euclaise/mathqa_programs huggingface dataset:
Problem: there are 780 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 130 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 780 . hence , we have m + f = 780 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 780 / 3 = 260 solving the three equations yields the solution f = 260 , m = 520 , and d = 260 . the number of female democratic participants equals half the female participants equals 260 / 2 = 130 . answer : a"
Answer: a
Python program:
a = 780 / 3
b = a * 4
c = b - 780
d = c / 2
Problem: there are 680 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 425 , b ) 345 , c ) 375 , d ) 380 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 680 . hence 3 x + 5 x = 680 solve for x 8 x = 680 x = 85 number of boys 3 x = 3 × 85 = 255 number of girls 5 x = 5 × 85 = 425 a"
Answer: a
Python program:
a = 680 / 5
b = a * 3
Problem: in a clothing store , there are 6 different colored neckties ( orange , yellow , green , blue , and indigo ) and 5 different colored shirts ( orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ?
Options: a ) 719 / 720 , b ) 1 / 120 , c ) 2 / 233 , d ) 3 / 543 , e ) 1 / 720
Rationale: 5 ties and 5 shirts . . . red tie can take any of 5 shirts . . orange can take any of the remaining 4 shirts yellow any of remaining 3 . . and so on till last indigo chooses the 1 remaining . . total ways = 5 * 4 * 3 * 2 * 1 = 120 out of this 120 , only 1 way will have same colour tie and shirt . . prob = 1 / 120 b
Answer: b
Python program:
a = 6 * 5
b = a * 4
c = 1 / b
Problem: 325 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 13 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "26 trees have 25 gaps between them , required distance ( 325 / 25 ) = 13 a"
Answer: a
Python program:
a = 26 - 2
b = a + 1 
c = 325 / b
Problem: in the coordinate plane , points ( x , 1 ) and ( 4 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x + y =
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 1 ) = ( 4 , 1 ) and ( 4 , y ) = ( 4,1 ) - - > x + y = 4 + 1 = 5 . answer : d"
Answer: d
Python program:
a = 4 * 4
b = 1 / 4
c = a * b
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 45 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 60
Rationale: "20 x + 45 = 21 ( x – 5 ) x = 60 answer : e"
Answer: e
Python program:
a = 20 + 1 
b = a * 5
c = b - 45
Problem: q and f represent two distinct digits . if the number 457 q 89 f is divisible by 36 , what is the value of ( q + f ) ?
Options: a ) a ) 9 , b ) b ) 3 , c ) c ) 12 , d ) d ) 6 , e ) e ) 10
Rationale: a no . divisible by 36 means it is div by 49 . to be div by 4 last 2 digits to be multiple of 4 so , f could be either 2 or 6 only similarly for a number to be div by 9 its sum must be multiple of 9 first . filtering we find q could be either 1 , 47 only . to be divisible by 9 only 1 works . ( if we choose f = 6 then q have to be 6 but as per condition qf are distinct ) so q = 1 f = 2 ans : - 3 . b
Answer: b
Python program:
a = reminder - (
Problem: the total population of dogs in a community is estimated to be 50 % male and 50 % female . the total number of black dogs is 20 % greater than the total number of male black dogs . if the total number of female dogs is 8 times more than the number of female black dogs what percentage of male dogs is black ?
Options: a ) 84.4 , b ) 70.2 , c ) 80.1 , d ) 60.8 , e ) 62.5
Rationale: since we are dealing in percentage let us pick 100 as the number of black male dogs . that means that the total number of black dogs is = 120 ( 20 % more ) , therefore the number of black female dogs is 20 . the total number of female dogs is 8 x the number of black female = 20 * 8 = 160 female dogs . male dogs are 50 % of the dogs , and because there are 160 female dogs , then there must also be 160 male dogs therefore percentage of male dogs that are black = 100 / 160 * 100 = 62.5 correct option is e
Answer: e
Python program:
a = 20 / 50
b = 1 - a
c = b * 100
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0003 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d"
Answer: d
Python program:
a = 0 / 3
Problem: the ratio 25 : 50 expressed as percent equals to
Options: a ) 50 % , b ) 85 % , c ) 25 % , d ) 75 % , e ) none of above
Rationale: "explanation : actually it means 25 is what percent of 50 , which can be calculated as , ( 25 / 50 ) * 100 = 25 * 2 = 50 answer : option a"
Answer: a
Python program:
a = 25 / 50
b = a * 100
Problem: a man is 22 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 19 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 22 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 22 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 20 answer : d"
Answer: d
Python program:
a = 2 * 2
b = a - 2
c = 22 - b
d = 2 - 1
e = c / d
Problem: 18 beavers , working together in a constant pace , can build a dam in 8 hours . how many hours will it take 36 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 8 .
Rationale: "total work = 18 * 8 = 144 beaver hours 36 beaver * x = 144 beaver hours x = 144 / 36 = 4 answer : b"
Answer: b
Python program:
a = 8 * 18
b = a / 36
Problem: 2 + 4
Options: a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: d
Answer: d
Python program:
a = 2 / 4
b = a * 100
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 30 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 30 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 30 / 10 = 3 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 3 = 18 kms . . . answer - b"
Answer: b
Python program:
a = 4 + 6 
b = 30 / a
c = 4 * b
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 6 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 24 hr , e ) 26 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 6 ) = 1 / 26 leak will empty the tank in 26 hrs . answer : e"
Answer: e
Python program:
a = 1 / 2
b = 2 * 6
c = b + 1 
d = c / 6
e = 1/(d)
f = a - e
g = 1/(f)
Problem: 10 people went to a hotel for combine dinner party 5 of them spent rs . 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 240 , e ) none of these
Rationale: "solution : let average expenditure of 10 people be x . then , 10 x = 20 * 5 + 5 * ( x + 4 ) ; or , 10 x = 20 * 5 + 5 x + 20 ; or , x = 24 ; so , total money spent = 24 * 10 = rs . 240 . answer : option d"
Answer: d
Python program:
a = 5 * 20
b = 10 - 5
c = b * 4
d = a + c 
e = 10 - 5
f = 10 - e
g = d / f
h = g * 10
Problem: a sum is divided among w , x and y in such a way that for each rupee w gets , x gets 30 paisa and y gets 20 paisa . if the share of w is rs . 10 , what is the total amount ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: w : x : y = 100 : 30 : 20 20 : 6 : 4 20 - - - 10 30 - - - ? = > 15 answer : d
Answer: d
Python program:
a = 20 / 10
b = 30 / a
Problem: a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 4 new workers . how many different ways can she assign the new workers ?
Options: a ) 1485 , b ) 2700 , c ) 3300 , d ) 4860 , e ) 5400
Rationale: whatever : my take selecting team of 4 out of 12 to assign to the shifts = 12 c 4 = 495 ways . now 4 out of 12 means total of 3 group possible . so putting them in shifts = counting methode : first , second , third , = 3 * 2 * 1 = 6 here alt and alt are the same : so 6 / 2 = 3 ways . total ways of selecting = ( selecting 4 out of 12 ) * arranging those teams in shifts = 495 * 3 = 1485 ans : a
Answer: a
Python program:
a = 12 / 4
b = math.factorial(a)
c = b / 2
d = math.factorial(12)
e = 12 - 4
f = math.factorial(e)
g = math.factorial(4)
h = f * g
i = d / h
j = c * i
Problem: a car was driving at 66 km / h for 30 minutes , and then at 100 km / h for another 45 minutes . what was its average speed ?
Options: a ) 84 . , b ) 75 . , c ) 70 . , d ) 65 . , e ) 54 .
Rationale: "driving at 66 km / h for 30 minutes , distance covered = 60 * 1 / 2 = 30 km driving at 100 km / h for 45 minutes , distance covered = 100 * 3 / 4 = 75 km average speed = total distance / total time = 105 / 1.25 = 84 km / h answer : a"
Answer: a
Python program:
a = 30 + 45 
b = 30 / a
c = b * 66
d = 30 + 45 
e = 45 / d
f = e * 100
g = c + f 
h = 30 + 45 
i = h / const_60
j = g / i
Problem: if the price of a book is first decreased by 30 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 16 , c ) 37 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . decreased by 30 % = 70 then increased 20 % on rs 70 = 70 + 14 = 84 net change in price = 100 - 84 = 16 answer : b"
Answer: b
Python program:
a = 100 * 30
b = a / 100
c = 100 - b
d = c / 100
e = 100 * 20
f = e / 100
g = 100 + f 
h = g / 100
i = d * h
j = i * 100
k = 100 - j
Problem: a man can do a piece of work in 10 days , but with the help of his son , he can do it in 4 days . in what time can the son do it alone ?
Options: a ) 13 / 2 , b ) 17 / 3 , c ) 15 / 2 , d ) 20 / 3 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 10 ) = 3 / 20 the son alone can do the work in 20 / 3 days answer is d"
Answer: d
Python program:
a = 10 * 4
b = 10 - 4
c = a / b
Problem: find the next term 88 , 62 , . . ?
Options: a ) - 2 , b ) - 4 , c ) - 6 , d ) - 8 , e ) - 9
Rationale: 8 , 8 , 6 , 2 , x i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - x should be ` ` 6 ' ' 2 - x = 6 x = - 4 answer : b
Answer: b
Python program:
a = 88 - 62
Problem: the cash difference between the selling prices of an book at a profit of 2 % and 4 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 52 : 33 , c ) 51 : 52 , d ) 45 : 53 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 102 % of x / 104 % of x = 102 / 104 = 51 / 52 = 51 : 52 c"
Answer: c
Python program:
a = 100 + 2 
b = 100 + 4 
c = a / b
Problem: how long does a train 100 m long running at the speed of 75 km / hr takes to cross a bridge 135 m length ?
Options: a ) 11.3 sec , b ) 12.1 sec , c ) 13.1 sec , d ) 16.5 sec , e ) 12.7 sec
Rationale: "speed = 75 * 5 / 18 = 20.8 m / sec total distance covered = 100 + 135 = 235 m . required time = 235 / 20.8 ' = 11.3 sec . answer : a"
Answer: a
Python program:
a = 100 + 135 
b = 75 * const_0_2778
c = a / b
Problem: what is the smallest positive integer x , such that 7000 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18
Rationale: "take out the factors of 7000 x that will come 10 ^ 3 * 7 . for perfect cube you need every no . raise to the power 3 . for 7000 x to be a perfect cube , need two 7 that means 49 . e is the answer ."
Answer: d
Python program:
a = 3 + 4
Problem: if x = 1 - 5 t and y = 2 t - 1 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 3 / 2 , c ) 2 / 3 , d ) 2 / 7 , e ) 0
Rationale: "we are given x = 1 – 5 t and y = 2 t – 1 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 5 t for x and 2 t – 1 for y in the equation x = y . this gives us : 1 – 5 t = 2 t – 1 2 = 7 t 2 / 7 = t the answer is d ."
Answer: d
Python program:
a = 1 + 2 
b = 2 + 5 
c = a / b
Problem: a person buys an article at $ 1200 . at what price should he sell the article so as to make a profit of 40 % ?
Options: a ) 1670 , b ) 1600 , c ) 1680 , d ) 1900 , e ) 1230
Rationale: c 1680 cost price = $ 1200 profit = 40 % of 1200 = $ 480 selling price = cost price + profit = 1200 + 480 = 1680
Answer: c
Python program:
a = 40 / 100
b = 1200 * a
c = 1200 + b
Problem: there is a 75 % chance that tigers will not win at all during the whole season . there is a 25 % chance that germany will not play at all in the whole season . what is the greatest possible probability that the tigers will win and germany will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: there is a 75 % chance that tigers will not win at all during the whole season we can infer that there is 25 % chance tigers will win . similarly there is a 25 % chance that germany will not play at all in the whole season we can also infer that there is 75 % chance that germany will play . answer d
Answer: d
Python program:
a = 2 * 5
b = 2 * 5
c = a * b
d = 25 / c
e = 1 - d
f = 2 * 5
g = 2 * 5
h = f * g
i = 75 / h
j = 1 - i
k = e * j
Problem: in the coordinate plane , points ( x , 8 ) and ( 20 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x * y =
Options: a ) 120 , b ) 100 , c ) 135 , d ) 140 , e ) 160
Rationale: line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 8 ) = ( 32 , 8 ) and ( 20 , y ) = ( 20,5 ) - - > x * y = 32 * 5 = 160 . answer : e
Answer: e
Python program:
a = 20 * 4
b = 8 / 4
c = a * b
Problem: find the sum of first 35 odd numbers
Options: a ) 4900 , b ) 3000 , c ) 1250 , d ) 1200 , e ) 1225
Rationale: "explanation : n 2 = 352 = 1225 answer : option e"
Answer: e
Python program:
a = 35 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 35 / e
g = f / 2
h = 35 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 35 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: bill is golfing with 3 friends and can either buy generic golf tees that are packaged by the dozen or the higher quality aero flight tees that come by the pair . what is the minimum number of packages of aero flight tees bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome , if he will buy no more than 2 packages of the generic golf tees ?
Options: a ) 16 , b ) 10 , c ) 28 , d ) 4 , e ) 2
Rationale: at least 20 golf tees for each member of his foursome = total of at least 4 * 20 = 80 tees . 2 packages of the generic golf tees , that are packaged by the dozen = 2 * 12 = 24 tees . so , bill must by at least 16 aero tees . they come by the pair , hence he must by at least 56 / 2 = 28 packages of aero flight tees . answer : c .
Answer: c
Python program:
a = 3 + 1 
b = a * 20
c = 2 * 12
d = b - c
e = d / 2
Problem: a man ' s speed with the current is 20 kmph and speed of the current is 3 kmph . the man ' s speed against the current will be
Options: a ) 11 kmph , b ) 12 kmph , c ) 14 kmph , d ) 17 kmph , e ) none of these
Rationale: "explanation : if you solved this question yourself , then trust me you have a all very clear with the basics of this chapter . if not then lets solve this together . speed with current is 20 , speed of the man + it is speed of the current speed in still water = 20 - 3 = 17 now speed against the current will be speed of the man - speed of the current = 17 - 3 = 14 kmph option c"
Answer: c
Python program:
a = 20 - 3
b = a - 3
Problem: country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 24 million , b ) $ 120 million , c ) $ 144 million , d ) $ 240 million , e ) $ 888 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 388 mill / 2 month i . e . $ 194 mill / month difference / month = 194 - 120 = 74 difference / year = $ 74 mill * 12 = $ 988 mill answer : e"
Answer: e
Python program:
a = 12 / 2
b = 388 * a
c = 1 * 44
d = b - c
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 70 % of the total school population of x students , what is x ?
Options: a ) 113 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = x / 100 * 70 / 100 * x = > x ^ 2 = 9 * 10000 / 7 = > x = 113 a"
Answer: a
Python program:
a = 90 * 100
b = 70 / 100
c = a / b
d = math.sqrt(c)
Problem: what is the remainder when 43 ^ 88 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 88 has the form 4 k so the units digit of 43 ^ 88 is 1 . the remainder when dividing by 5 is 1 . the answer is b ."
Answer: b
Python program:
a = 5 / 2
b = 43 * 43
c = a - b
Problem: how many factors of 990 are odd numbers greater than 1 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: when factorized , 990 has 5 prime factors . of these prime factors 4 are odd and 1 is even . hence total number of odd factors is 2 * 2 * 2 * 2 ( 16 ) , which includes 1 . the total number of odd factors greater than 1 are 15 . ( option c )
Answer: c
Python program:
a = 10 * 2
b = 990 / a
Problem: square a has an area of 25 square centimeters . square b has a perimeter of 12 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 9 / 25 , b ) 1 / 5 , c ) 16 / 25 , d ) 3 / 5 , e ) 6 / 25
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 12 , then its side is 12 / 4 = 3 and the area is 3 ^ 2 = 9 empty space between the squares is 25 - 9 = 16 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 16 / 25 . answer : c"
Answer: c
Python program:
a = 12 / 4
b = a ** 2
c = 25 - b
d = c / 25
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ 26.50 per metre is rs . 5300 , what is the length of the plot in metres ?
Options: a ) 40
b ) 50
c ) 60
d ) 70
e ) 80
Rationale: let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 / 26.50 m = 200 m . 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m . answer : c
Answer: c
Python program:
a = 5300 / 26
b = a / 2
c = 2 * 20
d = b - c
Problem: two trains 150 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.18 , b ) 7.12 , c ) 7.16 , d ) 7.55 , e ) 7.82
Rationale: "t = ( 150 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.82 answer : e"
Answer: e
Python program:
a = 150 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: a train running at the speed of 50 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 125 m , b ) 150 m , c ) 187 m , d ) 167 m , e ) 197 m
Rationale: "speed = 50 * 5 / 18 = 125 / 9 m / sec length of the train = speed * time = 125 / 9 * 9 = 125 m answer : a"
Answer: a
Python program:
a = 50 * 1000
b = a / 3600
c = b * 9
Problem: two - third of a positive number and 25 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 144 / 25 , e ) 146 / 25
Rationale: "let the number be x . then , 2 / 3 x = 25 / 216 * 1 / x x 2 = 25 / 216 * 3 / 2 = 25 / 144 x = 5 / 12 answer : a"
Answer: a
Python program:
a = 25 * 3
b = 216 * 2
c = a / b
d = math.sqrt(c)
Problem: if 50 % of ( x - y ) = 40 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 11 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "50 % of ( x - y ) = 40 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 40 / 100 ) ( x + y ) 5 ( x - y ) = 4 ( x + y ) x = 9 y x = 9 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 9 y ) x 100 ) = 11 % answer is b ."
Answer: b
Python program:
a = 50 - 40
b = 50 + 40 
c = a / b
d = c * 100
Problem: a certain quantity of 60 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 60 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 60 ml and 25 ml is 35 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 35 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 25 % . therefore , 25 out of 35 is 5 / 7 and e is the answer ."
Answer: e
Python program:
a = 35 - 25
b = 60 - 35
c = a / b
d = c + 1 
e = 1/(d)