euclaise/mathqa_programs huggingface dataset:
Problem: in a recent election , geoff received 0.5 percent of the 5,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 2,571 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 54 , c ) 52 , d ) 60 , e ) 63
Rationale: "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 25 votes he needs 2571 more votes so : 25 + 2571 = 2596 now what ' s the problem wants ? ? a x % . . . . . . . . 2596 is what % of total votes 5000 . . . . . . . . translating : 2596 = x / 100 * 5000 - - - x = 52 % . . . . . . . . . . c"
Answer: c
Python program:
a = 100 / 2
b = a + 0
Problem: a bus trip of 360 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "the time is the distance / speed . the time difference is 1 hour . 360 / v - 360 / ( v + 5 ) = 1 360 ( v + 5 ) - 360 v = ( v ) ( v + 5 ) 1800 = ( v ) ( v + 5 ) 40 * 45 = ( v ) ( v + 5 ) v = 40 mph the answer is b ."
Answer: b
Python program:
a = 360 * 5
b = a * 4
c = 5 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 5
g = f / 2
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 41 ° is ?
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 51.5 m 2 , d ) 53 m 2 , e ) 59 m 2
Rationale: "41 / 360 * 22 / 7 * 12 * 12 = 51.5 m 2 answer : c"
Answer: c
Python program:
a = 12 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 41 / g
i = f * h
Problem: 10 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 60
Rationale: "i came up with ( a ) 25 think of 100 people total : from the first fact , 10 of these are women with fair hair . from the second fact , these 10 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 10 equals the number of fair haired men , which is 15 men with fair hair . add this 15 to the 10 women and get 25 fair haired men and women out of 100 total men and women . 25 % a"
Answer: a
Python program:
a = 10 / 40
b = a * 100
Problem: a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) rs . 3919
b ) rs . 3910
c ) rs . 3997
d ) rs . 3900
e ) rs . 3902
Rationale: area = ( l + b – d ) d ( 80 + 60 – 10 ) 10 = > 1300 m 2 1300 * 3 = rs . 3900 answer : d
Answer: d
Python program:
a = 80 + 60 
b = a - 10
c = b * 10
d = c * 3
Problem: it takes 50 identical printing machines 8 hours to print 500,000 posters . how long would it take 40 of these machines to print the same total ?
Options: a ) 10 hr , b ) 12 hr , c ) 12 hr 24 min , d ) 12 hr , 40 min , e ) 13 hr , 20 min
Rationale: "50 machines finish the job in 8 hours . we do not have to take care of the 500 ' 000 posters , it does not matter . 40 machines means , 20 % less of capacity and therefore 20 % longer to work for a certain job . 8 * 1.2 = 9 hr , 36 min answer a . . hi reto , since you are looking time for 40 machines it is 25 % less so will take 25 % more . . ans 8 * 1.25 = 10 hrs . . a )"
Answer: a
Python program:
a = 50 / 8
b = 500 / 0
c = a + b
Problem: a man bought 40 shares of rs . 60 at 5 discount , the rate of dividend being 1212 % the rate of interest obtained is
Options: a ) 13.64 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 %
Rationale: explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 5 = rs . 55 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 55 ) interest obtained = 40 × 7.5 × 100 / 40 × 55 = 13.64 % answer : option a
Answer: a
Python program:
a = 40 * 60
b = 1212 / 100
c = a * b
d = 60 - 5
e = 40 * d
f = c / e
Problem: the average of numbers 0.54204 , 0.54203 , 0.54202 and 0.54201 is ?
Options: a ) 0.54202 , b ) 0.54204 , c ) 0.542022 , d ) 0.542025 , e ) none
Rationale: "answer average = ( 0.54204 + 0.54203 + 0.54202 + 0.54201 ) / 4 = 2.1681 / 4 = 0.542025 correct option : d"
Answer: d
Python program:
a = 0 * 54204
b = 0 * 54204
c = a + b 
d = c / 0
Problem: 0.007 x 0.45 = ?
Options: a ) 0.00315 , b ) 0.0315 , c ) 0.315 , d ) 0.0351 , e ) none of them
Rationale: "7 x 45 = 315 sum of decimal places = 5 therefore , 0.007 x 0.45 = 0.00315 answer is a ."
Answer: a
Python program:
a = 0 / 7
b = a * 100
Problem: one fourth of one third of two fifth of a number is 15 . what will be 40 % of that number
Options: a ) 140 , b ) 150 , c ) 180 , d ) 200 , e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 15 then x = 15 * 30 = 450 40 % of 450 = 180 answer : option c"
Answer: c
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3 
e = 2 / d
f = c * e
g = 15 / f
h = g * 40
i = h / 100
Problem: a certain candy manufacturer reduced the weight of candy bar m by 25 percent buy left the price unchanged . what was the resulting percent increase in the price per ounce of candy bar m ?
Options: a ) 20 , b ) 30 , c ) 34 , d ) 35 , e ) 33.33
Rationale: "assume 1 oz candy cost $ 1 before . now price remain same $ 1 but weight of candy reduces to 0.75 oz new price of candy = 1 / 0.75 = 1.3333 price increase 33.33 % e"
Answer: e
Python program:
a = 25 / 100
b = 1 - a
c = 1 / b
d = c * 100
e = d - 100
Problem: apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 11.67 and for 36 kgs of apples is 12.48 then the cost of first 10 kgs of apples is
Options: a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 3.62 , e ) 3.61
Rationale: "ans : by framing equations we get 30 l + 3 q = 11.67 30 l + 6 q = 12.48 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 0.362 cost of 10 kgs of apples = 0.362 x 10 = 3.62 answer : d"
Answer: d
Python program:
a = 33 - 30
b = 12 - 48
c = 36 - 33
d = b / c
e = a * d
f = 11 - 67
g = f / 30
h = g * 10
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 76800 ?
Options: a ) 81000 , b ) 97200 , c ) 27772 , d ) 29889 , e ) 22312
Rationale: 76800 * 9 / 8 * 9 / 8 = 97200 . answer : b
Answer: b
Python program:
a = 1 / 8
b = a * 76800
c = 76800 + b 
d = 1 / 8
e = 1 / 8
f = e * 76800
g = 76800 + f 
h = d * g
i = c + h
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 48 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2400 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 48 = 30 x = 2400 km answer is d"
Answer: d
Python program:
a = 30 * 48
Problem: kamal obtained 96 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 79 , e ) none
Rationale: "sol . average = 96 + 65 + 82 + 67 + 85 / 5 ) = ( 395 / 5 ) = 79 . answer d"
Answer: d
Python program:
a = 96 + 65 
b = a + 82 
c = b + 67 
d = c + 85 
e = 1 + 4 
f = d / e
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ?
Options: a ) 17 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e"
Answer: e
Python program:
a = 32 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: evaluate : 6702.5 + 670.25 + 67.025 + 6.7025 + 0.67025
Options: a ) 7447.14775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6702.5 670.25 67.025 6.7025 + 0.67025 - - - - - - - - - - - - - - - 7447.14775 answer is a ."
Answer: a
Python program:
a = 670 * 25
b = a * 6
c = 6702 - 5
Problem: a cylindrical can has a radius of 4 centimeters and a height of 24 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 4 * 24 = 192 pi answer is d ."
Answer: d
Python program:
a = 4 * 24
b = 2 * math.pi
c = a * b
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 12 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 20 min .
Rationale: the ratio is 2 : 3 = gym : ride , so ( 12 ) ( 3 / 2 ) = 18 minutes at the gym , and 18 + 12 = 30 minutes exercise , so ( 2 / 3 ) ( 30 ) = 20 minutes yoga . answer : e
Answer: e
Python program:
a = 2 + 3 
b = 3 / a
c = 12 * b
d = 2 + 3 
e = 3 / d
f = 2 + 3 
g = 3 / f
h = e * g
i = c / h
Problem: the probability that a man will be alive for 10 more yrs is 3 / 4 & the probability that his wife will alive for 10 more yrs is 3 / 7 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 1 / 7 , d ) 3 / 4 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 7 ans . ( c )"
Answer: c
Python program:
a = 3 / 4
b = 3 - a
c = 3 / 7
d = 3 - c
e = b * d
Problem: a jar of 264 marbles is divided equally among a group of marble - players . if 2 people join the group , each one would receive 1 marble less . how many people are there in the group today ?
Options: a ) 20 , b ) 21 . , c ) 22 , d ) 23 , e ) 24
Rationale: "only 22 and 24 divide 264 perfectly , assume initially , there are 22 people , , each will get 12 marbles two people join , then 24 will get 11 marble each . hence answer e = 24"
Answer: e
Python program:
a = 264 * 2
b = a * 4
c = 2 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 2
g = f / 2
Problem: two numbers are in the ratio 3 : 4 . if the sum of numbers is 63 , find the numbers .
Options: a ) 27 and 36 . , b ) 25 and 30 . , c ) 23 and 44 . , d ) 63 and 12 . , e ) 12 and 36 .
Rationale: "sum of the terms of the ratio = 3 + 4 = 7 sum of numbers = 63 therefore , first number = 3 / 7 × 63 = 27 second number = 4 / 7 × 63 = 36 therefore , the two numbers are 27 and 36 . answer is a"
Answer: a
Python program:
a = 3 * 63
b = a * 100
c = 4 * 63
d = b + c
Problem: a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food , and 1 / 8 of his salary on conveyance . if he has rs 1400 left with him , find his expenditure on food and conveyance
Options: a ) 3200 , b ) 3400 , c ) 3600 , d ) 3800 , e ) 4000
Rationale: "if his salary is x , then x - x * ( 2 / 5 + 3 / 10 + 1 / 8 ) = 1400 x ( 1 - 33 / 40 ) = 1400 x = 1400 * 40 / 7 = rs 8000 expenditure on food and conveyance = 8000 * 3 / 10 + 8000 * 1 / 8 = 2400 + 1000 = 3400 answer : b"
Answer: b
Python program:
a = 2 / 5
b = 3 / 10
c = a + b 
d = 1 / 8
e = c + d 
f = 1 - e
g = 1400 / f
h = 3 / 10
i = g * h
j = 2 / 5
k = 3 / 10
l = j + k 
m = 1 / 8
n = l + m 
o = 1 - n
p = 1400 / o
q = 1 / 8
r = p * q
s = i + r
Problem: a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 54 , b ) 51 , c ) 59 , d ) 55 , e ) 52
Rationale: "for 40 hrs = 40 * 14 = 560 excess = 976 - 560 = 416 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 416 / 24.5 = 18.82 = 19 approx . total hrs = 40 + 19 = 59 answer c 59"
Answer: c
Python program:
a = 14 * 40
b = 976 - a
c = 100 + 75 
d = 14 * c
e = d / 100
f = b / e
g = 40 + f
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 3 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 360 , b ) 487 , c ) 481 , d ) 729 , e ) 268
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 3 = 360 answer : a"
Answer: a
Python program:
a = 24 * 20
Problem: the ratio of the incomes of a and b is 2 : 3 and the ratio of their expenditure is 1 : 2 . if at the end of the year , each saves $ 500 then the income of a is ?
Options: a ) $ 1000 , b ) $ 1500 , c ) $ 1200 , d ) $ 900 , e ) $ 1100
Rationale: "let the income of a and b be $ 2 x and $ 3 x let their expenditures be $ y and $ 2 y 2 x - y = 500 - - - - - - - 1 ) 3 x - 2 y = 500 - - - - - - - 2 ) from 1 ) and 2 ) x = 500 a ' s income = 2 x = 2 * 500 = $ 1000 answer is a"
Answer: a
Python program:
a = 2 / 2
b = a * 500
Problem: the compound and the simple interests on a certain sum at the same rate of interest for two years are rs . 11730 and rs . 10200 respectively . find the sum
Options: a ) rs . 17037 , b ) rs . 17000 , c ) rs . 17276 , d ) rs . 170287 , e ) rs . 171881
Rationale: explanation : the simple interest for the first year is 10200 / 2 is rs . 5100 and compound interest for first year also is rs . 5100 . the compound interest for second year on rs . 5100 for one year so rate of the interest = ( 100 * 1530 ) / ( 5100 * 1 ) = 30 % p . a . so p = ( 100 * 10200 ) / ( 30 * 2 ) = rs . 17000 answer : b
Answer: b
Python program:
a = 100 * 10200
b = 11730 - 10200
c = b * 100
d = 10200 / 2
e = c / d
f = e * 2
g = a / f
Problem: the sum of two numbers is 8 and the sum of their squares is 120 . find the product of the two numbers .
Options: a ) 25 , b ) 24 , c ) 23 , d ) 21 , e ) 28
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 8 a ^ 2 + b ^ 2 = 120 so , 8 ^ 2 = 120 + 2 ab 2 ab = 120 - 64 2 ab = 56 ab = 28 ans e
Answer: e
Python program:
a = 8 ** 2
b = 120 - a
c = b / 2
Problem: if the cost price of 121 chocolates is equal to the selling price of 77 chocolates , the gain percent is :
Options: a ) 56.14 % , b ) 57.44 % , c ) 57.14 % , d ) 56.34 % , e ) 57.87 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 77 chocolates = rs . 77 ; s . p . of 77 chocolates = rs . 121 . . ' . gain % = 44 * 100 / 77 = 57.14 % answer : c"
Answer: c
Python program:
a = 121 - 77
b = 77 / a
c = 100 / b
Problem: a library has an average of 500 visitors on sundays and 140 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 550
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 500 * 5 + 140 * 25 ) / 30 = 6000 / 30 = 200 answer : b ) 200"
Answer: b
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 500
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 140
l = e + k 
m = l / 30
Problem: a man can row his boat with the stream at 6 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: "ds = 6 us = 4 s = ? s = ( 6 - 4 ) / 2 = 1 kmph answer : a"
Answer: a
Python program:
a = 6 - 4
b = a / 2
Problem: a man buys 100 lts of liquid which contains 25 % of the liquid and the rest is water . he then mixes it with 90 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 81 , b ) 75 , c ) 72.63 , d ) 73 , e ) 76
Rationale: 25 % in 100 lts is 25 . so water = 100 - 25 = 75 lts . 30 % of 90 lts = 27 . so water in 2 nd mixture = 90 - 27 = 63 lts . now total quantity = 100 + 90 = 190 lts . total water in it will be 75 + 63 = 138 lts . % of water = ( 100 * 138 ) / 190 = 72.63 answer : c
Answer: c
Python program:
a = 100 - 25
b = 100 * a
c = 100 - 30
d = 90 * c
e = b + d 
f = 100 + 90 
g = e / f
Problem: a train running at the speed of 60 km / hr crosses a pole in 3 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 170 meter , c ) 156 meter , d ) 168 meter , e ) 50 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 3 = 50 meter answer : e"
Answer: e
Python program:
a = 60 * 1000
b = a / 3600
c = b * 3
Problem: the sale price sarees listed for rs . 750 after successive discount is 20 % and 15 % is ?
Options: a ) 227 , b ) 570 , c ) 342 , d ) 680 , e ) 230
Rationale: "750 * ( 80 / 100 ) * ( 85 / 100 ) = 570 answer : b"
Answer: b
Python program:
a = 750 * 20
b = a / 100
c = 750 - b
d = 750 * 20
e = d / 100
f = 750 - e
g = f * 15
h = g / 100
i = c - h
Problem: operation # is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 10 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Python program:
a = 10 + 3 
b = 10 + a 
c = b / 2
Problem: a room of 8 m 44 cm long and 3 m 50 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 73850 , b ) 73805 , c ) 844 , d ) 350 , e ) 2
Rationale: "explanation : area of the room = 844 * 350 sq cm size of largest square tile = h . c . f of 844 cm and 350 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 844 * 350 ) / ( 2 * 2 ) = 73850 answer : a ) 73850"
Answer: a
Python program:
a = 8 * 100
b = a + 44 
c = 3 * 100
d = c + 50 
e = b * d
f = 8 * 100
g = f + 44 
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
Problem: a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 45 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 287 , b ) 279 , c ) 270 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 45 - 40 ) = 8 hours so , the two trains meet at 6 p . m . the two trains meet 6 * 45 = 270 km away from mumbai . answer : c"
Answer: c
Python program:
a = 40 * 1
b = 45 - 40
c = a / b
d = c * 45
Problem: he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 90 kg
Rationale: "explanation : total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 62 + 28 ) kg = 90 kg . answer : e"
Answer: e
Python program:
a = 3 * 5
b = a + 62
Problem: the price of a jacket is reduced by 20 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 35 , c ) 48.1 , d ) 65 , e ) 66.67
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 20 % , therefore bringing down the price to $ 80 . 3 ) again it is further discounted by 25 % , therefore bringing down the price to $ 60 . 4 ) now 60 has to be added byx % in order to equal the original price . 60 + ( x % ) 60 = 100 . solving this eq for x , we get x = 66.67 ans is e ."
Answer: e
Python program:
a = 100 - 20
b = 100 - 20
c = 25 / 100
d = b * c
e = a - d
f = 100 - e
g = 100 - 20
h = 100 - 20
i = 25 / 100
j = h * i
k = g - j
l = f / k
m = 100 * l
Problem: a cylindrical can has a radius of 3 centimeters and a height of 12 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 72 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 3 * 12 = 72 pi answer is b ."
Answer: b
Python program:
a = 3 * 12
b = 2 * math.pi
c = a * b
Problem: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 9.00 ?
Options: a ) 40 , b ) 60 , c ) 90 , d ) 120 , e ) 108
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 9 ( 1 / 12 ) * x = 9 x = 108 answer : e"
Answer: e
Python program:
a = 1 / 0
b = 0 / 50
c = a - b
d = 9 / 0
Problem: a man took a loan from a bank at the rate of 11 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 16363.64 , b ) rs . 10 , 000.64 , c ) rs . 15 , 000,64 , d ) rs . 21 , 353.64 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 11 x 3 ) = rs . 16363.64 . answer a"
Answer: a
Python program:
a = 5400 * 100
b = 3 * 11
c = a / b
d = const_60 / 4
e = d * 100
f = c / e
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 98 , what is the difference between the ages of patrick and monica ?
Options: a ) 32 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 98 x = 2 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 2 = 32 answer a"
Answer: a
Python program:
a = 5 * 5
b = 3 * 3
c = 3 * 5
d = b + c 
e = 5 * 5
f = d + e 
g = 98 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k 
m = 5 * 5
n = l + m 
o = 98 / n
p = i * o
q = h - p
Problem: three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is - .
Options: a ) 5 / 12 , b ) 4 / 13 , c ) 5 / 17 , d ) 3 / 12 , e ) 8 / 9
Rationale: "using question number 11 and 12 , we get the probability as 1 - ( 1 / 36 + 5 / 9 ) = 5 / 12 answer a"
Answer: a
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: six dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 6 dots that do not form an equilateral triangle ?
Options: a ) 18
b ) 17
c ) 16
d ) 15
e ) 14
Rationale: the total number of ways we can choose three dots is 6 c 3 = 20 . we can form two equilateral triangles from these six dots . there are 20 - 2 = 18 combinations which do not form an equilateral triangle . the answer is a .
Answer: a
Python program:
a = math.factorial(6)
b = math.factorial(3)
c = math.factorial(3)
d = b * c
e = a / d
f = e - 2