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 |
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a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days | a | multiply(divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2))), 2) | 6 boysand 8 girls can do job in 10 days , 26 boys & 48 women do work in 2 days find time taken by 15 boys and 20 girls to do same work | 6 b + 8 g = 1 / 10 ( 1 day work ) - - - - - - > ( i ) 26 b + 48 w = 1 / 2 - - - - - - - - > ( ii ) divide both sides by 2 in ( i ) and multiply both sides by 5 now we get 15 b + 20 b = 1 / 4 so ans . is 4 days . answer : a | a = 48 * 2
b = 8 * 10
c = a - b
d = 6 * 10
e = 26 * 2
f = d - e
g = c / f
h = g * 2
|
a ) a ) 300 , b ) b ) 290 , c ) c ) 280 , d ) d ) 270 , e ) e ) 66 | a | subtract(add(200, 350), 250) | a , b and c have rs . 250 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ? | "a + b + c = 250 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 250 - - - - - - - - - - - - - - - - c = 300 answer : a" | a = 200 + 350
b = a - 250
|
a ) 22 , b ) 38 , c ) 62 , d ) 122 , e ) 118 | e | multiply(2, divide(divide(1947, add(const_10, const_1)), const_3)) | a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * β¦ * n until the product is divisible by 1947 , what is the value of n ? | "factorise 1947 . . 3 * 11 * 59 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 59 = 118 . . ans : e" | a = 10 + 1
b = 1947 / a
c = b / 3
d = 2 * c
|
a ) 4.25 hr , b ) 3.6 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr | b | divide(72, add(14, 6)) | a boat can travel with a speed of 14 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 72 km downstream . | "speed of boat in still water = 14 km / hr speed of the stream = 6 km / hr speed downstream = ( 14 + 6 ) = 20 km / hr time taken to travel 72 km downstream = 72 Γ’ Β β 20 = 3.6 hours answer is b" | a = 14 + 6
b = 72 / a
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a ) 1021 , b ) 1041 , c ) 1061 , d ) 1081 , e ) 1101 | c | add(multiply(divide(add(40, 60), const_2), add(subtract(60, 40), const_1)), add(divide(subtract(60, 40), const_2), const_1)) | if x is equal to the sum of the integers from 40 to 60 , inclusive , and y is the number of even integers from 40 to 60 , inclusive , what is the value of x + y ? | "x = 40 + 41 + . . . + 60 = 21 ( 50 ) = 1050 y = 11 x + y = 1061 the answer is c ." | a = 40 + 60
b = a / 2
c = 60 - 40
d = c + 1
e = b * d
f = 60 - 40
g = f / 2
h = g + 1
i = e + h
|
a ) 35 years , b ) 45 years , c ) 52 years , d ) 54 years , e ) none of these | c | add(36, const_1) | the average age of 36 students in a group is 15 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ? | "explanation : age of the teacher = ( 37 * 16 - 36 * 15 ) years = 52 years . answer : c" | a = 36 + 1
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a ) 99 , b ) 18 , c ) 100 , d ) 17 , e ) 12 | c | divide(rectangle_area(40, 20), rectangle_area(4, 2)) | how many paying stones , each measuring 4 m * 2 m are required to pave a rectangular court yard 40 m long and 20 m board ? | "40 * 20 = 4 * 2 * x = > x = 100 answer : c" | a = rectangle_area / (
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a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 1.9 kmph . | c | multiply(const_3_6, divide(12, 36)) | convert the 12 / 36 m / s into kilometers per hour ? | "15 / 36 m / s = 12 / 36 * 18 / 5 = 1 ( 1 / 5 ) = 1.2 kmph . answer : c" | a = 12 / 36
b = const_3_6 * a
|
a ) 22 , b ) 67 , c ) 200 , d ) 288 , e ) 111 | b | add(multiply(divide(const_100, const_2), const_10), power(18, const_3)) | a two digit number is 18 less than the sum of the squares of its digits . how many such numbers are there ? | "option 2 only 47 and 67 satisfy the condition answer : b" | a = 100 / 2
b = a * 10
c = 18 ** 3
d = b + c
|
a ) 3 / 4 , b ) 9 / 16 , c ) 16 / 3 , d ) 4 / 3 , e ) 3 / 16 | b | divide(power(3, const_2), power(4, const_2)) | rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 4 , what is the ratio of rectangle a β s area to rectangle b β s area ? | "the area of rectangle a is ab . c = 4 a / 3 and d = 4 b / 3 . the area of rectangle b is cd = 16 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 16 ab / 9 ) = 9 / 16 . the answer is b ." | a = 3 ** 2
b = 4 ** 2
c = a / b
|
a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 35.71429 , e ) 64.5 | d | divide(multiply(25, add(const_4, const_1)), const_2) | to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 7 / 10 of its present ? | "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 7 x / 10 hence , number of buckets needed = 25 x / ( 7 x / 10 ) = ( 25 Γ 10 ) / 7 = 35.71429 answer is d ." | a = 4 + 1
b = 25 * a
c = b / 2
|
a ) 17 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 37 kg | e | subtract(add(multiply(40, const_2), multiply(46, const_2)), multiply(45, const_3)) | the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 46 kg , then the weight of b is : | "let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 46 = 92 hence 80 + 92 - 144 = 37 ans = 37 answer : e" | a = 40 * 2
b = 46 * 2
c = a + b
d = 45 * 3
e = c - d
|
a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 9 : 5 | e | divide(add(multiply(4, 5), multiply(3, divide(add(5, 3), const_2))), add(multiply(4, 3), multiply(3, divide(add(5, 3), const_2)))) | two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 2 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ? | "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 4 and 2 parts , respectively . this will give us in the final mixture ( 5 + 4 ) : ( 3 + 2 ) , which means 9 : 5 answer e ." | a = 4 * 5
b = 5 + 3
c = b / 2
d = 3 * c
e = a + d
f = 4 * 3
g = 5 + 3
h = g / 2
i = 3 * h
j = f + i
k = e / j
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | divide(subtract(30, divide(30, 2)), add(1, 2)) | in covering a distance of 30 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is : | "abhay speed = x sameer speed = y ( 30 / x ) - ( 30 / y ) = 2 . . . . 1 - ( 30 / 2 x ) + ( 30 / y ) = 1 . . . - 2 solving 1 and 2 we get 6 x = 30 x = 5 answer e" | a = 30 / 2
b = 30 - a
c = 1 + 2
d = b / c
|
a ) 980 , b ) 1130 , c ) 1440 , d ) 1610 , e ) 1820 | d | divide(add(subtract(2.05, divide(65, const_100)), multiply(divide(divide(10, 100), 100), 250)), divide(divide(10, 100), 100)) | a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.05 ? | the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.05 - $ 0.65 = $ 1.40 the charge for the next 1300 grams is $ 1.30 which leaves a charge of $ 0.10 the weight is somewhere between 1550 and 1650 . the answer is d . | a = 65 / 100
b = 2 - 5
c = 10 / 100
d = c / 100
e = d * 250
f = b + e
g = 10 / 100
h = g / 100
i = f / h
|
['a ) 38', 'b ) 36', 'c ) 40', 'd ) 56', 'e ) 64'] | a | subtract(subtract(add(const_10, multiply(14.25, 2)), const_0_25), const_0_25) | the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 14.25 , what is the perimeter of the garden , in feet ? | perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 14.25 ( p ^ 2 ) / 16 = 2 p + 9 p ^ 2 = 32 p + 228 p ^ 2 - 32 p - 228 = 0 p ^ 2 - 38 p + 6 p - 228 = 0 p ( p - 38 ) + 6 ( p + 38 ) = 0 ( p - 38 ) ( p + 6 ) = 0 p = 38 or - 6 discarding negative value , p = 38 answer is a | a = 14 * 25
b = 10 + a
c = b - const_0_25
d = c - const_0_25
|
a ) 223.78 , b ) 37.78 , c ) 24.6 , d ) 278.88 , e ) 123.0 | e | divide(61.50, divide(const_4, 2)) | a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 1 / 2 % his yearly income diminishes by rs . 61.50 . his capital is | "explanation : capital = rs . x , then 1 / 2 x = 61.5 x = 123.00 answer : e ) rs . 123.00" | a = 4 / 2
b = 61 / 50
|
a ) 475 , b ) 700 , c ) 220 , d ) 400 , e ) none of these | a | add(380, multiply(380, divide(20, const_100))) | a fruit seller had some oranges . he sells 20 % oranges and still has 380 oranges . how many oranges he had originally ? | explanation : he sells 20 % of oranges and still there are 380 oranges remaining = > 80 % of oranges = 380 β ( 80 Γ total oranges ) / 100 = 380 β total oranges / 100 = 4.75 β total oranges = 4.75 Γ 100 = 475 answer : option a | a = 20 / 100
b = 380 * a
c = 380 + b
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a ) a ) 59 , b ) b ) 30 , c ) c ) 63 , d ) d ) 65 , e ) e ) 67 | b | divide(add(25, 36), const_2) | find the mean proportional between 25 & 36 ? | "formula = β a Γ b a = 25 and b = 36 β 25 Γ 36 = 5 Γ 6 = 30 b" | a = 25 + 36
b = a / 2
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a ) 7 / 98 , b ) 1 / 70 , c ) 1 / 98 , d ) 1 / 96 , e ) 1 / 68 | b | inverse(multiply(2, 7)) | the compound ratio of 2 / 5 , 6 / 7 , 1 / 3 and 1 / 8 is given by ? | "2 / 5 * 6 / 7 * 1 / 3 * 1 / 8 = 12 / 840 = 1 / 70 answer : b" | a = 2 * 7
b = 1/(a)
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a ) 100 and 80 , b ) 100 and 90 , c ) 100 and 110 , d ) 70 and 100 , e ) 100 and 70 | e | add(multiply(const_100, const_100), divide(multiply(310, 7), add(add(divide(multiply(7, 10), 5), 7), 10))) | p , q and r can do a work in 5 , 7 and 10 days respectively . they completed the work and got rs . 310 . what is the share of q and r respectively ? | the ratio of their working rates = 1 / 5 : 1 / 7 : 1 / 10 = 14 : 10 : 7 . since , they work together , the share of q = 10 / 31 * 310 = rs . 100 the share of r = 7 / 31 * 310 = rs . 70 the share of q and r respectively is rs . 100 and rs . 70 answer : e | a = 100 * 100
b = 310 * 7
c = 7 * 10
d = c / 5
e = d + 7
f = e + 10
g = b / f
h = a + g
|
a ) 14.2 , b ) 16.5 , c ) 17 , d ) 17.5 , e ) 18 | e | divide(divide(multiply(add(16, 18), add(divide(subtract(18, 16), 16), const_1)), const_2), add(divide(subtract(18, 16), 16), const_1)) | what is the average ( arithmetic mean ) of the numbers 16 , 17 , 18 , 19 and 20 ? | "{ 16 , 17 , 18 , 19 , 20 } = { 18 - 2,18 - 1 , 18 , 18 + 1,18 + 2 } - - > the average = 18 . answer : e ." | a = 16 + 18
b = 18 - 16
c = b / 16
d = c + 1
e = a * d
f = e / 2
g = 18 - 16
h = g / 16
i = h + 1
j = f / i
|
a ) 270 , b ) 289 , c ) 267 , d ) 261 , e ) 552 | d | multiply(divide(841, add(add(multiply(12, 8), multiply(16, 9)), multiply(18, 6))), multiply(16, 9)) | a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ? | "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 841 = 261 answer : d" | a = 12 * 8
b = 16 * 9
c = a + b
d = 18 * 6
e = c + d
f = 841 / e
g = 16 * 9
h = f * g
|
a ) s . 2.66 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 2.1 | a | multiply(divide(divide(multiply(divide(21, const_100), 100), 10), multiply(divide(21, const_100), 100)), const_100) | a reduction of 21 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ? | "100 * ( 21 / 100 ) = 21 - - - 10 ? - - - 1 = > rs . 2.1 100 - - - 79 ? - - - 2.1 = > rs . 2.66 answer : a" | a = 21 / 100
b = a * 100
c = b / 10
d = 21 / 100
e = d * 100
f = c / e
g = f * 100
|
a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000 | a | multiply(const_1000, divide(1, 500)) | 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 / 500 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 / 500 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 / 1000 n = 10 satisfies this . a" | a = 1 / 500
b = 1000 * a
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a ) 19 , b ) 2 , c ) 5 , d ) 6 , e ) 8 | a | subtract(multiply(add(floor(divide(1156, 25)), const_1), 25), 1156) | what is the least number should be added to 1156 , so the sum of the number is completely divisible by 25 ? | "( 1156 / 25 ) gives remainder 6 6 + 19 = 25 , so we need to add 19 answer : a" | a = 1156 / 25
b = math.floor(a)
c = b + 1
d = c * 25
e = d - 1156
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a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | d | divide(subtract(multiply(4, 21), add(add(4, 5), 7)), 4) | the youngest of 4 children has siblings who are 4 , 5 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ? | x + ( x + 4 ) + ( x + 5 ) + ( x + 7 ) = 84 4 x + 16 = 84 4 x = 68 x = 17 the answer is d . | a = 4 * 21
b = 4 + 5
c = b + 7
d = a - c
e = d / 4
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a ) 3999 , b ) 7799 , c ) 2500 , d ) 2772 , e ) 6250 | e | divide(multiply(500, const_100), 2) | a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 500 when the rate to profit rises from 5 to 7 percent . find the capital of b ? | "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 500 b capital = 37500 * 1 / 6 = 6250 . answer : e" | a = 500 * 100
b = a / 2
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a ) 50 sec , b ) 190 sec , c ) 287 sec , d ) 74 sec , e ) 697 sec | b | subtract(divide(multiply(const_1, const_1000), divide(50, 10)), 10) | in a kilometer race , a beats b by 50 meters or 10 seconds . what time does a take to complete the race ? | "explanation : time taken by b run 1000 meters = ( 1000 * 10 ) / 50 = 200 sec . time taken by a = 200 - 10 = 190 sec . answer b" | a = 1 * 1000
b = 50 / 10
c = a / b
d = c - 10
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a ) 7 km , b ) 6 km , c ) 8 1 / 8 km , d ) 9 km , e ) 5 km | c | add(multiply(add(6, divide(const_1, const_2)), subtract(add(5, divide(const_3, const_4)), add(4, divide(const_1, const_2)))), const_2) | two men a and b start from place x walking at 4 Β½ kmph and 5 ΒΎ kmph respectively . how many km apart they are at the end of 6 Β½ hours if they are walking in the same direction ? | rs = 5 ΒΎ - 4 Β½ = 1 ΒΌ t = 6 Β½ h . d = 5 / 4 * 13 / 2 = 65 / 8 = 8 1 / 8 km answer : c | a = 1 / 2
b = 6 + a
c = 3 / 4
d = 5 + c
e = 1 / 2
f = 4 + e
g = d - f
h = b * g
i = h + 2
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a ) 30 , b ) 32 , c ) 40 , d ) 36 , e ) 38 | a | divide(add(subtract(multiply(25, 8), add(multiply(2, 20), multiply(3, 26))), 8), 3) | the average of 8 numbers is 25 , that of the first 2 is 20 and of the next 3 is 26 . the sixth number is less than the seventh by 4 , and less than the eighth by 6 . the last number is | explanation : sum of all the numbers = 25 * 8 = 200 sum of first two numbers = 40 sum of next three numbers ( i . e . , 3 rd , 4 th and 5 th ) = 78 so , sum of first five numbers = 118 and sum of 6 th , 7 th and 8 th number = 82 assuming sixth number to be x , we get 7 th number = x + 4 and 8 th number = x + 6 . so , x + ( x + 4 ) + ( x + 6 ) = 82 = > x = 24 . hence , last number ( 8 th number ) = 30 . answer : a | a = 25 * 8
b = 2 * 20
c = 3 * 26
d = b + c
e = a - d
f = e + 8
g = f / 3
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a ) 10 , b ) 9 , c ) 20 , d ) 25 , e ) 30 | b | multiply(6, divide(18, 12)) | 18 : 12 seconds : : ? : 6 minutes | 18 * 6 = 12 * x x = 9 answer : b | a = 18 / 12
b = 6 * a
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a ) 120 , b ) 150 , c ) 100 , d ) 240 , e ) 200 | c | multiply(multiply(18, const_0_2778), 20) | a ship going at the speed of 18 km / hr crosses a light house in 20 seconds . what is the length of the train ? | speed = ( 18 x 5 / 18 ) = 5 m / sec . length of the train = ( speed x time ) . length of the train = 5 x 20 m = 100 m . answer : c | a = 18 * const_0_2778
b = a * 20
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a ) 28 , b ) 27 , c ) 26 , d ) 25 , e ) 29 | d | divide(10, subtract(const_1, multiply(12, divide(const_1, 20)))) | matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days peter stops and peter completes the remaining work in 10 days . in how many days matt complete the work separately . | together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 10 < = > x = 10 / ( 8 / 20 ) = 25 d | a = 1 / 20
b = 12 * a
c = 1 - b
d = 10 / c
|
a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 7 , e ) e ) 16 | d | multiply(7, 1) | set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 7 ? | "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d" | a = 7 * 1
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a ) 9 % , b ) 8 % , c ) 7 % , d ) 3 % , e ) 6 % | a | divide(multiply(add(30, const_100), subtract(const_100, 30)), const_100) | a number is increased by 30 % and then decreased by 30 % . find the net increase or decrease per cent . | "let the number be 100 . increase in the number = 30 % = 30 % of 100 = ( 30 / 100 Γ£ β 100 ) = 30 therefore , increased number = 100 + 30 = 130 this number is decreased by 30 % therefore , decrease in number = 30 % of 130 = ( 30 / 100 Γ£ β 130 ) = 3900 / 100 = 39 therefore , new number = 130 - 39 = 91 thus , net decreases = 100 - 91 = 9 hence , net percentage decrease = ( 9 / 100 Γ£ β 100 ) % = ( 900 / 100 ) % = 9 % answer : a" | a = 30 + 100
b = 100 - 30
c = a * b
d = c / 100
|
a ) 5 , b ) 9 , c ) 4 , d ) 10 , e ) 3 | b | divide(subtract(27, power(3, 2)), 2) | if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 27 , find the value of ab . | "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 27 - 9 = 18 ab = 9 . answer is b ." | a = 3 ** 2
b = 27 - a
c = b / 2
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a ) 4 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph | a | divide(subtract(19, 11), const_2) | a man can row his boat with the stream at 19 km / h and against the stream in 11 km / h . the man ' s rate is ? | "ds = 19 us = 11 s = ? s = ( 19 - 11 ) / 2 = 4 kmph answer : a" | a = 19 - 11
b = a / 2
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a ) 30 % , b ) 37 % , c ) 65 % , d ) 35 % , e ) 45 % | d | multiply(subtract(const_1, multiply(divide(50, const_100), add(divide(30, const_100), const_1))), const_100) | kamal ' s salary was decreased by 50 % and subsequently increased by 30 % . how much percent does he lose ? | explanation : solution : let original salary = rs . 100 . new final salary = 130 % of ( 50 % of rs . 100 ) = rs . ( 130 / 100 * 50 / 100 * 100 ) = rs . 65 . . ' . decrease = 35 % answer : d | a = 50 / 100
b = 30 / 100
c = b + 1
d = a * c
e = 1 - d
f = e * 100
|
a ) 3 / 8 , b ) 9 / 10 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4 | b | divide(subtract(add(divide(divide(add(add(multiply(const_100, multiply(const_2, add(const_1, const_4))), multiply(const_4, const_100)), multiply(const_4, multiply(const_2, add(const_1, const_4)))), 20.000), 10), 10), 6), 20.000) | a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 10 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ? | "x * 6 / 100 * 1 + ( 20000 - x ) * 10 / 100 * 1 = 1440 6 x - 8 x = 144000 - 200000 = > - 2 x = - 4000 = > x = 2000 so 18000 / 20000 = 9 / 10 answer - b" | a = 1 + 4
b = 2 * a
c = 100 * b
d = 4 * 100
e = c + d
f = 1 + 4
g = 2 * f
h = 4 * g
i = e + h
j = i / 20
k = j / 10
l = k + 10
m = l - 6
n = m / 20
|
a ) 24 , b ) 25 , c ) 28 , d ) 30 , e ) 32 | c | multiply(divide(multiply(42, 3), add(add(2, 3), 4)), 2) | the ratio of a to b to c is 2 to 3 to 4 , and a , b , c are positive integers . if the average ( arithmetic mean ) of the 3 numbers is 42 , what is the value of a ? | let a = 2 k , b = 3 k , and c = 4 k . a + b + c = 2 k + 3 k + 4 k = 9 k since the average is 42 : 9 k / 3 = 42 3 k = 42 k = 14 then a = 28 . the answer is c . | a = 42 * 3
b = 2 + 3
c = b + 4
d = a / c
e = d * 2
|
a ) a ) 166 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158 | a | add(multiply(18, 9), 4) | what is the dividend . divisor 18 , the quotient is 9 and the remainder is 4 | "d = d * q + r d = 18 * 9 + 4 d = 166 answer : a" | a = 18 * 9
b = a + 4
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a ) 435 , b ) 570 , c ) 480 , d ) 520 , e ) 550 | a | divide(174, divide(subtract(70, subtract(const_100, 70)), const_100)) | in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 174 votes . find the total number of valid votes ? | "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 174 = > 4 x / 10 = 174 = > 4 x = 1740 = > x = 435 . answer : a" | a = 100 - 70
b = 70 - a
c = b / 100
d = 174 / c
|
a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11 | a | divide(1320, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14)) | if the wheel is 14 cm then the number of revolutions to cover a distance of 1320 cm is ? | "2 * 22 / 7 * 14 * x = 1320 = > x = 15 answer : a" | a = 3 * 100
b = 1 * 10
c = a + b
d = c + 4
e = d / 100
f = 2 * e
g = f * 14
h = 1320 / g
|
a ) 37 km / hr , b ) 53 km / hr , c ) 36 km / hr , d ) 26 km / hr , e ) 87 km / hr | b | divide(divide(subtract(125, multiply(multiply(8, const_0_2778), 8)), 8), const_0_2778) | a train 125 m long passes a man , running at 8 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ? | "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 8 = 45 = > x = 53 km / hr . answer : b" | a = 8 * const_0_2778
b = a * 8
c = 125 - b
d = c / 8
e = d / const_0_2778
|
a ) 1 : 2 , b ) 1 : 3 , c ) 3 : 1 , d ) 1 : 5 , e ) 1 : 4 | c | divide(add(divide(multiply(62.5, 4), const_100), divide(multiply(87.5, 4), const_100)), add(subtract(4, divide(multiply(62.5, 4), 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 4 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 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 2 + 7 / 2 = 6 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6 : 2 = 3 : 1 . answer : c" | a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d
f = 62 * 5
g = f / 100
h = 4 - g
i = 87 * 5
j = i / 100
k = 4 - j
l = h + k
m = e / l
|
a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | d | divide(880, divide(add(14, 8), const_2)) | the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 880 square meters , what is the depth of the channel ( in meters ) ? | "1 / 2 * d * ( 14 + 8 ) = 880 d = 80 the answer is d ." | a = 14 + 8
b = a / 2
c = 880 / b
|
a ) 0.004 , b ) 0.02775 , c ) 2.775 , d ) 3.6036 , e ) 36.036 | b | inverse(add(divide(1, 0.03), divide(1, 0.37))) | 1 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ? | approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 1 / 36 = . 02 something answer ( b ) | a = 1 / 0
b = 1 / 0
c = a + b
d = 1/(c)
|
a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.8 , e ) 2.22 | e | divide(100, multiply(162, const_0_2778)) | in what time will a train 100 m long cross an electric pole , it its speed be 162 km / hr ? | "speed = 162 * 5 / 18 = 45 m / sec time taken = 100 / 45 = 2.22 sec . answer : e" | a = 162 * const_0_2778
b = 100 / a
|
a ) 345 , b ) 342 , c ) 343 , d ) 342 , e ) 341 | b | multiply(412, subtract(add(floor(divide(956734, 412)), const_1), divide(956734, 412))) | which number need to add to 956734 to get a number exactly divisible by 412 ? | "956734 / 412 = 2322 and reminder = 70 . 412 - 70 = 342 so , the next number divisible by 412 is 342 places in front of 956734 which means 342 + 956734 = 957076 342 should be added to 956734 b" | a = 956734 / 412
b = math.floor(a)
c = b + 1
d = 956734 / 412
e = c - d
f = 412 * e
|
a ) 1250 m , b ) 1110 m , c ) 2000 m , d ) 1000 m , e ) 1300 m | c | multiply(divide(multiply(15, const_1000), const_60), 40) | a man walking at a rate of 15 km / hr crosses a bridge in 40 minutes . the length of the bridge is ? | "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 40 minutes = 15 / 18 * 40 * 60 = 2000 m answer is c" | a = 15 * 1000
b = a / const_60
c = b * 40
|
['a ) 10', 'b ) 100', 'c ) 1000', 'd ) 10000', 'e ) 50'] | c | divide(multiply(11, const_1000), circumface(1.75)) | a circular wheel radius is 1.75 m . for covering 11 k . m how much time it revolve ? | distance traveled in 1 round = perimeter = { 2 * 22 / 7 * 175 / 100 } m = 11 m total no . of revolution in covering 11 km = 11000 / 11 = 1000 answer c | a = 11 * 1000
b = a / circumface
|
a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90 | b | multiply(divide(multiply(divide(1, 12), const_3), divide(divide(1, 30), const_2)), 2) | in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ? | "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b" | a = 1 / 12
b = a * 3
c = 1 / 30
d = c / 2
e = b / d
f = e * 2
|
a ) 850 , b ) 900 , c ) 950 , d ) 1000 , e ) 2000 | b | divide(0.0006688, 0.0000150) | 0.0006688 / 0.0000150 x 19.85 = ? | "explanation : ? = 6688 / 150 x 19.85 = 45 x 20 = 900 answer : option b" | a = 0 / 6688
|
a ) 9 , b ) 8 , c ) 0 , d ) 2 , e ) 1 | b | divide(multiply(lcm(const_100, 8), gcd(const_100, 8)), const_100) | find the highest value of ' a ' so that 365 a 24 is divisible by 8 . | "explanation : given , number is divisible by 8 only if ' a 24 ' is divisible by 8 . . : highest value of a is ' 8 ' . answer : option b" | a = math.lcm(100, 8)
b = math.gcd(100, 8)
c = a * b
d = c / 100
|
a ) 0 , b ) 12 , c ) 13 , d ) 40 , e ) 25 | d | divide(multiply(12, 70), 21) | in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 70 as quotient . what is the correct quotient ? | "12 * 70 = 840 840 % 21 = 40 answer : d" | a = 12 * 70
b = a / 21
|
a ) 4615 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154 | a | divide(multiply(5000, divide(6, const_100)), divide(6.5, const_100)) | last year a certain bond price with a face value of 5000 yielded 6 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ? | interest = 0.06 * 5000 = 0.065 * selling price - - > selling price = 0.06 * 5000 / 0.065 - - > selling price = ~ 4,615 answer : a . | a = 6 / 100
b = 5000 * a
c = 6 / 5
d = b / c
|
a ) 8 , b ) 6 , c ) 7 , d ) 10 , e ) 9 | d | power(multiply(4, power(5, 2)), 5) | if 5 log ( 4 * 5 ^ 2 ) = x , find x | "5 ( log 2 ^ 2 * 5 ^ 2 ) = x 5 log ( 5 * 2 ) ^ 2 = x 5 * 2 log ( 5 * 2 ) = x 10 log 10 = x log 10 base 10 = 1 so 10 * 1 = x x = 10 answer : d" | a = 5 ** 2
b = 4 * a
c = b ** 5
|
a ) 18.75 , b ) 19.75 , c ) 26.89 , d ) 21.75 , e ) 22.75 | c | subtract(multiply(divide(const_100, 58), divide(multiply(60, 84), const_100)), 60) | there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 58 % | "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 58 / 100 = 50.40 so x = 26.89 answer : c" | a = 100 / 58
b = 60 * 84
c = b / 100
d = a * c
e = d - 60
|
a ) 19 , b ) 14 , c ) 13 , d ) 10 , e ) 12 | b | multiply(multiply(divide(7, 5), divide(14, 7)), 5) | the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 14 . if p invested the money for 5 months , find for how much time did q invest the money ? | "7 * 5 : 5 * x = 7 : 14 x = 14 answer : b" | a = 7 / 5
b = 14 / 7
c = a * b
d = c * 5
|
a ) 9300 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000 | a | subtract(subtract(7500, multiply(7500, divide(10, const_100))), multiply(subtract(7500, multiply(7500, divide(10, const_100))), divide(10, const_100))) | the population of a town is 7500 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ? | "formula : ( after = 100 denominator ago = 100 numerator ) 7500 Γ£ β 100 / 90 Γ£ β 100 / 90 = 9259 a )" | a = 10 / 100
b = 7500 * a
c = 7500 - b
d = 10 / 100
e = 7500 * d
f = 7500 - e
g = 10 / 100
h = f * g
i = c - h
|
a ) $ 880 , b ) $ 1050 , c ) $ 1280 , d ) $ 1460 , e ) $ 1640 | e | multiply(surface_rectangular_prism(3, 7, 2), 20) | a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 7 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ? | "the total surface area is 2 ( 2 * 3 + 3 * 7 + 2 * 7 ) = 82 square feet the total cost is 82 * $ 20 = $ 1640 the answer is e ." | a = surface_rectangular_prism * (
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | divide(16, 24) | how many of the positive factors of 24 , 16 and how many common factors are there in numbers ? | "factors of 24 - 1 , 2 , 3 , 4 , 8 , 12 and 24 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 4 answer d" | a = 16 / 24
|
a ) 25 , b ) 66 , c ) 18 , d ) 19 , e ) 01 | a | divide(multiply(divide(multiply(12.5, 50), const_100), const_100), 25) | a company pays 12.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ? | "explanation : dividend on 1 share = ( 12.5 * 50 ) / 100 = rs . 6.25 rs . 25 is income on an investment of rs . 100 rs . 6.25 is income on an investment of rs . ( 6.25 * 100 ) / 25 = rs . 25 answer : a" | a = 12 * 5
b = a / 100
c = b * 100
d = c / 25
|
a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21 | b | add(13, const_2) | a box contains 10 tablets of medicine a and 13 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted . | "the worst case scenario will be if we remove all 13 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 13 + 2 = 15 tablets . answer : b ." | a = 13 + 2
|
a ) 154 , b ) 161 , c ) 168 , d ) 175 , e ) 182 | b | subtract(lcm(24, 8), 7) | what is the smallest number which , when increased by 7 , is divisible by 7 , 8 , and 24 ? | "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 7 = 161 . the answer is b ." | a = math.lcm(24, 8)
b = a - 7
|
a ) 7500 , b ) 6500 , c ) 8125 , d ) 9125 , e ) none of them | d | multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100)) | find the simple interest on rs . 73,000 at 16 2 / 3 % per year for 9 months . | "p = rs . 73000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 73,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9125 answer is d ." | a = 2 * 3
b = a * 100
c = b * 100
d = 3 * 3
e = d * 100
f = 3 + 2
g = f * 2
h = e * g
i = c + h
j = 16 * 3
k = j + 2
l = k / 3
m = i * l
n = 3 * 3
o = 2 * 3
p = 2 * o
q = n / p
r = m * q
s = 1 / 100
t = r * s
|
a ) 1245 , b ) 1430 , c ) 1540 , d ) 1600 , e ) 1635 | e | multiply(divide(subtract(2, 6), subtract(1365, const_1)), 1365) | find large number from below question the difference of 2 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 = 2 - 6
b = 1365 - 1
c = a / b
d = c * 1365
|
a ) 4.5 kmph , b ) 9.5 kmph , c ) 7.5 kmph , d ) 8.5 kmph , e ) 5.5 kmph | d | divide(add(13, 4), const_2) | calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes at 13 km / hr downstream and 4 km / hr upstream . | "speed in still water = ( 13 + 4 ) 1 / 2 kmph = 8.5 kmph . answer : d" | a = 13 + 4
b = a / 2
|
a ) 7 / 4 , b ) 4 / 3 , c ) 15 / 4 , d ) 10 / 3 , e ) 64 / 21 | e | max(divide(subtract(const_1, multiply(add(divide(const_1, add(const_4, const_2)), divide(const_1, 7)), const_2)), divide(const_1, 7)), const_3) | two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 7 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ? | rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 7 combined = 13 / 42 work done in 2 days = 13 / 21 work left = 8 / 21 rate * time = work left 1 / 8 * time = 8 / 21 time = 64 / 21 e | a = 4 + 2
b = 1 / a
c = 1 / 7
d = b + c
e = d * 2
f = 1 - e
g = 1 / 7
h = f / g
i = max(h)
|
a ) 18 % , b ) 20 % , c ) 22 % , d ) 23 % , e ) 25 % | c | multiply(divide(subtract(divide(add(const_100, 10), subtract(const_10, const_3)), divide(const_100, const_10)), divide(const_100, const_10)), const_100) | car dealership x , the total profit from sales increased by 10 percent over the previous years , while the number of cars sold decreased by 10 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year . | "let profit be x and cars sold be y originally profit / car = x / y now it is 1.1 x / 0.9 y = 11 / 9 ( x / y ) increase in profit per car = ( ( 2 / 9 ) ( x / y ) ) / ( x / y ) * 100 = 22.22 % answer = c" | a = 100 + 10
b = 10 - 3
c = a / b
d = 100 / 10
e = c - d
f = 100 / 10
g = e / f
h = g * 100
|
a ) 56 , b ) 59 , c ) 63 , d ) 71 , e ) 92 | a | add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 28)), 28) | of 70 players on a football team , 28 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? | "total = 70 thrower = 28 rest = 70 - 28 = 42 left handed = 42 / 3 = 14 right handed = 28 if all thrower are right handed then total right handed is 28 + 28 = 56 so a . 56 is the right answer" | a = 1 / 3
b = 1 - a
c = 70 - 28
d = b * c
e = d + 28
|
a ) $ 5 , b ) $ 12.75 , c ) $ 51.75 , d ) $ 100.75 , e ) $ 105 | b | subtract(subtract(multiply(500, power(add(const_1, divide(10, const_100)), 2)), 500), subtract(multiply(power(add(const_1, divide(5, const_100)), 2), 900), 900)) | on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 900 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim β s investment in the first 2 years was how much greater than the total amount of interest earned by lana β s investment in the first 2 years ? | "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 900 ( 1.05 ) ^ 2 = 900 ( 1.1025 ) = 992.25 thus , tim earned 105 dollars , while lana earned 92.25 dollars the difference is $ 12.75 and the answer is b ." | a = 10 / 100
b = 1 + a
c = b ** 2
d = 500 * c
e = d - 500
f = 5 / 100
g = 1 + f
h = g ** 2
i = h * 900
j = i - 900
k = e - j
|
['a ) 30', 'b ) 24', 'c ) 12', 'd ) 8', 'e ) 9'] | c | subtract(subtract(multiply(9, 3), add(3, const_4)), multiply(const_4, 2)) | a cube of sides 9 is first painted red and then cut into smaller cubes of side 3 . how many of the smaller cube have painted on exactly 2 sides ? | n = side of big cube / side of small cube and no . of smaller cubes with two surfaces painted is ( n - 2 ) * 12 ( 3 - 2 ) * 12 = 12 ans answer : c | a = 9 * 3
b = 3 + 4
c = a - b
d = 4 * 2
e = c - d
|
a ) 500.2 , b ) 320.0 , c ) 220.5 , d ) 100.1 , e ) 230.2 | c | multiply(power(add(divide(divide(10, const_2), const_100), const_1), const_2), 5000) | sam invested rs . 5000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ? | "p = rs . 5000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 5000 * ( 1 + 5 / 100 ) 2 ] = ( 5000 * 21 / 20 * 21 / 20 ) = rs . 220.50 answer : c" | a = 10 / 2
b = a / 100
c = b + 1
d = c ** 2
e = d * 5000
|
a ) $ 1000 , b ) $ 950 , c ) $ 1500 , d ) $ 1150 , e ) $ 1250 | c | divide(1000, subtract(const_1, divide(20, const_100))) | a person incurs 20 % loss by selling a watch for $ 1000 . at what price should the watch be sold to earn 20 % profit ? | "let the new selling price be $ x ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 20 ) / 1000 = ( 100 + 20 ) / x x = 120 * 1000 / 80 = 1500 answer is c" | a = 20 / 100
b = 1 - a
c = 1000 / b
|
a ) 33 / 7 , b ) 43 / 7 , c ) 24 / 7 , d ) 19 / 7 , e ) none | c | inverse(add(inverse(12), add(inverse(24), inverse(6)))) | a , b and c can complete a piece of work in 24 , 6 and 12 days respectively . working together , they will complete the same work in : | if a can do a piece of work in n days , then a ' s 1 day ' s work = 1 / n ( a + b + c ) ' s 1 day ' s work = 1 / 24 + 1 / 6 + 1 / 12 = 7 / 24 so , all the three together will complete the job in = 24 / 7 days answer : c | a = 1/(12)
b = 1/(24)
c = 1/(6)
d = b + c
e = a + d
f = 1/(e)
|
a ) 35 , b ) 36 , c ) 37 , d ) 40 , e ) 45 | d | multiply(multiply(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), divide(40, const_60)), add(const_1, divide(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), 3))) | a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is : | "according to given condition vt = ( v + 3 ) ( t - 2 / 3 ) vt = ( v - 2 ) ( t + 2 / 3 ) here v is velocity in kmph , t is time in hours and 2 / 3 is value of 40 min in hour on solving we will get t = 10 / 3 and and v = 12 so distance = ( 10 / 3 ) * 12 = 40 kms answer : d" | a = 2 * 3
b = a * 2
c = 3 - 2
d = b / c
e = 40 / const_60
f = d * e
g = 2 * 3
h = g * 2
i = 3 - 2
j = h / i
k = j / 3
l = 1 + k
m = f * l
|
a ) 15 min , b ) 15 1 / 7 min , c ) 17 1 / 7 min , d ) 7 1 / 7 min , e ) 7 2 / 7 min | a | add(multiply(20, subtract(const_1, multiply(add(inverse(20), inverse(30)), const_3))), 60) | two pipes a and b can fill a cistern in 20 and 30 minutes respectively , and a third pipe c can empty it in 60 minutes . how long will it take to fill the cistern if all the three are opened at the same time ? | "1 / 20 + 1 / 30 - 1 / 60 = 4 / 60 60 / 4 = 15 answer : a" | a = 1/(20)
b = 1/(30)
c = a + b
d = c * 3
e = 1 - d
f = 20 * e
g = f + 60
|
a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | d | multiply(divide(10, const_100), multiply(5, 28)) | a shoe merchant has declared a 10 % rebate in prices . how much rebate would one get if he purchases 5 pairs of shoes at rs . 28 each ? | explanation : 5 shirts * rs . 28 = rs . 140 rebate = 10 % * 140 = 14 correct option : d | a = 10 / 100
b = 5 * 28
c = a * b
|
a ) 13.3 , b ) 38.3 , c ) 35.3 , d ) 31.3 , e ) 33.3 | e | divide(subtract(multiply(8, 20), multiply(5, 12)), 3) | if the average of 8 digits is 20 and the average of 5 of them is 12 , calculate the average of the remaining 3 numbers ? | "explanation : total of the 8 digits - 8 * 20 = 160 total of the 5 digits - 5 * 12 = 60 total of the remaining 3 digits - 160 - 60 = 100 average of the remaining 3 numbers = 100 / 3 = 33.3 answer : e" | a = 8 * 20
b = 5 * 12
c = a - b
d = c / 3
|
a ) 30 % , b ) 49 % , c ) 90 % , d ) 100 % , e ) none of these | b | multiply(const_100, divide(subtract(add(multiply(const_100, divide(120, const_100)), const_100), multiply(const_100, add(const_1, divide(12, const_100)))), add(multiply(const_100, divide(120, const_100)), const_100))) | in a restaurant , the profit is 120 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ? | "explanation : let c . p . = rs . 100 . then , profit = rs . 120 , s . p . = rs . 220 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 220 . profit = rs . ( 220 - 112 ) = rs . 108 . required percentage = ( 108 / 220 * 100 ) % = 49 % appox answer : b" | a = 120 / 100
b = 100 * a
c = b + 100
d = 12 / 100
e = 1 + d
f = 100 * e
g = c - f
h = 120 / 100
i = 100 * h
j = i + 100
k = g / j
l = 100 * k
|
a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 272 | d | subtract(multiply(const_10, 150), add(multiply(3, 100), multiply(5, 150))) | a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ? | "10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 β 1050 = 450 answer : d" | a = 10 * 150
b = 3 * 100
c = 5 * 150
d = b + c
e = a - d
|
a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 % | c | multiply(divide(10, subtract(30, 10)), const_100) | a shop owner sells 30 mtr of cloth and gains sp of 10 mtrs . find the gain % ? | "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 30 m cloth ) β ( c . p . of 30 m cloth ) selling price of 20 m cloth = selling price of 30 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 20 m cloth = rs . 2000 and s . p . of 20 m cloth = rs . rs . 3000 profit % = 10 Γ 100 = 50 % 20 profit of 50 % was made by the merchant . c" | a = 30 - 10
b = 10 / a
c = b * 100
|
a ) 3.5 , b ) 4 , c ) 4.5 , d ) 3 , e ) 5 | d | multiply(divide(divide(multiply(const_10, 40), const_100), const_2), divide(60, 40)) | a certain dark blue paint contains 40 percent blue pigment and 60 percent red pigment by weight . a certain green paint contains 40 percent blue pigment and 60 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ? | 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 6 = 3 grams of red pigment | a = 10 * 40
b = a / 100
c = b / 2
d = 60 / 40
e = c * d
|
a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 % | b | add(const_10, divide(add(25, 25), const_2)) | in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds x in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ? | "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out x : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b" | a = 25 + 25
b = a / 2
c = 10 + b
|
a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | divide(13, 3) | if ( a β b ) is 13 more than ( c + d ) and ( a + b ) is 3 less than ( c β d ) , then ( a β c ) is : | "( a β b ) β ( c + d ) = 13 and ( c β d ) β ( a + b ) = 3 = > ( a β c ) β ( b + d ) = 13 and ( c β a ) β ( b + d ) = 3 = > ( b + d ) = ( a β c ) β 13 and ( b + d ) = ( c β a ) β 3 = > ( a β c ) β 13 = ( c β a ) β 3 = > 2 ( a β c ) = 10 = > ( a β c ) = 5 answer : e" | a = 13 / 3
|
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | e | subtract(1,400, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2)) | how many integers between 1 and 1,400 are divisible by 25 , and 35 ? | "lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e" | a = 2 * 100
b = 3 + 4
c = b * 10
d = a + c
e = d + 2
f = 1 - 400
|
a ) 3 / 10 , b ) 10 / 3 , c ) 1 / 3 , d ) 5 , e ) 6 / 3 | b | inverse(add(divide(const_1, 5), divide(const_1, 10))) | rahul can done a work in 5 days and meena can done a work in 10 days . in how many days that both are work together ? | a ' s one day work = 1 / 5 b ' s one day work = 1 / 10 a + b = 1 / 5 + 1 / 10 = 10 + 5 / 50 = 10 / 3 days ans : option b | a = 1 / 5
b = 1 / 10
c = a + b
d = 1/(c)
|
a ) 424 , b ) 448 , c ) 1408 , d ) 710 , e ) 223 | a | divide(multiply(const_1000, 1), multiply(add(const_3, divide(add(multiply(const_3, const_4), const_2), power(add(multiply(const_4, const_2), const_2), const_2))), 0.75)) | a bicycle wheel has a diameter of 0.75 m . how many complete revolutions does it make in 1 km ? | "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.75 m ) = 424.6 . hence 424 complete revolutions . answer a" | a = 1000 * 1
b = 3 * 4
c = b + 2
d = 4 * 2
e = d + 2
f = e ** 2
g = c / f
h = 3 + g
i = h * 0
j = a / i
|
a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000 | b | add(multiply(multiply(const_4, const_10), const_1000), divide(subtract(multiply(multiply(const_4, const_2), const_1000), multiply(divide(15, const_100), multiply(multiply(const_4, const_10), const_1000))), divide(20, const_100))) | country x taxes each of its citizens an amount equal to 15 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ? | equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b . | a = 4 * 10
b = a * 1000
c = 4 * 2
d = c * 1000
e = 15 / 100
f = 4 * 10
g = f * 1000
h = e * g
i = d - h
j = 20 / 100
k = i / j
l = b + k
|
a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 70 | b | add(multiply(sqrt(10), const_10), const_3) | if a ^ 2 + b ^ 2 = 10 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ? | "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 10 - 20 = - 10 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 10 + 20 = 30 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 30 - 10 = 20 b" | a = math.sqrt(10)
b = a * 10
c = b + 3
|
a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26 | c | add(add(11, divide(subtract(11, 5), 2)), 8) | a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 8 , ab = 5 and ac = 11 , what is the length of ae ? | "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 8 = 22 the answer is c ." | a = 11 - 5
b = a / 2
c = 11 + b
d = c + 8
|
a ) 2 / 25 , b ) 4 / 75 , c ) 7 / 75 , d ) 3 / 5 , e ) 4 / 45 | e | multiply(subtract(const_1, divide(1, 3)), multiply(divide(2, 3), divide(1, 5))) | on a windy day , out of every 3 sand dunes formed , only 1 remains . out of 5 blown - out sand - dunes , 1 has treasure and only 2 out of 3 sand dunes formed have lucky coupons . find the probability that the blown - out sand dune will contain both the things . | probability of sand dune blown out = 2 / 3 probability that it has treasure = 1 / 5 probability that it has lucky coupon = 2 / 3 total probability = 2 / 3 * 1 / 5 * 2 / 3 = 4 / 45 answer : e | a = 1 / 3
b = 1 - a
c = 2 / 3
d = 1 / 5
e = c * d
f = b * e
|
a ) 515 . , b ) 545 . , c ) 618 . , d ) 674 . , e ) 666 . | d | add(250, 423) | in the faculty of reverse - engineering , 250 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ? | "answer is d : 674 solution : total number of students studying both are 423 + 250 - 134 = 539 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 539 , so 100 % is approx . 674 ." | a = 250 + 423
|
a ) 2.5 , b ) 3 , c ) 4 , d ) 4.5 , e ) 5 | a | divide(triangle_area_three_edges(const_4.0, 3, 5), divide(triangle_perimeter(2, 3, 5), const_2)) | what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 2 , 3 and 5 ? | "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 5 / 2 = 2.5 ans . a" | a = triangle_area_three_edges / (
|
a ) rs . 3800 , b ) rs . 3900 , c ) rs . 4000 , d ) rs . 4200 , e ) rs . 4400 | b | add(multiply(divide(4000, add(multiply(15, divide(4, 10)), 2)), 3), multiply(multiply(divide(4, 10), divide(4000, add(multiply(15, divide(4, 10)), 2))), 12)) | the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is | "let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . b" | a = 4 / 10
b = 15 * a
c = b + 2
d = 4000 / c
e = d * 3
f = 4 / 10
g = 4 / 10
h = 15 * g
i = h + 2
j = 4000 / i
k = f * j
l = k * 12
m = e + l
|
a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 7 / 64 , e ) 3 / 5 | d | divide(const_2, 7) | if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 7 children have two children of the same sex and one of the opposite sex ? | "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 7 = 7 c 2 total possible outcomes - 2 ^ 7 ( each child can be either a girl or a boy ) probability = 2 c 1 * 7 c 2 / 2 ^ 7 = 2 * 7 / 2 * 2 * 2 * 2 * 2 * 2 * 2 = 7 / 64 ans = d" | a = 2 / 7
|
a ) 94 % , b ) 92 % , c ) 95 % , d ) 93 % , e ) 97 % | c | subtract(const_100, multiply(divide(divide(10, 10), multiply(2, const_10)), const_100)) | instead of multiplying a number by 2 , the number is divided by 10 . what is the percentage of error obtained ? | let the number be x the right number is 2 x the wrong number is x / 10 error is ( 2 x - x / 10 ) = 19 x / 10 percentage of error is ( ( 19 x / 10 ) / 2 x ) * 100 = 95 % answer : c | a = 10 / 10
b = 2 * 10
c = a / b
d = c * 100
e = 100 - d
|
a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 7 | d | subtract(divide(subtract(90, 50), subtract(54, 50)), const_1) | for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 54 units per day , what is the value of n ? | "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 54 * ( n + 1 ) - - > n = 9 . or as 40 extra units increased the average for n + 1 days by 4 units per day then 40 / ( n + 1 ) = 4 - - > n = 9 . answer d ." | a = 90 - 50
b = 54 - 50
c = a / b
d = c - 1
|
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