euclaise/mathqa_programs huggingface dataset:
Problem: by how much does the larger root of the equation 2 a ^ 2 + 5 a = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: for 2 a ^ 2 + 5 a = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .
Answer: e
Python program:
a = 5 ** 2
b = 2 * 12
c = b * 4
d = a + c 
e = math.sqrt(d)
f = 5 + e 
g = 2 * 2
h = f / g
i = 5 ** 2
j = 2 * 12
k = j * 4
l = i + k 
m = math.sqrt(l)
n = 5 - m
o = 2 * 2
p = n / o
q = h - p
Problem: if x + 1 / x = 2 then find x 2 + 1 / x 2
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: if x + 1 / x = p = = > x ^ 2 + 1 / x ^ 2 = p ^ 2 - 2 ans = 2 ^ 2 - 2 = 2 answer : b
Answer: b
Python program:
a = 2 / 1
Problem: the faces of a triangular prism are to be painted by 5 different colors . in how many ways can be this be done ?
Options: a ) a . 720
b ) b . 256
c ) c . 1
d ) d . 120
e ) e . 36
Rationale: if i have to paint 5 sides with 5 different colour . . . first face can have 5 c 1 options , 2 nd would have 4 c 1 , and subsequent ones would have 3 c 1 , 2 c 1 and 1 options respectively . total options = 5 c 1 x 4 c 1 x 3 c 1 x 2 c 1 x 1 = 120 distinct ways correct answer - d
Answer: d
Python program:
a = math.factorial(5)
b = a / 1000
Problem: three interviewers , a , b , and c are interviewing 30 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer a admitted 10 applicants , b admitted 12 applicants , and c admitted 15 applicants , at least how many applicants get the admission ?
Options: a ) 6 , b ) 2 , c ) 0 , d ) 8 , e ) 12
Rationale: "if a admitted 10 are overlapping with b admission of 12 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : c"
Answer: c
Python program:
a = 10 + 12 
b = a + 15 
c = b - 30
Problem: during a sale of 30 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies . the store still makes a profit of 12 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: "hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . b"
Answer: b
Python program:
a = 12 / 100
b = a + 1 
c = 30 / 100
d = 1 - c
e = 20 - 14
f = e / 20
g = d * f
h = b / g
i = h - 1
j = i * 100
Problem: there are two cubes with ratio between volume is 125 : 64 . then what is the value of length of each cube ?
Options: a ) 25 : 16
b ) 16 : 25
c ) 4 : 5
d ) 5 : 4
e ) 150 : 96
Rationale: given 6 a 12 : a 22 = 150 : 96 then a 12 : a 22 = 25 : 16 a 1 : a 2 = 5 : 4 so the answer is d
Answer: d
Python program:
a = 1 / 3
b = 125 ** a
c = 1 / 3
d = 64 ** c
e = b / d
Problem: how many positive integers less than 247 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 41 , c ) 42 , d ) 53 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 41 , as all the other choices are very far away . the numbers 244 will come and complete the list that ’ s ( naughty or nice ) under 250 . answer choice b is correct here .
Answer: b
Python program:
a = 4 + 4 
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: ram , who is half as efficient as krish , will take 36 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 36 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 36 days is 36 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 36 w / 3 w = 12 days answer b"
Answer: b
Python program:
a = 1 / 36
b = 36 / 2
c = 1 / b
d = a + c 
e = 1/(d)
Problem: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 24 different signs . if the company used 22 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 24 signs ?
Options: a ) 246 , b ) 248 , c ) 92 , d ) 15,128 , e ) 30,256
Rationale: "# of 2 - letter codes possible from 24 different signs = 24 * 24 . # of 2 - letter codes possible from 22 different signs = 22 * 22 . the difference = 24 ^ 2 - 22 ^ 2 = ( 24 - 22 ) ( 24 + 22 ) = 92 . answer : c ."
Answer: c
Python program:
a = 24 - 22
b = 22 * a
c = 24 - 22
d = b * c
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 5 as remainder
Options: a ) 1637 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1635
Rationale: let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 5 5 x = 1360 x = 272 large number = 272 + 1365 = 1637 a
Answer: a
Python program:
a = 1365 - 5
b = 6 - 1
c = a / b
d = c * 6
e = d + 5
Problem: the sum of ages of 10 children born at the intervals of 1 years each is 105 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 2 , d ) 7 , e ) 6
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 , ( x + 3 ) , ( x + 4 ) , ( x + 5 ) , ( x + 6 ) , ( x + 7 ) , ( x + 8 ) , and ( x + 9 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) + ( x + 7 ) + ( x + 8 ) + ( x + 9 ) = 105 10 x = 60 x = 6 age of the youngest child = x = 6 years . answer : e"
Answer: e
Python program:
a = 105 / 10
b = a - 1
c = b - 1
Problem: a pipe can fill a cistern in 33 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 33 minutes 1 / 11 part filled in = 33 * 1 / 11 = 3 minutes answer is c"
Answer: c
Python program:
a = 1 / 11
b = 33 * a
Problem: a wooden cube whose edge length is 8 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 46.3 % , b ) 50.4 % , c ) 54.2 % , d ) 57.8 % , e ) 61.3 %
Rationale: "there are a total of 8 * 8 * 8 = 512 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 6 * 6 * 6 = 216 cubes . the number of cubes with at least one side painted red is 512 - 216 = 296 cubes the probability that a cube has at least one side painted red is 296 / 512 which is about 57.8 % the answer is d ."
Answer: d
Python program:
a = 1 * 4
b = volume_cube / (
c = 1 - b
d = 100 * c
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 36 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 36 days whole work will be done by y in 36 * 5 / 4 = 45 days answer is a
Answer: a
Python program:
a = 8 / 40
b = 1 - a
c = 1/(b)
d = 36 * c
Problem: mr . hanson has a pool of money from which to give out christmas bonuses to his 5 employees . he wants all his employees to have identical bonuses , but when he divides them out , he finds he has 2 dollars left over , as the payroll system will only accept whole dollar amounts . the next christmas , mr . hanson discovers the pool for the bonuses is 3 times the size . this time , how much money will be left over ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: set x = to amount of money for bonuses , and y to be the amount of each individual bonus . x = 5 * y + 2 . 3 x = 15 * y + 6 3 x = 3 * 5 * y + 6 3 x = 5 ( 3 ( y + 1 ) ) + 1 remainder is then 1 , so option b .
Answer: b
Python program:
a = 5 - 3
b = a - 1
Problem: calculate 469138 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4690910862 , d ) 4586870843 , e ) none
Rationale: "answer 469138 x 9999 = 469138 x ( 10000 - 1 ) = 4691380000 - 469138 = 4690910862 . option : c"
Answer: c
Python program:
a = 469138 * 9999
Problem: the cash difference between the selling prices of an book at a profit of 8 % and 16 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 52 : 33 , c ) 52 : 53 , d ) 27 : 29 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 108 % of x / 116 % of x = 108 / 116 = 27 / 29 = 27 : 29 d"
Answer: d
Python program:
a = 100 + 8 
b = 100 + 16 
c = a / b
Problem: if a rectangular billboard has an area of 117 square feet and a perimeter of 44 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 117 and a perimeter of 44 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 117 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 117 , so the correct answer is let ' s test answer d : 9 if . . . the shorter side = 9 . . . the area = 117 . . . . 117 / 9 = 13 = the longer side perimeter = 9 + 9 + 13 + 13 = 44 d"
Answer: d
Python program:
a = 44 / 2
b = 44 / 2
c = b ** 2
d = 4 * 117
e = c - d
f = math.sqrt(e)
g = a - f
h = g / 2
Problem: bird is flying 120 km / hr between b to r . two trains at b to r at 60 kmph . the distance traveled by the bird before it is killed ?
Options: a ) 90 kms . , b ) 100 kms . , c ) 110 kms . , d ) 120 kms . , e ) 130 kms .
Rationale: it will depend on the distance between b and r . if distance between b and r is 120 kms , time taken by trains before collision = 120 / ( 60 + 60 ) = 1 hr distance traveled by bird in 1 hr = 120 kms . so the distance traveled by the bird before it is killed = 120 kms . answer : d
Answer: d
Python program:
a = 60 + 60 
b = 120 / a
c = b * 120
Problem: a = 5 ^ 15 - 125 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get none different values and answer is a . . . ."
Answer: a
Python program:
a = 3 * 4
b = 15 - a
Problem: in a 600 m race , the ratio of the speeds of two contestants a and b is 5 : 4 . a has a start of 100 m . then , a wins by :
Options: a ) 200 m , b ) 20 m , c ) 403 m , d ) 20 m , e ) 23 m
Rationale: to reach the winning post a will have to cover a distance of ( 600 - 100 ) m , i . e . , 500 m . while a covers 5 m , b covers 4 m . while a covers 500 m , b covers 4 x 500 / 5 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 200 m behind . a wins by 200 m . answer : a
Answer: a
Python program:
a = 600 - 100
b = a * 4
c = b / 5
d = 600 - c
Problem: at present the ratio between the ages of arun and deepak is 2 : 3 . after 5 years , arun ' s age will be 25 years . what is the age of deepak at present ?
Options: a ) 20 years , b ) 30 years , c ) 15 years , d ) 25 years , e ) 28 years
Rationale: "let the present ages of arun and deepak be 2 x years and 3 x years respectively 2 x + 5 = 25 2 x = 20 x = 10 deepak ' s age = 3 x = 30 years answer is b"
Answer: b
Python program:
a = 25 - 5
b = a * 3
c = b / 2
Problem: the length of the bridge is 200 m , which a 100 m long train cross in 60 sec . then what is the speed of train ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 10 , e ) 8
Rationale: speed = length / time length = ( 200 + 100 ) = 300 m time = 60 sec speed = 300 / 60 = 5 m / sec answer b
Answer: b
Python program:
a = 200 + 100 
b = a / 60
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × e , what is the value of e ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × e = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x e = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x e = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x e e = 7 ^ 2 = 49 answer d"
Answer: d
Python program:
a = 105 ** 3
b = 21 * 25
c = b * 45
d = a / c
Problem: if i earn a profit 50 $ in a day and i have 9 employees . after keeping 10 percent profit for me , and distribute remianing money equally among my employees then how much each employee would get ?
Options: a ) $ 3 , b ) $ 7 , c ) $ 1 , d ) $ 5 , e ) $ 9
Rationale: since i earned $ 50 sp 10 percent would be 5 $ and 45 $ would remain . dividing 45 by 9 , each employee would get 5 $ each and hince option d is correct .
Answer: d
Python program:
a = 100 - 10
b = 50 * a
c = 100 * 9
d = b / c
Problem: a 14 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 175 , b ) rs . 92 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 14 , investment = rs . ( 100 / 8 x 14 ) = rs . 175 ∴ market value of rs . 100 stock = rs . 175 answer a"
Answer: a
Python program:
a = 100 / 8
b = a * 14
Problem: in the third grade of windblown school there are 84 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 84 failed in math = 84 / 3 = 28 failed in literature = 84 / 6 = 14 the least failed in both can be 0 while max can be 14 answer a"
Answer: a
Python program:
a = 84 / 3
b = 84 / 6
c = min(a)
Problem: the diameters of two spheres are in the ratio 1 : 2 what is the ratio of their volumes ?
Options: a ) 1 : 9 , b ) 1 : 2 , c ) 1 : 8 , d ) 1 : 1 , e ) 1 : 6
Rationale: "1 : 8 answer : c"
Answer: c
Python program:
a = 1 / 4
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 25 each with brokerage being 2.5 % .
Options: a ) 237 , b ) 320 , c ) 177 , d ) 166 , e ) 111
Rationale: "explanation : cost of each share = ( 25 + 2.5 % of 25 ) = rs . 25.625 therefore , number of shares = 8200 / 25.625 = 320 answer : b"
Answer: b
Python program:
a = 2 / 5
b = 25 + a 
c = 8200 / b
d = math.floor(c)
Problem: find the distance covered by a man walking for 30 min at a speed of 10 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 20 / 60 = 5 km answer is d"
Answer: d
Python program:
a = 10 * 1000
b = a / const_60
c = 30 * b
d = c / 1000
Problem: a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , one - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 7 / 5 , d ) 5 / 7 , e ) 3 / 2
Rationale: "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were right - handed - - > 6 * 1 / 3 = 2 were right - handed and 4 left - handed . the number of right - handed players who were not at practice that day is 9 - 2 = 7 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 7 / 5 . answer : c ."
Answer: c
Python program:
a = 1 / 2
b = 2 / 3
c = 1 - b
d = 2 / 3
e = 1 - d
f = 2 / 3
g = e * f
h = c - g
i = a - h
j = 1 / 2
k = 2 / 3
l = 1 - k
m = 2 / 3
n = l * m
o = j - n
p = i / o
Problem: a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 4 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 5 : 11 , e ) 7 : 3
Rationale: "container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 4 ounces in the ratio 1 : 3 or , x + 3 x = 4 gives x ( alcohol ) = 1 and remaining water = 3 mixing both we have alcohol = 4 + 1 and water = 8 + 3 ratio thus alcohol / water = 5 / 11 answer d"
Answer: d
Python program:
a = 1 + 2 
b = 1 / a
c = 12 * b
d = 1 + 3 
e = 1 / d
f = 4 * e
g = c + f 
h = 12 + 4 
i = 1 + 2 
j = 1 / i
k = 12 * j
l = 1 + 3 
m = 1 / l
n = 4 * m
o = k + n 
p = h - o
q = g / p
Problem: the number which exceeds 16 % of it by 84 is :
Options: a ) 100 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 84 x - 16 / 100 x = 84 x - 4 / 25 x = 84 21 / 25 x = 84 x = ( 84 x 25 / 21 ) = 100 answer a"
Answer: a
Python program:
a = 84 * 100
b = 100 - 16
c = a / b
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 21 in two years , at the same percent rate per annum ?
Options: a ) rs . 520 , b ) rs . 480 , c ) rs . 420 , d ) rs . 200 , e ) rs . 600
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 21 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 21 – 20 ) / 20 ] * 100 = 5 % p . a . let the principal be rs . x time = t = 2 years % rate = 5 % p . a . si = ( prt / 100 ) 20 = ( x * 5 * 2 ) / 100 x = rs . 200 answer : d"
Answer: d
Python program:
a = 21 - 20
b = a * 100
c = b / 2
Problem: ratio between rahul and deepak is 4 : 3 , after 4 years rahul age will be 32 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 20 , d ) 21 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 4 = 32 = > x = 7 so deepak age is = 3 ( 7 ) = 21 option d"
Answer: d
Python program:
a = 32 - 4
b = a * 3
c = b / 4
Problem: a train 850 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 510 , b ) 450 , c ) 500 , d ) 520 , e ) 589
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 850 + x ) / 60 = 65 / 3 x = 450 m . answer : option b"
Answer: b
Python program:
a = 78 - 1
b = a * const_0_2778
c = 850 / b
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 140 of the workers of that company are men , how many of the workers are women ?
Options: a ) 85 , b ) 95 , c ) 105 , d ) 120 , e ) 210
Rationale: "20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 80 * 1 + 40 * 2 ) / 3 = 160 / 3 % are men total = 120 * 300 / 160 = 225 no . of women = 225 - 140 = 85 a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 3
c = 20 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 40 / 100
i = g * h
j = e + i 
k = 140 / j
l = 1 / 3
m = 20 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 40 / 100
t = r * s
u = p - t
v = n + u 
w = k * v
Problem: if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a ∪ b ) = 6 / 15 find p ( a | b )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a ∪ b ) / p ( b ) p ( a | b ) = ( 6 / 15 ) / ( 4 / 15 ) = 3 / 2 . c"
Answer: c
Python program:
a = 6 / 15
b = 2 / 15
c = a / b
Problem: worker a takes 8 hours to do a job . worker b takes 6 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 24 / 7 , e ) 80 / 9
Rationale: "one day work of a = 1 / 8 one day work of b = 1 / 6 so one day work of a and b together = 1 / 8 + 1 / 6 = 7 / 24 so total days required = 24 / 7 answer : d"
Answer: d
Python program:
a = 1 / 8
b = 1 / 6
c = a + b 
d = 1 / c
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 7 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54 , b ) 32 , c ) 75 , d ) 28 , e ) 11
Rationale: "a / 8 = 7 * 7 = > a = 7 * 7 * 8 x * 2 x = 7 * 7 * 8 x = 14 = > 2 x = 28 answer : d"
Answer: d
Python program:
a = square_area * (
b = a / 8
c = 1/(2)
d = math.sqrt(b)
Problem: how many numbers from 32 to 97 are exactly divisible by 9 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' b ' 32 / 9 = 3 and 97 / 9 = 10 = = > 10 - 3 = 7 numbers"
Answer: b
Python program:
a = 97 / 9
b = math.floor(a)
c = b * 9
d = 32 / 9
e = math.floor(d)
f = e + 1 
g = f * 9
h = c - g
i = h / 9
j = i + 1
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 4 ) , how many units is p from the y - axis ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "the x - axis is 4 units from the point p . thus the y - axis is 8 units from the point p . the answer is c ."
Answer: c
Python program:
a = 4 * 2