euclaise/mathqa_programs huggingface dataset:
Problem: john had a stock of 700 books in his bookshop . he sold 50 on monday , 82 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 26.5 % , b ) 50 % , c ) 46.5 % , d ) 56.5 % , e ) 60 %
Rationale: "let n be the total number of books sold . hence n = 50 + 82 + 64 + 78 + 135 = 280 let m be the books not sold m = 700 - n = 700 - 280 = 420 percentage books not sold / total number of books = 420 / 700 = 0.60 = 60 % correct answer e"
Answer: e
Python program:
a = 50 + 82 
b = 60 + 48 
c = a + b 
d = c + 40 
e = 700 - d
f = e / 700
g = f * 100
Problem: if it takes a tub 4 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 36 seconds , d ) 2 minutes , 14 seconds , e ) 4 minutes , 12 seconds
Rationale: "if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 4 minutes to drain 5 / 7 th of tub it takes 4 * ( 7 / 5 ) minutes to drain the entire tub and 4 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 8 / 5 minutes or 1 3 / 5 minutes or 1 minute 36 seconds so answer is c"
Answer: c
Python program:
a = 5 / 7
b = 1 - a
c = 5 / 7
d = b + c
Problem: a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this ordert ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75
Rationale: i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . t = 12.5 * 6 = 75 . e
Answer: e
Python program:
a = 1 / 3
b = 1000 ** a
c = b ** 2
d = c * 4
e = 1 / 3
f = 1000 ** e
g = f ** 2
h = d + g 
i = 1 / 3
j = 1000 ** i
k = j ** 2
l = h + k 
m = 4 * 2
n = l / m
Problem: when a merchant imported a certain item , he paid a 9 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 85.50 , what was the total value of the item ?
Options: a ) $ 1,150 , b ) $ 1,350 , c ) $ 1,550 , d ) $ 1,750 , e ) $ 1,950
Rationale: "let x be the value in excess of $ 1,000 . 0.09 x = 85.5 x = $ 950 the total value was $ 950 + $ 1,000 = $ 1,950 . the answer is e ."
Answer: e
Python program:
a = 9 / 100
b = 85 / 50
c = b + 1 
d = c / 1
e = math.floor(d)
Problem: how many different 3 - digit multiples of 5 can be composed of digits 2 , 7 , 4 , and 5 if none of the digits is repeated ?
Options: a ) 3 , b ) 6 , c ) 10 , d ) 12 , e ) 18
Rationale: = 3 c 2 x 2 = 6 can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 3 possible choices . x can be any of the 2 possible choices . 2 + 3 + 1 = 6 b
Answer: b
Python program:
a = 7 * 4
b = a - 4
c = b / 4
Problem: in a class of 38 children , 19 play tennis , 21 play squash and 10 play neither sport . ( 1 ) how many children play both sports ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 19
Rationale: 28 play some sport 19 + 21 - both = 28 both = 12 answer is b
Answer: b
Python program:
a = 19 + 21 
b = 38 - 10
c = a - b
Problem: a train 440 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 72 sec , b ) 24 sec , c ) 44 sec , d ) 62 sec , e ) 21 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 440 * 3 / 55 ] sec = 8 sec answer : b"
Answer: b
Python program:
a = 440 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: firm a ' s revenues are described by the equation ra = 17.12 x and its costs by ca = 12.87 x + 2400 . firm b ' s revenues are described by the equation rb = 13.27 x and its costs by cb = 8.77 x + 1500 . ( x denotes the quantity of sales ) . if a ' s volume of sales increases from 1000 to 3000 over the same period that b ' s volume increases from 2000 to 3000 , the percent increase in profits for the firm with the biggest dollar increase in profits is
Options: a ) 20 % , b ) 30 % , c ) 60 % , d ) 50 % , e ) 33 %
Rationale: ok , i do not know whether it is exactly what you want to hear but i did it that way : first look at difference between revenue and variable cost = > take the bigger one ( b ) which gives you : 4.5 x - 1500 just plug in 2000 and 3000 . you get 7500 and 12000 ( difference 4500 ) . 4500 > 0.5 * 7500 so 30 % b
Answer: b
Python program:
a = 13 - 27
b = a * 1000
c = 13 - 27
d = c * 2000
e = d - 1500
f = b / e
g = f * 100
h = g / 2
Problem: how many seconds will a 500 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 33 , b ) 87 , c ) 30 , d ) 88 , e ) 77
Rationale: "explanation : distance = 500 m speed of the train relative to man = ( 63 - 3 ) km / hr = 60 km / hr = m / s = m / s time taken to pass the man = distance / speed = sec = 30 sec answer : c ) 30"
Answer: c
Python program:
a = 63 - 3
b = a * const_0_2778
c = 500 / b
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 9 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 18 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 9 work in 1 day b alone can do ( 1 / 6 - 1 / 9 ) = 1 / 18 work in 1 day = > complete work can be done in 18 days by b answer : option c"
Answer: c
Python program:
a = 1/(6)
b = 1/(9)
c = a - b
d = 1/(c)
Problem: √ 6 percent of 6 √ 6 =
Options: a ) 0.3 , b ) 0.25 , c ) 0.1 , d ) 0.95 , e ) 0.35
Rationale: "the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : √ 2 ≈ 1.4 √ 3 ≈ 1.7 √ 5 ≈ 2.2 √ 6 ≈ 2.4 so , √ 6 percent of 6 √ 6 ≈ 2.4 percent of ( 6 ) ( 2.4 ) ≈ ( 2.4 / 100 ) ( 14.4 ) ≈ 34.56 / 100 ≈ 0.34 check the answer choices to see that e is the only answer that ' s close . answer : e"
Answer: e
Python program:
a = math.sqrt(6)
b = math.sqrt(6)
c = a * b
d = c * 6
e = d / 100
Problem: 20 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 24 , b ) 18 , c ) 17 , d ) 16 , e ) 10
Rationale: "binders books days 20 1400 21 x 1600 20 x / 20 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 24 answer : a"
Answer: a
Python program:
a = 1600 / 20
b = 20 * 21
c = 1400 / b
d = a / c
Problem: a man can do a job in 20 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 7.1 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 20 + 1 / 20 + 1 / 25 ) = 7 / 50 so , all three together will complete the work in 300 / 47 = 7.1 days . answer : c"
Answer: c
Python program:
a = 1 / 25
b = 1 / 20
c = 1 / 20
d = b + c 
e = a + d 
f = 1 / e
Problem: what will be the vulgar fraction of 0.4
Options: a ) 3 / 5 , b ) 2 / 5 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.4 = 40 / 100 = 2 / 5 option b"
Answer: b
Python program:
a = 0 / 4
b = circle_area / (
Problem: in a school 10 % of the boys are same in number as 1 / 4 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 2 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 4 g 10 b / 100 = g / 4 b = 5 g / 2 b / g = 5 / 2 b : g = 5 : 2 answer is a"
Answer: a
Python program:
a = 10 / 100
b = 1 / 4
c = a / b
Problem: the volume of a cistern is 840 cubic meters and water is flowing into the cistern . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate , in cubic meters per minutes , at which the water is flowing into the cistern ?
Options: a ) 0.125
b ) 0.25
c ) 0.5
d ) 0.75
e ) not enough information to determine the rate
Rationale: there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate . the correct answer is e .
Answer: e
Python program:
a = 840 * 1000
b = 0 * 5
c = a / b
d = c / 1000
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 4 litres from vessel p is mixed with 6 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 31 : 1 , b ) 31 : 4 , c ) 31 : 8 , d ) 31 : 9 , e ) 31 : 2
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 6 = 21 / 4 litres quantity of alcohol in the mixture formed = 5 / 2 + 21 / 4 = 31 / 4 = 7.75 litres as 10 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 7.75 : 2.25 = 31 : 9 . answer : d"
Answer: d
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 4 - g
i = 87 * 5
j = i / 100
k = 6 - j
l = h + k 
m = e / l
Problem: a number whose fifth part increased by 2 is equal to its fourth part diminished by 2 is ?
Options: a ) 160 , b ) 80 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 2 = ( n / 4 ) - 2 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 4 â ‡ ’ ( 5 n - 4 n ) / 20 = 4 â ˆ ´ n = 80 option : b"
Answer: b
Python program:
a = 2 + 2 
b = 1 / 2
c = 1 + 2 
d = 1 / c
e = b - d
f = a / e
Problem: if an object travels at four feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 14400 , e ) 18000
Rationale: "speed = 4 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 4 = 1800 x 10 = 14400 answer d"
Answer: d
Python program:
a = 3 * const_60
b = a * const_60
Problem: a 230 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 250 m , d ) 260 m , e ) 270 m
Rationale: "speed = ( 120 + 80 ) km / h ( because direction is opposite hence relative velocity is added ) = 500 / 9 m / s time = 9 sec let the lenght of second train is x total distance covered = 230 + x therefore , d = speed * time thus 230 + x = 500 / 9 * 9 x = 500 - 230 = 270 m answer : e"
Answer: e
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 230
Problem: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 90 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 90 , c ) 100 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 180 - - 2 subtracting 1 from 2 we have c - a = 90 ; answer : b"
Answer: b
Python program:
a = 90 * 2
b = 45 * 2
c = a - b
Problem: ? x 240 = 173 x 240
Options: a ) 173 , b ) 685 , c ) 865 , d ) 495 , e ) 534
Rationale: "let y x 240 = 173 x 240 then y = ( 173 x 240 ) / 240 = 173 answer : a"
Answer: a
Python program:
a = 173 * 240
b = a / 240
Problem: at a summer camp with 900 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 900 campers will the 8 - to 12 - year - olds represent ?
Options: a ) 64 % , b ) 66 2 / 3 % , c ) 62 % , d ) 60 % , e ) 56 %
Rationale: "total - 900 participants campers are aged 8 to 12 = ( 1 / 2 ) * 900 = 450 next year , campers are aged 8 to 12 = ( 4 / 3 ) * 450 = 600 percentage = ( 600 / 900 ) * 100 = 66 2 / 3 % answer : option b"
Answer: b
Python program:
a = 8 * 100
b = 1000 + a 
c = b / 2
d = 1 / 3
e = d + 1 
f = c * e
g = 8 * 100
h = 1000 + g 
i = f / h
j = i * 100
k = j * 3
l = 8 * 100
m = 1000 + l 
n = m / 2
o = 1 / 3
p = o + 1 
q = n * p
r = 8 * 100
s = 1000 + r 
t = q / s
u = t * 100
v = u * 3
w = v / 10
x = k + w
Problem: a rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles , all of the same size . the minimum number of such tiles is :
Options: a ) 425
b ) 430
c ) 440
d ) 450
e ) 460
Rationale: l = 378 cm and b = 525 cm maximum length of a square tile = hcf of ( 378,525 ) = 21 cm number of tiles = ( 378 × 525 ) / ( 21 × 21 ) = ( 18 × 25 ) = 450 answer is d .
Answer: d
Python program:
a = 3 * 78
b = 5 * 25
c = a * b
d = 3 + 4 
e = d * 3
f = e ** 2
g = c / f
Problem: 12 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages
Options: a ) a ) 35 , b ) b ) 34 , c ) c ) 42 , d ) d ) 25 , e ) e ) 26
Rationale: explanation : let the present age of p and q be 3 x and 4 x respectively . twelve years ago , p was half of q in age = > 2 ( 3 x – 12 ) = ( 4 x – 12 ) = > 6 x – 24 = 4 x – 12 = > 2 x = 12 = > x = 6 7 x = 7 * 6 = 42 answer : option c
Answer: c
Python program:
a = 3 + 4 
b = 12 * 2
c = 12 * 2
d = c - 12
e = b - d
f = 3 * 2
g = f - 4
h = e / g
i = a * h
Problem: a can do a piece of work in 6 days and b can do it in 6 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 1 / 2 , c ) 3 / 4 , d ) 9 / 11 , e ) 10 / 11
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 6 ( a + b ) ’ s one day work = 1 / 6 + 1 / 6 = 2 / 3 = = > time = 3 / 2 = 1 1 / 2 days answer : option b"
Answer: b
Python program:
a = 1 / 6
b = 1 / 6
c = a + b 
d = 1 / c
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 20 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 20 = 6 k + 4 k k = 2 total red ' s in bag a will be 2 k = 4 c"
Answer: c
Python program:
a = 3 * 2
b = a + 4 
c = 20 / b
Problem: a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number n is
Options: a ) 74 , b ) n = 75 , c ) n = 175 , d ) n = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Python program:
a = 34 * 2
b = 34 * 2
c = 8 * 5
d = b - c
e = 5 - 1
f = d / e
g = a + f
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 190 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 4.2
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 190 / 45 = $ 4.2 answer : e ."
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = b * 190
d = 190 - c
e = 1 / 2
f = 5 - e
g = d / f
Problem: a train is travelling at 48 kmph . it crosses another train having half of its length , travelling in opposite direction at 42 kmph , in 12 seconds . it also passes a railway platform in 45 seconds . what is the length of the platform ?
Options: a ) 400 m , b ) 500 m , c ) 600 m , d ) 550 m , e ) 700 m
Rationale: speed of i train = 48 kmph length of i train = 2 x m speed of sec train = 42 kmph length of seconf train = x m dist = ( 2 x + x ) = 3 x m time = 12 sec = 90 * 5 / 18 = 25 m / s x = 100 length of first train = 2 x = 200 m time taken = 45 sec speed of first train = 48 kmph = 48 * 5 / 18 = 40 / 3 m / s length of the platform = y metre 200 + y = 45 * 45 / 3 = 600 y = 400 answer a
Answer: a
Python program:
a = 45 * 48
b = a * const_0_2778
c = 48 + 42 
d = c * const_0_2778
e = d * 12
f = 3 / 2
g = e / f
h = b - g
Problem: if 3 / p = 6 and 3 / q = 15 then p – q = ?
Options: a ) 3 / 19 , b ) 3 / 11 , c ) 3 / 17 , d ) 3 / 10 , e ) 3 / 13
Rationale: explanation : 3 p 3 p = 6 , p = 3636 = 1212 and 3 q 3 q = 15 , q = 315315 = 1515 then p – q = 1 / 2 – 1 / 5 = 3 / 10 answer : d
Answer: d
Python program:
a = 3 / 6
b = 3 / 15
c = a - b
Problem: light glows for every 13 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 381 times , c ) 382 times , d ) 392 times , e ) 482 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 13 ) = 382 times . answer : c"
Answer: c
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 13
Problem: in an election , candidate a got 80 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 380800 , c ) 356500 , d ) 356800 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 80 % therefore , the number of valid votes polled in favour of candidate a = 80 % of 476000 = 80 / 100 × 476000 = 38080000 / 100 = 380800 b )"
Answer: b
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 80 / 100
e = c * d
Problem: if n = 2 ^ 0.1 and n ^ b = 16 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 40 , d ) 5 / 3 , e ) 80 / 3
Rationale: 10 / 100 = 1 / 10 n = 2 ^ 1 / 10 n ^ b = 2 ^ 4 ( 2 ^ 1 / 10 ) ^ b = 2 ^ 4 b = 40 answer : c
Answer: c
Python program:
a = math.log(16)
b = 2 ** 0
c = math.log(b)
d = a / c
Problem: the maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 37 , c ) 99 , d ) 277 , e ) 19
Rationale: explanation : required number of students = h . c . f of 1001 and 910 = 9 answer : a ) 91
Answer: a
Python program:
a = math.gcd(1001, 910)
Problem: a will states that the estate would be divided among 6 sons with the remainder donated to charity . one stipulation in the will is that no one among the sons can receive an amount within 12 % of another ' s amount . if one of the beneficiaries received $ 30000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 6 sons ?
Options: a ) $ 4096 , b ) $ 14043 , c ) $ 7892 , d ) $ 17736 , e ) $ 15336
Rationale: 1 st - 30000 . 2 nd - 0.88 * 30000 = 26400 3 rd - 0.88 * 26400 = 23232 4 th - 0.88 * 23232 = 20 , 444.16 5 th - 0.88 * 20 , 444.16 = ~ 17 , 990.86 6 th - 0.88 * 17 , 990.86 = ~ 15 , 831.96 range = 30000 - 15831 = 14168 answer : b .
Answer: b
Python program:
a = 12 / 100
b = 30000 * a
c = b * 4
Problem: calculate 469111 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4690640889
Rationale: answer 469111 x 9999 = 469111 x ( 10000 - 1 ) = 4691110000 - 469111 = 4690640889 . option : e
Answer: e
Python program:
a = 469111 * 9999
Problem: simple interest on a certain sum at a certain annual rate of interest is 1 / 25 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is :
Options: a ) 5 % , b ) 2 % , c ) 6 % , d ) 8 % , e ) 3 %
Rationale: "explanation : let sum = x . then , s . i . = x / 25 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 25 ? r ^ 2 = 100 / 25 = 4 r = 2 hence , rate of interest = 2 % . answer : b"
Answer: b
Python program:
a = 1 / 25
b = a * 100
c = math.sqrt(b)
d = math.floor(c)
e = d * 10
f = e + 1 
g = f / 3
Problem: two numbers are in the ratio of 1 : 2 . if 9 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 9 ) / ( y + 9 ) = 3 / 5 = > x = 18 and y = 36 answer : e"
Answer: e
Python program:
a = 1 * 9
Problem: bookman purchased 60 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 660 , how many paperback copies were sold ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "the bookman had 10 hardback ad 60 - 10 = 50 paperback copies ; 14 copies were sold , hence 60 - 14 = 46 copies were left . let # of paperback copies left be p then 10 p + 20 ( 46 - p ) = 660 - - > 10 p = 260 - - > p = 26 # of paperback copies sold is 50 - 26 = 24 answer : b"
Answer: b
Python program:
a = 60 - 10
b = a * 10
c = 10 * 20
d = b + c 
e = d - 660
f = math.gcd(60, 10)
g = f * 20
h = e - g
i = h / 10
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 760 ; each of his remaining paychecks was $ 30 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 783 , e ) $ 775
Rationale: "= ( 760 * 6 + 790 * 20 ) / 26 = 783 answer is d . posted from my mobile device"
Answer: d
Python program:
a = 760 + 30 
b = a * 30
c = 6 * 760
d = b + c 
e = d / 26
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 30 km apart , if they walk in the same direction ?
Options: a ) 15 hours , b ) 6 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 30 = 15 hours answer is a"
Answer: a
Python program:
a = 12 - 10
b = a / 30
Problem: if a ' s salary is 20 % less than b ' s salary , by how much percentage is b ' s salary more than a ' s ?
Options: a ) 25 % , b ) 15 % , c ) 30 % , d ) 32 % , e ) 40 %
Rationale: "required percentage = [ 100 * 20 / ( 100 - 20 ) ] % = 25 % answer is a"
Answer: a
Python program:
a = 100 - 20
b = 100 - a
c = 100 - 20
d = c / 100
e = b / d
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 5 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 6 , b ) 1 , c ) 5 , d ) 4 , e ) 7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 5 ? - - - 1 = > rs . 4 100 - - - 80 ? - - - 4 = > rs . 5 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a * 100
c = b / 5
d = 20 / 100
e = d * 100
f = c / e
g = f * 100
Problem: find 103 × × 10
Options: a ) 106 / 19 , b ) 108 / 12 , c ) 108 / 19 , d ) 108 / 15 , e ) 108 / 11
Rationale: "by taking 100 as a base we can easily get the answer for the above question within seconds . 103 is 3 more than 100 and 105 is 5 more than 100 so we will write add the excess of the second number to first number or excess of first number to second number as show below to get left most digits and multiply the excesses to get the right most two digits . note : always remember if you get a single digit number put zero in the left two make it a two digit number to get the right most two digits . answer : d"
Answer: d
Python program:
a = 103 / 10