euclaise/mathqa_programs huggingface dataset:
Problem: what is the dividend . divisor 14 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 131 , c ) c ) 148 , d ) d ) 158 , e ) e ) 160
Rationale: "d = d * q + r d = 14 * 9 + 5 d = 126 + 5 d = 131 answer b"
Answer: b
Python program:
a = 14 * 9
b = a + 5
Problem: shop offered 30 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 800 , c ) 600 , d ) 700 , e ) 750
Rationale: "sp * ( 70 / 100 ) = 560 sp = 8 * 100 = > cp = 800 answer : b"
Answer: b
Python program:
a = 30 / 100
b = 1 - a
c = 560 / b
Problem: if q = { 1 , 7 , 18 , 20 , 29 , 33 } , how much less is the mean of the numbers in q than the median of the numbers in q ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 1 + 7 + 18 + 20 + 29 + 33 ) / 6 = 18 median = ( 18 + 20 ) / 2 = 19 difference = 1 option a
Answer: a
Python program:
a = 18 + 20 
b = a / 2
c = 1 + 7 
d = c + 18 
e = d + 20 
f = e + 29 
g = f + 33 
h = 2 * 3
i = g / h
j = b - i
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 20 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 86 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 20 % more than company a ' s assets which is 120 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 60 a + b = 160 kw = 120 kw / ( a + b ) * 100 = 120 / 160 * 100 = 75 % b"
Answer: b
Python program:
a = 100 + 20 
b = 100 + 20 
c = b / 2
d = 100 + c 
e = a / d
f = e * 100
Problem: a bowl of fruit contains 12 apples and 23 oranges . how many oranges must be removed so that 60 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 15 , d ) 17 , e ) 20
Rationale: "number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 60 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 12 + ( 23 - x ) = 35 - x 12 / ( 35 - x ) = 6 / 10 = > 20 = 35 - x = > x = 15 answer c"
Answer: c
Python program:
a = 12 + 23 
b = 60 / 100
c = a * b
d = c - 12
e = 60 / 100
f = d / e
Problem: if a town of 25,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) 26000 , b ) 27000 , c ) 28000 , d ) 29000 , e ) 30000
Rationale: "let population in the beginning = 100 at the end of 1 st year population = 100 + 1 % of 100 = 100 + 1 = 101 at the end of 2 nd year population = 101 + 1 % of 101 = 101 + 1 approx = 102 approx ( on the lower side because 1 % of 101 is greater than 1 ) at the end of 3 rd year population = 102 + 1 % of 102 = 102 + 1 approx = 103 approx ( on the lower side because 1 % of 102 is greater than 1 ) at the end of 4 th year population = 103 + 1 % of 103 = 103 + 1 approx = 104 approx ( on the lower side because 1 % of 103 is greater than 1 ) at the end of 5 th year population = 104 + 1 % of 104 = 104 + 1 approx = 105 approx ( on the lower side because 1 % of 104 is greater than 1 ) i . e . 5 % greater than 25000 = 25000 + 5 % of 25000 = 25000 + 1250 = 26250 ( on the lower side ) i . e . population must be greater than 26250 but since the closest option is 26000 so answer : option a"
Answer: a
Python program:
a = 3 + 4 
b = 5 * a
c = b * 100
d = 3 + 4 
e = d + 3 
f = c * e
Problem: one ton has 2100 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 ) 1680 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2100 pound = 13 * 2100 * 16 ounces . hence the answer is ( 13 * 2100 * 16 ) / 260 = 1680 . answer : a ."
Answer: a
Python program:
a = 13 * 2100
b = a * 16
c = 16 * 16
d = c + 4 
e = b / d
Problem: the salary of a worker is first increased by 25 % and afterwards reduced by 25 % . what is the net change in the worker ' s salary ?
Options: a ) 3.25 % increase , b ) 3.25 % decrease , c ) 6.25 % increase , d ) 6.25 % decrease , e ) no change
Rationale: "let x be the original salary . the final salary is 0.75 ( 1.25 x ) = 0.9375 x the answer is d ."
Answer: d
Python program:
a = 25 + 100 
b = 25 + 100 
c = b * 25
d = c / 100
e = a - d
f = 100 - e
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 13 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 10
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 13 = > m = 39 answer a"
Answer: a
Python program:
a = 2 / 3
b = 13 / a
c = b - 13
Problem: perimeter of front wheel = 30 , back wheel = 20 . if front wheel revolves 240 times . how many revolutions will the back wheel take ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 360 , e ) 480
Rationale: sice the distance covered by both the wheels should be same so let x be the no . of revolutions by the back wheel so 240 * 2 * pie * 30 = x * 2 * pie * 20 so x = 360 . answer : d
Answer: d
Python program:
a = 30 * 240
b = a / 20
Problem: 15 litres of mixture contains 25 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 20.83 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 %
Rationale: alcohol in the 15 litres of mix . = 25 % of 15 litres = ( 25 * 15 / 100 ) = 3.75 litres water in it = 15 - 3.75 = 11.25 litres new quantity of mix . = 15 + 3 = 18 litres quantity of alcohol in it = 3.75 litres percentage of alcohol in new mix . = 3.75 * 100 / 18 = 20.83 % answer is a
Answer: a
Python program:
a = 15 + 3 
b = 100 - 25
c = b / 100
d = c * 15
e = d + 3 
f = a - e
g = 15 + 3 
h = f / g
i = h * 100
Problem: rs . 800 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 800 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1052 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 800 ) = rs . 156 rate = ( 100 x 156 / 800 x 3 ) = 6 1 / 2 % new rate = ( 6 1 / 2 + 4 ) % = 10 1 / 2 % new s . i . = rs . ( 800 x 21 / 2 x 3 / 100 ) rs . 252 . ∴ new amount = rs . ( 800 + 252 ) = rs . 1052 . answer c"
Answer: c
Python program:
a = 956 - 800
b = a * 100
c = 800 * 3
d = b / c
e = d + 4 
f = 800 * e
g = f * 3
h = g / 100
i = 800 + h
Problem: a certain college ' s enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 17.5 % , b ) 24 % , c ) 30 % , d ) 35 % , e ) 38 %
Rationale: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 120 and enrollment in 1993 will be 120 * 1.15 = 138 increase in 1993 from 1991 = 138 - 100 = 38 answer : e"
Answer: e
Python program:
a = 100 + 20 
b = 100 + 15 
c = b / 100
d = a * c
e = d - 100
Problem: sonika deposited rs . 6200 which amounted to rs . 7200 after 5 years at simple interest . had the interest been 3 % more . she would get how much ?
Options: a ) 9680 , b ) 8130 , c ) 8134 , d ) 8556 , e ) 9808
Rationale: "( 6200 * 5 * 3 ) / 100 = 930 7200 - - - - - - - - 8130 answer : b"
Answer: b
Python program:
a = 3 / 100
b = 7200 - 6200
c = b / 5
d = c / 6200
e = a + d 
f = e * 6200
g = f * 5
h = g + 6200
Problem: a bag of potatoes weighs 50 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 50 ÷ 5 = 10 . answer : c"
Answer: c
Python program:
a = 50 / 1
Problem: if x is a positive integer , then the least value of x for which x ! is divisible by 100,000 is ? can someone please explain intuitively what the question is asking ?
Options: a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30
Rationale: in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d .
Answer: d
Python program:
a = 10 / 2
b = a * 4
Problem: there is enough provisions for 600 men in an army camp for 25 days . if there were 200 men less , how long will the provision last ?
Options: a ) 50 days , b ) 60 days , c ) 70 days , d ) 75 days , e ) 90 days
Rationale: exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 200 * d 2 d 2 = 600 * 25 / 200 = 75 days . answer : d
Answer: d
Python program:
a = 600 * 25
b = a / 200
Problem: a person spent rs . 8,550 from his salary on food and 8,640 on house rent . after that he was left with 40 % of his monthly salary . what is his monthly salary ?
Options: a ) 38,650 , b ) 28,650 , c ) 48,650 , d ) 68,650 , e ) 18,650
Rationale: "total money spent on food and house rent = 8,550 + 8,640 = 17,190 which is 100 - 40 = 60 % of his monthly salary ∴ his salary = 17190 x 100 / 60 = 28650 answer : b"
Answer: b
Python program:
a = 4 + 1 
b = a * 100
c = b + 40 
d = math.sqrt(100)
e = c / d
Problem: when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 62 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 26 = 62 - x or , 4 x = 88 or , x = 22 . answer : e"
Answer: e
Python program:
a = 62 + 26 
b = 3 + 1 
c = a / b
Problem: find the principle on a certain sum of money at 6 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 979 , b ) 1288 , c ) 2778 , d ) 2682 , e ) 1021
Rationale: "1120 = p [ 1 + ( 6 * 12 / 5 ) / 100 ] p = 979 answer : a"
Answer: a
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 6
e = d / 100
f = e + 1 
g = 1120 / f
Problem: my watch gains 5 min every hour . how many degrees the second hand moves in every min ?
Options: a ) 300 , b ) 350 , c ) 390 , d ) 400 , e ) 450
Rationale: gain 5 min every 1 hr degrees moves = = > 390 answer c
Answer: c
Python program:
a = 3600 / 10
b = 5 + const_60 
c = a * b
d = c / const_60
Problem: if 5 cats can kill 5 rats in 5 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 5 minutes
Rationale: "it will take 5 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 5 minutes , so 100 cats can kill 100 rats in 5 minutes answer e"
Answer: e
Python program:
a = 5 * 1
Problem: 4.2 x 4.2 - 1.9 x 1.9 / 2.3 x 6.1 is equal to :
Options: a ) 2 , b ) 1 , c ) 3 , d ) 4 , e ) 8
Rationale: "given expression = ( a 2 - b 2 ) / ( a + b ) ( a - b ) = ( a 2 - b 2 ) / ( a 2 - b 2 ) = 1 . answer is b ."
Answer: b
Python program:
a = 4 * 2
b = 1 * 9
c = a - b
d = c / 2
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 4 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 288 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
Rationale: "since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 4 ) or $ 288 . the best answer is therefore a . answer : a ."
Answer: a
Python program:
a = 2 / 3
b = 36 * a
c = 1 / 3
d = b / c
e = 2 * 0
Problem: calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10 % of its volume is occupied by concrete ?
Options: a ) 6000 , b ) 5400 , c ) 3800 , d ) 4700 , e ) 2500
Rationale: "explanation : let ' b ' be the nuber of bricks . = > 10 x 4 / 100 x 5 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x b = > 10 x 20 x 90 = 15 x 2 x b = > b = 6000 answer is a"
Answer: a
Python program:
a = 4 / 100
b = 10 * a
c = b * 5
d = 10 / 100
e = 1 - d
f = c * e
g = 25 / 100
h = 15 / 100
i = g * h
j = 8 / 100
k = i * j
l = f / k
Problem: in how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 28400 , b ) 28500 , c ) 28600 , d ) 28700 , e ) 28800
Rationale: "number of ways = 2 * 5 ! * 5 ! = 28800 answer is e"
Answer: e
Python program:
a = math.factorial(5)
b = math.factorial(5)
c = a * b
Problem: the average monthly salary of laborers and supervisors in a factory is rs . 1250 per month ; where as the average monthly salary of 6 supervisors is rs . 2450 . if the average monthly salary of the laborers is rs . 850 find the number of laborers ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "2450 850 \ / 1250 / \ 400 1200 1 : 3 1 - - > 6 3 - - > ? 18 answer : e"
Answer: e
Python program:
a = 2450 * 6
b = 1250 * 6
c = a - b
d = 1250 - 850
e = c / d
f = e * 2
g = f - 4
h = g - 2
Problem: in a digital circuit which was to implement ( a b ) + ( a ) xor ( b ) , the designer implements ( a b ) ( a ) xor ( b ) what is the probability of error in it ?
Options: a ) 25 % , b ) 35 % , c ) 75 % , d ) 45 % , e ) 55 %
Rationale: a b ab a xor b ( ab ) + ( a xor b ) ( ab ) ( a xor b ) 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 so , we are getting 3 wrong answers out of 4 probability of error is 3 / 4 = 75 % answer : c
Answer: c
Python program:
a = 3 / 4
b = a * 100
Problem: if 4 men can colour 48 m long cloth in 2 days , then 5 men can colour 36 m long cloth in
Options: a ) 1.2 day , b ) 2.0 days , c ) 3 days , d ) 4.2 days , e ) 5 days
Rationale: the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 5 = 1.2 day . a
Answer: a
Python program:
a = 4 * 2
b = 48 / a
c = b * 5
d = 36 / c
Problem: a man gains 10 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 120 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 110 / 100 ) x = 11 x / 10 new s . p . = 2 ( 11 x / 10 ) = 22 x / 10 profit = 22 x / 10 - x = 12 x / 10 profit % = ( profit / c . p . ) * 100 = > ( 12 x / 10 ) * ( 1 / x ) * 100 = 120 % option b"
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = b * 2
d = c - 1
e = d * 100
f = e + 100
Problem: man 1 does a work in 10 days and man 2 does the same work in 15 days . in how many days they together will do the same work ?
Options: a ) 10 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: man 1 day work = 1 / 10 man 2 day work = 1 / 15 both work = 1 / 10 + 1 / 15 = = = > 3 + 2 / 30 = = > 1 / 6 answer c
Answer: c
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1 / c
Problem: from a container having pure milk , 20 % is replaced by water and the process is repeated thrice . at the end of the third operation , the milk is
Options: a ) 40 % pure , b ) 50 % pure , c ) 51.2 % pure , d ) 58.8 % pure , e ) none
Rationale: "solution let total quantity of original milk = 100 gm . milk after first operation = 80 % of 1000 ‹ = › 800 gm . milk after second operation = 80 % of 800 ‹ = › 640 gm . milk after third operation = 80 % of 640 ‹ = › 512 gm . strength of final mixtures = 51.2 % . answer c"
Answer: c
Python program:
a = 100 - 20
b = a / 100
c = b ** 3
d = c * 100
Problem: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 6 ?
Options: a ) 5 , b ) 12 , c ) 10 , d ) 20 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 6 ? 9 ^ 6 = ( 3 ^ 2 ) ^ 6 = 3 ^ 12 b . 12"
Answer: b
Python program:
a = 9 - 6
b = a * 6
Problem: 1396 x 1396
Options: a ) 1948816 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1396 x 1396 = ( 1396 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 4 ) 2 - ( 4 x 1400 x 4 ) = 1948816 . answer : option a"
Answer: a
Python program:
a = 1396 / 1396
b = a * 100
Problem: a man invested rs . 4940 in rs . 10 shares quoted at rs . 9.50 . if the rate of dividend be 14 % , his annual income is
Options: a ) 708 , b ) 718 , c ) 738 , d ) 748 , e ) 728
Rationale: "market value of a share = rs . 9.50 investment = rs . 4940 number of shares = 4940 / 9.50 = 520 face value of a share = rs . 10 dividend = 14 % dividend per share = ( 10 × 14 ) / 100 = rs . 1.4 his annual income = 520 × 1.4 = rs . 728 answer is e ."
Answer: e
Python program:
a = 14 / 100
b = 4940 / 9
c = b * 10
d = a * c
Problem: if 20 gallons of grape juice are added to 40 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 ) 34 % , e ) 40 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.10 = 4 gallons of grape juice . 40 × 0.90 = 36 gallons of other components . if we add 20 gallons of grape juice , we will end up with 24 gallons of grape juice and 36 gallons of other components , and we will have a total of 60 gallons of the mixture . so 24 / 60 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 40 / 100 = 40 % . the correct answer is choice ( e )"
Answer: e
Python program:
a = 10 / 100
b = a * 40
c = b + 20 
d = 40 + 20 
e = c / d
f = e * 100
Problem: the l . c . m . of two numbers is 30 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 25 , b ) 32 , c ) 40 , d ) 53 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 30 or x = 5 . the numbers are 10 and 15 . hence , required sum = ( 10 + 15 ) = 25 . answer : option a"
Answer: a
Python program:
a = 2 * 3
b = 30 / a
c = b * 3
d = 2 * 3
e = 30 / d
f = e * 2
g = c + f
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 12 more blue balls than white balls , and twice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 12 more blue balls than white balls . . . equation # 2 : y = 12 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 2 y solve equation # 2 for z : z = y - 12 now , we can replace both x and z with y in equation # 1 2 y + y + ( y - 12 ) = 100 4 y - 12 = 100 4 y = 112 y = 28 there are 28 blue balls . this is 15 more than the number of white balls , so z = 16 . that ' s the answer . just as a check , x = 56 , and 56 + 28 + 16 = 100 . answer = 16 , ( e )
Answer: e
Python program:
a = 12 * 3
b = 100 - a
c = b / 4
Problem: bill and jane play a simple game involving two fair dice , each of which has 6 sides numbered from 1 to 6 ( with an equal chance of landing on any side ) . bill rolls the dice and his score is the total of the two dice . jane then rolls the dice and her score is the total of her two dice . if jane ’ s score is higher than bill ’ s , she wins the game . what is the probability the jane will win the game ?
Options: a ) 15 / 36 , b ) 175 / 432 , c ) 575 / 1296 , d ) 583 / 1296 , e ) 1 / 2
Rationale: there are three possible outcomes in the game : 1 . b wins 2 . j wins 3 . draw so , 1 = p ( j ) + p ( b ) + p ( draw ) 1 = p ( j ) + p ( b ) + p ( draw ) the probability of b winning or j winning the game is same . so , 1 = 2 ∗ p ( j ) + p ( draw ) 1 = 2 ∗ p ( j ) + p ( draw ) so , we need to calculate the probability of a draw . a draw can happen when both will have the same sum . the possible sums are - 2 , 34 , 56 , 78 , 910 , 1112 prob . of each sum is - 2 - 11 - 1 / 36 3 - 1 2 , 2 1 - 2 / 36 4 - 1 3 , 2 2 , 3 1 - 3 / 36 5 - 1 4 , 2 3 , 3 2 , 41 - 4 / 36 6 - 1 5 , 2 4 , 3 3 , 4 2 , 5 1 - 5 / 36 7 - 1 6 , 2 5 , 3 4 , 4 3 , 5 2 , 61 - 6 / 36 8 - 2 6 , 3 5 , 4 4 , 5 3 , 6 2 , - 5 / 36 9 - 3 6 , 4 5 , 5 4 , 63 - 4 / 36 10 - 4 6 , 5 5 , 6 4 - 3 / 36 11 - 5 6 , 6 5 - 2 / 36 12 - 6 6 - 1 / 36 now , since both have to get the same sum , the probability will be same for both and the combined probability will be the square of the probabilities i . e . 2 - ( 1 / 36 ) ^ 2 3 - ( 2 / 36 ) ^ 2 etc . squaring the probabilities and adding them will give 146 / 1296 so , p ( d ) = 146 / 1296 1 = 2 * p ( j ) + p ( d ) 2 * p ( j ) = 1150 / 1296 p ( j ) = 575 / 1296 ans . c
Answer: c
Python program:
a = 6 - 1
b = a * 6
c = 6 - 1
d = c * 2
e = d + 1 
f = b * e
g = f / 6
h = g * 2
i = 6 * 6
j = h + i 
k = 6 * 6
l = k ** 2
m = j / l
n = 1 - m
o = n / 2
Problem: the total age of a and b is 11 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 11 + b + c = > a ? c = 11 + b ? b = 11 = > c is younger than a by 11 years answer : option a"
Answer: a
Python program:
a = 11 * 1
Problem: if the sides of a triangle are 30 cm , 40 cm and 50 cm , what is its area ?
Options: a ) 400 , b ) 500 , c ) 550 , d ) 600 , e ) 700
Rationale: "the triangle with sides 30 cm , 40 cm and 50 cm is right angled , where the hypotenuse is 50 cm . area of the triangle = 1 / 2 * 40 * 30 = 600 cm 2 answer : option d"
Answer: d
Python program:
a = 40 * 50
b = a / 2
Problem: the area of an equilateral triangle is subtracted from its base , and the perimeter is then added to this total , the result is 4 . what is the height of the equilateral triangle if its base is 2 ?
Options: a ) 2
b ) 3
c ) 4
d ) 5
e ) 6
Rationale: an eqilateral triangle means all sides are equal ; therefore , base = side . the equation is ; base - area + perimeter = b - a + p = b - 1 / 2 bh + 3 b , and b = 2 . so , 2 - 2 / 2 h + 6 = 4 , and 8 - h = 4 . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : c
Answer: c
Python program:
a = 2 - 4
b = 2 * 3
c = a + b
Problem: ( 6 ! - 4 ! ) / 5 ! = ?
Options: a ) 29 / 5 , b ) 28 / 3 , c ) 27 / 6 , d ) 25 / 4 , e ) 29 / 6
Rationale: ( 6 ! - 4 ! ) / 5 ! ( 4 ! * 5 * 6 - 4 ! ) / 5 ! 4 ! ( 5 * 6 - 1 ) / 4 ! * 5 29 / 5 answer a
Answer: a
Python program:
a = math.factorial(6)
b = math.factorial(4)
c = a - b
d = math.factorial(5)
e = c / d
Problem: a sum of money is sufficient to pay p ' s wages for 24 days and q ' s wages for 40 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: let the total money be $ x p ' s 1 day work = $ x / 24 q ' s 1 day work = $ x / 40 p + q 1 day work = $ x / 15 money is sufficient to pay the wages of both for 15 days answer is d
Answer: d
Python program:
a = 1 / 24
b = 1 / 40
c = a + b 
d = 1 / c