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 ) 200 , b ) 400 , c ) 800 , d ) 600 , e ) 1200 | d | divide(42, subtract(204.07, add(const_100, add(multiply(const_4, const_10), const_2)))) | when positive integer n is divided by positive integer j , the remainder is 42 . if n / j = 204.07 , what is value of j ? | "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.07 here 204 is the quotient . given that remainder = 42 so , 204.07 = 204 + 42 / j so , j = 600 answer : d" | a = 4 * 10
b = a + 2
c = 100 + b
d = 204 - 7
e = 42 / d
|
a ) 2736900 , b ) 2738800 , c ) 2658560 , d ) 2716740 , e ) none of them | b | multiply(8796, power(223, 8796)) | 8796 x 223 + 8796 x 77 = ? | "= 8796 x ( 223 + 77 ) ( by distributive law ) = 8796 x 300 = 2638800 answer is b" | a = 223 ** 8796
b = 8796 * a
|
a ) 333 , b ) 500 , c ) 887 , d ) 250 , e ) 132 | d | divide(12.50, divide(5, const_100)) | an agent , gets a commission of 5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth | "explanation : let the total sale be rs . x . then , 5 % . of x = 12.50 < = > ( 5 / 100 * x ) = 125 / 10 < = > x = 250 . answer : d" | a = 5 / 100
b = 12 / 50
|
a ) 75625 , b ) 68225 , c ) 72325 , d ) 71225 , e ) 72225 | a | multiply(121, power(5, 4)) | 121 x 5 ^ 4 = ? | explanation : 121 × 5 ^ 4 = 121 × ( 10 / 2 ) ^ 4 = ( 121 × 10000 ) / 16 = 7.5625 × 10000 = 75625 answer is a | a = 5 ** 4
b = 121 * a
|
a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8 | a | divide(multiply(6, 10), multiply(6, 10)) | the number n is h , 284 , where h represents the 10 ' s digit . if n is divisible by 6 , what is the value of h ? | if the number is divisible by 6 , then the sum of the digits must also be divisible by both 3 and 2 . only 1 yields such a number . answer : a | a = 6 * 10
b = 6 * 10
c = a / b
|
a ) 220 meter , b ) 225 meter , c ) 140 meter , d ) 235 meter , e ) none of these | c | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 360) | a 360 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ? | "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 360 / 9 = 500 / 9 = > x + 360 = 500 = > x = 140 so the length of the train is 140 meters option c" | a = 120 + 80
b = a * const_0_2778
c = b * 9
d = c - 360
|
a ) 22 sec , b ) 20 sec , c ) 15 sec , d ) 23 sec , e ) 16 sec | d | divide(add(100, 250), multiply(54, const_0_2778)) | how long does a train 100 m long traveling at 54 kmph takes to cross a station of 250 m in length ? | "d = 100 + 245 = 345 m s = 54 * 5 / 18 = 15 t = 345 * 1 / 15 = 23 sec answer : d" | a = 100 + 250
b = 54 * const_0_2778
c = a / b
|
a ) 4.5 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | c | multiply(multiply(divide(6, subtract(5, 3)), 3), subtract(const_1, multiply(add(divide(const_1, multiply(2, divide(multiply(5, divide(6, subtract(5, 3))), 3))), divide(const_1, multiply(5, divide(6, subtract(5, 3))))), 2))) | the ratio of efficiency of a is to c is 5 : 3 . the ratio of no . of days taken by b is to c is 2 : 3 . a takes 6 days less than c , when a and c completes the work individually . b and c left the work after 2 days . the no of days taken by a to finish the remaining work ? | a : b : c efficiency 10 : 9 : 6 no of days 9 x : 10 x : 15 x given = > 15 x - 9 x = 6 hence , x = 1 number of days taken by a = 9 and daily work done = 10 number of days taken by b = 10 and daily work done = 9 ( total work = 90 ) number of days taken by c = 15 and daily work done = 6 work done by b and c in initial 2 days = 30 rest work = 60 number of days required by a to finish = 60 / 10 = 6 days answer : c | a = 5 - 3
b = 6 / a
c = b * 3
d = 5 - 3
e = 6 / d
f = 5 * e
g = f / 3
h = 2 * g
i = 1 / h
j = 5 - 3
k = 6 / j
l = 5 * k
m = 1 / l
n = i + m
o = n * 2
p = 1 - o
q = c * p
|
a ) m , b ) m , c ) m , d ) m , e ) m | c | divide(16, subtract(divide(16, 10), 6)) | a train covers a distance of 16 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 16 / 10 * 60 ) km / hr = ( 96 * 5 / 18 ) m / sec = 80 / 3 m / sec . length of the train = 80 / 3 * 6 = 160 m . answer : c" | a = 16 / 10
b = a - 6
c = 16 / b
|
a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 42 kmph | e | subtract(multiply(divide(280, 9), const_3_6), 70) | a man sitting in a train which is traveling at 70 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ? | "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 70 ) kmph = 42 kmph . answer : e" | a = 280 / 9
b = a * const_3_6
c = b - 70
|
a ) 652 , b ) 589 , c ) 456 , d ) 620 , e ) 784 | e | multiply(divide(add(add(add(add(add(16, 8), 24), 32), 40), 48), add(const_2, const_4)), divide(add(24, 32), const_2)) | if s = { 8 , 16 , 24 , 32 , 40 , 48 } , what is the product of mean and median of the numbers in s ? | mean = ( 8 + 16 + 24 + 32 + 40 + 48 ) / 6 = 28 median = ( 24 + 32 ) / 2 = 28 product = 28 * 28 = 784 option e | a = 16 + 8
b = a + 24
c = b + 32
d = c + 40
e = d + 48
f = 2 + 4
g = e / f
h = 24 + 32
i = h / 2
j = g * i
|
a ) 2.5 , b ) 3.2 , c ) 4.0 , d ) 6.5 , e ) 8.0 | b | divide(divide(0.2, const_0_25), const_0_25) | after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.2 cubic inches , what is the original volume of the cubic ice , in cubic inches ? | "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.2 x = 3.2 alternate solution : try to backsolve . initial volume = 3.2 after one hour - - > ( 1 / 4 ) 3.2 = 0.8 after two hours - - > ( 1 / 4 ) 0.8 = 0.2 answer : b" | a = 0 / 2
b = a / const_0_25
|
a ) 74 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 % | a | multiply(divide(subtract(multiply(const_100, divide(35, const_100)), multiply(subtract(const_100, multiply(divide(const_1, const_4), const_100)), divide(22, const_100))), multiply(divide(const_1, const_4), const_100)), const_100) | one fourth of a solution that was 22 % sugar by weight was replaced by a second solution resulting in a solution that was 35 percent sugar by weight . the second solution was what percent sugar by weight ? | "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.22 + 1 / 4 * x = 1 * 0.35 - - > x = 0.74 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.22 + 25 * x = 100 * 0.35 - - > x = 0.74 . answer : a ." | a = 35 / 100
b = 100 * a
c = 1 / 4
d = c * 100
e = 100 - d
f = 22 / 100
g = e * f
h = b - g
i = 1 / 4
j = i * 100
k = h / j
l = k * 100
|
a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2 | a | divide(171, divide(14.5, 1.45)) | if 2994 ã · 14.5 = 171 , then 29.94 ã · 1.45 = ? | "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 171 in the place of 2994 / 14.5 ] = 171 / 10 = 17.1 answer is a ." | a = 14 / 5
b = 171 / a
|
a ) 300 , b ) 320 , c ) 360 , d ) 410 , e ) 420 | a | divide(27, subtract(204.09, add(const_100, add(multiply(const_4, const_10), const_2)))) | when positive integer n is divided by positive integer j , the remainder is 27 . if n / j = 204.09 , what is value of j ? | "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.09 here 204 is the quotient . given that remainder = 27 so , 204.09 = 204 + 27 / j so , j = 300 answer : a" | a = 4 * 10
b = a + 2
c = 100 + b
d = 204 - 9
e = 27 / d
|
a ) 140 , b ) 100 , c ) 125 , d ) 175 , e ) 225 | a | divide(subtract(multiply(divide(840, const_3), const_4), 840), const_2) | there are 840 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? | "female = x male = 840 - x x / 2 + 840 - x / 4 = 1 / 3 * ( 840 ) = 280 x = 280 x / 2 = 140 is supposed to be the answer m is missing something correct option a" | a = 840 / 3
b = a * 4
c = b - 840
d = c / 2
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | e | divide(const_1, add(divide(const_1, 7), divide(divide(const_1, 7), const_3))) | p alone can complete a job in 7 days . the work done by q alone in one day is equal to one - sixth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ? | "p ' s rate is 1 / 7 q ' s rate is 1 / 42 the combined rate is 1 / 7 + 1 / 42 = 1 / 6 if they work together , the job will take 6 days . the answer is e ." | a = 1 / 7
b = 1 / 7
c = b / 3
d = a + c
e = 1 / d
|
a ) rs . 10000 , b ) rs . 11000 , c ) rs . 12000 , d ) rs . 9000 , e ) rs . 8500 | b | subtract(multiply(4, 10000), add(add(8000, 15000), 6000)) | there are 4 members in a family . their average income is rs . 10000 per month . 3 members get rs . 8000 , rs . 15000 , rs . 6000 respectively . therefore what is the income of the fourth member of the family ? | explanation total income of 3 members = rs . ( 8000 + 15000 + 6000 ) = rs . 29000 . required income = rs . [ ( 10000 x 4 ) – 29000 ] = rs . ( 40000 – 29000 ) = rs . 11000 . answer b | a = 4 * 10000
b = 8000 + 15000
c = b + 6000
d = a - c
|
a ) - 12 , b ) 12 , c ) - 1 / 12 , d ) 1 / 12 , e ) 3 | b | divide(multiply(add(15, 3), 2), 3) | if ( 3 / 2 ) x - 3 = 15 what is the value of x ? | ( 3 / 2 ) x - 3 = 15 = > 3 x - 6 = 30 = > 3 x = 36 = > x = 12 answer : b | a = 15 + 3
b = a * 2
c = b / 3
|
a ) 3.58 , b ) 3.68 , c ) 3.78 , d ) 3.88 , e ) 3.98 | b | multiply(divide(multiply(add(8, 1.2), subtract(8, 1.2)), add(add(8, 1.2), subtract(8, 1.2))), const_2) | a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ? | "m = 8 s = 1.2 ds = 8 + 1.2 = 9.2 us = 8 - 1.2 = 6.8 x / 9.2 + x / 6.8 = 1 x = 3.68 . answer : b" | a = 8 + 1
b = 8 - 1
c = a * b
d = 8 + 1
e = 8 - 1
f = d + e
g = c / f
h = g * 2
|
a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 16 , d ) 9 : 9 , e ) 9 : 5 | c | divide(add(multiply(3000, 6), multiply(multiply(3000, const_2), 6)), multiply(8000, add(6, 6))) | a and b invests rs . 3000 and rs . 8000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ? | "( 3 * 6 + 6 * 6 ) : ( 8 * 12 ) 54 : 96 = > 9 : 16 . answer : c" | a = 3000 * 6
b = 3000 * 2
c = b * 6
d = a + c
e = 6 + 6
f = 8000 * e
g = d / f
|
a ) 34 , b ) 77 , c ) 36 , d ) 56 , e ) 91 | d | divide(multiply(add(90, 50), const_2), 5) | a rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ? | "explanation : perimeter of the plot = 2 ( 90 + 50 ) = 280 m no of poles = 280 / 5 = 56 m answer : d" | a = 90 + 50
b = a * 2
c = b / 5
|
a ) $ 4.50 , b ) $ 5.10 , c ) $ 9.30 , d ) $ 5.50 , e ) $ 5.60 | c | add(3.20, multiply(divide(subtract(9.80, 3.20), add(5, subtract(sqrt(2), 1))), 5)) | the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 9.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ? | "i tried using time / rate approach : - initial price difference = 9.80 - 3.20 = 6.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 6.6 = t ( 5.4 x ) - > t = ( 6.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 6.6 / 5.4 = 9.3 answer c ." | a = 9 - 80
b = math.sqrt(2)
c = b - 1
d = 5 + c
e = a / d
f = e * 5
g = 3 + 20
|
a ) one , b ) two , c ) four , d ) five , e ) six | d | subtract(4, const_4) | how many two - element subsets of { 1,2 , 3,4 } are there that do not contain the pair of elements 2 and 4 ? | "{ 1,2 } , { 1,3 } , { 1,4 } , { 2,3 } , { 3,4 } . or : c 24 − 1 = 5 answer : d ." | a = 4 - 4
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a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | a | divide(subtract(subtract(add(add(19, 16), 12), 4), 39), const_2) | at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 19 employees are trained to work in the family buffet , 16 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ? | 39 = 19 + 16 + 12 - 4 - 2 x 2 x = 19 + 16 + 12 - 4 - 39 = 43 - 39 = 4 x = 2 a | a = 19 + 16
b = a + 12
c = b - 4
d = c - 39
e = d / 2
|
['a ) 6', 'b ) 5', 'c ) 8', 'd ) 6', 'e ) 3'] | c | add(divide(divide(square_edge_by_area(784), const_2), divide(add(const_3, const_4), const_3)), const_2) | there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle ? | let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c | a = square_edge_by_area / (
b = a / 2
c = 3 + 4
d = c / 3
e = b + d
|
a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0 | b | subtract(5.2, floor(5.2)) | for any number z , z * is defined as the greatest positive even integer less than or equal to z . what is the value of 5.2 – 5.2 * ? | "since z * is defined as the greatest positive even integer less than or equal to z , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 – 5.2 * = 5.2 - 4 = 1.2 answer : b ." | a = math.floor(5, 2)
b = 5 - 2
|
a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 850 , e ) $ 900 | d | divide(multiply(250, multiply(multiply(const_2, const_100), const_100)), divide(multiply(multiply(const_2, const_100), const_100), const_4)) | if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 17,000 is invested at the same interest rate , what is the interest from the investment ? | "5000 * r * t / 100 = 250 rt = 5 17000 * 5 / 100 = 850 answer is d" | a = 2 * 100
b = a * 100
c = 250 * b
d = 2 * 100
e = d * 100
f = e / 4
g = c / f
|
a ) 87 , b ) 18 , c ) 17 , d ) 36 , e ) 10 | d | divide(divide(1600, 20), divide(1400, multiply(30, 21))) | 30 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ? | binders books days 30 1400 21 x 1600 20 x / 30 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 36 answer : d | a = 1600 / 20
b = 30 * 21
c = 1400 / b
d = a / c
|
a ) 51 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease | a | subtract(const_100, multiply(power(divide(30, const_100), const_2), const_100)) | if the radius of a circle is decreased 30 % , what happens to the area ? | "area of square = pi * radius ^ 2 new radius = 0.7 * old radius so new area = ( 0.7 ) ^ 2 old area = > 0.49 of old area = > 49 % old area ans : a" | a = 30 / 100
b = a ** 2
c = b * 100
d = 100 - c
|
a ) 3377 , b ) 2678 , c ) 5460 , d ) 1976 , e ) 1671 | c | divide(multiply(divide(multiply(5000, add(const_100, 4)), const_100), add(const_100, 5)), const_100) | find the amount on rs . 5000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ? | "5000 * 104 / 100 * 105 / 100 = > 5460 answer : c" | a = 100 + 4
b = 5000 * a
c = b / 100
d = 100 + 5
e = c * d
f = e / 100
|
a ) 233 , b ) 690 , c ) 287 , d ) 771 , e ) 191 | b | subtract(multiply(410, 9), subtract(multiply(430, 9), 870)) | the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 410 per month . the salary of the new supervisor is : | "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 410 = 3690 salary of the new supervisor = 3690 â ˆ ’ 3000 = 690 answer : b" | a = 410 * 9
b = 430 * 9
c = b - 870
d = a - c
|
a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | c | add(4, 6) | if there are 4 peanuts in a box and mary puts 6 more peanuts inside , how many peanuts are in the box ? | 6 + 4 = 10 correct answer is c ) 10 | a = 4 + 6
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a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129 | e | divide(subtract(subtract(multiply(const_100, const_10), const_1), add(multiply(add(const_10, const_4), 7), 5)), 7) | how many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ? | "explanatory answer step 1 : find the first and last term of the series the smallest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 103 . the largest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 999 . the series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an a . p ( arithmetic progression ) with the first term being 103 and the last term being 999 . the common difference of the sequence is 7 . step 2 : compute the number of terms in an a . p , the last term l = a + ( n - 1 ) * d , where ' a ' is the first term , ' n ' is the number of terms of the series and ' d ' is the common difference . therefore , 999 = 103 + ( n - 1 ) * 7 or 999 - 103 = ( n - 1 ) * 7 or 896 = ( n - 1 ) * 7 so , n - 1 = 128 or n = 129 choice e is the correct answer ." | a = 100 * 10
b = a - 1
c = 10 + 4
d = c * 7
e = d + 5
f = b - e
g = f / 7
|
a ) 6 , b ) 12 , c ) 18 , d ) 32 , e ) 48 | c | multiply(9, const_2) | if ( 10 ^ 4 * 3.456789 ) ^ 9 is written as a single term , how many digits would be to the right of the decimal place ? | "3.456789 ^ 9 has 6 * 9 = 54 decimal places . 10 ^ 36 moves the decimal place to the right 36 places . ( 10 ^ 4 * 3.456789 ) ^ 9 has 54 - 36 = 18 digits after the decimal point . the answer is c ." | a = 9 * 2
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a ) 2.5 % , b ) 15 % , c ) 120 % , d ) 35 % , e ) 250 % | c | multiply(divide(divide(30, const_100), divide(25, const_100)), const_100) | if c is 30 % of a and 25 % of b , what percent of a is b ? | "answer = c 30 a / 100 = 25 b / 100 b = 30 a / 25 = 120 a / 100 = 120 %" | a = 30 / 100
b = 25 / 100
c = a / b
d = c * 100
|
a ) s . 50 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60 | a | divide(multiply(subtract(24, 20), const_100), const_2) | find the principal which yields a simple interest of rs . 20 and compound interest of rs . 24 in two years , at the same percent rate per annum ? | "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 24 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 24 – 20 ) / 20 ] * 100 = 20 % p . a . let the principal be rs . x time = t = 2 years % rate = 20 % p . a . si = ( prt / 100 ) 20 = ( x * 20 * 2 ) / 100 x = rs . 50 answer : a" | a = 24 - 20
b = a * 100
c = b / 2
|
a ) 60 , b ) 61.2 , c ) 3240 , d ) 3,600 , e ) 3,672 | c | multiply(0.9, const_3600) | the moon revolves around the earth at a speed of approximately 0.9 kilometers per second . this approximate speed is how many kilometers per hour ? | "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.9 * 3600 = 3240 kilometers per hour . option c is correct" | a = 0 * 9
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a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70 | a | multiply(subtract(const_100, 80), subtract(divide(const_100, 60), divide(80, 80))) | john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 60 miles per hour , what is v in miles per hour ? | "let distance be d . we can find the total time & equate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 60 = > v = 30 answer : a" | a = 100 - 80
b = 100 / 60
c = 80 / 80
d = b - c
e = a * d
|
a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90 | a | subtract(divide(multiply(divide(150, 5), 12), 2), 150) | the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 150 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ? | "let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 150 / ( 150 + x ) = 5 / 6 x = 30 the answer is a ." | a = 150 / 5
b = a * 12
c = b / 2
d = c - 150
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a ) 346 , b ) 368 , c ) 375 , d ) 337 , e ) 325 | e | divide(1300, const_3) | divide rs . 1300 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ? | "a + b + c = 1300 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1300 = > 325 answer : e" | a = 1300 / 3
|
a ) 2 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km | a | divide(add(divide(7, const_60), divide(8, const_60)), divide(const_1, 8)) | a boy is travelling from his home to school at 4 km / hr and reached 7 min late . next day he traveled at 8 km / hr and reached 8 min early . distance between home and school ? | "let the distance be x t 1 = x / 4 hr t 2 = x / 8 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 4 - x / 8 = 1 / 4 x / 8 = 1 / 4 x = 2 km answer is a" | a = 7 / const_60
b = 8 / const_60
c = a + b
d = 1 / 8
e = c / d
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a ) $ 1206.60 , b ) $ 1363.63 , c ) $ 1263.63 , d ) $ 1463.53 , e ) $ 1163.03 | b | multiply(2500, divide(inverse(4), add(inverse(6), add(inverse(2), inverse(4))))) | a , b and c , each working alone can complete a job in 2 , 4 and 6 days respectively . if all three of them work together to complete a job and earn $ 2500 , what will be c ' s share of the earnings ? | "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 6 ( or 2 / 12 ) 1 day work of the combined workforce is ( 1 / 2 + 1 / 4 + 1 / 6 ) = 11 / 12 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 6 / 11 * 2500 = $ 1363.63 hence : b" | a = 1/(4)
b = 1/(6)
c = 1/(2)
d = 1/(4)
e = c + d
f = b + e
g = a / f
h = 2500 * g
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a ) 25 , b ) 34 , c ) 50 , d ) 60 , e ) 100 | d | divide(multiply(6, 200), divide(200, const_10)) | according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 5 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ? | orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 5 oz can = 300 oz / 5 oz = 60 answer d , 60 cans | a = 6 * 200
b = 200 / 10
c = a / b
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a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21 | c | divide(subtract(add(multiply(10, divide(subtract(multiply(20, 30), multiply(30, 18)), subtract(20, 10))), multiply(20, subtract(30, divide(subtract(multiply(20, 30), multiply(30, 18)), subtract(20, 10))))), multiply(30, 16)), subtract(20, 16)) | each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ? | if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 2 : 3 , the number of 20 - pound boxes must be 9 . we need to remove 15 of the 20 - pound boxes . the answer is c . | a = 20 * 30
b = 30 * 18
c = a - b
d = 20 - 10
e = c / d
f = 10 * e
g = 20 * 30
h = 30 * 18
i = g - h
j = 20 - 10
k = i / j
l = 30 - k
m = 20 * l
n = f + m
o = 30 * 16
p = n - o
q = 20 - 16
r = p / q
|
a ) 30 minutes , b ) 17 minutes , c ) 15 minutes , d ) 6 minutes , e ) 12 minutes | d | subtract(add(divide(const_1, 18), divide(const_1, 15)), divide(const_1, 54)) | two pipes can fill a tank in 18 minutes and 15 minutes . an outlet pipe can empty the tank in 54 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ? | "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 15 - 1 / 54 = ( 15 + 18 - 5 ) / 270 = 28 / 270 = 14 / 135 so , the tank becomes full in 6 minutes . answer : d" | a = 1 / 18
b = 1 / 15
c = a + b
d = 1 / 54
e = c - d
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a ) 5600 , b ) 600 , c ) 6400 , d ) 7200 , e ) none of these | c | divide(multiply(multiply(8, 6), 22.5), divide(divide(multiply(multiply(25, 11.25), 6), const_100), const_100)) | how many bricks each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall 8 m x 6 m x 22.5 m | "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 25 x 11.25 x 6 ) = 6400 answer : c" | a = 8 * 6
b = a * 22
c = 25 * 11
d = c * 6
e = d / 100
f = e / 100
g = b / f
|
a ) $ 160 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360 | a | subtract(subtract(500, divide(multiply(500, 2), 5)), multiply(subtract(subtract(20, divide(multiply(20, 3), 5)), const_1), 20)) | a prize of $ 500 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ? | total value of the prize = $ 500 number of people = 20 2 / 5 of 500 ( = $ 200 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 500 - 200 = $ 300 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 300 - 140 = $ 160 , hence a is the correct answer . | a = 500 * 2
b = a / 5
c = 500 - b
d = 20 * 3
e = d / 5
f = 20 - e
g = f - 1
h = g * 20
i = c - h
|
a ) 11 , b ) 78 , c ) 60 , d ) 28 , e ) 81 | c | divide(multiply(divide(divide(add(100, 100), 8), const_3), const_2), const_0_2778) | two trains , each 100 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ? a . 30 km / hr b . 45 km / hr | let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 8 = 3 x = > x = 25 / 3 . so , speed of the faster train = 50 / 3 = 50 / 3 * 18 / 5 = 60 km / hr . answer : c | a = 100 + 100
b = a / 8
c = b / 3
d = c * 2
e = d / const_0_2778
|
a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 90 | e | divide(90, divide(add(multiply(subtract(10, 9), const_60), subtract(40, 10)), const_60)) | a car going at 40 miles per hour set out on an 90 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ? | "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 40 m per hour = 1.5 hours distance travelled by car a = 40 * 1.5 = 60 miles since car b catches up car a at 10 : 30 , time = 90 mins = 3 / 2 hour speed of car b = 60 / ( 3 / 2 ) = 90 miles per hour answer e" | a = 10 - 9
b = a * const_60
c = 40 - 10
d = b + c
e = d / const_60
f = 90 / e
|
a ) 5655 , b ) 1366 , c ) 6444 , d ) 7266 , e ) none of these | b | divide(multiply(multiply(6, 4), 20.5), divide(divide(multiply(multiply(30, 12), 10), const_100), const_100)) | how many bricks each measuring 30 cm x 12 cm x 10 cm , will be needed to build a wall 6 m x 4 m x 20.5 m | explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 600 x 400 x 20.5 ) / ( 30 x 12 x 10 ) = 1366 answer : b | a = 6 * 4
b = a * 20
c = 30 * 12
d = c * 10
e = d / 100
f = e / 100
g = b / f
|
a ) 300 , b ) 245 , c ) 600 , d ) 743 , e ) 215 | c | multiply(1800, divide(inverse(8), add(inverse(12), add(inverse(6), inverse(8))))) | a , b and c can do a work in 6 , 8 and 12 days respectively doing the work together and get a payment of rs . 1800 . what is b ’ s share ? | c 600 wc = 1 / 6 : 1 / 8 : 1 / 12 = > 4 : 3 : 2 3 / 9 * 1800 = 600 | a = 1/(8)
b = 1/(12)
c = 1/(6)
d = 1/(8)
e = c + d
f = b + e
g = a / f
h = 1800 * g
|
a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | a | divide(factorial(subtract(add(const_4, 01), const_1)), multiply(factorial(01), factorial(subtract(const_4, const_1)))) | how many positive integers less than 50 have a reminder 01 when divided by 4 ? | "1 also gives the remainder of 1 when divided by 4 . so , there are total of 13 numbers . answer : a ." | a = 4 + 1
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
|
a ) 46.7 % , b ) 47.3 % , c ) 48.4 % , d ) 50.6 % , e ) 51.8 % | a | multiply(divide(add(1, 3), add(add(2, 2), add(1, 3))), const_100) | the proportion of water to alcohol in solution a is 2 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ? | "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 3 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 6 + 3 v / 10 = 14 v / 30 = 7 v / 15 . the concentration of alcohol is 7 / 15 = 46.7 % the answer is a ." | a = 1 + 3
b = 2 + 2
c = 1 + 3
d = b + c
e = a / d
f = e * 100
|
a ) 40 , b ) 54 , c ) 50 , d ) 39 , e ) none | c | divide(100, 2) | a worker makes a toy in every 2 h . if he works for 100 h , then how many toys will he make ? | "no . of toys = 100 / 2 = 50 answer : c" | a = 100 / 2
|
a ) 15 , b ) 35 , c ) 75 , d ) 25 , e ) 85 | c | multiply(divide(subtract(56, 32), 32), const_100) | a book is bought for $ 32 and sold for $ 56 . what is the profit in percentage ? | 56 / 32 = 1.75 the answer is c . | a = 56 - 32
b = a / 32
c = b * 100
|
a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48 | e | divide(multiply(divide(90, const_100), 24), divide(70, const_100)) | an alloy weighing 24 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ? | "in 24 ounces , gold is 24 * ( 70 / 100 ) = 16.8 ounces . now we add x ounces of pure gold to make it 90 % gold . so 16.8 + x = ( 24 + x ) * 90 / 100 = > x = 48 . answer is e ." | a = 90 / 100
b = a * 24
c = 70 / 100
d = b / c
|
a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | c | divide(subtract(multiply(4, 20), add(add(4, 5), 8)), 4) | the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 20 , what is the age of the youngest sibling ? | "x + ( x + 3 ) + ( x + 5 ) + ( x + 8 ) = 80 4 x + 16 = 80 4 x = 64 x = 16 the answer is c ." | a = 4 * 20
b = 4 + 5
c = b + 8
d = a - c
e = d / 4
|
a ) 14.83 , b ) 14.81 , c ) 14.91 , d ) 14.82 , e ) 14.12 | c | divide(multiply(34, 136), 310) | on a map the distance between two mountains is 310 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ? | "explanation : since 310 inch = 136 km so 1 inch = 136 / 310 km so 34 inch = ( 136 ã — 34 ) / 310 = 14.91 km answer : c" | a = 34 * 136
b = a / 310
|
a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500 | b | add(multiply(const_2, 100), 100) | brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 100 meters . they next meet after sally has run 100 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ? | "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 100 = 200 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 100 meters , thus the circumference is 200 + 100 = 300 meters . answer : b ." | a = 2 * 100
b = a + 100
|
a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | a | subtract(power(3, 2), 3) | for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 3 ” 3 ? | "3 ” 3 = 9 - 3 = 6 answer : a" | a = 3 ** 2
b = a - 3
|
a ) 4500 , b ) 3200 , c ) 3400 , d ) 2761 , e ) 2882 | b | divide(multiply(multiply(3, 32), multiply(2, const_1000)), multiply(const_1, const_60)) | a river 3 m deep and 32 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ? | "( 2000 * 3 * 32 ) / 60 = 3200 m 3 answer : b" | a = 3 * 32
b = 2 * 1000
c = a * b
d = 1 * const_60
e = c / d
|
a ) 4436 toys , b ) 5487 toys , c ) 6113 toys , d ) 1875 toys , e ) 1375 toys | d | divide(7500, 5) | a factory produces 7500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ? | "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 7500 / 4 = 1875 toys correct answer d" | a = 7500 / 5
|
['a ) 140 %', 'b ) 350 %', 'c ) 450 %', 'd ) 600 %', 'e ) 700 %'] | d | multiply(const_100, divide(multiply(surface_cube(1), surface_cube(7)), surface_cube(7))) | if a 7 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ? | the area a of the large cube is 7 * 7 * 6 = 294 square cm . the area of the 343 small cubes is 7 * 7 * 7 * 6 = 7 a , an increase of 600 % . the answer is d . | a = surface_cube * (
b = a / surface_cube
c = 100 * b
|
a ) 58 , b ) 59 , c ) 60 , d ) 62 , e ) 63 | e | divide(add(110, 142), 4) | a student chose a number , multiplied it by 4 , then subtracted 142 from the result and got 110 . what was the number he chose ? | "let x be the number he chose , then 4 ⋅ x − 142 = 110 4 x = 252 x = 63 correct answer e" | a = 110 + 142
b = a / 4
|
a ) $ 0 , b ) $ 8 , c ) $ 4 , d ) $ 12 , e ) $ 15 | b | subtract(multiply(divide(56, subtract(const_1, divide(30, const_100))), subtract(const_1, divide(20, const_100))), 56) | a merchant purchased a jacket for $ 56 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ? | "actual cost = $ 56 sp = actual cost + mark up = actual cost + 30 % sp = 56 * 100 / 70 on sale sp = 80 / 100 ( 56 * 100 / 70 ) = 64 gross profit = $ 8 answer is b" | a = 30 / 100
b = 1 - a
c = 56 / b
d = 20 / 100
e = 1 - d
f = c * e
g = f - 56
|
a ) 33 , b ) 77 , c ) 24 , d ) 55 , e ) 71 | c | divide(multiply(3, const_3), subtract(divide(add(divide(multiply(3, const_3), 6), add(divide(multiply(3, const_3), 3), divide(multiply(3, const_3), 4))), const_2), divide(multiply(3, const_3), 3))) | a and b can do a piece of work in 3 days , b and c in 4 days , c and a in 6 days . how long will c take to do it ? | "2 c = ¼ + 1 / 6 – 1 / 3 = 1 / 12 c = 1 / 24 = > 24 days answer : c" | a = 3 * 3
b = 3 * 3
c = b / 6
d = 3 * 3
e = d / 3
f = 3 * 3
g = f / 4
h = e + g
i = c + h
j = i / 2
k = 3 * 3
l = k / 3
m = j - l
n = a / m
|
a ) 25 seconds , b ) 28 seconds , c ) 30 seconds , d ) 35 seconds , e ) 40 seconds | c | multiply(multiply(subtract(divide(500, multiply(subtract(63, 3), const_0_2778)), const_1), const_10), const_2) | how many seconds will a 500 meter 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 | "explanation : relative speed = 63 - 3 = 60 km / hr = 60 * ( 5 / 18 ) = 50 / 3 m / sec time taken to pass the man will be 500 â ˆ — 3 / 50 = 30 seconds answer is c" | a = 63 - 3
b = a * const_0_2778
c = 500 / b
d = c - 1
e = d * 10
f = e * 2
|
a ) 69 miles , b ) 88 miles , c ) 96 miles , d ) 102.8 miles , e ) 112 miles | d | divide(multiply(multiply(subtract(21, 3), add(21, 3)), 10), add(add(21, 3), subtract(21, 3))) | the current in a river is 3 mph . a boat can travel 21 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ? | "upstream speed = 21 - 3 = 18 mph downstream speed = 21 + 3 = 24 mph d / 18 + d / 24 = 10 hours solving for d we get d = 102.8 answer : d" | a = 21 - 3
b = 21 + 3
c = a * b
d = c * 10
e = 21 + 3
f = 21 - 3
g = e + f
h = d / g
|
a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104 | e | divide(subtract(multiply(180, divide(add(const_100, 50), const_100)), 10), add(divide(add(const_100, 50), const_100), const_1)) | if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 180 pounds . what is leo ' s current weight ? | l + k = 180 and so k = 180 - l l + 10 = 1.5 k = 1.5 ( 180 - l ) 2.5 l = 260 l = 104 the answer is e . | a = 100 + 50
b = a / 100
c = 180 * b
d = c - 10
e = 100 + 50
f = e / 100
g = f + 1
h = d / g
|
a ) 338 m , b ) 778 m , c ) 200 m , d ) 276 m , e ) 360 m | e | subtract(divide(1200, const_2), 240) | if the perimeter of a rectangular garden is 1200 m , its length when its breadth is 240 m is ? | "2 ( l + 240 ) = 1200 = > l = 360 m answer : e" | a = 1200 / 2
b = a - 240
|
a ) 7 : 5 , b ) 2 : 9 , c ) 7 : 2 , d ) 2 : 2 , e ) 2 : 8 | a | divide(divide(1, 35), power(divide(1, 2), 2)) | the volumes of two cones are in the ratio 1 : 35 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ? | "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 35 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 7 / 5 i . e . h 1 : h 2 = 7 : 5 answer : a" | a = 1 / 35
b = 1 / 2
c = b ** 2
d = a / c
|
a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20 | c | divide(subtract(sqrt(add(multiply(multiply(144, 2), const_4), power(2, 2))), 2), 2) | a jar of 144 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ? | "144 = 16 * 9 = 18 * 8 there are 16 people in the group today . the answer is c ." | a = 144 * 2
b = a * 4
c = 2 ** 2
d = b + c
e = math.sqrt(d)
f = e - 2
g = f / 2
|
a ) 115 min , b ) 215 min , c ) 315 min , d ) 415 min , e ) none of these | a | divide(divide(400, multiply(20, const_0_2778)), const_60) | how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr | "explana ɵ on : we know that , time = distancespeedspeed = 20 km / hr = 20 ∗ 518 m / sec = 509 m / sec time = ( 400 ∗ 950 ) = 72 sec = 115 min answer : op ɵ on a" | a = 20 * const_0_2778
b = 400 / a
c = b / const_60
|
a ) 7.59 , b ) 7.79 , c ) 7.99 , d ) 8.19 , e ) 8.39 | c | divide(add(7, 10), add(divide(7, 10), divide(10, 7))) | a cyclist rides a bicycle 7 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 7 km / hr . what is the average speed for the entire trip ? | distance = 17 km time = 7 / 10 + 10 / 7 = ( 49 + 100 ) / 70 = 149 / 70 hours average speed = ( 17 * 70 ) / 149 = 7.99 km / h the answer is c . | a = 7 + 10
b = 7 / 10
c = 10 / 7
d = b + c
e = a / d
|
a ) 28 sec , b ) 89 sec , c ) 85 sec , d ) 16 sec , e ) 15 sec | b | divide(add(240, 650), divide(240, 24)) | a train 240 m long passed a pole in 24 sec . how long will it take to pass a platform 650 m long ? a . 65 | speed = 240 / 24 = 10 m / sec . required time = ( 240 + 650 ) / 10 = 89 sec . answer : b | a = 240 + 650
b = 240 / 24
c = a / b
|
a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20 | c | subtract(subtract(multiply(5, 5), add(5, const_4)), power(const_2, const_2)) | if the radius of a circle that centers at the origin is 5 , how many k points on the circle have integer coordinates ? | "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : k = c" | a = 5 * 5
b = 5 + 4
c = a - b
d = 2 ** 2
e = c - d
|
a ) 2262016 , b ) 2250000 , c ) 12000 , d ) 2262000 , e ) 2250016 | a | multiply(divide(1504, 1504), const_100) | 1504 x 1504 = ? | "1504 x 1504 = ( 1504 ) 2 = ( 1500 + 4 ) 2 = ( 1500 ) 2 + ( 4 ) 2 + ( 2 x 1500 x 4 ) = 2250000 + 16 + 12000 = 2250016 + 12000 = 2262016 a" | a = 1504 / 1504
b = a * 100
|
a ) 21 , b ) 20 , c ) 19 , d ) 18 , e ) 15 | d | subtract(23, add(floor(divide(9, const_2)), const_1)) | marcella has 23 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ? | marcella has 23 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 23 pairs of shoes minus the 5 ' destroyed ' pairs yields 20 pairs that still fulfill the requirements . answer : d | a = 9 / 2
b = math.floor(a)
c = b + 1
d = 23 - c
|
a ) 27636 , b ) 27640 , c ) 27647 , d ) 27713 , e ) 27675 | d | divide(multiply(add(multiply(3, const_100), 21), add(multiply(7, const_100), 77)), multiply(subtract(21, add(multiply(const_2, const_4), const_2)), subtract(21, add(multiply(const_2, const_4), const_2)))) | a room 3 m 21 cm long and 7 m 77 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 = ( 321 x 777 ) cm 2 . size of largest square tile = h . c . f . of 321 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 321 × 777 ) / ( 3 × 3 ) = 27713 answer : option d" | a = 3 * 100
b = a + 21
c = 7 * 100
d = c + 77
e = b * d
f = 2 * 4
g = f + 2
h = 21 - g
i = 2 * 4
j = i + 2
k = 21 - j
l = h * k
m = e / l
|
a ) 30 % , b ) 31 % , c ) 20 % , d ) 33.33 % , e ) 40 % | d | multiply(divide(subtract(20, 15), 15), const_100) | a shopkeeper sold 15 articles at the cost price of 20 articles . then find the profit % or lost % | "here 15 articles selling price = 20 articles cost price so the difference = 20 - 15 = 5 % of profit = 5 * 100 / 15 = 33.33 % correct option is d" | a = 20 - 15
b = a / 15
c = b * 100
|
a ) rs . 2400 , b ) rs . 2490 , c ) rs . 2500 , d ) rs . 2550 , e ) rs . 2600 | a | multiply(12, divide(1600, subtract(multiply(6, 2), 4))) | the price of 2 saris and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ? | let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . a | a = 6 * 2
b = a - 4
c = 1600 / b
d = 12 * c
|
a ) 9 , b ) 15 , c ) 36 , d ) 45 , e ) none | c | multiply(4, divide(180, multiply(5, 4))) | two numbers are in ratio 4 : 5 and their lcm is 180 . the smaller number is | solution : let two numbers be 4 x and 5 x ; their lcm = 180 and hcf = x ; now , 1 st number * 2 nd number = lcm * hcf or , 4 x * 5 x = 180 * x ; or , 20 x = 180 ; or , x = 9 ; then , the smaller number = 4 * 9 = 36 . answer : option c | a = 5 * 4
b = 180 / a
c = 4 * b
|
['a ) 177 cm', 'b ) 100 cm', 'c ) 86 cm', 'd ) 64 cm', 'e ) 87 cm'] | d | divide(volume_cube(1), volume_cube(divide(25, const_100))) | how many cubes of 25 cm edge can be put in a cubical box of 1 m edge . | number of cubes = 100 â ˆ — 100 â ˆ — 100 / 25 â ˆ — 25 â ˆ — 25 = 64 note : 1 m = 100 cm answer : d | a = volume_cube / (
|
a ) 3488 , b ) 3778 , c ) 7200 , d ) 1800 , e ) 2881 | c | multiply(multiply(const_3, const_60), const_60) | if an object travels at two feet per second , how many feet does it travel in one hour ? | "explanation : if an object travels at 2 feet per second it covers 2 x 60 feet in one minute , and 2 x 60 x 60 feet in one hour . answer = 7200 answer : c ) 7200" | a = 3 * const_60
b = a * const_60
|
a ) 99 , b ) 112 , c ) 118 , d ) 124 , e ) 130 | d | divide(496, add(3, const_1)) | an apple orchard grows red and green apples . on the first day of harvest , 496 apples are collected . there are 3 times as many red apples as there are green apples . how many green apples were harvested ? | let x be the number of green apples . there were 496 total apples ; there are three times as many red apples as green apples . therefore , x + 3 x = 496 4 x = 496 x = 124 answer : d | a = 3 + 1
b = 496 / a
|
a ) 7 : 8 , b ) 8 : 3 , c ) 3 : 8 , d ) 8 : 7 , e ) 7 : 1 | b | divide(multiply(subtract(10, const_1), 3), multiply(7, 3)) | 100 liters of a mixture contains milk and water in the ratio 7 : 3 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ? | "quantity of milk in 100 liters if mix = 100 * 7 / 10 = 70 liters quantity of milk in 110 liters of new mix = 80 + 10 = 80 liters quantity of water in it = 110 - 80 = 30 liters ratio of milk and water in new mix = 80 : 30 = 8 : 3 answer is b" | a = 10 - 1
b = a * 3
c = 7 * 3
d = b / c
|
a ) 16 : 5 , b ) 14 : 5 , c ) 16 : 7 , d ) 19 : 5 , e ) none of these | d | divide(add(divide(multiply(62.5, 2), const_100), divide(multiply(87.5, 4), const_100)), add(subtract(2, divide(multiply(62.5, 2), const_100)), subtract(4, divide(multiply(87.5, 4), const_100)))) | two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ? | "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres as 6 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5 . answer : d" | a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d
f = 62 * 5
g = f / 100
h = 2 - g
i = 87 * 5
j = i / 100
k = 4 - j
l = h + k
m = e / l
|
a ) 24 , b ) 48 , c ) 84 , d ) 72 , e ) 80 | c | divide(12, subtract(const_1, sqrt(divide(36, 49)))) | a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 36 / 49 . how many marbles are in the bag ? | ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 36 / 49 - - > ( x - 12 ) ^ 2 = 36 / 49 x ^ 2 square rooting u have x - 12 / x = 6 / 7 or 7 x - 6 x = 84 or x = 84 c | a = 36 / 49
b = math.sqrt(a)
c = 1 - b
d = 12 / c
|
a ) 24 , b ) 25 , c ) 32 , d ) 39 , e ) 43 | c | add(add(divide(multiply(add(subtract(405, 270), 15), const_2), const_10), divide(divide(multiply(add(subtract(405, 270), 15), const_2), const_10), const_10)), const_1) | 288 ã · ? ã — 15 + 270 = 405 | "explanation : 288 ã · ? ã — 15 = 405 - 270 = 135 ( 288 ã — 15 ) / ? = 135 ? = ( 288 ã — 15 ) / 135 = 32 answer : option c" | a = 405 - 270
b = a + 15
c = b * 2
d = c / 10
e = 405 - 270
f = e + 15
g = f * 2
h = g / 10
i = h / 10
j = d + i
k = j + 1
|
a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320 | b | subtract(multiply(multiply(add(4, const_1), add(4, const_1)), multiply(4, 4)), multiply(multiply(add(4, const_1), add(4, const_1)), 4)) | how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 7 , and the digit 2 can be used only once ? | "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 7 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 2 = 160 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 2 = 10 . thus there are 160 - 10 = 150 such numbers . answer : b ." | a = 4 + 1
b = 4 + 1
c = a * b
d = 4 * 4
e = c * d
f = 4 + 1
g = 4 + 1
h = f * g
i = h * 4
j = e - i
|
a ) $ 54.00 , b ) $ 89.60 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80 | b | divide(multiply(subtract(1720, 600), 8), const_100) | a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 8 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ? | "correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.08 ( $ 1120 ) = $ 89.60 . the correct answer is b ." | a = 1720 - 600
b = a * 8
c = b / 100
|
a ) 1 / 6 , b ) 2 , c ) 5 / 2 , d ) 6 , e ) 32 | d | multiply(add(5, const_1), divide(log(2), log(2))) | what is the value of ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) ? | using the identity ( loga b ) ( logb c ) = loga c repeatedly , we obtain ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) = log 2 64 = 6 correct answer d | a = 5 + 1
b = math.log(2)
c = math.log(2)
d = b / c
e = a * d
|
a ) 12.21 , b ) 283 , c ) 16.8 , d ) 318 , e ) 32.4 | c | multiply(15, 375) | the h . c . f . of two numbers is 15 and their l . c . m . is 420 . if one of the numbers is 375 , then the other is : | "other number = ( 15 x 420 ) / 375 = 16.8 . answer : c" | a = 15 * 375
|
a ) 500 , b ) 620 , c ) 450 , d ) 360 , e ) 440 | d | add(add(add(add(add(add(const_12, const_2), const_1), add(add(const_12, const_2), add(add(add(add(add(const_2, const_4), const_4), subtract(const_10, const_1)), add(add(const_2, const_4), const_4)), add(const_10, const_2)))), add(add(add(const_12, const_2), const_1), const_1)), 10), add(const_2, const_4)) | what is the sum of all the multiples of 10 between 0 and 85 ? | "the multiples of 10 between 0 and 85 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 . if these are all added together , the result is 360 . final answer : d" | a = 12 + 2
b = a + 1
c = 12 + 2
d = 2 + 4
e = d + 4
f = 10 - 1
g = e + f
h = 2 + 4
i = h + 4
j = g + i
k = 10 + 2
l = j + k
m = c + l
n = b + m
o = 12 + 2
p = o + 1
q = p + 1
r = n + q
s = r + 10
t = 2 + 4
u = s + t
|
a ) 1456 , b ) 1563 , c ) 1546 , d ) 1643 , e ) 1635 | e | multiply(divide(subtract(1365, 15), subtract(6, const_1)), 6) | find large number from below question the difference of two no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ? | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e" | a = 1365 - 15
b = 6 - 1
c = a / b
d = c * 6
|
a ) - 16 , b ) - 13 , c ) - 4 , d ) - 2 , e ) 12 | c | add(2, 10) | if | x + 2 | = 10 , what is the sum of all the possible values of x ? | "there will be two cases x + 2 = 10 or x + 2 = - 10 = > x = 8 or x = - 12 sum of both the values will be - 12 + 8 = - 4 answer : c" | a = 2 + 10
|
a ) 5 , b ) 7 , c ) 9 , d ) 12 , e ) 14 | c | divide(18, subtract(const_4, const_2)) | in a group of cows and chickens , the number of legs was 18 more than twice the number of heads . the number of cows was : | "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 18 more than twice the number of heads . therefore , 2 × ( x + y ) + 18 = 4 x + 2 y . or , 2 x + 2 y + 18 = 4 x + 2 y . or , 2 x + 18 = 4 x [ subtracting 2 y from both sides ] . or , 18 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 18 = 2 x . or , x = 9 [ dividing by 2 on both sides ] . therefore , the number of cows = 9 . correct answer : c ) 9" | a = 4 - 2
b = 18 / a
|
a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 42 , d ) 2 , e ) 30 | c | divide(const_1, multiply(divide(3.5, 5), const_60)) | before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 3.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ? | pete covered 3.5 * 60 = 210 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 210 = 1 / 42 . answer : c . | a = 3 / 5
b = a * const_60
c = 1 / b
|
a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10 | c | subtract(642, add(multiply(multiply(multiply(5, 7), 9), const_2), 4)) | what least number should be subtracted from 642 so that the remainder when divided by 5 , 7 , and 9 will leave in each case the same remainder 4 ? | "the lcm of 5 , 7 , and 9 is 315 . the next multiple is 2 * 315 = 630 . 630 + { remainder } = 630 + 4 = 634 , which is 8 less than 642 . answer : c ." | a = 5 * 7
b = a * 9
c = b * 2
d = c + 4
e = 642 - d
|
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