63 kmph , find the speed of the stream ? | "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 63 / 3 = 21 kmph . answer : d" | a = 63 * 2
b = a / 3
c = 63 - b
|
a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10 | a | divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 6600), const_100) | if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 6600 ? | "required difference = [ 3 ½ % of rs . 6600 ] – [ 3 1 / 3 % of rs . 6600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 6600 = 1 / 6 % of rs . 6600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 6600 ] = rs . 11 . answer is a ." | a = 1 / 2
b = a + 3
c = 1 / 3
d = c + 3
e = b - d
f = e * 6600
g = f / 100
|
a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 14 minutes , e ) 12 minutes | d | divide(multiply(7, 10), add(speed(10, 10), speed(multiply(2, 10), 5))) | working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 7 x boxes ? | "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 7 x / 5 x * 10 = 14 min ans : d" | a = 7 * 10
b = speed + (
c = 2 * 10
d = a / b
|
a ) 70 % , b ) 50 % , c ) 100 % , d ) 60 % , e ) 55 % | a | multiply(divide(subtract(add(320, const_100), add(25, const_100)), add(320, const_100)), const_100) | in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , approximately what percentage of the selling price is the profit ? | "cp . = rs . 100 . = > profit = rs . 320 , s . p . = rs . 420 . new c . p . = 125 % of rs . 100 = rs . 125 new s . p . = rs . 420 . profit = rs . ( 420 - 125 ) = rs . 295 . req = ( 295 / 420 * 100 ) = = > 70 % answer a" | a = 320 + 100
b = 25 + 100
c = a - b
d = 320 + 100
e = c / d
f = e * 100
|
a ) 65 meters , b ) 75 meters , c ) 85 meters , d ) 95 meters , e ) 55 meters | b | multiply(divide(multiply(subtract(50, 32), const_1000), const_3600), 15) | 2 trains in same direction at 50 km / hr , 32 km / hr . a man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train ? | relative speed = 18 k / hr = 5 m / sec distance covered = length of faster train = 5 * 15 = 75 meters answer : b | a = 50 - 32
b = a * 1000
c = b / 3600
d = c * 15
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.