euclaise/mathqa_programs huggingface dataset:
Problem: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 40 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 21 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 40 pints will require 9 / 17 * 40 = 21 pints . . c"
Answer: c
Python program:
a = 3 * 2
b = 4 * 3
c = a / b
d = 40 * c
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 72 kmph and 90 kmph . in how much time will the trains cross each other ?
Options: a ) 80 / 8 , b ) 80 / 9 , c ) 80 / 5 , d ) 80 / 3 , e ) 80 / 1
Rationale: "relative speed = ( 72 + 90 ) * 5 / 18 = 9 * 5 = 45 mps . the time required = d / s = ( 100 + 100 + 200 ) / 45 = 400 / 45 = 80 / 9 sec . answer : b"
Answer: b
Python program:
a = 72 + 90 
b = a * const_0_2778
c = 100 / b
Problem: a fruit seller sells mangoes at the rate of rs . 13 per kg and thereby loses 25 % . at what price per kg , he should have sold them to make a profit of 15 % ?
Options: a ) rs . 11.81 , b ) rs . 19.93 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 75 : 13 = 115 : x x = ( 13 ã — 115 / 75 ) = rs . 19.93 hence , s . p per kg = rs . 19.93 answer b"
Answer: b
Python program:
a = 100 + 15 
b = 13 * a
c = 100 - 25
d = b / c
Problem: mahesh can do a piece of work in 40 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 60
Rationale: "work done by mahesh in 60 days = 20 * 1 / 40 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 2 = 60 days answer is e"
Answer: e
Python program:
a = 1 / 40
b = 20 * a
c = 1 - b
d = c / 30
e = 1 / d
Problem: a store ’ s selling price of $ 2240 for a certain printer would yield a profit of 40 percent of the store ’ s cost for the printer . what selling price would yield a profit of 50 percent of the printer ’ s cost ?
Options: a ) $ 2800 , b ) $ 2464 , c ) $ 2650 , d ) $ 2732 , e ) $ 2400
Rationale: "1.4 x = 2240 x = 2240 / 1.4 so , 1.5 x = 2240 * 1.5 / 1.4 = 2400 answer : - e"
Answer: e
Python program:
a = 40 / 100
b = 1 + a 
c = b * original_price_before_gain
Problem: a contractor undertakes to built a walls in 50 days . he employs 50 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 20 , e ) none of these
Rationale: "50 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 50 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 50 × 25 × 0.6 / 25 × 0.4 = 75 men answera"
Answer: a
Python program:
a = 100 - 40
b = a / 100
c = 50 * b
d = 4 / 10
e = c / d
Problem: convert 500 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 500 mile = 500 * 1609.34 = 804670 meters answer is c"
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 500
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 12 , and k < m < r < s < t . if t is 20 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 18 , c ) 19 , d ) 20 , e ) 22
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 12 which means that in effect , all numbers are equal to 12 . if the largest number is 20 , it is 8 more than 12 . we need r to be maximum so k and m should be as small as possible to get the average of 12 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 11 less than 12 and 2 is 10 less than 12 which means k and m combined are 21 less than the average . 20 is already 8 more than 12 and hence we only have 21 - 8 = 13 extra to distribute between r and s . since s must be greater than r , r can be 12 + 6 = 18 and s can be 12 + 7 = 19 . so r is 18 . answer ( d )"
Answer: d
Python program:
a = 12 * 5
b = a - 20
c = b / 2
d = c - 2
Problem: a work as fast as b . if b can complete a work in 36 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 12 days , b ) 3 days , c ) 4 days , d ) 5 days , e ) 6 days
Rationale: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 18 b ' s 1 day work = 1 / 36 a + b 1 day work = 1 / 18 + 1 / 36 = 3 / 36 = 1 / 12 a and b can finish the work in 12 days answer is a"
Answer: a
Python program:
a = 1/(36)
b = 1/(36)
c = 2 * b
d = a + c 
e = 1/(d)
Problem: a car covers a distance of 200 km in 2 hours 40 minutes , whereas a jeep covers the same distance in 2 hours . what is the ratio of t
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 4 : 5 , d ) 5 : 4 , e ) 8 : 7
Rationale: a 3 : 4
Answer: a
Python program:
a = const_60 * 2
b = const_60 * 2
c = b + 40 
d = a / c
Problem: the average of 13 numbers is 60 . average of the first 7 of them is 54 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 25 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 54 = 378 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 378 - 780 = 25 . answer : a"
Answer: a
Python program:
a = 8 * 61
b = 13 * 60
c = 54 * 7
d = b - c
e = a - d
Problem: a man is 22 years older than his son . in three years , his age will be thrice the age of his son . the present age of this son is
Options: a ) 8 years , b ) 2 years , c ) 7 years , d ) 8 years , e ) 5 years
Rationale: "let ' s son age is x , then father age is x + 22 . = > 3 ( x + 3 ) = ( x + 22 + 3 ) = > 3 x + 9 = x + 25 = > 2 x = 16 years = 8 years answer : d"
Answer: d
Python program:
a = 2 * 2
b = a - 2
c = 22 - b
d = 2 - 1
e = c / d
Problem: for each color copy , print shop x charges $ 1.20 and print shop y charges $ 1.70 . how much greater is the charge for 70 color copies at print shop y than at print shop x ?
Options: a ) $ 27 , b ) $ 29 , c ) $ 31 , d ) $ 33 , e ) $ 35
Rationale: the difference in the two prices is $ 1.70 - $ 1.20 = $ 0.50 for each color copy . each color copy will cost an extra $ 0.50 at print shop y . 70 * $ 0.50 = $ 35 the answer is e .
Answer: e
Python program:
a = 1 * 7
b = 1 * 2
c = a - b
Problem: pipe a fills a tank of capacity 850 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 42 minutes , b ) 51 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 850 = 50 * n = > n = 17 here n = number of cycles . total time = 17 * 3 = 51 as in one cycle there are 3 minutes . thus 51 minutes answer : b"
Answer: b
Python program:
a = 40 + 30 
b = a - 20
c = 850 / b
d = c * 3
Problem: a picnic attracts 240 persons . there are 80 more men than women , and 80 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 110 , d ) 120 , e ) 200
Rationale: "adult + children = 240 let , children = y then , adult = y + 80 i . e . y + ( y + 80 ) = 240 i . e . y = 80 i . e . adult = 80 + 80 = 160 adults include only men and women i . e . men + women = 160 let women , w = x then men , m = x + 80 i . e . x + ( x + 20 ) = 2 x + 80 = 160 i . e . x = 40 i . e . men , m = 40 + 80 = 120 answer : option d"
Answer: d
Python program:
a = 240 - 80
b = a / 2
c = b + 80 
d = c - 80
e = d / 2
f = e + 80
Problem: tap a runs 3 liters of water per minute into a bucket that has a total volume of 36 liters . tap b fills a third of the bucket in 20 mins . working together how long will it take both taps to fill the bucket ?
Options: a ) 10 minutes , b ) 1.5 hours , c ) 9 hours and 12 minutes , d ) 15 hours , e ) 1 hour and 48 minutes .
Rationale: pipe a has a rate of 3 liters per minute which equals a rate of 180 liters per hour . pipe b has a rate of 36 liters per hour . 180 + 36 ( a + b ) = together they have a rate of 2000 liters per hour . 36 ( the bucket ) / 216 = 1 / 6 = 10 minutes answer - a
Answer: a
Python program:
a = 36 / 3
b = 1 / a
c = 20 * 3
d = 1 / c
e = b + d 
f = 1/(e)
Problem: what is the smallest integer that is multiple of 5 , 7,11
Options: a ) a ) 70 , b ) b ) 35 , c ) c ) 385 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 5 , 7 and 11 which is 385 . the answer is c ."
Answer: c
Python program:
a = 3 + 4
Problem: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 22000 . what is the share of c ?
Options: a ) rs . 2250 , b ) rs . 3375 , c ) rs . 6000 , d ) rs . 5625 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 22000 ] = rs . 6000 answer : option c"
Answer: c
Python program:
a = 2 / 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 1 
f = 1/(e)
g = 22000 * f
Problem: if the radius of a circle is decreased 40 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 64 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.6 * old radius so new area = ( 0.6 ) ^ 2 old area = > 4 / 25 of old area = > 36 % old area ans : e"
Answer: e
Python program:
a = 40 / 100
b = a ** 2
c = b * 100
d = 100 - c
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9 - sided polygon ) ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 9
Rationale: "from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 6 = 1 / 3 . the answer is b ."
Answer: b
Python program:
a = 9 - 3
b = 9 * a
c = b / 2
d = 9 / c
Problem: if 10 gallons of grape juice are added to 30 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 32.5 % , e ) 50 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 30 × 0.10 = 3 gallons of grape juice . 30 × 0.90 = 27 gallons of other components . if we add 10 gallons of grape juice , we will end up with 13 gallons of grape juice and 36 gallons of other components , and we will have a total of 40 gallons of the mixture . so 13 / 40 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 32,5 % . the correct answer is choice ( d )"
Answer: d
Python program:
a = 10 / 100
b = a * 30
c = b + 10 
d = 30 + 10 
e = c / d
f = e * 100
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 12 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32
Rationale: "3.456789 ^ 12 has 6 * 12 = 72 decimal places . 10 ^ 48 moves the decimal place to the right 48 places . ( 10 ^ 4 * 3.456789 ) ^ 12 has 72 - 48 = 24 digits after the decimal point . the answer is c ."
Answer: c
Python program:
a = 12 * 2
Problem: convert 150 inches into centimeter ?
Options: a ) 312 cm , b ) 381 cm , c ) 350 cm , d ) 310 cm , e ) 354 cm
Rationale: "1 inch = 2.54 cm 150 inches = 110 * 2.54 = 381 cm answer is b"
Answer: b
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 150
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: one day eesha started 30 min late from home and reached her office 50 min late while driving 25 % slower than her usual speed . how much time in min does eesha usually take to reach her office from home ?
Options: a ) 22 , b ) 60 , c ) 88 , d ) 26 , e ) 18
Rationale: we know that speed is inversely proportional to time while she drives 25 % slower means she drove at 3434 ( s ) we know that d = s x t when speed became 3434 ( s ) then time taken should be 4343 ( t ) i . e , she has taken 4343 ( t ) - t extra to cover the distance . extra time = t 3 t 3 = 20 min ( as 20 min late due to slow driving ) actual time t = 60 minutes answer : b
Answer: b
Python program:
a = 25 / 100
b = 1 - a
c = 50 - 30
d = b * c
e = 25 / 100
f = d / e
Problem: the sum of three consecutive even numbers is 24 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 24 , e ) 34
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 24 6 p = 24 = > p = 4 . the middle number is : 4 p = 16 . answer : b"
Answer: b
Python program:
a = 24 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 24 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 24 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 24 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: two trains of equal length , running with the speeds of 50 and 40 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 5.55 sec , b ) 4.55 sec , c ) 5.95 sec , d ) 6.55 sec , e ) 9.55 sec
Rationale: "rs = 50 - 40 = 10 * 5 / 18 = 50 / 18 t = 50 d = 50 * 50 / 18 = 1250 / 9 rs = 50 + 40 = 90 * 5 / 18 = 25 t = 1250 / 9 * 1 / 25 = 5.55 sec answer : a"
Answer: a
Python program:
a = 50 - 40
b = const_0_2778 * a
c = b * 50
d = 50 + 40 
e = const_0_2778 * d
f = 1/(e)
g = c * f
Problem: daniel went to a shop and bought things worth rs . 40 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) a ) 34.7 , b ) b ) 20 , c ) c ) 21.3 , d ) d ) 21.5 , e ) e ) 22
Rationale: "total cost of the items he purchased = rs . 40 given that out of this rs . 40 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 40 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 40 − 0.3 − x ) = 30 ⇒ ( 40 − 0.3 − x ) = 5 ⇒ x = 40 − 0.3 − 5 = 34.7 ans - a"
Answer: a
Python program:
a = 30 / 100
b = 40 - a
c = 30 / 6
d = b - c
Problem: if 6 men can colour 48 m long cloth in 2 days , then 2 men can colour 36 m long cloth in
Options: a ) 1 day , b ) 2.1 days , c ) 3 days , d ) 4.5 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 6 × 2 = 4 m no . of days required to paint 36 m cloth by 6 men = 36 / 4 × 2 = 4.5 day . d"
Answer: d
Python program:
a = 6 * 2
b = 48 / a
c = b * 2
d = 36 / c
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts five hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 10 , e ) e ) 5
Rationale: the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 5 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 5 + t ) = 40 * t t = 15 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 15 / 60 = 10 hrs time taken by a = 5 + t = 5 + 15 = 20 hrs time taken by k = 10 hrs so k starts 20 - 10 = 10 hrs after a . ( answer d )
Answer: d
Python program:
a = 40 - 30
Problem: the decimal 0.1 is how many times greater than the decimal ( 0.001 ) ^ 4 ?
Options: a ) 10 ^ 8 , b ) 10 ^ 9 , c ) 10 ^ 10 , d ) 10 ^ 11 , e ) 10 ^ 12
Rationale: "0.1 = 10 ^ - 1 ( 0.001 ) ^ 4 = ( 10 ^ - 3 ) ^ 4 = 10 ^ - 12 10 ^ 11 * 10 ^ - 12 = 10 ^ - 1 the answer is d ."
Answer: d
Python program:
a = 0 ** 1
b = 0 / 1
Problem: in what time will a train 400 meters long cross an electric pole , if its speed is 144 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 10 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 400 / 40 = 10 seconds answer : c"
Answer: c
Python program:
a = 144 * const_0_2778
b = 400 / a
Problem: p software has coding line 5 % more than n , n software has coding line 5 / 2 more than m . m software has 108 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 397 , d ) 109 , e ) 110
Rationale: "m s / w has 108 line of code n s / w has = 108 + 108 * 5 / 2 = 378 line of code p s / w 5 % more n ' code 378 + 18.9 = 396.9 or 397 line of code answer : c"
Answer: c
Python program:
a = 108 / 2
b = 108 + a
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 2 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 11 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 2 * x hence , a 1 + a 2 + . . + a 20 + n = 22 x so , the fraction asked = 2 x / 22 x = 1 / 11 answer c"
Answer: c
Python program:
a = 1 * 1
b = 20 / 2
c = b + 21 
d = c / 4
e = d * 2
f = e - 2
g = f - 3
h = a / g
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 20,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 116000 , e ) 188871
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 20,000 is made = 96,000 + 20,000 = rs . 1 , 16,000 answer : d"
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 20 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: mary works in a restaurant a maximum of 60 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 300 , b ) 420 , c ) 560 , d ) 320 , e ) 400
Rationale: mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 40 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 40 ) = $ 400 . the total amount is $ 160 + $ 400 = $ 560 answer c 560 .
Answer: c
Python program:
a = 60 * 8
b = 60 - 20
c = 25 / 100
d = 8 * c
e = b * d
f = a + e
Problem: how many seconds will a 600 m long train take to cross a man walking with a speed of 4 km / hr in the direction of the moving train if the speed of the train is 64 km / hr ?
Options: a ) 30 , b ) 36 , c ) 50 , d ) 44 , e ) 60
Rationale: "speed of train relative to man = 64 - 4 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 600 * 3 / 50 = 36 sec . answer : b"
Answer: b
Python program:
a = 64 - 4
b = a * const_0_2778
c = 600 / b
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 40 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 4 : 5 , b ) 9 : 25 , c ) 5 : 4 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 20 / speed b since the times are same , 50 pi / speed a = 40 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 4 correct option : c"
Answer: c
Python program:
a = 50 / 2
b = circumface / (
Problem: if ( 2 ^ 13 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 7 , b ) 13 , c ) 15 , d ) 16 , e ) 23
Rationale: "given 2 ^ 13 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 13 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans b on comparing the power of 2 = > m = 13"
Answer: b
Python program:
a = 10 / 5
b = a ** 4
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 36,000 , what will be the amount a receives ?
Options: a ) 15120 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 36000 × 21 / 50 = 15,120 answer is a .
Answer: a
Python program:
a = 5000 * 10
b = 4000 + 5000 
c = b + 5000 
d = a - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 3 * 12
i = h * 1000
j = 5000 * 10
k = i / j
l = g * k
Problem: a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution . if 500 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 10.00 , b ) 15.00 , c ) 11.50 , d ) 10.50 , e ) 9.75
Rationale: "we are given that a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container when we have 500 cubic centimeters of solution , we can set up a proportion . we can say : “ 20 grams of glucose is to 1000 cubic centimeters of solution as x grams of glucose is to 500 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 20 / 1000 = x / 500 when we cross multiply we obtain : ( 20 ) ( 500 ) = 1000 x 10000 = 1000 x 10 = x there are 10.00 grams of glucose in the solution in the container . the answer is a ."
Answer: a
Python program:
a = 20 / 1000
b = 500 * a