euclaise/mathqa_programs huggingface dataset:
Problem: a reduction of 30 % in the price of salt enables a lady to obtain 10 kgs more for rs . 200 , find the original price per kg ?
Options: a ) 7.5 , b ) 8.99 , c ) 8.0 , d ) 9.2 , e ) 8.57
Rationale: "answer : 200 * ( 30 / 100 ) = 60 - - - 10 ? - - - 1 = > rs . 6 200 - - - 140 ? - - - 6 = > rs . 8.57 . answer : e"
Answer: e
Python program:
a = 30 / 100
b = a * 200
c = b / 10
d = 30 / 100
e = d * 200
f = c / e
g = f * 100
Problem: if a is a positive integer and 10 ^ a – 74 in decimal notation has digits whose sum is 440 , what is the value of a ?
Options: a ) 40 , b ) 44 , c ) 45 , d ) 46 , e ) 50
Rationale: answer e = 50 we have ( 10 ^ a ) - 74 , where the sum of the digits is 440 . 100 - 74 = 26 , so we already have 2 + 6 = 8 from the 440 . because we have a power of 10 , we will have numbers like 100 , 1000 , 10000 and so on . this minus 74 rests 26 and a lot of 9 s . e . g : 1000 - 74 = 9926 . so dividing the 432 / 9 = 48 , that ` s the number of 9 s . and we have 2 other numbers ( 2 and 6 ) wich were 00 before the subtraction . so we have 48 + 2 as an a = 50
Answer: e
Python program:
a = 2 + 3 
b = 10 * a
Problem: if x = 7 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.001 , c ) 0.25 , d ) 4 , e ) 8
Rationale: quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.001 answer : b
Answer: b
Python program:
a = 2 / 2
b = a / 1000
Problem: a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 10 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 20 , d ) 22.5 , e ) 27
Rationale: producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 10 % of the final price - - > ( final price ) * 0.9 = $ 18 - - > ( final price ) = $ 20 . answer : c .
Answer: c
Python program:
a = 100 + 10 
b = a / 100
c = 15 * b
d = 100 + 20 
e = d / 100
f = c * e
Problem: if integer k is equal to the sum of all even multiples of 5 between 300 and 610 , what is the greatest prime factor of k ?
Options: a ) 32 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: "if we break down what the stem is asking what is the sum of all mult of 10 between 300 and 610 . using arithmetic progression to find n : 610 = 300 + ( n - 1 ) 10 310 + 10 = 10 n 320 = 10 n = > n = 32 the sum would be : 32 * mean mean = [ 610 + 300 ] / 2 = 455 32 * 455 a"
Answer: a
Python program:
a = 610 / 5
b = math.floor(a)
c = b * 5
d = 300 / 5
e = math.floor(d)
f = e * 5
g = c - f
h = g / 5
i = h + 1 
j = i / 2
Problem: one ton has 2200 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 1760 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: 16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2200 pound = 13 * 2200 * 16 ounces . hence the answer is ( 13 * 2200 * 16 ) / 260 = 1760 . answer : a .
Answer: a
Python program:
a = 13 * 2200
b = a * 16
c = 16 * 16
d = c + 4 
e = b / d
Problem: find the greatest number which leaves the same remainder when it divides 25 , 62 and 105 .
Options: a ) 1 , b ) 8 , c ) 12 , d ) 16 , e ) none of these
Rationale: "105 - 62 = 43 62 - 25 = 37 105 - 25 = 80 the h . c . f of 37 , 43 and 80 is 1 . answer : a"
Answer: a
Python program:
a = 62 - 25
b = a / 2
Problem: if 16 ^ y = 2 ^ 16 , what is y ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "16 ^ y = 2 ^ 4 y = 2 ^ 16 4 y = 16 y = 4 the answer is b ."
Answer: b
Python program:
a = 16 / 2
Problem: an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 25 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1305 , b ) 1545 , c ) 1375 , d ) 1345 , e ) 1455
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 25 % of the gaskets to x = 15 gaskets = 25 * 10 + 20 * 5 = 250 + 100 = 350 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 60 % to z = 36 gaskets = 25 * 10 = 250 + 20 * 26 = 770 thus , total money earned 350 + 225 + 770 = 1345 answer is d"
Answer: d
Python program:
a = 4 / 5
b = 25 * a
c = 25 / 100
d = 60 * c
e = 60 - d
f = 25 / 100
g = 60 * f
h = e - g
i = h - 10
j = b * i
k = 25 * 10
l = j + k 
m = 25 / 100
n = 60 * m
o = 25 * n
p = 25 / 100
q = 60 * p
r = 25 * q
s = o + r 
t = l + s
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 20 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: answer : a .
Answer: a
Python program:
a = 20 * 4
b = a / 2
c = 20 + 5 
d = b + c
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 5 years ?
Options: a ) 3277 , b ) 2977 , c ) 9492 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 5 answer : c"
Answer: c
Python program:
a = 100 * 100
b = 4 * a
c = 3 / 4
d = c ** 5
e = b * d
Problem: what is the length of a bridge ( in meters ) , which a train 148 meters long and travelling at 45 km / h can cross in 30 seconds ?
Options: a ) 211 , b ) 219 , c ) 227 , d ) 235 , e ) 243
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 148 = 227 meters the answer is c ."
Answer: c
Python program:
a = 45 * const_0_2778
b = a * 30
c = b - 148
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 4 / 7 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 7 / 10 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 8
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 3 / 4 * 4 / 7 x = 3 / 7 x % loaded by day crew = x / ( x + 3 / 7 x ) = 7 / 10 answer a"
Answer: a
Python program:
a = 7 * 4
b = 7 * 4
c = 3 * 4
d = b + c 
e = a / d
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 11 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 88 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,11 = 11 / 100 x = 80 * 11 / 100 x = 8.8 8.8 / 10 = 0.88 = 88 % , answer c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 11 * b
d = c / 10
e = d * 100
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 63
Rationale: f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a
Answer: a
Python program:
a = 30 * 2
b = 12 / 3
c = 3 / b
d = a * c
Problem: one year before the age of pramila was 4 times than her daughter swati . after 6 years the age of pramila will be 24 year greater than the age of swati . then calculate the ratio of ages of pramila and swati ?
Options: a ) 5 : 3 , b ) 16 : 3 , c ) 11 : 3 , d ) 11 : 5 , e ) 9 : 4
Rationale: let 1 year before age of swati = x years and age of pramila = 4 x years swati present age = ( x + 1 ) and pramila present age = ( 4 x + 1 ) after 6 year age of swati = ( x + 7 ) , age of pramila = ( 4 x + 7 ) so , 4 x + 7 - ( x + 7 ) = 243 x = 24 , x = 8 . ratio = ( 4 x + 7 ) : ( x + 1 ) = 33 : 9 = 11 : 3 answer c
Answer: c
Python program:
a = 4 - 1
b = 24 + a 
c = 4 - 1
d = b / c
e = 24 + d 
f = 4 - 1
g = 24 + f 
h = 4 - 1
i = g / h
j = e / i
Problem: somehow or other i got talked into buying something on the installment plan . i ' m notsure i got a good deal . the payments to date , according to my checkbook , have reached rs . 96 . the second year cost rs . 2.00 more than the first year ; the third year cost rs . 3.00 more thanthe second ; and the fourth year cost me rs . 4.00 more than the third . what were mypayments the first year ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: let payments for the first year = x given , x + x + 2 + x + 5 + x + 9 = 96 4 x + 16 = 96 x = 20 answer : b
Answer: b
Python program:
a = 2 + 3 
b = a + 4 
c = 2 + 3 
d = b + c 
e = d + 2 
f = 96 - e
g = f / 4
Problem: if x is a sum of all even integers on the interval 23 . . . 65 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 21 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 24 + 16 + . . . + 64 = ( largest + smallest ) / 2 * ( # of terms ) = ( 24 + 64 ) / 2 * 21 = 44 * 16 . gcd of 21 and 44 * 21 is 21 . answer : b ."
Answer: b
Python program:
a = 23 - 10
b = a + 2 
c = 23 - 10
d = c + 2 
e = b * d
Problem: a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability w that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes w = 15 / 36 . answer : c ."
Answer: c
Python program:
a = 12 + 3 
b = 1 / 6
c = b ** 2
d = a * c
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 750 resolutions ?
Options: a ) 277 m , b ) 704 m , c ) 278 m , d ) 288 m , e ) 1056 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 750 resolutions . = 750 * 2 * 22 / 7 * 22.4 = 105600 cm = 1056 m answer : e"
Answer: e
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 750
i = h / 100
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 450 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 370 , b ) 365 , c ) 360 , d ) 380 , e ) 350
Rationale: "c 450 * t = 1 km = > t = 1 / 450 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 450 + 2 / 3600 ) = 1 = > v = 360 km / h"
Answer: c
Python program:
a = 1 / 450
b = 3600 * a
c = b + 2 
d = c / 3600
e = 1 / d
Problem: a sum of rs . 2795 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1642 , b ) 1640 , c ) 1720 , d ) 2795 , e ) 6386
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2795 - x ) * 3 * 5 ) / 100 24 x / 100 = 41925 / 100 - 15 x / 100 39 x = 41925 = > x = 1075 second sum = 2795 – 1075 = 1720 answer : c"
Answer: c
Python program:
a = 3 * 5
b = a * 2795
c = 3 * 5
d = 8 * 3
e = c + d 
f = b / e
g = 2795 - f
Problem: in one year , the population , of a village increased by 25 % and in the next year , it decreased by 25 % . if at the end of 2 nd year , the population was 18750 , what was it in the beginning ?
Options: a ) 7787 , b ) 8000 , c ) 1988 , d ) 1277 , e ) 20000
Rationale: "x * 125 / 100 * 75 / 100 = 18750 x * 0.9375 = 18750 x = 18750 / 0.9375 = > 20000 answer : e"
Answer: e
Python program:
a = 25 / 100
b = 1 - a
c = 18750 / b
d = 25 / 100
e = 1 + d 
f = c / e
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 85 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1529.41 , e ) 1625
Rationale: "300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 85 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 85 = 1529.41 d is the answer"
Answer: d
Python program:
a = 300 * 100
b = a / 30
c = b + 300 
d = 85 / 100
e = c / d
Problem: if 85 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 70.5 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 85 % of 3 / 5 of x = 36 85 / 100 * 3 / 5 * x = 36 x = ( 36 * 100 / 51 ) = 70.5 required number = 70.5 . correct option : c"
Answer: c
Python program:
a = 85 / 100
b = 3 / 5
c = a * b
d = 36 / c
Problem: a jar contains a mixture of ab in the ratio 3 : 2 . when 10 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 18 , b ) 15 , c ) 16 , d ) 20 , e ) 25
Rationale: "10 litres of mixture that is replaced will contain 6 litres of a and 4 litres of b ( as a : b = 3 : 2 ) let the initial volume of the mixture be 3 k + 2 k = 5 k so by condition , [ 3 k - 6 ] / [ 2 k - 4 + 10 ] = 2 / 3 9 k - 18 = 4 k - 8 + 20 5 k = 12 + 18 k = 6 solve for k which is k = 6 so initial volume of liquid a = 3 k = 18 litres answer : a"
Answer: a
Python program:
a = 3 * 2
b = 2 * 2
c = a + b 
d = 3 * 2
e = d - 2
f = 10 / e
g = c * f
h = 3 + 2 
i = g / h
j = i * 3
Problem: √ 3 percent of 3 √ 3 =
Options: a ) 5.2 , b ) 1.0 , c ) 0.1 , d ) 2.0 , e ) 5.0
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 so , √ 3 percent of 3 √ 3 ≈ 1.7 percent of ( 3 ) ( 1.7 ) ≈ ( 1.7 / 100 ) ( 5.1 ) ≈ 8.67 / 100 ≈ 0.08 check the answer choices to see that c is the only answer that ' s close . answer : c"
Answer: c
Python program:
a = math.sqrt(3)
b = math.sqrt(3)
c = a * b
d = c * 3
e = d / 100
Problem: machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 40 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 10 minutes ?
Options: a ) 20 , b ) 50 , c ) 60 , d ) 40 , e ) 30
Rationale: "machine b produces 100 part in 40 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 40 / 2 = 20 minutes . now , machine a produces 100 parts in 20 minutes which is 100 / 20 = 5 parts / minute . 5 parts x a total of 10 minutes = 50 b"
Answer: b
Python program:
a = 100 / 40
b = a * 2
c = b * 10
Problem: an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the cases ?
Options: a ) 8 : 6 , b ) 8 : 7 , c ) 8 : 9 , d ) 8 : 4 , e ) 8 : 1
Rationale: let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer : b
Answer: b
Python program:
a = 3 * 2
b = a * 4
c = 7 * 3
d = b / c
Problem: of the diplomats who attended a summit conference : 20 spoke french , 32 did not speak english and 20 % of the diplomats spoke neither french nor english . if 10 % of the diplomats spoke both french and english , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer
Answer: d
Python program:
a = 32 - 20
b = 10 / 100
c = a / b
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 $ 1400 left with him , find his expenditure on food .
Options: a ) $ 400 , b ) $ 1400 , c ) $ 3400 , d ) $ 2400 , e ) $ 4400
Rationale: "part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) = 7 / 40 let the monthly salary be $ x then ( 7 / 40 ) of x = 1400 x = 8000 expenditure on food = $ 2400 option d"
Answer: d
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: in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 82 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 63 . , b ) 73 . , c ) 81 , d ) 91 , e ) 108
Rationale: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 82 % of 250 = 205 are boys who play soccer . girls who play soccer = 45 . total girls who do not play soccer = 108 - 45 = 63 . correct option : a"
Answer: a
Python program:
a = 420 - 312
b = 250 * 82
c = b / 100
d = 250 - c
e = a - d
Problem: x , a , z , and b are single digit positive integers . x = 1 / 5 a . z = 1 / 5 b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 36 , b ) 33 , c ) 44 , d ) 64 , e ) 56
Rationale: a = 5 x , b = 5 z therefore ( 5 x * 10 + 5 z ) - ( 10 x + z ) = ( 5 - 1 ) ( 10 x + z ) = . ( 10 x + z ) number should be divisible by 4 b
Answer: b
Python program:
a = 5 * 5
b = 5 * 10
c = a + b 
d = 5 * 10
e = d + 5 
f = c - e
g = f + 10 
h = g + 3
Problem: how much water should be added to 10 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 10 + x ) ) ) 2 = 5 % * ( 10 + x ) - - - - - - - - > x = 30 answer : c"
Answer: c
Python program:
a = 2 * 100
b = 75 / 100
c = b * 20
d = 20 - c
e = a / d
f = e - 10
Problem: on a game show , a contestant is given 3 keys , each of which opens exactly one of 3 identical boxes . the first box contains $ 5 , the second $ 500 , and the third $ 5000 . the contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it . what is the probability that a contestant will win more than $ 5000 ?
Options: a ) 1 / 9 , b ) 4 / 6 , c ) 3 / 6 , d ) 1 / 2 , e ) 1 / 6
Rationale: let ' s call the boxes that contain $ 5 , $ 500 , and $ 5000 , respectively , box a , box b , box c . these are opened , respectively , by key a , key b , and key c . we want to know the probability of winning more than $ 5000 . notice that if the distribution of keys is : box a = key b box b = key a box c = key c then the contestant wins exactly $ 5000 , not more than $ 5000 . the only configuration that leads to winning more than $ 1000 is : box a = key a box b = key b box c = key c i . e . , getting all three keys correct . that ' s the only way to be more than $ 5000 . so , really , the question can be rephrased : what is the probability of guessing the order of keys so that each key matches the correct box ? well , for a set of three items , the number of possible permutations is 3 ! = 3 * 2 * 1 = 6 . of those 6 possible permutations , only one of them leads to all three keys being paired with the right box . so , the answer is probability = 1 / 6 answer : e
Answer: e
Python program:
a = math.factorial(3)
b = 1 / a
Problem: sakshi can do a piece of work in 20 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 20 : x ⇒ x = ( 20 x 4 / 5 ) ⇒ x = 16 days . hence , tanya takes 16 days is complete the work . answer b"
Answer: b
Python program:
a = 25 / 100
b = 1 + a 
c = 20 / b
Problem: there are 18 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 987 , b ) 177 , c ) 357 , d ) 267 , e ) 380
Rationale: "the total number of stations = 20 from 20 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in ² ⁰ p ₂ ways . ² ⁰ p ₂ = 20 * 19 = 380 . answer : e"
Answer: e
Python program:
a = 18 + 1 
b = 18 + 1 
c = b + 1 
d = a * c
Problem: a boat traveled upstream 90 miles at an average speed of ( v - 3 ) miles per hour and then traveled the same distance downstream at an average speed of ( v + 3 ) miles per hour . if the trip upstream took a half hour longer than the trip downstream , then how many hours did it take the boat to travel downstream ?
Options: a ) 2.5 , b ) 2.4 , c ) 2.3 , d ) 2.2 , e ) 2.1
Rationale: 90 / ( v - 3 ) = 90 / ( v + 3 ) + 0.5 hours = > 90 ( v + 3 ) = ( v - 3 ) [ 90 + 0.5 v + 1.5 ] 90 v + 270 = ( v - 3 ) ( 183 / 2 + v / 2 ) 180 v + 540 = ( v - 3 ) ( 183 + v ) = 183 v - 549 + v ^ 2 - 3 v v ^ 2 - 1089 = 0 = > v = 33 miles / hr = > time downstream = 90 / 36 = 30 / 12 = 5 / 2 = 2.5 hrs answer a 2.5
Answer: a
Python program:
a = 90 * 3
b = 90 * 3
c = a + b 
d = 1 / 2
e = 3 * 3
f = d * e
g = c - f
h = 1 / 2
i = g / h
j = math.sqrt(i)
k = j + 3 
l = 90 / k
Problem: in a certain country 1 / 3 of 4 = 6 . assuming the same proportion , what would be the value of 1 / 6 of 20 ?
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 25
Rationale: "b 15"
Answer: b
Python program:
a = 3 / 4
b = a * 20
Problem: working together , a and b can do a job in 6 days . b and c can do the same job in 10 days , while c and a can do it in 7.5 days . how long will it take if all a , b and c work together to complete the job ?
Options: a ) 4 days , b ) 5 days , c ) 8 days , d ) 9 days , e ) 10 days
Rationale: a and b 1 day work = 1 / 6 b and c 1 day work = 1 / 10 c and a 1 day work = 1 / 7.5 a , b , c 1 day work = ( 1 / 6 + 1 / 10 + 1 / 7.5 ) * 1 / 2 = 1 / 5 so a . b . c completes work in 5 days answer : b
Answer: b
Python program:
a = 1/(6)
b = 1/(10)
c = a + b 
d = 1/(7)
e = c + d 
f = e / 2
g = 1/(f)
Problem: from below option 49 is divisible by which one ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 4 , d ) d ) 5 , e ) e ) 7
Rationale: 49 / 7 = 7 e
Answer: e
Python program:
a = math.sqrt(49)