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 ) 120', 'b ) 80', 'c ) 60', 'd ) 40', 'e ) none of these'] | c | sqrt(divide(2400, divide(const_2, const_3))) | the breadth of a rectangular hall is two - thirds of its length . if the area of the hall is 2400 sq metres , what is the length in metres ? | let the length of the rectangular hall be ‘ x ’ m , then the breadth of the rectangular hall = 2 x ⁄ 3 m . area of hall = 2 x ⁄ 3 × x = 2 x 2 ⁄ 3 or , 2 x 2 ⁄ 3 = 2400 or x = 60 m answer c | a = 2 / 3
b = 2400 / a
c = math.sqrt(b)
|
a ) $ 960 , b ) $ 1,350 , c ) $ 1,650 , d ) $ 2,050 , e ) $ 2,250 | c | divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 5.50), const_1000) | a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.50 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ? | "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 5.5 $ then total value is 300 * 5.5 = 1650 . imo option c is correct answer . ." | a = 3 * 100
b = 8 * 10
c = a + b
d = c + 4
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 5
j = i / 1000
|
a ) 76 , b ) 5776 , c ) 304 , d ) 5184 , e ) none | d | power(multiply(4, 18), const_2) | find √ ? / 18 = 4 ? | "answer let √ n / 18 = 4 then √ n = 18 x 4 = 72 ∴ n = 72 x 72 = 5184 . correct option : d" | a = 4 * 18
b = a ** 2
|
a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 15.76 % , e ) none of these | d | add(divide(multiply(add(const_100, add(divide(multiply(add(const_100, subtract(6, 1)), subtract(6, 1)), const_100), subtract(6, 1))), subtract(6, 1)), const_100), add(divide(multiply(add(const_100, subtract(6, 1)), subtract(6, 1)), const_100), subtract(6, 1))) | the population of a city increases by 6 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ? | actual increase in population = 5 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 5 / 100 ) ^ 3 = 115.7625 ∴ required percentage = 15.7625 % answer : d | a = 6 - 1
b = 100 + a
c = 6 - 1
d = b * c
e = d / 100
f = 6 - 1
g = e + f
h = 100 + g
i = 6 - 1
j = h * i
k = j / 100
l = 6 - 1
m = 100 + l
n = 6 - 1
o = m * n
p = o / 100
q = 6 - 1
r = p + q
s = k + r
|
a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 21 | e | divide(add(add(6, const_4), subtract(34, const_4)), const_2) | find the average of all the numbers between 6 and 34 which are divisible by 6 . | "solution average = ( ( 12 + 18 + 24 + 30 ) / 5 ) = 84 / 4 = 21 . answer e" | a = 6 + 4
b = 34 - 4
c = a + b
d = c / 2
|
a ) 6 hours , b ) 3 hours , c ) 2 hours , d ) 5 hours , e ) 4 hours | b | divide(const_1, subtract(divide(const_1, 2), subtract(divide(const_1, 2), divide(const_1, 3)))) | a can do a piece of work in 3 hours ; b and c together can do it in 2 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ? | "a ' s 1 hour work = 1 / 3 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 3 + 1 / 2 ) = 5 / 6 b ' s 1 hour work = ( 5 / 6 - 1 / 2 ) = 1 / 3 b alone will take 3 hours to do the work . answer : b" | a = 1 / 2
b = 1 / 2
c = 1 / 3
d = b - c
e = a - d
f = 1 / e
|
a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) 5 : 2 | b | divide(sqrt(16), sqrt(9)) | two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is ? | "answer : option b let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 16 : â ˆ š 9 = 4 : 3" | a = math.sqrt(16)
b = math.sqrt(9)
c = a / b
|
a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 9.23 % | e | multiply(divide(divide(subtract(950, 650), 650), 5), const_100) | at what rate percent on simple interest will rs . 650 amount to rs . 950 in 5 years ? | "300 = ( 650 * 5 * r ) / 100 r = 9.23 % answer : e" | a = 950 - 650
b = a / 650
c = b / 5
d = c * 100
|
a ) 288889 , b ) 556677 , c ) 555681 , d ) 267788 , e ) 268811 | c | multiply(subtract(subtract(divide(559981, 987), const_4), const_0_33), 987) | a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and the other digits are correct , then the correct answer would be : | "explanation : 987 = 3 * 7 * 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 = > ( sum of digits = 28 , not divisible by 3 ) 555181 = > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by each one of 3 , 7 , 47 . answer : c ) 555681" | a = 559981 / 987
b = a - 4
c = b - const_0_33
d = c * 987
|
a ) $ 1600 , b ) $ 1850 , c ) $ 2250 , d ) $ 2400 , e ) $ 2750 | c | add(divide(87.5, divide(7, const_100)), 1000) | when leo imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that leo paid was $ 87.50 , what was the total value of the item ? | let the value of the item be $ x , then 0.07 ( x − 1000 ) = 87.5 - - > x − 1000 = 1250 x − 1000 = 1250 - - > x = 2250 . answer : c . | a = 7 / 100
b = 87 / 5
c = b + 1000
|
a ) 20 % , b ) 18 % , c ) 16 % , d ) 25 % , e ) 15 % | e | divide(multiply(15.90, const_100), add(15.90, const_100)) | the annual interest rate earned by an investment increased by 6 percent from last year to this year . if the annual interest rate earned by the investment this year was 15.90 percent , what was the annual interest rate last year ? | "let i = interest rate i ( this year ) = i ( last year ) + 0.06 i ( last year ) = 1.06 i ( last year ) 15.90 = 1.06 x i ( last year ) i ( last year ) = 15.90 / 1.06 = 1590 / 106 = 15 % answer : e" | a = 15 * 90
b = 15 + 90
c = a / b
|
a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 34 seconds , e ) 28 seconds | e | divide(add(divide(multiply(3.7, add(12, 2)), subtract(4.2, 3.7)), add(12, 2)), 4.2) | john and steve are speed walkers in a race . john is 12 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ? | let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 12 + 2 - - - > 0.5 t = 14 - - - > t = 28 seconds . e is the correct answer . | a = 12 + 2
b = 3 * 7
c = 4 - 2
d = b / c
e = 12 + 2
f = d + e
g = f / 4
|
a ) 1200 , b ) 1152 , c ) 1189 , d ) 1190 , e ) 100 | b | multiply(add(189, 3), 6) | i chose a number and divide it by 6 . then i subtracted 189 from the result and got 3 . what was the number i chose ? | "let x be the number i chose , then x / 6 − 189 = 3 x / 6 = 192 x = 1152 answer is b ." | a = 189 + 3
b = a * 6
|
a ) s . 1200 , b ) s . 800 , c ) s . 1400 , d ) s . 1000 , e ) s . 920 | b | divide(400, multiply(divide(5, const_100), 10)) | a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 400 more . what was the sum ? | "at 5 % more rate , the increase in s . i for 10 years = rs . 400 ( given ) so , at 5 % more rate , the increase in si for 1 year = 400 / 10 = rs . 40 / - i . e . rs . 40 is 5 % of the invested sum so , 1 % of the invested sum = 40 / 5 therefore , the invested sum = 40 × 100 / 5 = rs . 800 answer : b" | a = 5 / 100
b = a * 10
c = 400 / b
|
a ) 29798 , b ) 27908 , c ) 78902 , d ) 26000 , e ) 27991 | d | divide(divide(divide(multiply(multiply(multiply(26, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5) | a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 26 m * 2 m * 0.75 m ? | "26 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 26 = 1 / 1000 * x = > x = 26000 answer : d" | a = 26 * 100
b = 2 * 100
c = a * b
d = 0 * 75
e = c * d
f = e / 20
g = f / 10
h = g / 7
|
a ) 21 , b ) 23 , c ) 26 , d ) 27 , e ) 29 | a | sqrt(462) | the product of two successive numbers is 462 . which is the smaller of the two numbers ? | a 21 from the given alternatives , 21 × 22 = 462 ∴ smaller number = 21 | a = math.sqrt(462)
|
a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20 | b | divide(30, const_2) | in a group of ducks and cows , the total number of legs are 30 more than twice the number of heads . find the total number of cows . | "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 30 + 2 ( c + d ) = > d + 2 c = 15 + c + d = > 2 c = 15 + c = > c = 15 i . e . , total number of cows = 15 answer is b ." | a = 30 / 2
|
a ) 40 meter , b ) 45 meter , c ) 50 meter , d ) 55 meter , e ) none of these | c | divide(multiply(divide(multiply(subtract(46, 36), const_1000), const_3600), 36), const_2) | two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is ? | "explanation : let the length of each train is x meter distance will be x + x = 2 x relative speed = 46 - 36 = 10 km / hr = 10 * ( 5 / 18 ) = 25 / 9 m / sec distance = speed * time 2 x = 25 / 9 ∗ 36 2 x = 100 = > x = 50 so length of both the trains are 50 meters option c" | a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 36
e = d / 2
|
a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 33.33 % , e ) 66.65 % | d | multiply(divide(25, subtract(const_100, 25)), const_100) | if a ' s height is 25 % less than that of b , how much percent b ' s height is more than that of a ? | "excess of b ' s height over a ' s = [ ( 25 / ( 100 - 25 ) ] x 100 % = 33.33 % answer : d )" | a = 100 - 25
b = 25 / a
c = b * 100
|
a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 % | c | subtract(const_100, divide(multiply(add(const_100, 12), subtract(const_100, 24)), const_100)) | the tax on a commodity is diminished by 24 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ? | "100 * 100 = 10000 76 * 112 = 8512 10000 - - - - - - - 1488 100 - - - - - - - ? = 15 % answer : c" | a = 100 + 12
b = 100 - 24
c = a * b
d = c / 100
e = 100 - d
|
a ) 6 â ½ days , b ) 1 â ½ days , c ) 8 â ½ days , d ) 5 â ½ days , e ) 2 â ½ days | b | multiply(5, subtract(2, add(inverse(5), inverse(add(6, divide(2, 3)))))) | a and b can do a piece of work in 6 2 / 3 days and 5 days respectively . they work together for 2 days and then a leaves . in how many days after that b will complete the work alone . | "explanation : 3 / 20 * 2 + ( 2 + x ) / 5 = 1 x = 1 â ½ days answer : b" | a = 1/(5)
b = 2 / 3
c = 6 + b
d = 1/(c)
e = a + d
f = 2 - e
g = 5 * f
|
a ) 1.5 kmph . , b ) 0.91 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 0.98 kmph . | e | multiply(const_3_6, divide(13, 48)) | convert the 13 / 48 m / s into kilometers per hour ? | "13 / 48 m / s = 13 / 48 * 18 / 5 = 49 / 50 = 0.98 kmph . answer : e" | a = 13 / 48
b = const_3_6 * a
|
a ) 18 cm , b ) 16 cm , c ) 40 cm , d ) 20 cm , e ) 50 cm | c | divide(const_100, const_3) | the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ? | "let bresdth x cm length = 2 x cm new l = ( 2 x - 5 ) cm new breadth = ( x + 5 ) new area = ( 2 x - 5 ) sq cm = ( 2 x - 5 ) ( x + 5 ) = 2 x 2 + 75 x = 20 cm l = 2 x - 2 = 2 * 20 = 40 cm answer c" | a = 100 / 3
|
a ) 3 / 5 , b ) 7 / 15 , c ) 11 / 15 , d ) 19 / 30 , e ) 23 / 30 | d | subtract(1, add(divide(1, 6), divide(1, 5))) | there is a total of 90 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 6 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ? | "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 30 / 30 - 5 / 30 - 6 / 30 = 19 / 30 the answer is d ." | a = 1 / 6
b = 1 / 5
c = a + b
d = 1 - c
|
a ) 67 , b ) 69 , c ) 77 , d ) 79 , e ) 81 | c | multiply(divide(divide(multiply(21, add(21, const_1)), const_2), 21), 7) | what is the average of first 21 multiples of 7 ? | "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 7 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 77 c" | a = 21 + 1
b = 21 * a
c = b / 2
d = c / 21
e = d * 7
|
a ) 3 , b ) 6 , c ) 7.2 , d ) 5 , e ) 9 | d | multiply(divide(20, const_100), 20) | uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 14 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ? | "answer is d . x / x + 36 = 1 / 5 x = 9 14 - 9 = 5" | a = 20 / 100
b = a * 20
|
a ) 47 , b ) 55 , c ) 28 , d ) 66 , e ) 11 | b | multiply(divide(25, subtract(6, const_1)), subtract(12, const_1)) | at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 25 seconds . how long does it tick at 12 ′ o clock | "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 25 / 5 = 5 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 5 = 55 secs . answer : b" | a = 6 - 1
b = 25 / a
c = 12 - 1
d = b * c
|
a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95 | d | add(multiply(const_2, const_3), subtract(const_100, const_10)) | a number is said to be prime saturated if the product of all the different positive prime factors of q is less than the square root of q . what is the greatest two digit prime saturated integer ? | "q 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ." | a = 2 * 3
b = 100 - 10
c = a + b
|
a ) 7 km , b ) 6 km , c ) 3 1 / 8 km , d ) 9 km , e ) 5 km | c | add(multiply(add(2, divide(const_1, const_2)), subtract(add(5, divide(const_3, 4)), add(4, divide(const_1, const_2)))), const_2) | two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 2 ½ hours if they are walking in the same direction ? | "rs = 5 ¾ - 4 ½ = 1 ¼ t = 2 ½ h . d = 5 / 4 * 5 / 2 = 25 / 8 = 3 1 / 8 km answer : c" | a = 1 / 2
b = 2 + a
c = 3 / 4
d = 5 + c
e = 1 / 2
f = 4 + e
g = d - f
h = b * g
i = h + 2
|
a ) 3000 , b ) 1500 , c ) 1800 , d ) 9000 , e ) 2500 | d | multiply(multiply(const_3, const_60), const_60) | if an object travels at 85 feet per second , how many feet does it travel in 30 minutes ? | "if an object travels at 85 feet per second it covers 85 x 60 feet in one minute , and 5 x 60 x 30 feet in 30 minutes . answer = 9000 answer : d" | a = 3 * const_60
b = a * const_60
|
a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km | a | multiply(10, divide(20, subtract(14, 10))) | if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is : | "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a" | a = 14 - 10
b = 20 / a
c = 10 * b
|
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | a | floor(sqrt(divide(53900, multiply(multiply(multiply(11, 7), 5), 2)))) | in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 53900 . how many times did he participate in the competition ? | "53900 = 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 7 times . the answer is a ." | a = 11 * 7
b = a * 5
c = b * 2
d = 53900 / c
e = math.sqrt(d)
f = math.floor(e)
|
a ) 31 , b ) 25 , c ) 35 , d ) 45 , e ) 75 | a | multiply(divide(subtract(multiply(divide(40, 100), 300), multiply(divide(15, 100), multiply(300, divide(60, 100)))), 300), 100) | 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 15 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ? | "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 15 % = 27 responded as satisfied , so remaining satisfied are 120 - 27 = 93 so 93 is what percentage of 300 - 31 % so the answer should be a" | a = 40 / 100
b = a * 300
c = 15 / 100
d = 60 / 100
e = 300 * d
f = c * e
g = b - f
h = g / 300
i = h * 100
|
a ) 58 kgs , b ) 58.85 kgs , c ) 58.7 kgs , d ) 59 kgs , e ) 59.85 kgs | c | divide(add(multiply(58.4, 20), subtract(62, 56)), 20) | the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 62 kg . what is the correct weight ? | "actual total weight is ( 20 x 58.4 - 56 + 62 ) = 1174 kgs actual average weight is 1174 / 20 = 58.7 kgs c" | a = 58 * 4
b = 62 - 56
c = a + b
d = c / 20
|
a ) 36 , b ) 26 , c ) 97 , d ) 26 , e ) 19 | a | divide(multiply(18, 34), 17) | 34 men can complete a piece of work in 18 days . in how many days will 17 men complete the same work ? | "explanation : let the required number of days be a . then , less men , more days ( indirect proportion ) 17 : 34 : : 18 : a 17 x a = 34 x 18 a = ( 34 x 18 ) / 17 a = 36 answer : a" | a = 18 * 34
b = a / 17
|
a ) 56 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these | b | add(multiply(8, 2.5), 60) | the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ? | "b 80 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg ." | a = 8 * 2
b = a + 60
|
a ) 13 √ 4 , b ) 13 √ 2 , c ) 13.4 √ 2 , d ) 12 √ 4 , e ) 13 √ 9 | c | sqrt(multiply(add(power(divide(48, const_4), const_2), power(divide(24, const_4), const_2)), const_2)) | the perimeter of one square is 48 cm and that of another is 24 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ? | "4 a = 48 4 a = 24 a = 12 a = 6 a 2 = 144 a 2 = 36 combined area = a 2 = 180 = > a = 13.4 d = 13.4 √ 2 answer : c" | a = 48 / 4
b = a ** 2
c = 24 / 4
d = c ** 2
e = b + d
f = e * 2
g = math.sqrt(f)
|
a ) 30000 , b ) 50000 , c ) 45000 , d ) 20000 , e ) 60000 | c | multiply(divide(30000, 2), 3) | p and q invested in a business . the profit earned was divided in the ratio 2 : 3 . if p invested rs 30000 , the amount invested by q is | "let the amount invested by q = q 30000 : q = 2 : 3 ⇒ 30000 × 3 = 2 q ⇒ q = ( 30000 × 3 ) / 2 = 45000 answer is c ." | a = 30000 / 2
b = a * 3
|
a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160 | b | divide(30, subtract(add(const_1, divide(12.5, const_100)), subtract(const_1, divide(25, const_100)))) | the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number q ? | ( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = q answer : b | a = 12 / 5
b = 1 + a
c = 25 / 100
d = 1 - c
e = b - d
f = 30 / e
|
a ) 23 years , b ) 28 years , c ) 21 years , d ) 20 years , e ) 19 years | b | divide(subtract(30, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | a man is 30 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ? | "let present age of the son = x years then , present age the man = ( x + 30 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 30 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 28 answer : b" | a = 2 * 2
b = a - 2
c = 30 - b
d = 2 - 1
e = c / d
|
a ) 1 / 1008 , b ) 1 / 6400 , c ) 1 / 6550 , d ) 1 / 6660 , e ) 1 / 4096 | e | divide(multiply(add(add(const_100, const_60), const_1), 4), const_100) | what is the value of ( 4 ) ^ - 6 ? | "4 ^ - 6 = 1 / ( 4 ) ^ 6 = 1 / 4096 answer : e" | a = 100 + const_60
b = a + 1
c = b * 4
d = c / 100
|
a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 3 | e | divide(1080, multiply(divide(60, const_10), 60)) | machine x takes 60 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce | machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 60 so , x = 60 . hence 6 x = 6 * 60 = 360 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 360 = 3 hence option ( e ) . | a = 60 / 10
b = a * 60
c = 1080 / b
|
a ) 22 , b ) 35 , c ) 25 , d ) 99 , e ) 21 | b | divide(subtract(multiply(90, 5), multiply(5, 20)), subtract(90, 80)) | the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam . | "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 10 x = > x = 35 . answer : b" | a = 90 * 5
b = 5 * 20
c = a - b
d = 90 - 80
e = c / d
|
a ) 130 , b ) 272 , c ) 278 , d ) 277 , e ) 112 | a | multiply(divide(multiply(52, const_1000), const_3600), 9) | a train running at the speed of 52 km / hr crosses a pole in 9 seconds . find the length of the train ? | "speed = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec length of train ( distance ) = speed * time ( 130 / 9 ) * 9 = 130 meter answer : a" | a = 52 * 1000
b = a / 3600
c = b * 9
|
a ) 150 , b ) 450 , c ) 500 , d ) 650 , e ) 700 | a | divide(add(37, divide(1, 2)), divide(1, 4)) | how many 1 / 4 s are there in 37 1 / 2 ? | "required number = ( 75 / 2 ) / ( 1 / 4 ) = ( 75 / 2 x 4 / 1 ) = 150 . answer : a" | a = 1 / 2
b = 37 + a
c = 1 / 4
d = b / c
|
a ) 22 : 1 , b ) 22 : 3 , c ) 7 : 1 , d ) 5 : 3 , e ) 8 : 1 | a | divide(add(power(2, const_2.0), 2), add(add(2, 9), 2)) | if x : y = 2 : 9 , find the value of ( 2 x + 2 y ) : ( 5 x – y ) | "explanation : given : x / y = 2 / 9 ( 2 x + 2 y ) : ( 5 x – y ) = ( 2 * 2 + 2 * 9 ) : ( 5 * 2 – 9 ) = 22 : 1 answer : a" | a = 2 ** 2
b = a + 2
c = 2 + 9
d = c + 2
e = b / d
|
a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3 | c | multiply(subtract(1, divide(1, 8)), subtract(1, divide(subtract(1, divide(const_2.0, 8)), 1))) | for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 8 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ? | "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 8 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 8 = 7 / 8 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 7 / 8 = 4 / 9 - - - > p ( of burning out in a six mnth period ) = 1 - 4 / 9 = 4 / 7 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 7 / 8 * 4 / 7 = 1 / 2 ans c" | a = 1 / 8
b = 1 - a
c = 2 / 0
d = 1 - c
e = d / 1
f = 1 - e
g = b * f
|
a ) 40 sec , b ) 29 sec , c ) 26 sec , d ) 20 sec , e ) 34 sec | d | divide(360, multiply(subtract(90, 140), const_0_2778)) | a train 360 m long is running at a speed of 90 km / hr . in what time will it pass a bridge 140 m long ? | "speed = 90 * 5 / 18 = 25 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 25 = 20 sec answer : d" | a = 90 - 140
b = a * const_0_2778
c = 360 / b
|
a ) 187 , b ) 169 , c ) 152 , d ) 178 , e ) 175 | c | subtract(subtract(200, divide(multiply(200, 20), const_100)), divide(multiply(subtract(200, divide(multiply(200, 20), const_100)), 5), const_100)) | the sale price sarees listed for rs . 200 after successive discount is 20 % and 5 % is ? | "200 * ( 80 / 100 ) * ( 95 / 100 ) = 152 answer : c" | a = 200 * 20
b = a / 100
c = 200 - b
d = 200 * 20
e = d / 100
f = 200 - e
g = f * 5
h = g / 100
i = c - h
|
a ) 40 , b ) 80 , c ) 120 , d ) 160 , e ) 180 | d | multiply(divide(subtract(15, 5), divide(divide(15, const_2), const_2)), const_60) | bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy ’ s average speed . how many minutes does ben spend on his round trip ? | bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy ’ s average speed . how many minutes does ben spend on his round trip ? average speed = total distance / total time we know the total distance is 5 + 5 ( going from a to b then from b to a ) time = distance / speed time = 5 / 15 time = 1 / 3 hour average speed = ( 10 ) / ( 1 hr + 1 / 3 hr ) average speed ( bexi ) = 10 / 1.33 therefore , if ben ' s average speed is 1 / 2 of bexi ' s then his speed = 10 / 2.66 . this means it took him 2.66 hours to cover the same 10 miles bexi did . 2.66 hours = roughly 160 minutes . answer : d ) . 160 | a = 15 - 5
b = 15 / 2
c = b / 2
d = a / c
e = d * const_60
|
a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 260 | b | divide(add(1365, 15), subtract(6, const_1)) | the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ? | "x - y = 1365 divide larger number by the smaller , we get 6 as quotient and the 15 as remainder x / y = 6 quotient and 15 reminder convert this as x = 6 y + 15 apply this x in above eqn therefore , 6 y + 15 - y = 1365 5 y + 15 = 1365 y + 3 = 273 y = 270 answer : b" | a = 1365 + 15
b = 6 - 1
c = a / b
|
a ) 11 , b ) 92 , c ) 96 , d ) 174 , e ) 115 | c | multiply(multiply(divide(16, 4), 3), 8) | running at the same constant rate , 4 identical machines can produce a total of 16 bottles per minute . at this rate , how many bottles could 8 such machines produce in 3 minutes ? | "let ' s take the approach that uses the answer choices to eliminate wasted time . 16 / 4 = 4 . 8 machines = 32 per minute . 3 minutes worth = 96 bottles . looking at the answers it is clear . . . we can only choose ( c ) the correct answer is c ." | a = 16 / 4
b = a * 3
c = b * 8
|
a ) 10 years , b ) 4 years , c ) 6 years , d ) 15 years , e ) 16 years | b | divide(multiply(subtract(12, const_2), const_2), add(const_4, const_1)) | a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 12 , the how old is b ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 12 5 x = 10 x = 2 . hence , b ' s age = 2 x = 4 years . b )" | a = 12 - 2
b = a * 2
c = 4 + 1
d = b / c
|
a ) 792 , b ) 684 , c ) 492 , d ) 372 , e ) 340 | a | add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(300, const_100), const_1), const_3)) | how many digits are required to number a book containing 300 pages ? | "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 300 - ( 90 + 9 ) = 201 pages will require 201 * 3 = 603 digits . the total number of digits is 9 + 180 + 603 = 792 . the answer is a ." | a = 10 - 1
b = 10 - 1
c = b * 10
d = c * 2
e = a + d
f = 300 - 100
g = f + 1
h = g * 3
i = e + h
|
a ) 2 , b ) 2.5 , c ) 3 , d ) 3.25 , e ) 3.5 | c | divide(divide(multiply(add(4, 2), 4), 2), 4) | natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 4 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ? | "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 4 km / hour x / 3 = 4 x = 12 km the average speed while climbing = distance / time = 12 / 4 = 3 km / h the answer is c ." | a = 4 + 2
b = a * 4
c = b / 2
d = c / 4
|
a ) 25 , b ) 66 , c ) 77 , d ) 60 , e ) 44 | d | divide(multiply(36, 5), const_4) | there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 36 , then find the smaller number ? | "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 36 3 x = 36 = > x = 12 = > smaller number = 5 x = 60 . answer : d" | a = 36 * 5
b = a / 4
|
a ) 0 , b ) 1 , c ) - 1 , d ) - 2 , e ) 3 | a | add(1, subtract(1, 1)) | if x = 1 - q and y = 2 q + 1 , then for what value of q , x is equal to y ? | explanation : x = y < = > 1 - q = 2 q + 1 < = > 3 q = 0 < = > q = 0 . answer : a | a = 1 - 1
b = 1 + a
|
a ) a ) 426 , b ) b ) 306 , c ) c ) 207 , d ) d ) 204 , e ) e ) 297 | b | add(add(const_100, 2), multiply(divide(multiply(const_2, const_3), add(add(add(multiply(const_2, const_3), 3), add(multiply(const_2, const_3), 2)), multiply(const_2, const_3))), 782)) | if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 2 / 3 : 3 / 4 , then the third part is ? | given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 8 : 9 1 st part = 782 * 9 / 23 = rs . 306 . answer : b | a = 100 + 2
b = 2 * 3
c = 2 * 3
d = c + 3
e = 2 * 3
f = e + 2
g = d + f
h = 2 * 3
i = g + h
j = b / i
k = j * 782
l = a + k
|
a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,124 , e ) 2,628 | e | multiply(divide(250, 22.95), 250) | at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.65 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ? | "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ amount remaining = 2.2 - 1.65 = 0.55 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 250 $ = 250 * 10 + 20 * 6 + 8 * 1 = 2628 answer e" | a = 250 / 22
b = a * 250
|
a ) 4.7 kmph , b ) 5.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph | b | add(divide(1, divide(add(const_60, 48), const_60)), 5) | a start walking from a place at a uniform speed of 5 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b . | "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 5 + 5 / 9 = 5.55 answer b" | a = const_60 + 48
b = a / const_60
c = 1 / b
d = c + 5
|
a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22 | e | divide(multiply(choose(7, 2), choose(3, 1)), choose(add(add(7, 4), 3), 3)) | a jar contains only red , yellow , and orange marbles . if there are 3 red , 7 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? | "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 5 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 5 ) , which indeed is 5 / 22 . e" | a = math.comb(7, 2)
b = math.comb(3, 1)
c = a * b
d = 7 + 4
e = d + 3
f = math.comb(e, 3)
g = c / f
|
a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 7 | e | divide(49, add(add(2, 2), 1)) | if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 49 ) which of these integers could be the value of z ? | "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 49 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 50 incorrect c . 2 / 2 = 2 / 3 + 2 / 51 incorrect d . 2 / 3 = 2 / 4 + 2 / 54 incorrect e . 2 / 4 = 2 / 5 + 2 / 56 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case" | a = 2 + 2
b = a + 1
c = 49 / b
|
a ) 14700 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000 | a | multiply(add(divide(subtract(multiply(5000, const_10), add(add(4000, 5000), 5000)), const_3), add(4000, 5000)), divide(multiply(multiply(const_3, const_12), const_1000), multiply(5000, const_10))) | a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 35,000 , what will be the amount a receives ? | "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 35000 × 21 / 50 = 700 × 21 = 14700 answer is a ." | a = 5000 * 10
b = 4000 + 5000
c = b + 5000
d = a - c
e = d / 3
f = 4000 + 5000
g = e + f
h = 3 * 12
i = h * 1000
j = 5000 * 10
k = i / j
l = g * k
|
a ) 158 , b ) 161 , c ) 164 , d ) 167 , e ) 170 | d | add(divide(multiply(75, 9), 5), 32) | if t = 5 / 9 * ( k - 32 ) , and if t = 75 , then what is the value of k ? | k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 75 ) / 5 + 32 = 167 the answer is d . | a = 75 * 9
b = a / 5
c = b + 32
|
a ) 99 , b ) 9.9 , c ) 990 , d ) 0.99 , e ) 0.099 | c | divide(multiply(0.0077, 4.5), multiply(multiply(0.05, 0.1), 0.007)) | ( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = | "( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 450 / 5 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : c" | a = 0 * 77
b = 0 * 5
c = b * 0
d = a / c
|
a ) 22 , b ) 33 , c ) 17 , d ) 12 , e ) 88 | b | divide(2904, 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 2904 cm is ? | "2 * 22 / 7 * 14 * x = 2904 = > x = 33 answer : b" | a = 3 * 100
b = 1 * 10
c = a + b
d = c + 4
e = d / 100
f = 2 * e
g = f * 14
h = 2904 / g
|
a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 21.7 | b | subtract(25, add(multiply(divide(30, const_100), divide(const_100, 6)), divide(30, const_100))) | jerry went to a shop and bought things worth rs . 25 , out of which 30 $ went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ? | "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 $ is given as tax = > total tax incurred = 30 $ = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 b )" | a = 30 / 100
b = 100 / 6
c = a * b
d = 30 / 100
e = c + d
f = 25 - e
|
a ) 40 years , b ) 41 years , c ) 47 years , d ) 43 years , e ) 44 years | c | subtract(multiply(add(25, 2), add(19, 2)), multiply(25, 19)) | the average age of a class of 25 students is 19 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ? | "if age of the teacher was 19 , average would not have changed . since average increased by 2 , age of the teacher = 25 + 22 × 1 = 47 answer : c" | a = 25 + 2
b = 19 + 2
c = a * b
d = 25 * 19
e = c - d
|
a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 30 | e | add(add(6, 10), 6) | two spherical balls lie on the ground touching . if one of the balls has a radius of 6 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ? | "a straight line will join the two centers and the point of contact , thus making similar triangles . 4 / 6 = ( r - 10 ) / r 4 r = 6 r - 60 r = 30 the answer is e ." | a = 6 + 10
b = a + 6
|
a ) 54 , b ) 59 , c ) 60 , d ) 71 , e ) 92 | c | add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 40)), 40) | of 70 players on a football team , 40 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 = 40 rest = 70 - 40 = 30 left handed = 30 / 3 = 10 right handed = 20 if all throwe 0 r are right handed then total right handed is 40 + 20 = 60 so c . 60 is the right answer" | a = 1 / 3
b = 1 - a
c = 70 - 40
d = b * c
e = d + 40
|
a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,700 , e ) 48,500 | d | multiply(42500, const_1) | of the 13 employees in a certain department , 1 has an annual salary of 38000 , 2 have an annual salary of 45700 each , 2 have an annual salary of 42500 each , 3 have an annual salary of 40000 each and 5 have an annual salary of 48500 each . what is the median annual salary for the 13 employees ? | median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.7 so , answer is d . | a = 42500 * 1
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a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none | c | subtract(multiply(735, 4), multiply(650, subtract(4, const_1))) | average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ? | "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 650 x 3 rs . = 990 rs . correct option : c" | a = 735 * 4
b = 4 - 1
c = 650 * b
d = a - c
|
a ) 210 kms , b ) 30 kms , c ) 20 kms , d ) 40 kms , e ) none of these | a | multiply(divide(multiply(12, 5), subtract(7, 5)), 7) | a car travels a certain distance taking 7 hrs in forward journey , during the return journey increased speed 12 km / hr takes the times 5 hrs . what is the distance traveled | if x is the distance , then difference in speeds = x / 5 - x / 7 = 12 2 x / 35 = 12 x = 12 * 35 / 2 = 210 kms . answer : a | a = 12 * 5
b = 7 - 5
c = a / b
d = c * 7
|
a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4 | b | subtract(const_1, divide(20, divide(multiply(const_60, const_1), 1))) | a searchlight on top of the watch - tower makes 1 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 20 seconds ? | "1 revolutions per minute = 1 revolution every 60 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 60 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 20 seconds ) = 1 - p ( man in dark for max of 20 seconds ) = 1 - 20 / 60 = 1 - 1 / 3 = 2 / 3 or the other way would be : p ( man in dark for at least 20 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 60 seconds because that is the max . in this approach it would be 20 / 60 seconds = 1 / 3 . answer is b" | a = const_60 * 1
b = a / 1
c = 20 / b
d = 1 - c
|
a ) 20 % , b ) 42 % , c ) 44 % , d ) 85 % , e ) 84 % | d | multiply(subtract(const_1, divide(10, subtract(const_100, 30))), const_100) | exactly 10 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ? | "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 10 % of all reporters reporters covering politics / all reporters = 10 / 70 = 1 / 7 reporters not covering politics / all reporters = 6 / 7 = 85 % = d" | a = 100 - 30
b = 10 / a
c = 1 - b
d = c * 100
|
a ) 9 , b ) 24.8 , c ) 2 , d ) 3 , e ) 5 | e | multiply(divide(7, subtract(12, 5)), 5) | sachin is younger than rahul by 7 years . if the ratio of their ages is 5 : 12 , find the age of sachin | explanation : if rahul age is x , then sachin age is x - 7 , so , 12 x - 84 = 5 x 7 x = 84 x = 12 so sachin age is 12 - 7 = 5 answer : e ) 5 | a = 12 - 5
b = 7 / a
c = b * 5
|
a ) 72 , b ) 80 , c ) 88 , d ) 96 , e ) 104 | b | add(multiply(6, 5), 48) | in a 6 - sided polygon xqrstv ∠ x measures 48 ° less than the average ( arithmetic mean ) of the remaining 5 angles . what does ∠ x equal to , in degrees ? | the sum of interior angle in a polygon is ( n - 2 ) * 180 so for a six sided figure , ( 6 - 2 ) * 180 = 720 let the a . m of the other 5 angles be ' m ' - - > m * 5 + ∠ x = 720 , we know ∠ x = m - 48 - - > m * 5 + m - 48 = 720 , solving we get m = 128 hence ∠ x = 128 - 48 = 80 ans b . | a = 6 * 5
b = a + 48
|
a ) 200 m , b ) 180 m , c ) 272 m , d ) 210 m , e ) 267 m | a | subtract(multiply(220, divide(15, divide(15, const_3))), multiply(150, divide(18, divide(15, const_3)))) | a train crosses a platform of 150 m in 15 sec , same train crosses another platform of length 220 m in 18 sec . then find the length of the train ? | "length of the train be ‘ x ’ ( x + 150 ) / 15 = ( x + 220 ) / 18 5 x + 1100 = 6 x + 900 x = 200 m answer : a" | a = 15 / 3
b = 15 / a
c = 220 * b
d = 15 / 3
e = 18 / d
f = 150 * e
g = c - f
|
a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 6 | e | divide(30, 4) | if ( - 4 ) ^ ( 6 x ) = 4 ^ ( 30 + x ) and x is an integer , what is the value of x ? | "since x is an integer , ( - 4 ) ^ ( 6 x ) is always positive . so , 4 ^ 6 x = 4 ^ ( 30 + x ) 6 x = 30 + x 5 x = 30 x = 6 answer : e" | a = 30 / 4
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a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | b | inverse(subtract(inverse(5), inverse(10))) | working alone , a can complete a certain kind of job in 10 hours . a and d , working together at their respective rates , can complete one of these jobs in 5 hours . in how many hours can d , working alone , complete one of these jobs ? | "let total time taken by d to complete the job = d total time taken by a to complete the job = 10 work done by a in an hour 1 / a = 1 / 10 working together a and d can complete the job in 5 hours 1 / a + 1 / d = 1 / 5 = > 1 / d = 1 / 5 - 1 / a = 1 / 5 - 1 / 10 = 1 / 10 = > d = 10 hours answer b" | a = 1/(5)
b = 1/(10)
c = a - b
d = 1/(c)
|
a ) 41.6 sec , b ) 11 sec , c ) 88 sec , d ) 19 sec , e ) 10 sec | a | divide(360, multiply(subtract(45, 160), const_0_2778)) | a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 160 m long ? | "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 160 = 520 m required time = 520 * 2 / 25 = 41.6 sec answer : a" | a = 45 - 160
b = a * const_0_2778
c = 360 / b
|
a ) 5 , b ) 20 , c ) 30 , d ) 25 , e ) 15 | e | divide(add(10, 20), const_2) | man can row upstream at 10 kmph and downstream at 20 kmph , and then find the speed of the man in still water ? | us = 10 ds = 20 m = ( 10 + 20 ) / 2 = 15 answer : e | a = 10 + 20
b = a / 2
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a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 2.27 % | e | divide(const_100, 44) | at what rate percent of simple interest will a sum of money double itself in 44 years ? | "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 44 ) = 100 / 44 = 2.27 % answer : e" | a = 100 / 44
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a ) 2 / 3 , b ) 0.17 , c ) 3 / 2 , d ) 0.71 , e ) none of them | b | multiply(0.17, const_1) | which is greatest in 16 ( 2 / 3 ) % , 2 / 5 and 0.17 ? | 16 ( 2 / 3 ) % = [ ( 50 / 3 ) * ) 1 / 100 ) ] = 1 / 6 = 0.166 , 2 / 15 = 0.133 . clearly , 0.17 is the greatest . answer is b . | a = 0 * 17
|
a ) 351 , b ) 364 , c ) 416 , d ) 424 , e ) 450 | c | subtract(power(divide(add(41, const_1), 2), 2), power(divide(add(subtract(11, 2), const_1), 2), 2)) | the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 11 and 41 inclusive . | "we ' re dealing with a sequence of consecutive odd integers : 11 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 11 + 41 = 52 2 ) now look at the ' next smallest ' and the ' next biggest ' : 13 + 39 = 52 now we have proof that there is no middle term . we have 8 bunches of 52 . 8 ( 52 ) = 416 c" | a = 41 + 1
b = a / 2
c = b ** 2
d = 11 - 2
e = d + 1
f = e / 2
g = f ** 2
h = c - g
|
a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2 | e | add(const_2, const_3) | if 25 / 999 = 0.002 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ? | "0 . [ u ] 25 [ / u = 0.002002002002 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 2 . since 81 is multiple of 3 , the 81 st digit is 2 . answer e" | a = 2 + 3
|
a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3 | a | floor(divide(log(divide(620, 6.1)), log(10))) | if x is an integer and 6.1 × 10 ^ x is less than 620 what is the greatest possible value for x ? | if x = 2 6.1 × 10 ^ 2 = 610 < 620 so , x = 2 answer : a | a = 620 / 6
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | add(add(multiply(divide(2, 2), 2), divide(2, 2)), divide(2, 2)) | in the game of dubblefud , red balls , blue balls and green balls are each worth 2 , 4 and 5 points respectively . in a certain selection of balls , the product of the point values of the balls is 16000 . if the number of blue balls in this selection equals the number of green balls , how many red balls are in the selection ? | this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z ( given ) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of red balls = 4 hence d | a = 2 / 2
b = a * 2
c = 2 / 2
d = b + c
e = 2 / 2
f = d + e
|
a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64 | a | divide(choose(6, 4), inverse(multiply(power(divide(const_1, const_2), 4), power(divide(const_1, const_2), const_2)))) | the chance of rain on any given day in tel - aviv is 50 % . what is the probability q that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ? | "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days q = 15 / 64 ans a it is ." | a = math.comb(6, 4)
b = 1 / 2
c = b ** 4
d = 1 / 2
e = d ** 2
f = c * e
g = 1/(f)
h = a / g
|
a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1 | d | divide(subtract(multiply(4.5, const_2), 4.5), const_3) | a man can row 4.5 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ? | "speed of boat in still water ( b ) = 4.5 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.5 km / hr . answer : d" | a = 4 * 5
b = a - 4
c = b / 3
|
a ) 8 , b ) 11 , c ) 13 , d ) 15 , e ) 16 | b | divide(multiply(8261955, 11), 8261955) | what is the smallest no . which must be added to 8261955 so as to obtain a sum which is divisible by 11 ? | for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 8261955 , difference = ( 8 + 6 + 9 + 5 ) - ( 2 + 1 + 5 ) = 28 - 8 = 20 . the units digit is at odd place . so we add 2 to the number = > 8261955 + 2 = 8261957 now , ( 8 + 6 + 9 + 7 ) - ( 2 + 1 + 5 ) = 30 - 8 = 22 = > 22 is a multiple of 11 and hence 8261957 is also divisible by 11 b | a = 8261955 * 11
b = a / 8261955
|
a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 32 | e | multiply(3, power(subtract(40, multiply(divide(add(40, 20), add(3, 2)), 3)), 2)) | if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 2 y ^ 2 = ? | "3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 2 y ^ 2 = 2 * 16 = 32 answer is e" | a = 40 + 20
b = 3 + 2
c = a / b
d = c * 3
e = 40 - d
f = e ** 2
g = 3 * f
|
a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 6 / 20 , e ) 3 / 10 | d | divide(subtract(20, 14), 20) | a ’ s speed is 20 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ? | "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 14 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 6 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 6 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 14 meters ) to reach the finish line . so b should get a head start of 6 / 20 th of the race . answer ( d )" | a = 20 - 14
b = a / 20
|
a ) – 29 , b ) – 12 , c ) 12 , d ) 29 , e ) 168 | b | multiply(multiply(negate(2), subtract(7, 6)), subtract(7, subtract(7, 6))) | what is the product of all the possible values of x if x ^ 2 ( x + 2 ) + 7 x ( x + 2 ) + 6 ( x + 2 ) = 0 ? | x ^ 2 ( x + 2 ) + 7 x ( x + 2 ) + 6 ( x + 2 ) = 0 = > ( x + 2 ) ( x ^ 2 + 7 x + 6 ) = 0 = > ( x + 2 ) ( x + 1 ) ( x + 6 ) = 0 = > x = - 1 or - 2 or - 6 product = - 12 answer option - 12 answer : b | a = negate * (
b = 7 - 6
c = a * b
|
a ) 2 / 5 , b ) 3 / 5 , c ) 7 / 10 , d ) 7 / 20 , e ) 9 / 20 | e | add(divide(1, const_2.0), multiply(divide(1, 5), divide(1, 5))) | jar x is 1 / 5 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ? | "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 5 + p / 4 = 9 / 20 the answer is e ." | a = 1 / 2
b = 1 / 5
c = 1 / 5
d = b * c
e = a + d
|
a ) 40 , b ) 30 , c ) 35 , d ) 25 , e ) 45 | a | add(30, divide(subtract(760, multiply(16, 30)), multiply(16, divide(add(75, const_100), const_100)))) | a babysitter is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 30 hours per week . for any overtime hours worked in excess of 30 hours per week , the babysitter is paid a rate that is 75 % higher than his regular rate . if last week the babysitter earned $ 760 , how many total hours did she work that week ? | for 30 hrs = 30 * 16 = 480 excess = 760 - 480 = 280 for extra hours = . 75 ( 16 ) = 12 in addition to $ 16 . thus , 12 + 16 = 28 number of extra hrs = 280 / 28 = 10 total hrs = 30 + 10 = 40 answer a 40 | a = 16 * 30
b = 760 - a
c = 75 + 100
d = c / 100
e = 16 * d
f = b / e
g = 30 + f
|
a ) 25 kmph , b ) 40 kmph , c ) 35 kmph , d ) 46 kmph , e ) 50 kmph | b | divide(subtract(multiply(80, const_3), divide(multiply(multiply(80, const_3), const_2), const_3)), subtract(const_3, const_1)) | by travelling at 80 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ? | "let the time taken to reach the destination be 3 x hours . total distance = 80 * 3 x = 240 x km he covered 2 / 3 * 240 x = 160 x km in 1 / 3 * 3 x = x hours so , the remaining 80 x km , he has to cover in 2 x hours . required speed = 80 x / 2 x = 40 kmph . answer : b" | a = 80 * 3
b = 80 * 3
c = b * 2
d = c / 3
e = a - d
f = 3 - 1
g = e / f
|
a ) $ 240 , b ) $ 250 , c ) $ 260 , d ) $ 270 , e ) $ 280 | d | divide(594, add(divide(120, const_100), const_1)) | two employees m and n are paid a total of $ 594 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ? | 1.2 n + n = 594 2.2 n = 594 n = 270 the answer is d . | a = 120 / 100
b = a + 1
c = 594 / b
|
a ) 10 min , b ) 7 min , c ) 8.2 min , d ) 9.6 min , e ) 40 min | d | multiply(const_60, divide(subtract(50, 42), 50)) | excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 42 kmph . for how many minutes does the bus stop per hour ? | "d 9.6 min due to stoppages , it covers 8 km less . time taken to cover 9 km = ( 8 / 50 x 60 ) min = 9.6 min" | a = 50 - 42
b = a / 50
c = const_60 * b
|
a ) 64 , b ) 82 , c ) 128 , d ) 729 , e ) 1522 | d | power(2, multiply(const_2.0, const_3.0)) | tough and tricky questions : functions . let a be a positive integer . let n # a equal n ^ ( 2 a ) if a is odd and n ^ ( 3 a ) if a is even . then ( 2 # 3 ) + ( 2 # 3 ) – ( 3 # 3 ) is equal to | "answer : 3 ^ 6 + 3 ^ 6 - 3 ^ 6 = 3 ^ 6 = 729 ans d" | a = 2 * 0
b = 2 ** a
|
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