euclaise/mathqa_programs huggingface dataset:
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 e 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 e = 15 / 36 . answer : c ."
Answer: c
Python program:
a = 12 + 3 
b = 1 / 6
c = b ** 2
d = a * c
Problem: if 100 < x < 199 and 20 < y < 100 , then the product xy can not be equal to :
Options: a ) 1900 , b ) 19,303 , c ) 19 , 356.732 , d ) 19,502 , e ) 19,909
Rationale: "correct answer : ( a ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 100 * 20 . the largest value must be less than 199 * 100 . this means that 2000 < xy < 19,900 . ( a ) is outside of this range , so it is not a possible product of xy ."
Answer: a
Python program:
a = 100 + 1
Problem: if d | | d ' , d : 2 x - y = 1 and d ' : ( a - 1 ) x + 2 y = x - 2 , then find the value of a .
Options: a ) - 3 , b ) - 2 , c ) - 1 , d ) 0 , e ) 1
Rationale: d : 2 x − y = 1 , d ’ : ( a − 1 ) x + 2 y = x − 2 d : 2 x − y = 1 , d ′ : ( a − 1 ) x + 2 y = x − 2 d ∥ d ′ ⇒ md = m ′ dd ∥ d ′ ⇒ md = md ′ 2 x − y = 1 → y = 2 x − 1 → md = 22 x − y = 1 → y = 2 x − 1 → md = 2 ( a − 1 ) x + 2 y = x − 2 → 2 y = x ( 1 − a + 1 ) − 2 → 2 y = x ( 2 − a ) − 2 → ( a − 1 ) x + 2 y = x − 2 → 2 y = x ( 1 − a + 1 ) − 2 → 2 y = x ( 2 − a ) − 2 → y = x × ( 2 − a ) 2 − 1 → m ′ d = ( 2 − a ) 2 y = x × ( 2 − a ) 2 − 1 → md ′ = ( 2 − a ) 2 md = m ′ d → ( 2 − a ) 2 = 2 → 2 − a = 4 → a = − 2 answer : b - 2
Answer: b
Python program:
a = 2 * 2
b = 2 - a
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2500 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500
Rationale: solution : money compounded annually at x % triples in 112 / x years . we need to find the final amount of 2500 at the end of the 28 years . . compounded annually at 8 % by putting the value in formula it will give us = 2500 ( 1.08 ) ^ 28 there must be a relation between these two conditions ? x = 8 % so money will triple in 112 / 8 = 14 years so money will be 3 ^ 2 = 9 times in 28 years so 2500 * 9 = 22500 answer : e
Answer: e
Python program:
a = 112 / 8
b = 28 / a
c = 3 ** b
d = 2500 * c
Problem: let a be the event that a randomly selected two digit number is divisible by 3 and let b be the event that a randomly selected two digit number is divisible by 2 . what is p ( a and b ) ?
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 2
Rationale: "p ( a and b ) = 1 / 3 * 1 / 2 = 1 / 6 the answer is b ."
Answer: b
Python program:
a = 3 - 1
b = 3 - 1
c = b * 3
d = a / c
e = 3 - 1
f = e * 2
g = 3 - 1
h = g * 3
i = f / h
j = d * i
Problem: replace x with the appropriate number in 4 , 5 , 14 , 15 , 24 , 25 , x
Options: a ) 30 , b ) 29 , c ) 34 , d ) 21 , e ) 20
Rationale: c list of consecutive numbers that has an ' f ' in the spelling
Answer: c
Python program:
a = 14 - 5
b = 25 + a
Problem: the radius of a semi circle is 3.5 cm then its perimeter is ?
Options: a ) 32.8 , b ) 32.4 , c ) 32.1 , d ) 18 , e ) 32.9
Rationale: "diameter = 7 cm 1 / 2 * 22 / 7 * 7 + 7 = 18 answer : d"
Answer: d
Python program:
a = circumface / (
b = a + 2
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 71 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80
Rationale: "3 j + 2 s = 69 2 j + 3 s = 71 - - - - - - - - - - - - - - - - 5 j + 5 s = 140 - - - - ( divide by 5 ) - - - > j + s = 28 3 j + 2 s = j + 2 ( j + s ) = j + 56 = 69 - - - > j = 13 3 * 13 + 2 s = 69 39 + 2 s = 69 2 s = 30 s = 15 answer : d"
Answer: d
Python program:
a = 71 * 3
b = 69 * 2
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 165 kg then find the average weight of all the 7 rounds ?
Options: a ) 94.2 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 165 / 7 = 94.2 kgs answer : a"
Answer: a
Python program:
a = 1 + 3 
b = a * 165
c = b / 7
Problem: the area of a rectangular field is equal to 800 square meters . its perimeter is equal to 120 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 800 : area , l is the length and w is the width . 2 l + 2 w = 120 : perimeter l = 60 - w : solve for l ( 60 - w ) * w = 800 : substitute in the area equation w = 20 and l = 40 correct answer d"
Answer: d
Python program:
a = 120 / 2
b = 120 / 2
c = 120 / 2
d = b * c
e = 4 * 800
f = d - e
g = math.sqrt(f)
h = a - g
i = h / 2
Problem: lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 20 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "l = r l = 3 c r = c + 20 3 c = c + 20 c = 10 the answer is c ."
Answer: c
Python program:
a = 3 - 1
b = 20 / a
Problem: in a company , 48 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 85 % , b ) 80 % , c ) 75 % , d ) 70 % , e ) 65 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 52 % of all employees are women , so non - union women are 52 % - 18 % = 34 % 40 % of all employees are non - union . the percent of non - union employees who are women is 34 % / 40 % = 85 % the answer is a ."
Answer: a
Python program:
a = 100 - 48
b = 70 / 100
c = 60 * b
d = 60 - c
e = a - d
f = 100 - 60
g = e / f
h = 100 * g
Problem: by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 500 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.66 % , b ) 1.96 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 500 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 500 ) / 100 + ( 1.8 * 700 ) / 100 = 16.6 gms % of liquid x in resultant mixture = ( 16.6 / 1000 ) * 100 = 1.66 % a"
Answer: a
Python program:
a = 500 * 0
b = 700 * 1
c = a + b 
d = c / 1000
Problem: what number has a 5 : 1 ratio to the number 9 ?
Options: a ) 45 , b ) 50 , c ) 88 , d ) 52 , e ) 12
Rationale: "5 : 1 = x : 9 x = 45 answer : a"
Answer: a
Python program:
a = 9 * 5
Problem: there are 100 employees in a room . 99 % are president . how many managers must leave the room to bring down the percentage of president to 98 % ?
Options: a ) 1 , b ) 2 , c ) 46 , d ) 50 , e ) 97
Rationale: "we have 99 presidents and 1 director . that 1 director to compose 2 % of the total number of people , there must be 50 people in the room , hence 50 presidents must leave . answer : b ."
Answer: b
Python program:
a = 99 / 100
b = 100 * a
c = 98 / 100
d = 100 * c
e = b - d
f = 98 / 100
g = 1 - f
h = e / g
Problem: what is the compound interest paid on a sum of rs . 3000 for the period of 3 years at 10 % per annum .
Options: a ) 900 , b ) 930 , c ) 990 , d ) 993 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 interest % for 3 rd year = 10 + 10 % ( 10 + 11 ) = 10 + 2.1 = 12.1 total % of interest = 10 + 11 + 12.1 = 33.1 total interest = 33.1 % 3000 = 3000 * ( 33.1 / 100 ) = 993 answer d"
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 3
d = 3000 * c
e = d - 3000
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 15
Rationale: "3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 10 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 10 x = 15 since you need a 15 l solution , you must evaporate 35 of the original 50 l solution to get a 10 % solution . answer is a ."
Answer: a
Python program:
a = 50 / 100
b = a * 10
c = 50 - b
Problem: a person borrows rs . 6000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 120 rs , b ) 150 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 6000 * 6 * 2 ) / 100 ] - [ ( 6000 * 4 * 2 ) / 100 ] 720 - 480 = 240 gain in 1 year = ( 240 / 2 ) = 120 rs answer : a"
Answer: a
Python program:
a = 6000 * 6
b = a * 2
c = b / 100
d = 6000 * 4
e = d * 2
f = e / 100
g = c - f
h = g / 2
Problem: a person crosses a 1440 m long street in 12 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 7.2
Rationale: "speed = 1440 / ( 12 x 60 ) m / sec = 2 m / sec . converting m / sec to km / hr = 2 x ( 18 / 5 ) km / hr = 7.2 km / hr . answer : e"
Answer: e
Python program:
a = 1440 / 1000
b = 12 * const_60
c = b / 3600
d = a / c
Problem: an object thrown directly upward is at a height of h feet after t seconds , where h = - 14 ( t - 3 ) ^ 2 + 140 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 62 , b ) 68 , c ) 76 , d ) 84 , e ) 96
Rationale: "we see that h will be a maximum h = 140 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 14 ( 5 - 3 ) ^ 2 + 140 = - 14 ( 4 ) + 140 = 84 the answer is d ."
Answer: d
Python program:
a = negate * (
b = 3 + 2 
c = b - 3
d = c ** 2
e = a + d
Problem: rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage x .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % x = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Python program:
a = 2 * 10
b = 2 * 10
c = b + 1 
d = a * c
e = 25 / 100
f = e + 1 
g = 10 / f
h = 15 + 2 
i = g * h
j = d + i 
k = 653 - j
l = 2 * 10
m = 2 * 10
n = m + 1 
o = l * n
p = 25 / 100
q = p + 1 
r = 10 / q
s = 15 + 2 
t = r * s
u = o + t 
v = k / u
w = v * 100
Problem: the amount of time that three people worked on a special project was in the ratio of 2 to 3 to 4 . if the project took 90 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 18 hours , b ) 22 hours , c ) 25 hours , d ) 26 hours , e ) 20 hours
Rationale: "let the persons be a , b , c . hours worked : a = 2 * 90 / 9 = 20 hours b = 3 * 90 / 9 = 30 hours c = 4 * 90 / 9 = 40 hours c is the hardest worker and a worked for the least number of hours . so the difference is 40 - 20 = 20 hours . answer : e"
Answer: e
Python program:
a = 2 + 3 
b = a + 4 
c = 90 / b
d = c * 4
e = 2 + 3 
f = e + 4 
g = 90 / f
h = g * 2
i = d - h
Problem: a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 9 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 24 , e ) 27
Rationale: "i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 9 ) x solve for r , r = 33 33 - 9 = 24 mpg d"
Answer: d
Python program:
a = 462 - 336
b = a / 9
c = 336 / b
Problem: the ratio of the radius of two circles is 2 : 7 , and then the ratio of their areas is ?
Options: a ) 1 : 7 , b ) 2 : 9 , c ) 1 : 9 , d ) 4 : 49 , e ) 3 : 4
Rationale: "r 1 : r 2 = 2 : 7 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 4 : 49 answer : d"
Answer: d
Python program:
a = circle_area / (
Problem: karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many q miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) q = 24 miles . d is the correct answer ."
Answer: d
Python program:
a = 45 / 60
b = a * 4
c = b + 4 
d = 60 / 60
e = 45 / 60
f = d - e
g = c / f
h = g - 4
Problem: there are 7 thieves . they stole diamonds from a diamond merchant and ran away . while running , night sets in and they decide to rest in the jungle . when everybody was sleeping , two of them woke up and decided to divide the diamonds equally among themselves . but when they divided the diamonds equally , one diamond is left . so they woke up the 3 rd thief and tried to divide the diamonds equally again but still one diamond was left . then they woke up the 4 th thief to divide the diamonds equally again , and again one diamond was left . this happened with the 5 th and 6 th thief – one diamond was still left . finally , they woke up the 7 th thief and this time the diamonds were divided equally . how many diamonds did they steal in total ?
Options: a ) 1560 , b ) 1561 , c ) 1559 , d ) 1557 , e ) none of the above
Rationale: we need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2 , 3 , 4 , 5 , and 6 . the least common multiple of these numbers is 60 . so , we need a multiple of 7 that is 1 greater than a multiple of 60 . answer b
Answer: b
Python program:
a = 4 * 5
b = 7 + 3 
c = a * b
d = 4 * 5
e = c + d 
f = e + 3 
g = f * 7
Problem: in a race where 15 cars are running , the chance that car x will win is 1 / 4 , that y will win is 1 / 8 and that z will win is 1 / 12 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 11 / 24 , d ) 10 / 15 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 4 + 1 / 8 + 1 / 12 = 11 / 24 answer : c"
Answer: c
Python program:
a = 1 / 4
b = 1 / 8
c = a + b 
d = 1 / 12
e = c + d
Problem: find the compound interest on $ 26,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.93 , b ) 2552.26 , c ) 2524.23 , d ) 4098.25 , e ) 2512.23
Rationale: "principal = $ 26000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 26000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 30098.25 ci . = $ ( 30098.25 - 26000 ) = $ 4098.25 answer d ."
Answer: d
Python program:
a = 9 / 100
b = 1 + a 
c = b ** 20
d = 26 * 0
e = d - 26
Problem: some of 50 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 3 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "40 % is 20 % - points above 20 % and 10 % - points below 50 % . thus the ratio of 20 % - solution to 50 % - solution is 1 : 2 . 1 / 3 of the original paint was replaced . the answer is a ."
Answer: a
Python program:
a = 40 / 100
b = 50 / 100
c = a - b
d = 20 / 100
e = 50 / 100
f = d - e
g = c / f
Problem: shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 50 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 40 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 46
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 46 hence answer is e"
Answer: e
Python program:
a = 3 * 50
b = a - 50
c = b / 3
Problem: how many three digit numbers r are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples r - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Python program:
a = 1000 - 10
b = 78 * 78
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
Problem: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 60 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600
Rationale: "volume of pool = 60 * 150 * 10 cu . ft , 80 % full = 60 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 60 * 150 * 10 * 0.8 / 60 min = 1200 min c"
Answer: c
Python program:
a = 80 / 100
b = 60 * 150
c = b * 10
d = a * c
e = d / 60
Problem: a shopkeeper labeled the price of his articles so as to earn a profit of 50 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 35 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 150 . sp = rs . 150 - 10 % of 150 = rs . 150 - 15 = rs . 135 . gain = rs . 135 â € “ rs . 100 = rs . 35 therefore , gain / profit percent = 35 % . answer : option a"
Answer: a
Python program:
a = 100 + 50 
b = 100 + 50 
c = 10 / 100
d = b * c
e = a - d
f = e - 100
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 770 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 193 , c ) 195 , d ) 212 , e ) 213
Rationale: "total movies submitted are 770 . as per question we need to take 1 / 4 of 770 to be considered for top 10 movies = 192.25 approximate the value we 193 imo option b is the correct answer . . ."
Answer: b
Python program:
a = 770 / 4
Problem: 1 / 3 of girls , 1 / 2 of boys go to canteen . what factor and total number of classmates go to canteen .
Options: a ) 1 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 2 / 5 , e ) 2 / 3
Rationale: let total girls be 3 . . . and total boys be 2 . . . so total girls going to canteen = 1 boys going to canteen = 1 total no . of classmates = 5 ( only suppose . . . . . . to find out the factor of students going to canteen . . . ) factor of classmates going to canteen = 2 / 5 . answer : d
Answer: d
Python program:
a = 12 / 3
b = 12 / 2
c = a + b 
d = 12 + 12 
e = c / d
Problem: suraj has a certain average of runs for 9 innings . in the 10 th innings he scores 200 runs thereby increasing his average by 8 runs . what is his average after the 10 th innings ?
Options: a ) 149 , b ) 190 , c ) 128 , d ) 178 , e ) 190
Rationale: "to improve his average by 8 runs per innings he has to contribute 9 x 8 = 72 runs for the previous 8 innings . thus , the average after the 9 th innings = 200 - 72 = 128 . answer : c"
Answer: c
Python program:
a = 9 * 8
b = 200 - a
c = 10 - 9
d = b / c
Problem: at a particular graduation party with 220 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 12 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 36 , c ) 42 , d ) 68 , e ) 70
Rationale: "the correct method total = 220 . . 70 % of 220 = 154 got gifts . . 66 did not get gift , out of which 12 are males , so remaining 60 - 12 = 54 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 54 , 100 % = 54 * 100 / 60 = 90 . . ans 40 % of 90 = 36 b"
Answer: b
Python program:
a = 70 * 220
b = a / 100
c = 220 - b
d = c - 12
e = d * 100
f = 100 - 40
g = e / f
h = g * 40
i = h / 100
Problem: if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 3 = 1 / ( 2 * ( 10 ) ^ 3 ) , then m =
Options: a ) 4 , b ) 3 , c ) 1 , d ) 6 , e ) 8
Rationale: "1 / 5 ^ m * 1 / 4 ^ 3 = 2 * 1 / 2 ^ 3 * 5 ^ 3 * 8 2 ^ 3 * 5 ^ 3 * 8 / 4 ^ 3 = 5 ^ m or 5 ^ 3 = 5 ^ m m = 3 b"
Answer: b
Python program:
a = 1 / 4
b = a * 2
c = 1 / 5
d = c * 2
e = b + d 
f = 5 / 2
g = e - f
Problem: in town x , 64 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 34 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 42 are employed males , hence 22 % are employed females . ( employed females ) / ( total employed people ) = 22 / 64 = 34 % answer : d ."
Answer: d
Python program:
a = 64 - 42
b = a / 64
c = b * 100
Problem: if n divided by 7 has a remainder of 1 , what is the remainder when 3 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "as per question = > n = 7 p + 1 for some integer p hence 3 n = > 21 q + 3 = > remainder = > 6 for some integer q alternatively = > n = 2 > 3 n = > 3 = > 3 divided by 7 will leave a remainder 3 hence c"
Answer: c
Python program:
a = 3 * 1