euclaise/mathqa_programs huggingface dataset:
Problem: a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is :
Options: a ) 251 , b ) 253 , c ) 255 , d ) 257 , e ) 260
Rationale: "let the middle digit be x . then , 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digits is smaller than the unit ' s digit . hence , required number = 253 . option b"
Answer: b
Python program:
a = 10 / 2
b = a - 3
c = 100 * b
d = 10 / 2
e = d * 10
f = c + e 
g = f + 3
Problem: how many seconds will a train 110 meters long take to cross a railway platform 165 meters long if the speed of the train is 132 kmph ?
Options: a ) 6 sec , b ) 7.5 sec , c ) 8 sec , d ) 3 sec , e ) 10 sec
Rationale: "d = 110 + 165 = 275 s = 132 * 5 / 18 = 110 / 3 mps t = 275 * 3 / 110 = 7.5 sec b ) 7.5 sec"
Answer: b
Python program:
a = 165 + 110 
b = 132 * const_0_2778
c = a / b
Problem: 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations . what is the ratio of their speeds
Options: a ) 11 : 9 , b ) 13 : 9 , c ) 17 : 9 , d ) 21 : 9 , e ) none of these
Rationale: "explanation : we know total distance is 200 km if both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [ 110 + 90 = 200 km ] so ratio of their speed = 110 : 90 = 11 : 9 option a"
Answer: a
Python program:
a = 200 - 110
b = a / 110
c = 1/(b)
Problem: 50 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 180 / 7 , c ) 50.4 , d ) 64.8 , e ) 90
Rationale: "50 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 50 ) * 100 = 64.8 square feet answer : option d"
Answer: d
Python program:
a = 4 * 9
b = 50 / 100
c = a / b
Problem: a work can be finished in 13 days by ten women . the same work can be finished in fifteen days by ten men . the ratio between the capacity of a man and a woman is
Options: a ) 14 : 13 , b ) 13 : 15 , c ) 12 : 13 , d ) 13 : 12 , e ) 14 : 15
Rationale: work done by 10 women in 1 day = 1 / 13 work done by 1 woman in 1 day = 1 / ( 13 ã — 10 ) work done by 16 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 ã — 10 ) ratio of the capacity of a man and woman = 1 / ( 15 ã — 10 ) : 1 / ( 13 ã — 10 ) = 1 / 15 : 1 / 13 = 1 / 15 : 1 / 13 = 13 : 15 answer is b .
Answer: b
Python program:
a = 13 + 2 
b = a * 10
c = 1 / b
d = 13 * 10
e = 1 / d
f = c / e
Problem: if 213 × 16 = 3408 , then 1.6 × 213.0 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: solution 1.6 × 21.3 = ( 16 / 10 x 213 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8 . answer d
Answer: d
Python program:
a = 1 * 6
Problem: a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds . its length is
Options: a ) 100 , b ) 120 , c ) 130 , d ) 150 , e ) 140
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m . answer : option d"
Answer: d
Python program:
a = 2 - 1
b = 100 * a
Problem: the population of a bacteria colony doubles every day . if it was started 3 days ago with 3 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 1024 , c ) 768 , d ) 2048 , e ) 4096
Rationale: "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 answer : b"
Answer: b
Python program:
a = 3 + 1 
b = 3 ** a
c = b - 1
Problem: the h . c . f of two numbers is 15 and their l . c . m is 3300 . if one of the numbers is 225 , then the other is ?
Options: a ) 200 , b ) 210 , c ) 220 , d ) 230 , e ) 240
Rationale: "other number = ( 15 * 3300 ) / 225 = 220 . answer : c"
Answer: c
Python program:
a = 15 * 225
Problem: a bag marked at $ 80 is sold for $ 68 . the rate of discount is ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "rate of discount = 12 / 80 * 100 = 15 % answer is b"
Answer: b
Python program:
a = 80 - 68
b = a / 80
c = b * 100
Problem: { 5 , 6 , 3 , 8 , 4 } if we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values ?
Options: a ) 5 , b ) 7 , c ) 15 , d ) 12 , e ) 13
Rationale: median is the middle number of a sorted distribution . in case of even number of items , median will be the average of middle two values . the question asks fora new number that will cause the median of new set at 10 . mentionable that given set is already sorted and number of items of new set will be 5 + 1 = 6 . to get median 10 , the sum of 3 th 4 th term should be 20 i . e . 3 + 7 . so to keep the median 10 , the new item should be > = 7 answer is b
Answer: b
Python program:
a = 5 + 6 
b = a - 10
c = b + 1 
d = 5 + 6 
e = d - 10
f = c + e 
g = 5 + 6 
h = g - 10
i = f + h 
j = 5 + 6 
k = j - 10
l = i + k 
m = 5 + 6 
n = m - 10
o = l + n 
p = 5 + 6 
q = p - 10
r = o + q
Problem: the area of a rhombus is equal to the area of a square whose side length is 8 cm . if one of the diagonals is 16 cm what is the length of other diagonal ?
Options: a ) 4
b ) 8
c ) 12
d ) 16
e ) 20
Rationale: area of the square = 8 x 8 = 64 let ' l ' be the unknown diagonal 0.5 x 16 x ' l ' = 64 which gives ' l ' = 8 cm answer : b
Answer: b
Python program:
a = square_area * (
b = a / 2
Problem: the cost price of 7 articles is equal to the selling price of 5 articles . what is the profit percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "5 * sp = 7 * cp sp = 1.4 * cp the profit percent is 40 % . the answer is d ."
Answer: d
Python program:
a = 7 * 4
b = 4 + 1 
c = a / b
Problem: in a kilometer race , a beats b by 20 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 290 sec , b ) 190 sec , c ) 199 sec , d ) 192 sec , e ) 490 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 20 = 500 sec . time taken by a = 500 - 10 = 490 sec . answer : e"
Answer: e
Python program:
a = 1 * 1000
b = 20 / 10
c = a / b
d = c - 10
Problem: a positive number when decreased by 4 is equal to 21 times the reciprocal of the number . the number is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 12
Rationale: "sol . let the numbers be x . then , x - 4 = 21 / x ⇔ x 2 - 4 x - 21 = 0 ⇔ ( x - 7 ) ( x + 3 ) = 0 ⇔ x = 7 . answer c"
Answer: c
Python program:
a = 4 * 21
b = 4 ** 2
c = a + b 
d = math.sqrt(c)
e = d + 4 
f = e / 2
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 62.5 , d ) 82.5 , e ) 60.5
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5"
Answer: c
Python program:
a = 100 + 25 
b = 47 * 50
c = b / 100
d = 100 - 5
e = c / d
f = e * 100
Problem: a car consumes 210 liters of petrol weekly . for how many days will 1470 liters of petrol be sufficient ?
Options: a ) 38 , b ) 20 , c ) 28 , d ) 49 , e ) 10
Rationale: explanation : no explanation is available for this question ! answer : d
Answer: d
Python program:
a = 1470 / 210
b = 4 + 3 
c = a * b
Problem: one type of liquid contains 20 % of water and the second type of liquid contains 35 % of water . a glass is filled with 10 parts of 1 st liquid and 4 parts of 2 nd liquid . the percentage of water in the new mixture in the glass is ?
Options: a ) 22.15 % , b ) 23.5 % , c ) 24.3 % , d ) 25 % , e ) 29.6 %
Rationale: required percentage = ( 20 % of 10 + 35 % of 4 ) / 10 + 4 * 100 = 3.4 / 14 * 100 = 24.3 % answer is c
Answer: c
Python program:
a = 10 + 4 
b = 100 / a
c = 20 * 10
d = c / 100
e = 35 * 4
f = e / 100
g = d + f 
h = b * g
Problem: the sum of two consecutive integers is 61 . find the numbers .
Options: a ) 17 , 18 , b ) 30,31 , c ) 5 , 6 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 61 2 n + 1 = 61 2 n = 60 n = 30 answer : b"
Answer: b
Python program:
a = 61 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 61 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 61 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 61 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: cuboid volume and base area are 144 m ^ 3 and 18 m ^ 3 respectively . find the height of a cuboid ?
Options: a ) 5 m
b ) 12 m
c ) 6 m
d ) 8 m
e ) 10 m
Rationale: height of the cuboid = volume * base area = 144 / 18 = 8 metre answer is option d
Answer: d
Python program:
a = 144 / 18
Problem: how many positive even integers less than 100 contain digits 7 or 9 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 10
Rationale: "two digit numbers : 7 at tens place : 70 , 72,74 , 76,78 9 at tens place : 90 , 92,94 , 96,98 if 7 and 9 is at units place , the number cant be even total : 5 + 5 = 10 answer e"
Answer: e
Python program:
a = 7 * 2
Problem: in a group of 650 readers who read science fiction or literacy works or both , 250 read science fiction and 550 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 650 , b ) 250 , c ) 150 , d ) 100 , e ) 400
Rationale: "consider total number of reader n ( s u l ) = 650 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 550 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 650 = 250 + 550 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 800 - 650 n ( s â ˆ © l ) = 150 so people read both science fiction and literacy works are 150 answer : c"
Answer: c
Python program:
a = 250 + 550 
b = a - 650
Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in one half circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 360 , d ) 18,000 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 180 degrees = 18,000 anglets answer - d"
Answer: d
Python program:
a = 2 + 4 
b = 1 / a
c = 3600 / 10
d = c * 100
e = b * d
Problem: the speed of a car is 80 km in the first hour and 40 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 60 kmph , c ) 30 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "s = ( 80 + 40 ) / 2 = 60 kmph answer : b"
Answer: b
Python program:
a = 80 + 40 
b = a / 2
Problem: two trains 200 m and 250 m long run at the speed of 72 kmph and 18 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 18 sec
Rationale: "relative speed = 72 + 18 = 90 kmph * 5 / 18 = 25 m / s distance covered in crossing each other = 200 + 250 = 450 m required time = 450 * 1 / 25 = 18 sec answer is e"
Answer: e
Python program:
a = 200 + 250 
b = 72 + 18 
c = b * const_0_2778
d = a / c
Problem: the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 3000 ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 11 = 2048 < 3000 , then the greatest possible length of integer z is 11 . the answer is c ."
Answer: c
Python program:
a = 2 ** 10
b = math.log(a)
Problem: a cistern is filled by a tap in 4 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 45 , e ) 48
Rationale: "filling rate - leak rate = net rate 1 / 4.5 - leak rate = 1 / 5 leak rate = 2 / 9 - 1 / 5 = 1 / 45 the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = 4 + a 
c = 1 / b
d = 1 / 4
e = c - d
f = 1 / e
Problem: what is ( 19 ^ 7 + 19 ) / 19 ?
Options: a ) 45225766 , b ) 46855821 , c ) 47045882 , d ) 48925947 , e ) 49325989
Rationale: "( 19 ^ 7 + 19 ) / 19 = 19 * ( 19 ^ 6 + 1 ) / 19 = 19 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is c ."
Answer: c
Python program:
a = 19 ** 7
b = a + 19 
c = b / 19
Problem: a certain galaxy is known to comprise approximately 6 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 8,000 , d ) 12,000 , e ) 80,000
Rationale: "6 * 10 ^ 11 50 mln = 5 * 10 ^ 7 we divide 10 ^ 11 by 10 ^ 7 and we get ( 10 ^ 4 ) * 6 = 60,000 and divide by 5 . the result is 12,000 d"
Answer: d
Python program:
a = 6 * 10
b = a / 50
c = 10 ** 4
d = b * c
e = d / 1000
f = e * 6
Problem: what is the remainder when 4 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 4 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? e
Answer: e
Python program:
a = 5 / 2
b = 4 * 4
c = a - b
Problem: the present population of a town is 1000 . population increase rate is 25 % p . a . find the population of town before 1 years ?
Options: a ) 800 , b ) 1500 , c ) 1000 , d ) 750 , e ) 500
Rationale: "p = 1000 r = 25 % required population of town = p / ( 1 + r / 100 ) ^ t = 1000 / ( 1 + 25 / 100 ) = 1000 / ( 5 / 4 ) = 800 answer is a"
Answer: a
Python program:
a = 1000 * 25
b = a / 100
c = 1000 + b
Problem: a garrison of 400 men had a provision for 31 days . after 28 days 300 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 45 days , c ) 10 days , d ) 16 days , e ) 12 days
Rationale: "400 - - - 31 400 - - - 3 100 - - - ? 400 * 3 = 100 * x = > x = 12 days . answer : e"
Answer: e
Python program:
a = 31 - 28
b = a * 400
c = b / 300
Problem: a = { 0 , 1 , - 3 , 6 , - 8 } b = { - 1 , 2 , - 4 , 7 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab > 0 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 9 , e ) 1 / 2
Rationale: for the product of 2 numbers to be positive either both of them must be positive or both of them must be negative : p ( positive , positive ) = 2 / 5 * 2 / 4 = 4 / 20 ; p ( negative , negative ) = 2 / 5 * 2 / 4 = 4 / 20 . p = 4 / 20 + 4 / 20 = 8 / 20 = 2 / 5 . answer : c .
Answer: c
Python program:
a = 1 + 4 
b = 2 / a
c = 2 / 4
d = b * c
e = 1 + 4 
f = 2 / e
g = 2 / 4
h = f * g
i = d + h
Problem: two trains 140 m and 210 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 12.6 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 10.2 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 210 = 350 m . required time = 350 * 9 / 250 = 12.6 sec . answer : a"
Answer: a
Python program:
a = 140 + 210 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: john and david can finish a job together in 1 hours . if john can do the job by himself in 2 hours , what percent of the job does david do ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: you can also plug in numbers . for example , bob and alice work at a donut factory and make 10 donuts which is the job ( i picked this as a smart number ) . john on his own works 10 / 2 = 5 donuts per hour . john and david work 10 / 1 = 10 donuts per hour so david works 5 donuts / hour to find out the percentage , david works 5 donuts / hr x 1 hours = 5 donuts per hour . therefore 5 donuts / 10 donuts = 1 / 2 = 50 % answer : c
Answer: c
Python program:
a = 1/(2)
b = 1 - a
c = b * 100
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 17 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 17 ) / 5 = ( 5 x + 30 ) / 5 = x + 6 median = x + 4 thus mean - median = x + 6 - ( x + 4 ) = 2 answer = c"
Answer: c
Python program:
a = 2 + 4 
b = a + 7 
c = b + 17 
d = 4 + 1 
e = c / d
f = e - 4
Problem: a man rows his boat 84 km downstream and 60 km upstream , taking 4 hours each time . find the speed of the stream ?
Options: a ) 76 kmph , b ) 6 kmph , c ) 14 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "speed downstream = d / t = 84 / ( 4 ) = 21 kmph speed upstream = d / t = 60 / ( 4 ) = 15 kmph the speed of the stream = ( 21 - 15 ) / 2 = 3 kmph answer : e"
Answer: e
Python program:
a = 84 / 4
b = 60 / 4
c = a - b
d = c / 2
Problem: an iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm . if the sides of the sheet are in the ratio 1 : 5 , the sides are :
Options: a ) 10 cm 20 cm
b ) 2 cm 10 cm
c ) 100 cm 20 cm
d ) 30 cm 100 cm
e ) none
Rationale: sol . let the sides of the sheet be x and 5 x . then , ⇒ x * 5 x * 1 / 2 = 10 * 10 * 10 ⇒ 5 x ² = 2000 ⇒ x ² = 400 ⇒ x = 20 . ∴ the sides are 20 cm and 100 cm . answer a
Answer: a
Python program:
a = volume_cube / (
b = a / 0
c = math.sqrt(b)
Problem: a train is moving at a speed of 132 km / hour . if the length of the train is 110 meters , how long will it take to cross a railway platform 165 meters long .
Options: a ) 7 second , b ) 7.5 second , c ) 8 second , d ) 8.5 second , e ) none of these
Rationale: explanation : as we need to calculate answer in seconds , so first convert speed into meter / sec . we know 1 km / hr = 1 * ( 5 / 18 ) m / sec so , speed = 132 * ( 5 / 18 ) = 110 / 3 m / sec distance need to be covered in passing the platform = length of train + length of platform = 110 + 165 = 275 meters time = distance / speed = > time = 275 ∗ 3 / 110 = 15 / 2 = 7.5 seconds option b
Answer: b
Python program:
a = 110 + 165 
b = 132 * const_0_2778
c = a / b
Problem: 10 machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 8
Rationale: "another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 10 = 15 so we need 15 - 10 = 5 more machines . answer : d"
Answer: d
Python program:
a = 4 + 1 
b = 10 * a
c = b / 12
d = 4 + 1 
e = c - d
Problem: given a bag with 2 red balls and 3 yellow balls , you randomly select one of them , in order . if the second ball you take is yellow , what is the probability that the first one was also yellow ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 3 / 4 , d ) 1 / 3 , e ) 3 / 5
Rationale: this is a conditional probability question . basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow . so , possible options for this other ball would be : w , w , b , b ( as one yellow is already picked ) so the probability for that ball to be yellow too is 2 / 4 = 1 / 2 . option a
Answer: a
Python program:
a = 2 + 3 
b = a - 1
c = 2 / b
Problem: how many 4 - digit positive integers are multiple of each integer from 1 to 10
Options: a ) 1520 , b ) 2520 , c ) 3520 , d ) 5140 , e ) 7660
Rationale: "least no which could be divisible by integers [ 1,2 , 3,4 , 5,6 , 7,8 , 9,10 ] is the lcm of the said integers . lcm [ 1,2 , 3,4 , 5,6 , 7,8 , 9,10 ] = 2520 no the nos which are divisible by 2520 will be divisible by [ 1 , 2,3 , 4,5 , 6,7 , 8,9 ] there are 3 values possible between 1000 to 9999 they are 2520 x 1 = 2520 2520 x 2 = 5040 2520 x 3 = 7560 answer : b"
Answer: b
Python program:
a = 4 + 1 
b = 4 + 1 
c = a * b
d = 4 + 4 
e = 1 * 1
f = d * e
g = c * f
Problem: a water tank is one - fifth full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only one - fifth full , the time is ( 1 / 5 ) * 15 = 3 minutes the answer is a .
Answer: a
Python program:
a = 1 + 4 
b = 1 / a
c = 1 / 6
d = 1 / 10
e = c - d
f = 1 / e
g = b * f
Problem: jar y has 10 % more marbles than jar x . what percent of marbles from jar y need to be moved into x so that both jars have equal marbles
Options: a ) 4.54 % , b ) 9.09 % , c ) 10 % , d ) 11 % , e ) 12.25 %
Rationale: no ; the choices will be approximated only when gmat question explicitly mentions that ; here the answer is very close 4.54 , not 5 . jar y has 10 % more marbles than x y = 1.1 x if k marbles are taken out of y . the remaining marbles in jar y = 1.1 x - k if k marbles are added to x . the new marbles ' count in jar x = x + k and we know they are equal ; x + k = 1.1 x - k 2 k = 0.1 x k = 0.05 x the marbles taken out of y = 0.05 x question is : 0.05 x is what percent of marbles that was originally there in y i . e . 1.1 x 0.05 x 1.1 x ∗ 1000.05 x 1.1 x ∗ 100 0.05 x 1.1 x ∗ 1000.05 x 1.1 x ∗ 100 5011 = 4.54 ¯ ≈ 4.545011 = 4.54 ¯ ≈ 4.54 answer : a
Answer: a
Python program:
a = 100 + 10 
b = 100 + 10 
c = 100 + b 
d = c / 2
e = a - d
f = 100 + 10 
g = e / f
h = g * 100
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Python program:
a = 3 * 5
b = 3 + 5 
c = 5 + 2 
d = b * c
e = d / 2
f = a / e
Problem: a woman complete a journey in 10 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 544 km .
Rationale: "d 224 km . 0.5 x / 21 + 0.5 x / 24 = 10 - - > x / 21 + x / 24 = 20 - - > 15 x = 168 x 20 - - > x = ( 168 x 20 ) / 15 = 224 km ."
Answer: d
Python program:
a = 10 * 24
b = 24 + 21 
c = a / b
d = c * 21
e = d * 2
Problem: the speed of a train is 80 kmph . what is the distance covered by it in 6 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 18 kmph , d ) 8 kmph , e ) 12 kmph
Rationale: "80 * 6 / 60 = 8 kmph answer : d"
Answer: d
Python program:
a = 6 / const_60
b = a * 80
Problem: if 50 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 560 , b ) 540 , c ) 520 , d ) 440 , e ) 500
Rationale: we know 50 % people study biology , therefore the no of people not studying = 100 - 50 = 50 % > therefore the people not studying biology out of a total 880 people are = 50 % of 880 > ( 50 / 100 ) * 880 = 440 people d
Answer: d
Python program:
a = 880 / 100
b = 100 - 50
c = a * b
Problem: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 70 respectively . the sum is :
Options: a ) 1360 , b ) 1450 , c ) 1600 , d ) 1800 , e ) none
Rationale: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 70 / ( 85 - 70 ) = rs . 396.7 . answer e"
Answer: e
Python program:
a = 85 * 70
b = 85 - 70
c = a / b