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 ) 450 min , b ) 528 min , c ) 610 min , d ) 714 min , e ) 359 min | b | add(4.5, 3.75) | the jogging track in a sports complex is 726 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ? | "clearly , the two will meet when they are 726 m apart to be 4.5 + 3.75 = 8.25 km apart , they take 1 hour to be 726 m apart , they take 100 / 825 * 726 / 1000 = 242 / 2750 * 60 = 528 min . answer is b" | a = 4 + 5
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a ) 6 : 8 , b ) 6 : 1 , c ) 6 : 5 , d ) 6 : 7 , e ) 6 : 3 | d | divide(multiply(4, 3), multiply(7, 2)) | the marks obtained by vijay and amith are in the ratio 4 : 7 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ? | "4 : 7 3 : 2 - - - - - - - 12 : 21 : 14 12 : 14 6 : 7 answer : d" | a = 4 * 3
b = 7 * 2
c = a / b
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a ) 1000 , b ) 450 , c ) 720 , d ) 180 , e ) 400 | a | multiply(multiply(subtract(10, const_1), 10), divide(10, const_2)) | there are , in a certain league , 10 teams , and each team face another team for a total of 10 times . how many games are played in the season ? | "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 450 option a ." | a = 10 - 1
b = a * 10
c = 10 / 2
d = b * c
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a ) 35 , b ) 37 , c ) 38 , d ) 41 , e ) 42 | c | add(multiply(const_2, 10), add(8, 10)) | in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 8 years older than b , the present age of b is | "explanation : let b ' s age = x years . then , as age = ( x + 8 ) years . ( x + 8 + 10 ) = 2 ( x — 10 ) hence x = 38 . present age of b = 38 years answer : option c" | a = 2 * 10
b = 8 + 10
c = a + b
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a ) 38 , b ) 40 , c ) 42 , d ) 45 , e ) 50 | d | divide(multiply(60, const_2), add(divide(60, 36), const_1)) | an assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this ... | the time to produce the first 60 cogs is 60 / 36 = 5 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 8 / 3 ) hours = 45 cogs per hour . the answer is d . | a = 60 * 2
b = 60 / 36
c = b + 1
d = a / c
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a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3 | a | divide(subtract(add(multiply(7, 7), 5), 2), 13) | if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 2 is subtracted and divided by 13 ? | "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 2 ) / 13 = ( 54 - 2 ) / 13 = 4 answer : option a" | a = 7 * 7
b = a + 5
c = b - 2
d = c / 13
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a ) 4 , b ) 5 , c ) 8 , d ) 10.72 , e ) 15 | d | sqrt(subtract(power(14, const_2), power(subtract(sqrt(subtract(power(14, const_2), power(5, const_2))), 4), const_2))) | a ladder 14 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 5 feet from the base of the wall . if the top of the ladder slips down 4 feet , how many feet will the bottom of the ladder slip ? | "14 ^ 2 - 5 ^ 2 = 171 it means that the height is equal to 13.07 ~ = 13 . since the top of the ladder slips down 4 feet , then the height of the wall = 13 - 4 = 9 the bottom = sqrt ( 14 ^ 2 - 9 ^ 2 ) = sqrt ( 196 - 81 ) = 10.72 ans is d" | a = 14 ** 2
b = 14 ** 2
c = 5 ** 2
d = b - c
e = math.sqrt(d)
f = e - 4
g = f ** 2
h = a - g
i = math.sqrt(h)
|
a ) rs . 9009 , b ) rs . 9008 , c ) rs . 9002 , d ) rs . 9202 , e ) rs . 9001 | a | multiply(multiply(multiply(add(multiply(multiply(multiply(2, const_3), const_100), const_100), multiply(multiply(multiply(const_3, const_3), const_100), multiply(add(5, 2), 2))), divide(add(multiply(15, 5), 2), 5)), divide(multiply(5, 5), multiply(2, multiply(2, 5)))), divide(const_1, const_100)) | find the simple interest on rs . 78000 at 15 ( 2 / 5 ) % per annum for 9 months . | "explanation : p = rs . 78000 , r = 77 / 5 % p . a and t = 9 / 12 years = ¾ years therefore , s . i = ( p * r * t ) / 100 = ( 78000 * 77 / 5 * ¾ * 1 / 100 ) = rs . 9009 answer : a" | a = 2 * 3
b = a * 100
c = b * 100
d = 3 * 3
e = d * 100
f = 5 + 2
g = f * 2
h = e * g
i = c + h
j = 15 * 5
k = j + 2
l = k / 5
m = i * l
n = 5 * 5
o = 2 * 5
p = 2 * o
q = n / p
r = m * q
s = 1 / 100
t = r * s
|
a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 4 / 9 | e | subtract(add(divide(4, 9), divide(2, 3)), divide(6, 12)) | the instructions state that cheryl needs 4 / 9 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 6 / 12 square yards left that she did not use . what is the total amount of square yards o... | "total bought = 4 / 9 + 2 / 3 left part 6 / 12 - - - > 2 / 3 so used part 4 / 9 + 2 / 3 - 2 / 3 = 4 / 9 ans e" | a = 4 / 9
b = 2 / 3
c = a + b
d = 6 / 12
e = c - d
|
a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | c | divide(32, 51) | how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 32 / 51 ? | "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one... | a = 32 / 51
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a ) 360 , b ) 227 , c ) 268 , d ) 198 , e ) 176 | a | multiply(divide(870, add(add(multiply(12, 8), multiply(16, 9)), multiply(18, 6))), multiply(16, 9)) | a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ? | "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 870 = 360 answer : a" | a = 12 * 8
b = 16 * 9
c = a + b
d = 18 * 6
e = c + d
f = 870 / e
g = 16 * 9
h = f * g
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a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) none | a | sqrt(divide(multiply(multiply(const_pi, multiply(6, divide(6, const_2))), const_2), multiply(const_pi, const_4))) | the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each . the radius of the sphere is | "solution 4 î r 2 = 2 î 3 x 6 â ‡ ’ r 2 = ( 3 x 6 / 2 ) â ‡ ’ 9 â ‡ ’ r = 3 cm . answer a" | a = 6 / 2
b = 6 * a
c = math.pi * b
d = c * 2
e = math.pi * 4
f = d / e
g = math.sqrt(f)
|
a ) 19 , b ) 18 , c ) 16 , d ) 17 , e ) 14 | c | power(divide(96, divide(subtract(96, 24), sqrt(9))), const_2) | the speed of a railway engine is 96 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of co... | "the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is... | a = 96 - 24
b = math.sqrt(9)
c = a / b
d = 96 / c
e = d ** 2
|
a ) 800 , b ) 1400 , c ) 1000 , d ) 1100 , e ) 1200 | b | divide(multiply(subtract(870, 800), 4), divide(20, const_100)) | average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 870 . what was original rent of friend whose rent is increased ? | "0.2 x = 4 ( 870 - 800 ) 0.2 x = 280 x = 1400 answer b" | a = 870 - 800
b = a * 4
c = 20 / 100
d = b / c
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a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 5 / 3 , e ) 40 / 3 | e | divide(log(16), log(power(2, 0.3))) | if n = 2 ^ 0.3 and n ^ b = 16 , b must equal | "30 / 100 = 3 / 10 n = 2 ^ 3 / 10 n ^ b = 2 ^ 4 ( 2 ^ 3 / 10 ) ^ b = 2 ^ 4 b = 40 / 3 answer : e" | a = math.log(16)
b = 2 ** 0
c = math.log(b)
d = a / c
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a ) 25 , b ) 35 , c ) 23 , d ) 22 , e ) 33 | e | divide(subtract(multiply(95, 3), multiply(3, 40)), subtract(95, 90)) | the average mark of the students of a class in a particular exam is 90 . if 3 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam ? | "let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 3 ) students = 80 ( x - 3 ) 90 x - ( 3 * 40 ) = 95 ( x - 3 ) 165 = 5 x = > x = 33 answer : e" | a = 95 * 3
b = 3 * 40
c = a - b
d = 95 - 90
e = c / d
|
a ) 16.5 % , b ) 14 % , c ) 35 % , d ) 55 % , e ) 65 % | b | multiply(divide(subtract(3.5, 3), subtract(6.5, 3)), const_100) | a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 6.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs a... | the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.065 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 65 f - - > s = 6 f - - > f / s = 1 / 6 - - > f / ( s + f ) = 1 / (... | a = 3 - 5
b = 6 - 5
c = a / b
d = c * 100
|
a ) 8 , b ) 21 , c ) 24 , d ) 27 , e ) 30 | b | multiply(divide(const_1, add(add(add(divide(const_1, 7), multiply(3, divide(const_1, 7))), add(divide(const_1, 7), multiply(3, divide(const_1, 7)))), multiply(3, add(divide(const_1, 7), multiply(3, divide(const_1, 7)))))), const_60) | machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machin... | c = a + b d = 3 c = 3 ( a + b ) = 4 b then b = 3 a and c = 4 a the combined rate of the four machines is a + 3 a + 4 a + 12 a = 20 a machine a can complete the work in 420 minutes , so its rate is 1 / 420 of the work per minute . the combined rate is 20 / 420 = 1 / 21 so the work will be completed in 21 minutes . the a... | a = 1 / 7
b = 1 / 7
c = 3 * b
d = a + c
e = 1 / 7
f = 1 / 7
g = 3 * f
h = e + g
i = d + h
j = 1 / 7
k = 1 / 7
l = 3 * k
m = j + l
n = 3 * m
o = i + n
p = 1 / o
q = p * const_60
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a ) 10 , b ) 12 , c ) 18 , d ) 20 , e ) 15 | e | divide(divide(6000, 2), 200) | in a company the manager wants to give some gifts to all of the workers . in each block there are about 200 workers are there . the total amount for giving the gifts for all the workers is $ 6000 . the worth of the gift is 2 $ . how many blocks are there in the company ? | "each employee will get a gift worth of = $ 2 total employees = 6000 / 2 = 3000 total blocks = 3000 / 200 = 15 correct option is e" | a = 6000 / 2
b = a / 200
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a ) 500 , b ) 289 , c ) 350 , d ) 882 , e ) 281 | a | subtract(multiply(divide(300, 18), 48), 300) | a 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ? | "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 48 = 50 / 3 3 ( x + 300 ) = 2400 è x = 500 m . answer : a" | a = 300 / 18
b = a * 48
c = b - 300
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a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42 | c | multiply(divide(const_100, add(const_100, 12)), 45) | from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 12 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ? | "soln : - 12 x = 45 - - > 28 / 25 * x = 45 - - > x = 45 * 25 / 28 = 1125 / 28 = ~ 40 answer : c ." | a = 100 + 12
b = 100 / a
c = b * 45
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a ) 100 , b ) 150 , c ) 140 , d ) 200 , e ) 250 | d | divide(divide(multiply(add(100, 200), add(divide(subtract(200, 100), 100), const_1)), const_2), add(divide(subtract(200, 100), 100), const_1)) | what is the average ( arithmetic mean ) of the numbers 100 , 150 , 200 , 200 , 250 , and 300 ? | "{ 100 , 150 , 200 , 200 , 250 , 300 } = { 200 - 100,200 - 50 , 200 , 200,200 + 50,200 + 100 } - - > the average = 200 . answer : d ." | a = 100 + 200
b = 200 - 100
c = b / 100
d = c + 1
e = a * d
f = e / 2
g = 200 - 100
h = g / 100
i = h + 1
j = f / i
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a ) 1000 , b ) 1376 , c ) 1456 , d ) 1900 , e ) 1566 | b | add(multiply(14, 54), multiply(10, 62)) | andrew purchased 14 kg of grapes at the rate of 54 per kg and 10 kg of mangoes at the rate of 62 per kg . how much amount did he pay to the shopkeeper ? | "cost of 14 kg grapes = 54 × 14 = 756 . cost of 10 kg of mangoes = 62 x 10 = 620 . total cost he has to pay = 756 + 620 = 1376 b" | a = 14 * 54
b = 10 * 62
c = a + b
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a ) 100 m , b ) 75 m , c ) 120 m , d ) 50 m , e ) 70 m | b | multiply(multiply(subtract(50, 32), const_0_2778), 15) | two trains move in the same direction at speeds 50 kmph and 32 kmph respectively . a man in the slower train observes that 15 seconds elapse before the faster train completely passes by him . what is the length of faster train ? | since both trains move in same direction so : average speed = 50 - 32 = 18 kmph = 5 mps speeed = length of train / time length of train = 5 * 15 = 75 m answer : b | a = 50 - 32
b = a * const_0_2778
c = b * 15
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a ) 1 / 4 , b ) 1 / 5 , c ) 3 / 10 , d ) 1 / 11 , e ) none of above | c | divide(circle_area(divide(30, const_2)), const_2) | what will be the fraction of 30 % | "explanation : it will 30 * 1 / 100 = 3 / 10 option c" | a = 30 / 2
b = circle_area / (
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a ) 63 , b ) 64 , c ) 65 , d ) 76 , e ) 67 | c | multiply(39, 3) | jacob is 39 years old . he is 3 times as old as his brother . how old will jacob be when he is twice as old ? | "j = 39 ; j = 3 b ; b = 39 / 3 = 13 ; twice as old so b = 13 ( now ) + ( 13 ) = 26 ; jacob is 39 + 26 = 65 answer : c" | a = 39 * 3
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a ) 21.4 sec , b ) 77 sec , c ) 25 sec , d ) 18 sec , e ) 17 sec | a | divide(add(150, 100), multiply(42, const_0_2778)) | how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph ? | "d = 100 + 150 = 250 s = 42 * 5 / 18 = 11.7 mps t = 250 / 11.7 = 21.4 sec answer : a" | a = 150 + 100
b = 42 * const_0_2778
c = a / b
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a ) 10 sec , b ) 30 sec , c ) 40 sec , d ) 20 s , e ) 50 sec | d | divide(add(280, 120), multiply(add(42, 30), const_0_2778)) | two cars of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ? | d relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 s . | a = 280 + 120
b = 42 + 30
c = b * const_0_2778
d = a / c
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a ) 10 , b ) 19 , c ) 20 , d ) 21 , e ) 22 | a | subtract(add(6, 5), const_1) | a student is ranked 6 th from right and 5 th from left . how many students are there in totality ? | "from right 6 , from left 5 total = 6 + 5 - 1 = 10 answer : a" | a = 6 + 5
b = a - 1
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a ) 120 , b ) 360 , c ) 240 , d ) 182 , e ) 1000 | c | multiply(60, multiply(divide(12, 6), divide(20, 10))) | if 6 men can reap 60 acres of land in 10 days , how many acres of land can 12 men reap in 20 days ? | "6 men 60 acres 10 days 12 men ? 20 days 60 * 12 / 6 * 20 / 10 60 * 2 * 2 60 * 4 = 240 answer : c" | a = 12 / 6
b = 20 / 10
c = a * b
d = 60 * c
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a ) 98 , b ) 165 , c ) 180 , d ) 253 , e ) none of these | b | multiply(15, divide(165, 15)) | solve for x and check : 15 x = 165 | solution : dividing each side by 15 , we obtain ( 15 x / 15 ) = ( 165 / 15 ) therefore : x = 11 check : 15 x = 165 ( 15 * 11 ) = 165 165 = 165 answer : b | a = 165 / 15
b = 15 * a
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a ) 5 , b ) 8 , c ) 4 , d ) 7 , e ) 6 | e | inverse(add(divide(const_1, 10), divide(const_1, 15))) | if ram and gohul can do a job in 10 days and 15 days independently . how many days would they take to complete the same job working simultaneously ? | "if total work is x . ram rate of working = x / 10 per day . gohul rate of working = x / 15 per day . rate of work = ( x / 10 ) + ( x / 15 ) = 30 x / 5 x = 6 days answer is option e" | a = 1 / 10
b = 1 / 15
c = a + b
d = 1/(c)
|
a ) 64.19 , b ) 64.12 , c ) 40.5 , d ) 64.1 , e ) 64.11 | c | subtract(subtract(multiply(1000, power(add(divide(8, const_100), const_1), 4)), 1000), multiply(multiply(1000, divide(8, const_100)), 4)) | what will be the difference between simple and compound interest at 8 % per annum on a sum of rs . 1000 after 4 years ? | "s . i . = ( 1000 * 8 * 4 ) / 100 = rs . 320 c . i . = [ 1000 * ( 1 + 8 / 100 ) 4 - 1000 ] = rs . 360.5 difference = ( 360.5 - 320 ) = rs . 40.5 answer : c" | a = 8 / 100
b = a + 1
c = b ** 4
d = 1000 * c
e = d - 1000
f = 8 / 100
g = 1000 * f
h = g * 4
i = e - h
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a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 67.5 | e | multiply(divide(divide(add(divide(120, const_2), 120), 40), const_4), divide(120, const_2)) | a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 40 miles per hour . if the ride from marker a to marker b lasted 3 t... | "a - b = 120 miles b - c = 60 miles avg speed = 40 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 40 = 180 / 4 t t = 67.5 b - c = 67.5 mph answer e" | a = 120 / 2
b = a + 120
c = b / 40
d = c / 4
e = 120 / 2
f = d * e
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a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | b | divide(divide(add(add(add(add(add(add(add(add(add(add(50, 50), 97), 97), 97), 120), 125), 155), 199), 199), 239), add(const_10, const_1)), divide(add(add(add(add(add(add(add(add(add(add(50, 50), 97), 97), 97), 120), 125), 155), 199), 199), 239), add(const_10, const_1))) | company x sells a selection of products at various price points . listed below are unit sales made for one particular day . how many unit sales on that day were greater than the mean sale price but less than the median sale price ? $ 50 , $ 50 , $ 97 , $ 97 , $ 97 , $ 120 , $ 125 , $ 155 , $ 199 , $ 199 , $ 239 | taking the prices of products in ascending order ( already arranged ) $ 50 , $ 50 , $ 97 , $ 97 , $ 97 , $ 120 , $ 125 , $ 155 , $ 199 , $ 199 , $ 239 we see that median value is the 6 th value as there in total 11 values given arithmetic mean = total / number of entries = 1428 / 11 = 129.8181 we are asked to find how ... | a = 50 + 50
b = a + 97
c = b + 97
d = c + 97
e = d + 120
f = e + 125
g = f + 155
h = g + 199
i = h + 199
j = i + 239
k = 10 + 1
l = j / k
m = 50 + 50
n = m + 97
o = n + 97
p = o + 97
q = p + 120
r = q + 125
s = r + 155
t = s + 199
u = t + 199
v = u + 239
w = 10 + 1
x = v / w
y = l / x
|
a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18 | c | divide(subtract(multiply(15, subtract(40, 4)), multiply(15, 32)), 4) | the average age of an adult class is 40 years . 15 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ? | "let original strength = y then , 40 y + 15 x 32 = ( y + 15 ) x 36 â ‡ ’ 40 y + 480 = 36 y + 540 â ‡ ’ 4 y = 60 â ˆ ´ y = 15 c" | a = 40 - 4
b = 15 * a
c = 15 * 32
d = b - c
e = d / 4
|
a ) 100 / 6 , b ) 289 / 4 , c ) 128 / 7 , d ) 456 / 6 , e ) 1000 / 301 | e | divide(const_1, 0.301) | if log 10 2 = 0.3010 , then log 2 10 is equal to : | explanation : log 2 10 = 1 / log 102 = 1 / 0.3010 = 10000 / 3010 = 1000 / 301 answer e | a = 1 / 0
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a ) 64 and 15,625 , b ) 32 and 3,125 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 64 and 16,625 | b | add(power(divide(log(multiply(const_100, const_1000)), log(const_10)), subtract(divide(log(multiply(const_100, const_1000)), log(const_10)), const_1)), 0) | find two integers , neither of which ends in a zero , and whose product is exactly 00000 | 1 , 00,000 = 10 ^ 5 = 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 5 ) x ( 5 ^ 5 ) = 32 x 3125 so the numbers are 32 and 3,125 answer : b | a = 100 * 1000
b = math.log(a)
c = math.log(10)
d = b / c
e = 100 * 1000
f = math.log(e)
g = math.log(10)
h = f / g
i = h - 1
j = d ** i
k = j + 0
|
a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | e | add(6, 4) | set a consists of the integers from 4 to 15 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ? | a = { 4,5 , 6,7 , 8,9 , 10,11 , 12,13 , 14,15 } b = { 6 , 7,8 , 9,10 , 11,12 . . . 20 } thus we see that there are 10 distinct integers that are common to both . e is the correct answer . | a = 6 + 4
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a ) 1 / 64 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3 | a | multiply(divide(8, power(8, const_2)), divide(8, power(8, const_2))) | what is the probability that the sum of two dice will yield a 9 , and then when both are thrown again , their sum will again yield a 9 ? assume that each die has 8 sides with faces numbered 1 to 8 . | "solution - rolling dices is an independent event . the combinations to get 9 are ( 1,8 ) , ( 8,1 ) , ( 2,7 ) , ( 7,2 ) , ( 3,6 ) , ( 6,3 ) , ( 4,5 ) , ( 5,4 ) , and total combinations of both dices is 64 . the probability of getting 9 in first attempt is 8 / 64 = 1 / 8 . probability of getting 9 again in second attemp... | a = 8 ** 2
b = 8 / a
c = 8 ** 2
d = 8 / c
e = b * d
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a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 % | e | subtract(100, 20) | john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 20 . what is the percent decrease ? | "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 20 = 80 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 80 / 100 ) * 100 = ( 0.8 ) * 100 = 80 % . e" | a = 100 - 20
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a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50 | d | divide(80, const_2) | a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent q of the list price is the l... | "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is q = 40 % of 80 hence ... | a = 80 / 2
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a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | b | subtract(add(1, multiply(17, 4)), multiply(17, 4)) | how many two - digit numbers yield a remainder of 1 when divided by both 4 and 17 ? | easier to start with numbers that are of the form 17 p + 1 - - - > 18 , 35,52 , 69,86 . out of these , there is only one ( 69 ) is also of the form 4 q + 1 . thus 1 is the answer . b is the correct answer . | a = 17 * 4
b = 1 + a
c = 17 * 4
d = b - c
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a ) 33 , b ) 11 , c ) 96 , d ) 36 , e ) 91 | c | divide(multiply(120, 20), const_100) | the cost of an article is decreased by 20 % . if the original cost is $ 120 , find the decrease cost . | "original cost = $ 120 decrease in it = 20 % of $ 120 = 20 / 100 ã — 120 = 2400 / 100 = $ 24 therefore , decrease cost = $ 120 - $ 24 = $ 96 answer : c" | a = 120 * 20
b = a / 100
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a ) 1 , b ) undentified , c ) 3 , d ) 7 , e ) 5 | b | divide(log(multiply(3, 3)), log(const_10)) | 3 log 3 ( - 5 ) = ? | "since - 5 is not in the domain of function log 3 ( x ) , 3 log 3 ( - 5 ) is undefined correct answer b" | a = 3 * 3
b = math.log(a)
c = math.log(10)
d = b / c
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['a ) 13', 'b ) 12', 'c ) 4', 'd ) 16', 'e ) 18'] | a | divide(volume_cylinder(6, 12), volume_cylinder(const_2, 8)) | a cylinder with 6 meter radius and 12 meter height is filled to capacity with water . if the content of the cylinder is used to fill several smaller cylinders of 4 meter diameter and 8 meter height , how many smaller cylinders will be filled to capacity ? | calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 1357.17 smaller cylinder volume = 100.53 therefore the number of cylinders b that can be filled to capacity = 1357.17 / 100.53 = 13.5 answer is a only 13 smaller cylind... | a = volume_cylinder / (
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a ) 20940 , b ) 21009 , c ) 23000 , d ) 23450 , e ) 30000 | a | add(multiply(multiply(add(divide(3, const_100), divide(divide(subtract(19500, 12000), 4), 12000)), 12000), 4), 12000) | sonika deposited rs . 12000 which amounted to rs . 19500 after 4 years at simple interest . had the interest been 3 % more . she would get how much ? | "( 12000 * 4 * 3 ) / 100 = 1440 19500 - - - - - - - - 20940 answer : a" | a = 3 / 100
b = 19500 - 12000
c = b / 4
d = c / 12000
e = a + d
f = e * 12000
g = f * 4
h = g + 12000
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a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 17 | a | floor(divide(divide(subtract(add(multiply(16, const_100), 6), add(add(multiply(8, const_100), 8), 88)), const_10), add(const_10, const_1))) | 8 k 8 + k 88 - - - - - - - - 16 y 6 if k and y represent non - zero digits within the integers above , what is y ? | 8 k 8 k 88 - - - - - - - - 16 y 6 trial and error or just plug - in method might be the shortest way to solve this problem . though you can narrow down the possible values of k to just two : 7 and 8 - - > 8 * * + 7 * * = 16 * * or 8 * * + 8 * * = 16 * * ( k can not be less than 7 or 9 , as the result wo n ' t be 16 * *... | a = 16 * 100
b = a + 6
c = 8 * 100
d = c + 8
e = d + 88
f = b - e
g = f / 10
h = 10 + 1
i = g / h
j = math.floor(i)
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a ) 40 , b ) 50 , c ) 60 , d ) 200 , e ) 300 | e | multiply(divide(900, multiply(add(const_2, const_1), const_2)), const_2) | a rectangular garden is to be twice as long as it is wide . if 900 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ? | "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 900 so , 2 ( l + b ) = 900 or , l + b = 450 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ... | a = 2 + 1
b = a * 2
c = 900 / b
d = c * 2
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a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3 | c | floor(divide(log(divide(2, 2.134)), log(10))) | if x is an integer and 2.134 × 10 ^ x is less than 2 , 100,000 , what is the greatest possible value for x ? | "if x = 6 2.134 × 10 ^ 6 = 2 , 134,000 > 2 , 100,000 so , x = 5 answer : c" | a = 2 / 2
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
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a ) 5 , b ) 5 1 / 2 , c ) 4 4 / 5 , d ) 6 , e ) 9 1 / 2 | c | divide(multiply(const_4.0, 3), subtract(8, 3)) | a man can do a piece of work in 8 days , but with the help of his son , he can finish it in 3 days . in what time can the son do it alone ? | "son ' s 1 day work = 1 / 3 - 1 / 8 = 5 / 24 son alone can do the work in 24 / 5 days = 4 4 / 5 days answer is c" | a = 4 * 0
b = 8 - 3
c = a / b
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a ) 10 and 12 , b ) 9 and 11 , c ) 20 and 22 , d ) 8 and 10 , e ) 19 and 21 | c | add(add(multiply(10, 2), 2), multiply(multiply(10, 10), multiply(10, 2))) | caleb and kyle built completed the construction of a shed in 10 and half days . if they were to work separately , how long will it take each for each of them to build the shed , if it will take caleb 2 day earlier than kyle ? | work = ( a ) ( b ) / ( a + b ) where a and b are the individual times of each entity . here , we ' re told that ( working together ) the two workers would complete a job in 12 days . this means that ( individually ) each of them would take more than 10 days to do the job . answers e , a and c are illogical , since the ... | a = 10 * 2
b = a + 2
c = 10 * 10
d = 10 * 2
e = c * d
f = b + e
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a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12 | b | divide(divide(multiply(multiply(36, 12), 8), 72), 8) | in a manufacturing plant , it takes 36 machines 8 hours of continuous work to fill 8 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ? | "the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 8 * 36 / 72 * 12 / 8 = 6 ans b" | a = 36 * 12
b = a * 8
c = b / 72
d = c / 8
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a ) 6 , b ) 12 , c ) 9 , d ) 5 , e ) 2 | e | add(const_3, const_4) | what is the smallest positive integer x such that 864 x is the cube of a positive integer | "given 864 x is a perfect cube so we will take 1728 = 12 * 12 * 12 864 x = 1728 x = 1728 / 864 = 2 correct option is e" | a = 3 + 4
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a ) 70 , b ) 120 , c ) 100 , d ) 90 , e ) 110 | b | multiply(multiply(10, 4), 3) | at the beginning of the year , the ratio of boys to girls in high school x was 3 to 4 . during the year , 10 boys and twice as many girls transferred to another high school , while no new students joined high school x . if , at the end of the year , the ratio of boys to girls was 4 to 5 , how many boys were there in hi... | let the total number of boys and girls at the beginning of the year be 3 x and 4 x respectively . now 10 boys and 20 girls are transferred to another school . thus no . of boys and girls students left in the school x are 3 x - 10 and 4 x - 20 respectively . the ratio of these boys and girls students = 4 / 5 thus we hav... | a = 10 * 4
b = a * 3
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a ) 972 , b ) 990 , c ) 1098 , d ) 1305 , e ) 1405 | a | subtract(subtract(multiply(360, const_3), subtract(const_100, const_1)), subtract(const_10, const_1)) | the total number of digits used in numbering the pages of a book having 360 pages is | "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 261 ) = ( 9 + 180 + 783 ) = 972 . answer : a" | a = 360 * 3
b = 100 - 1
c = a - b
d = 10 - 1
e = c - d
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a ) 260 , b ) 258 , c ) 252 , d ) 250 , e ) 244 | c | subtract(negate(234), multiply(subtract(224, 228), divide(subtract(224, 228), subtract(222, 224)))) | 222 , 224 , 228 , 234 , 242 , ( . . . . ) | "explanation : the pattern is 2 , 4 , 6 , 8 , 10 , etc . hence 10 = 252 answer : c" | a = negate - (
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a ) 8 , b ) 12 , c ) 18 , d ) 24 , e ) 48 | b | divide(multiply(add(add(6, 4), 2), divide(2000, 2)), const_1000) | a 2000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ? | "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 1,000 by that net inflow to get the minutes ) - 12 min . answer b ." | a = 6 + 4
b = a + 2
c = 2000 / 2
d = b * c
e = d / 1000
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a ) 900 , b ) 980 , c ) 1600 , d ) 1240 , e ) 1400 | c | subtract(divide(4800, 2), divide(4800, 6)) | share rs . 4800 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ? | amount received by sanjay . 4 / 12 x 4800 = 1600 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1600 . c | a = 4800 / 2
b = 4800 / 6
c = a - b
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a ) 5.7 , b ) 6.0 , c ) 4.0 , d ) 9.7 , e ) 18.0 | c | divide(add(divide(divide(25, const_3), const_3), divide(multiply(divide(25, const_3), const_2), const_3)), const_2) | the total circumference of two circles is 25 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ? | "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 25 where 2 r = r thus : 2 π r + 4 π r = 25 6 π r = 25 r = approx 1.33 π r + 2 r π = 25 3 π r = 25 r = approx 2.65 r + r = approx 3.98 = 4.0 answer : c" | a = 25 / 3
b = a / 3
c = 25 / 3
d = c * 2
e = d / 3
f = b + e
g = f / 2
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a ) 757 , b ) 758 , c ) 718 , d ) 1200 , e ) 738 | d | divide(divide(multiply(144, const_1000), divide(const_60, const_1)), const_2) | the length of a train and that of a platform are equal . if with a speed of 144 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ? | "speed = [ 144 * 5 / 18 ] m / sec = 40 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 40 è x = 40 * 60 / 2 = 1200 answer : d" | a = 144 * 1000
b = const_60 / 1
c = a / b
d = c / 2
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a ) 347.4 , b ) 987.4 , c ) 877.4 , d ) 637.4 , e ) 667.4 | c | add(add(multiply(4, multiply(divide(24, 10), divide(multiply(20.50, 6), 2))), multiply(3, divide(multiply(20.50, 6), 2))), multiply(5, 20.50)) | the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 20.50 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ? | "c $ 877.40 let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 20.50 = 2 r a = 12 / 5 r and r = 61.5 a = 147.6 required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5 = 590.4 + 184.5 + 102.5 = $ 877.40" | a = 24 / 10
b = 20 * 50
c = b / 2
d = a * c
e = 4 * d
f = 20 * 50
g = f / 2
h = 3 * g
i = e + h
j = 5 * 20
k = i + j
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a ) 23 , b ) 18 , c ) 21 , d ) 24 , e ) 25 | b | divide(const_1, add(divide(const_1, 30), divide(divide(const_1, 30), 1.5))) | a is 1.5 times as fast as b . a alone can do the work in 30 days . if a and b working together in how many days will the work be completed ? | "a can finish 1 work in 30 days b can finish 1 / 1.5 work in 30 days - since a is 1.5 faster than b this means b can finish 1 work in 30 * 1.5 days = 45 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 45 * 30 / ( 45 + 30 ) = 20 * 30 / 50 = 18 days so... | a = 1 / 30
b = 1 / 30
c = b / 1
d = a + c
e = 1 / d
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a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 95 , d ) 1 , e ) 2 | c | divide(1, 95) | if the numbers 1 to 95 are written on 95 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ? | "there are 25 primes , 69 composite numbers from 1 to 95 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 95 . answer : c" | a = 1 / 95
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a ) 8 hrs , b ) 20 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs | b | multiply(divide(1, 6), 24) | a train running at 1 / 6 of its own speed reached a place in 24 hours . how much time could be saved if the train would have run at its own speed ? | "time taken if run its own speed = 1 / 6 * 24 = 4 hrs time saved = 24 - 4 = 20 hrs answer : b" | a = 1 / 6
b = a * 24
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a ) s : 1000 , b ) s : 1067 , c ) s : 1200 , d ) s : 1028 , e ) s : 1027 | c | divide(multiply(168, const_100), subtract(add(const_100, 4), subtract(const_100, 10))) | a watch was sold at a loss of 10 % . if it was sold for rs . 168 more , there would have been a gain of 4 % . what is the cost price ? | "90 % 104 % - - - - - - - - 14 % - - - - 168 100 % - - - - ? = > rs : 1200 answer : c" | a = 168 * 100
b = 100 + 4
c = 100 - 10
d = b - c
e = a / d
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a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | e | divide(const_1, subtract(divide(const_1, 2), divide(const_1, 3))) | a pump can fill a tank with a water in 2 hours . because of a leak , it took 3 hours to fill the tank . the leak can drain all the water of the full tank in how many hours ? | the rate of the pump + leak = 1 / 3 1 / 2 - leak ' s rate = 1 / 3 leak ' s rate = 1 / 2 - 1 / 3 = 1 / 6 the leak will empty the tank in 6 hours . the answer is e . | a = 1 / 2
b = 1 / 3
c = a - b
d = 1 / c
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['a ) becomes 8 times', 'b ) becomes 9 times', 'c ) is double', 'd ) becomes 6 times', 'e ) none'] | a | power(const_2, const_3) | if each edge of a cube is doubled , then its volume : | sol . let original edge = a . then , volume = a ³ new edge = 2 a . so , new volume = ( 2 a ) ³ = 8 a ³ ∴ volume becomes 8 times answer a | a = 2 ** 3
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a ) s . 28028 , b ) s . 28000 , c ) s . 28003 , d ) s . 28029 , e ) s . 24029 | b | subtract(52000, multiply(const_60, const_100)) | a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 52000 , then the share of a is ? | "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 52000 share of b = 7 / 13 ( 52000 ) = rs . 28000 answer : b" | a = const_60 * 100
b = 52000 - a
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a ) 6.9 , b ) 7.2 , c ) 7.5 , d ) 7.8 , e ) 8.1 | c | divide(add(18, 12), subtract(7.2, add(divide(18, 9), divide(12, 10)))) | on a trip , a cyclist averaged 9 miles per hour for the first 18 miles and 10 miles per hour for the remaining 12 miles . if the cyclist returned immediately via the same route and took a total of 7.2 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ? | "the time to go 30 miles was 18 / 9 + 12 / 10 = 2 + 1.2 = 3.2 hours . the average speed for the return trip was 30 miles / 4 hours = 7.5 mph . the answer is c ." | a = 18 + 12
b = 18 / 9
c = 12 / 10
d = b + c
e = 7 - 2
f = a / e
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a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 % | c | multiply(divide(subtract(60, 42), 60), const_100) | in town p , 60 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town p are females ? | "the percent of the population who are employed females is 60 - 42 = 18 % the percent of employed people who are female is 18 % / 60 % = 30 % . the answer is c ." | a = 60 - 42
b = a / 60
c = b * 100
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a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5 | e | multiply(divide(divide(100, 5), 100), const_2.0) | an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 5 ? | "n ( n + 1 ) to be divisible by 3 either n or n + 1 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 , 4 , 5 } , { 6 , 7 , 8 , 9 , 10 } , . . . , { 96 , 97 , 98 , 99,100 } there is exactly 1 numbers out of 5 satisfying the above condition . for example in { 1 , 2 , 3 , 4 , 5 } n can be : 4 or... | a = 100 / 5
b = a / 100
c = b * 2
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a ) 3 , b ) 4 , c ) 7 , d ) 32 , e ) 35 | c | subtract(38, reminder(3, 7)) | when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 38 ? | "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 38 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 7 more to make it 38 m + 38 answer - c" | a = 38 - reminder
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a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25 | e | add(divide(18, const_2), subtract(34, 18)) | jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 34 years old , and she stopped baby - sitting 12 years ago . what is the current age of the oldest person for whom jane could have baby - sat ? | "check two extreme cases : jane = 18 , child = 9 , years ago = 34 - 18 = 16 - - > child ' s age now = 9 + 16 = 25 ; jane = 22 , child = 11 , years ago = 34 - 22 = 12 - - > child ' s age now = 11 + 12 = 23 . answer : e ." | a = 18 / 2
b = 34 - 18
c = a + b
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a ) 1 / 12 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 24 , e ) 5 / 9 | a | multiply(multiply(multiply(divide(add(5, const_1), add(9, const_1)), divide(subtract(add(5, const_1), const_1), subtract(add(9, const_1), const_1))), divide(subtract(subtract(add(5, const_1), const_1), const_1), subtract(subtract(add(9, const_1), const_1), const_1))), divide(subtract(subtract(subtract(add(5, const_1), ... | each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 5 of the slips are the drawn , without replacement , what is the probability that all 5 have a odd number written on it ? | "key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 p ( ... | a = 5 + 1
b = 9 + 1
c = a / b
d = 5 + 1
e = d - 1
f = 9 + 1
g = f - 1
h = e / g
i = c * h
j = 5 + 1
k = j - 1
l = k - 1
m = 9 + 1
n = m - 1
o = n - 1
p = l / o
q = i * p
r = 5 + 1
s = r - 1
t = s - 1
u = t - 1
v = 9 + 1
w = v - 1
x = w - 1
y = x - 1
z = u / y
A = q * z
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a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5 % , e ) 6.0 % | d | multiply(divide(add(multiply(50, divide(4, const_100)), multiply(30, divide(10, const_100))), const_100), const_100) | of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what perc... | let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2 tax on others = 3 percentage = 5 / 100 = 5 % answer : d | a = 4 / 100
b = 50 * a
c = 10 / 100
d = 30 * c
e = b + d
f = e / 100
g = f * 100
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a ) 9 , b ) 8 , c ) 7 , d ) 10 , e ) 11 | a | multiply(divide(252, add(add(16, 28), 40)), const_3) | jeff has 252 ounces of peanut butter in 16 , 28 . and 40 ounce jars . he has an equal number of each sized jar . how many jars of peanut butter does jeff have ? | let p equal the number of each sized jar then 16 p + 28 p + 40 p = 252 84 p = 252 p = 3 therefore , the total number of jars of peanut butter jeff has = 3 p = 9 answer : a | a = 16 + 28
b = a + 40
c = 252 / b
d = c * 3
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a ) 189.2 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs | a | multiply(66, divide(multiply(86, 8), multiply(20, 12))) | if 20 men can build a wall 66 metres long in 12 days , what length of a similar can be built by 86 men in 8 days ? | "if 20 men can build a wall 66 metres long in 12 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 12 * 20 ) = 189.2 mtrs answer : a" | a = 86 * 8
b = 20 * 12
c = a / b
d = 66 * c
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['a ) 3.17 feet', 'b ) 3.2 feet', 'c ) 3.3 feet', 'd ) 3.4 feet', 'e ) 3.5 feet'] | a | divide(add(add(multiply(add(2, 10), 2), const_10), 4), add(2, 10)) | carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 4 inches tall . how tall are the sculpture andbase together ? | we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 4 = 38 38 / 12 = 3.17 feet answer : a | a = 2 + 10
b = a * 2
c = b + 10
d = c + 4
e = 2 + 10
f = d / e
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a ) 2.3 , b ) 2.6 , c ) 3.6 , d ) 4.5 , e ) 5 | e | divide(subtract(multiply(6, 2.5), add(multiply(2, 1.1), multiply(2, 1.4))), 2) | the average of 6 no . ' s is 2.5 . the average of 2 of them is 1.1 , while the average of the other 2 is 1.4 . what is the average of the remaining 2 no ' s ? | "sum of the remaining two numbers = ( 2.5 * 6 ) - [ ( 1.1 * 2 ) + ( 1.4 * 2 ) ] = 15 - ( 2.2 + 2.8 ) = 15 - 5 = 10 required average = ( 10 / 2 ) = 5 answer : e" | a = 6 * 2
b = 2 * 1
c = 2 * 1
d = b + c
e = a - d
f = e / 2
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a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 11,700 , e ) 19,600 | d | multiply(divide(add(200, 101), const_2), add(divide(subtract(200, 101), const_2), const_1)) | the sum of the first 92 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? | "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 92 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 92 positive even integers = 2550 sum of 1 st 100 odd numbers = ... | a = 200 + 101
b = a / 2
c = 200 - 101
d = c / 2
e = d + 1
f = b * e
|
a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 , e ) 5 / 4 | c | subtract(divide(subtract(21, const_1), add(19, const_1)), divide(add(9, const_1), subtract(31, const_1))) | a is an integer greater than 9 but less than 21 , b is an integer greater than 19 but less than 31 , what is the range of a / b ? | min value of a / b will be when b is highest and a is lowest - - - > a = 10 and b = 30 so , a / b = 1 / 3 max value of a / b will be when b is lowest and a is highest - - - > a = 20 and b = 20 so , a / b = 1 range is 1 - ( 1 / 3 ) = 2 / 3 . answer should be c | a = 21 - 1
b = 19 + 1
c = a / b
d = 9 + 1
e = 31 - 1
f = d / e
g = c - f
|
a ) 95 , b ) 90 , c ) 85 , d ) 78 , e ) 72 | e | divide(18, divide(subtract(100, 75), 100)) | if 18 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ? | "let x be the number of students in the school . 0.18 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.18 x / 0.25 = 0.72 x students went to the camping which is 72 % . the answer is e" | a = 100 - 75
b = a / 100
c = 18 / b
|
a ) 1 / 2 , b ) 3 / 4 , c ) 1 , d ) 2 , e ) 3 | a | subtract(1, multiply(divide(factorial(2), factorial(1)), power(divide(1, 1), 2))) | a couple decides to have 2 children . if they succeed in having 2 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 1 girl and 1 boy ? | "sample space = 2 ^ 2 = 4 . favourable events = { bg } , { gb } , probability = 2 / 4 = 1 / 2 . ans ( a ) ." | a = math.factorial(2)
b = math.factorial(1)
c = a / b
d = 1 / 1
e = d ** 2
f = c * e
g = 1 - f
|
a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 195 | e | divide(add(add(multiply(multiply(const_4, const_4), const_1000), multiply(5, const_100)), multiply(add(80, 5), 150)), 150) | a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces... | by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me . | a = 4 * 4
b = a * 1000
c = 5 * 100
d = b + c
e = 80 + 5
f = e * 150
g = d + f
h = g / 150
|
a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 50 | e | divide(subtract(75, 60), subtract(const_1, divide(70, const_100))) | a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 60 books in the spec... | "i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 60 books , thus 76 - 60 = 16 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 50 . answer : ... | a = 75 - 60
b = 70 / 100
c = 1 - b
d = a / c
|
a ) 59 , b ) 58 , c ) 60 , d ) 61 , e ) 12 | c | multiply(divide(100, add(add(divide(2, 3), divide(5, 2)), 2)), 5) | a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by c are ? | "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 15 / 25 * 100 = 60 answer : c" | a = 2 / 3
b = 5 / 2
c = a + b
d = c + 2
e = 100 / d
f = e * 5
|
a ) 10 , b ) 12 , c ) 42 , d ) 20 , e ) 22 | c | divide(subtract(multiply(12, subtract(50, 4)), multiply(12, 32)), 4) | the average age of an adult class is 50 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 years . find what was the original average age of the class ? | "let original strength = y then , 50 y + 12 x 32 = ( y + 12 ) x 46 â ‡ ’ 50 y + 384 = 46 y + 552 â ‡ ’ 4 y = 168 â ˆ ´ y = 42 c" | a = 50 - 4
b = 12 * a
c = 12 * 32
d = b - c
e = d / 4
|
a ) $ 300 , b ) $ 400 , c ) $ 450 , d ) $ 625 , e ) $ 750 | e | add(multiply(3, 150), multiply(divide(const_2, 3), multiply(3, 150))) | anne and katherine are both saving money from their summer jobs to buy bicycles . if anne had $ 150 less , she would have exactly 1 / 3 as much as katherine . and if katherine had twice as much , she would have exactly 3 times as much as anne . how much money have they saved together ? ( | if anne had $ 150 less , katherine would have three times more than anne . make this statement into an equation and simplify : 3 ( a – 150 ) = k 3 a – 450 = k and if katherine had twice as much , she would have three times more than anne : 2 k = 3 a substitute 3 a – 450 for k into the last equation and solve for a 2 ( ... | a = 3 * 150
b = 2 / 3
c = 3 * 150
d = b * c
e = a + d
|
a ) 145 , b ) 180 , c ) 181 , d ) 184 , e ) 150 | b | subtract(multiply(180, divide(15, divide(15, const_3))), multiply(120, divide(18, divide(15, const_3)))) | a train crosses a platform of 120 m in 15 sec , same train crosses another platform of length 180 m in 18 sec . then find the length of the train ? | "length of the train be ‘ x ’ x + 120 / 15 = x + 180 / 18 6 x + 720 = 5 x + 900 x = 180 m answer : option b" | a = 15 / 3
b = 15 / a
c = 180 * b
d = 15 / 3
e = 18 / d
f = 120 * e
g = c - f
|
a ) 5 / 32 , b ) 5 / 27 , c ) 1 / 27 , d ) 1 / 32 , e ) 27 / 32 | a | divide(subtract(32, 27), 32) | a ’ s speed is 32 / 27 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 32 meters , b covers 27 meters in that time . so if the race i... | a = 32 - 27
b = a / 32
|
a ) 17725 cm , b ) 15625 cm , c ) 12786 cm , d ) 12617 cm , e ) 12187 cm | b | divide(volume_cube(1), volume_cube(divide(4, const_100))) | how many cubes of 4 cm edge can be put in a cubical box of 1 m edge . | "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 4 * 4 * 4 = 15625 note : 1 m = 100 cm answer : b" | a = volume_cube / (
|
a ) 509 , b ) 624 , c ) 756 , d ) 832 , e ) 947 | a | subtract(375,600, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2)) | how many integers between 324,700 and 375,600 have tens digit 1 and units digit 3 ? | "the integers are : 324,713 324,813 etc . . . 375,513 the number of integers is 3756 - 3247 = 509 the answer is a ." | a = 2 * 100
b = 3 + 4
c = b * 10
d = a + c
e = d + 2
f = 375 - 600
|
['a ) 5 / ( √ 6 )', 'b ) 5 · √ ( 2 / 3 )', 'c ) 5 · √ ( 3 / 2 )', 'd ) 5 · √ 3', 'e ) 5 · √ 6'] | b | multiply(5, const_1) | if the space diagonal of cube c is 5 inches long , what is the length , in inches , of the diagonal of the base of cube c ? | n cube c , let ' s say that each side has side length x so , the diagonal = √ ( x ² + x ² + x ² ) = √ ( 3 x ² ) here , we ' re told that the diagonal has length 5 , so we can write : 5 = √ ( 3 x ² ) square both sides to get : 25 = 3 x ² divide both sides by 3 to get : 25 / 3 = x ² square root both sides : √ ( 25 / 3 ) ... | a = 5 * 1
|
a ) 145 m , b ) 786 m , c ) 566 m , d ) 546 m , e ) 445 m | a | multiply(divide(multiply(58, const_1000), const_3600), 9) | a train running at the speed of 58 km / hr crosses a pole in 9 sec . what is the length of the train ? | "speed = 58 * 5 / 18 = 145 / 9 m / sec length of the train = speed * time = 145 / 9 * 9 = 145 m answer : a" | a = 58 * 1000
b = a / 3600
c = b * 9
|
a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12 | d | multiply(multiply(2, add(const_1, const_1)), add(const_1, const_1)) | if x and y are both odd prime numbers and x < y , how many distinct positive integer w factors does 2 xy have ? | since 2 xy prime w factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer . | a = 1 + 1
b = 2 * a
c = 1 + 1
d = b * c
|
a ) 5 hrs , b ) 7 hrs , c ) 8 hrs , d ) 9 hrs 50 mins , e ) 9 hrs | e | multiply(6, multiply(divide(4, 2), divide(6000, 8000))) | if it takes 4 identical printing presses exactly 6 hours to print 8000 newspapers , how long would it take 2 of these presses to print 6000 newspapers ? | 4 presses - 8,000 newspapers - 6 hours ; 2 presses - 4,000 newspapers - 6 hours ; ( 360 mins ) 2 presses - 6,000 newspapers - 360 / 4000 * 6000 = 540 mins = 9 hrs answer : e | a = 4 / 2
b = 6000 / 8000
c = a * b
d = 6 * c
|
a ) 16 , b ) 12 , c ) 2 , d ) 3 , e ) 14 | d | add(const_10, 2) | if ( t - 8 ) is a factor of t ^ 2 - kt - 43 , then k = | "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 3 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ... | a = 10 + 2
|
a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46 | c | add(subtract(55, multiply(12, 1)), 1) | a batsman in his 12 th innings makes a score of 55 and thereby increases his average by 1 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ? | "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 1 ) + 55 ∴ x = 44 answer c" | a = 12 * 1
b = 55 - a
c = b + 1
|
a ) 1209 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 2535 | e | multiply(divide(subtract(2415, 15), subtract(21, const_1)), 21) | find large number from below question the difference of two numbers is 2415 . on dividing the larger number by the smaller , we get 21 as quotient and the 15 as remainder | "let the smaller number be x . then larger number = ( x + 2415 ) . x + 2415 = 21 x + 15 20 x = 2400 x = 120 large number = 120 + 2415 = 2535 answer : e" | a = 2415 - 15
b = 21 - 1
c = a / b
d = c * 21
|
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