euclaise/mathqa_programs huggingface dataset:
Problem: the average monthly income of a and b is rs . 5050 . the average monthly income of b and c is rs . 6250 and the average monthly income of a and c is rs . 5200 . what is the monthly income of a ?
Options: a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6200
Rationale: "explanation : let monthly income of a = a monthly income of b = b monthly income of c = c a + b = 2 × 5050 . . . . ( equation 1 ) b + c = 2 × 6250 . . . . ( equation 2 ) a + c = 2 × 5200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > a + b + a + c - ( b + c ) = ( 2 × 5050 ) + ( 2 × 5200 ) - ( 2 × 6250 ) = > 2 a = 2 ( 5050 + 5200 - 6250 ) = > a = 4000 i . e . , monthly income of a = 4000 answer is c"
Answer: c
Python program:
a = 2 * 5050
b = 2 * 5050
c = 2 * 6250
d = 2 * 5200
e = c - d
f = b + e 
g = f / 2
h = a - g
Problem: x , y , and z are different prime numbers . the product x ^ 3 * y ^ 2 * z ^ 1 is divisible by how many different positive numbers ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48
Rationale: "the exponents of x ^ 3 * y ^ 2 * z ^ 1 are 3 , 2 , and 1 . the number of factors is ( 3 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 24 the answer is a ."
Answer: a
Python program:
a = 2 ** 0
b = a - 4
Problem: a man is 28 years older than his son . in four years , his age will be twice the age of his son . the present age of this son is
Options: a ) 21 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 25 years
Rationale: "explanation : let ' s son age is x , then father age is x + 28 . = > 2 ( x + 4 ) = ( x + 28 + 4 ) = > 2 x + 8 = x + 32 = > x = 24 years answer : option d"
Answer: d
Python program:
a = 2 * 2
b = a - 2
c = 28 - b
d = 2 - 1
e = c / d
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 529 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 22 , e ) 23
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 529 / 3 = 176.33 sq m l b = 176.33 i . e . , l * l / 3 = 176.33 l ^ 2 = 529 = > l = 23 e"
Answer: e
Python program:
a = 529 / 3
b = a / 3
c = math.sqrt(b)
d = c * 3
Problem: walking at 5 / 6 th of its usual speed a cab is 8 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 40 m , d ) 50 m , e ) 62 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 8 m ut / 5 = 8 m ut = 40 m answer is c"
Answer: c
Python program:
a = 5 * 8
Problem: a and b can do a piece of work in 4 days . b and c can do it in 12 days and a and c in 16 days . working together they will complete the work in how many days ?
Options: a ) 4.05 days , b ) 5.05 days , c ) 14.76 days , d ) 8.05 days , e ) 15.05 days
Rationale: "a + b = 1 / 4 b + c = 1 / 12 c + a = 1 / 16 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ( a + b + c ) = 1 / 4 + 1 / 12 + 1 / 16 = 19 / 48 a + b + c = 19 / 96 96 / 19 = 5.05 days answer : b"
Answer: b
Python program:
a = 1/(16)
b = 1/(4)
c = 1/(12)
d = b + c 
e = a + d 
f = e / 2
g = 1/(f)
Problem: a certain machine produces 780 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 4 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 74,880 , d ) 100,000 , e ) 168,000
Rationale: "since 7 days consist of 24 * 4 hours the total is 96 hours . since every hour the machine produces 780 units of product p the total product during 96 hours is 96 * 780 = 74,880 . correct option : d"
Answer: d
Python program:
a = 4 * 10
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 39 ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "first , let ' s translate the expression 21 # 39 , using the definition given : 21 # 39 = 21 × 24 × 27 × 30 × 33 × 36 × 39 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 39 = 3 ^ 7 ( 7 × 8 × 9 × 10 × 11 × 12 × 13 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 39 = 3 ^ 7 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) × 11 × ( 2 ^ 2 × 3 ) × 13 ) let ' s group the prime bases : 21 # 39 = 2 ^ 6 × 3 ^ 10 × 5 × 7 × 11 × 13 the sum of the exponents is 6 + 10 + 1 + 1 + 1 + 1 = 20 the answer is d ."
Answer: d
Python program:
a = 2 + 2 
b = 3 + a 
c = 2 + 2 
d = b + c 
e = 2 + 2 
f = 3 + e 
g = d + f
Problem: the cost of 3 pens and 5 pencils is rs . 200 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 150 , e ) rs . 600
Rationale: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 200 15 x + 5 x = rs . 200 x = 200 / 20 = 10 : . cost of 1 pen = 5 x = 5 x 10 = 50 : . cost of 12 pens , i . e . ( one dozen ) = 50 x 12 = rs . 600 answer : option e"
Answer: e
Python program:
a = 3 * 4
b = 3 + 1 
c = 200 / b
d = a * c
Problem: the captain of a cricket team of 11 members is 25 years old and the wicket keeper is 5 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: "let the average age of the whole team be x years . 11 x - ( 25 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is c ."
Answer: c
Python program:
a = 25 + 5 
b = 25 + a 
c = 3 * 0
d = b - c
e = d / 2
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 72 % percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 48 % , b ) 54 % , c ) 60 % , d ) 64 % , e ) 68 %
Rationale: 72 % is 8 % - points below 80 % and 17 % - points above 55 % . so the ratio of solution p to solution q is 17 : 8 . mixture p is 17 / 25 = 68 % of the volume of mixture pq . the answer is e .
Answer: e
Python program:
a = 72 / 100
b = 55 / 100
c = a - b
d = 72 / 100
e = 55 / 100
f = d - e
g = 80 / 100
h = 72 / 100
i = g - h
j = f + i 
k = c / j
l = k * 100
Problem: there are 3 girls and 6 boys . how many kids are there ?
Options: a ) 10 , b ) 19 , c ) 20 , d ) 9 , e ) 12
Rationale: d
Answer: d
Python program:
a = 3 / 6
Problem: two numbers n and 16 have lcm = 48 and gcf = 8 . find n .
Options: a ) 11 , b ) 32 , c ) 24 , d ) 48 , e ) 50
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 * n = 48 * 8 n = 48 * 8 / 16 = 24 correct answer c"
Answer: c
Python program:
a = 48 * 8
b = a / 16
Problem: if y > 0 , ( 2 y ) / 5 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: can be reduced to 2 y / 5 + 3 y / 10 = 2 y / 5 = 70 % d
Answer: d
Python program:
a = 2 / 5
b = 3 / 10
c = a + b 
d = 100 * c
Problem: convert 200 inches into centimeter ?
Options: a ) 512 cm , b ) 520 cm , c ) 508 cm , d ) 510 cm , e ) 554 cm
Rationale: "1 inch = 2.54 cm 200 inches = 200 * 2.54 = 508 cm answer is c"
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 200
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: if an object travels at seven feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 25200 , e ) 18000
Rationale: "speed = 7 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 7 = 25200 answer d"
Answer: d
Python program:
a = 3 * const_60
b = a * const_60
Problem: evaluate : 2344 - 12 * 3 * 2 = ?
Options: a ) 2337 , b ) 1227 , c ) 3327 , d ) 5457 , e ) 7677
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 2344 - 12 * 3 * 2 = 2344 - 8 = 2337 correct answer a"
Answer: a
Python program:
a = 12 * 3
b = a * 2
c = 2344 - b
Problem: a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 22.5 , e ) 27
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 20 % of the final price - - > ( final price ) * 0.8 = $ 18 - - > ( final price ) = $ 22.5 . answer : d ."
Answer: d
Python program:
a = 100 + 20 
b = a / 100
c = 15 * b
d = 100 + 20 
e = d / 100
f = c * e
Problem: the product of x and y is a constant . if the value of x is increased by 80 % , by what percentage must the value of y be decreased ?
Options: a ) 45 % , b ) 55 % , c ) 35 % , d ) 40 % , e ) 44.44 %
Rationale: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.8 x ( 180 ) i . e . 180 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 180 = 55.55 i . e . y decreases from 100 to 55.55 i . e . decrease of 44.44 % answer : option e"
Answer: e
Python program:
a = 100 + 80 
b = 100 / a
c = 1 - b
d = c * 100
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 90 km / hr
Options: a ) 8.5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 4 seconds
Rationale: "first convert speed into m / sec speed = 90 * ( 5 / 18 ) = 25 m / sec time = distance / speed = 100 / 25 = 4 seconds answer : e"
Answer: e
Python program:
a = 90 * const_0_2778
b = 100 / a
Problem: the roof of an apartment building is rectangular and its length is 7 times longer than its width . if the area of the roof is 847 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 66 . , d ) 44 . , e ) 46 .
Rationale: "answer is c : 66 let w be the width , so length is 7 w . therefore : w * 7 w = 847 , solving for , w = 11 , so 7 w - w = 6 w = 6 * 11 = 66"
Answer: c
Python program:
a = 847 / 7
b = math.sqrt(a)
c = b * 7
d = 847 / 7
e = math.sqrt(d)
f = c - e
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 3000 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 600 , e ) 1200
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 3000 = > 5 parts out of 15 parts is rs . 3000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 3000 ) = rs . 1200 answer : e"
Answer: e
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 3000
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 12 , c ) 9 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = 9 years . answer : c"
Answer: c
Python program:
a = 15 * 15
b = 4 * 14
c = 10 * 16
d = b + c 
e = a - d
Problem: the circumferences of two circles are 660 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 2996 sq m , b ) 4774 sq m , c ) 4312 sq m , d ) 2768 sq m , e ) 2786 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 660 and 2 ∏ l = 704 s = 660 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 330 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 330 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 330 - 352 ) ( 330 + 352 ) / ∏ = ( 22 ) ( 682 ) / ( 22 / 7 ) = 4774 sq m answer : b"
Answer: b
Python program:
a = 2 * math.pi
b = 704 / a
c = circle_area - (
Problem: p is 30 % more efficient than q . p can complete a work in 23 days . if p and q work together , how much time will it take to complete the same work ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 13 , e ) 15
Rationale: "work done by p in 1 day = 1 / 23 let work done by q in 1 day = q q × ( 130 / 100 ) = 1 / 23 = > q = 100 / ( 23 × 130 ) = 10 / ( 23 × 13 ) work done by p and q in 1 day = 1 / 23 + 10 / ( 23 × 13 ) = 23 / ( 23 × 13 ) = 1 / 13 = > p and q together can do the work in 13 days option d"
Answer: d
Python program:
a = 30 / 100
b = a + 1 
c = b * 23
d = 30 / 100
e = d + 1 
f = e + 1 
g = c / f
Problem: suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have
Options: a ) 4
b ) 6
c ) 9
d ) 10
e ) 5
Rationale: to arrange them as described i did as follows on my scratch paper ( see the file attached ) , where i counted 4 sides and bottom , hence 4 + 1 = 5 . e
Answer: e
Python program:
a = 4 + 1 
b = a + 1
Problem: the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 48 , e ) 50
Rationale: "so , according to a mean of a set of even numbers from 0 to 100 = ( 0 + 100 ) / 2 = 50 and mean of a set of even numbers from 0 to 50 = ( 0 + 50 ) / 2 = 25 difference = 50 - 25 = 25 answer : b ."
Answer: b
Python program:
a = 50 + 0 
b = a / 2
c = 100 + 0 
d = c / 2
e = b - d
Problem: how many positive integers less than 10,000 are such that the product of their digits is 30 ?
Options: a ) 12 , b ) 24 , c ) 36 , d ) 38 , e ) 50
Rationale: "30 = 1 * 30 , 2 * 15 , 3 * 10 , 5 * 6 we have the option of using single digits 1,2 , 3,5 and 6 no : of four digit numbers such that the product is 30 the possible combinations are using digits ( 1,2 , 3,5 ) & ( 1,1 , 5 , 6 ) such that the product 30 . no : of different combinations possible using ( 1,2 , 3,5 ) = 4 ! = 24 no : of different combinations possible using ( 5,6 , 1,1 ) = 4 ! / 2 ! = 12 ( ' 1 ' is repeated twice ) total 4 digit numbers so that the product is 30 is 24 + 12 = 36 no : of three digit numbers such that the product is 30 the possible combinations are using digits ( 2,3 , 5 ) & ( 1 , 5,6 ) no : of different combinations possible using ( 2 , 3,5 ) = 3 ! = 6 no : of different combinations possible using ( 1 , 5,6 ) = 3 ! = 6 total 3 digit numbers so that the product is 30 is 6 + 6 = 12 no : of 2 digit numbers such that the product is 30 is 2 ( 56 and 65 ) total numbers under 10000 such that the product is 30 is 36 + 12 + 2 = 50 e"
Answer: e
Python program:
a = 4 + 30 
b = a - 1
c = math.factorial(b)
d = math.factorial(30)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the speed at which a man can row a boat in still water is 16 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 100 metres ?
Options: a ) 23 , b ) 27 , c ) 28 , d ) 12 , e ) 18
Rationale: speed of the boat downstream = 16 + 4 = 20 kmph = 20 * 5 / 18 = 5.55 m / s hence time taken to cover 100 m = 100 / 5.55 = 18 seconds . answer : e
Answer: e
Python program:
a = 16 + 4 
b = a * const_0_2778
c = 100 / b
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 2 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 10 %
Rationale: "per quarter , interest = 2 % so for a year , interest = 8 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 8 % answer = 8.25 % = answer : d"
Answer: d
Python program:
a = 2 * 4
Problem: the sale price sarees listed for rs . 390 after successive discount is 14 % and 15 % is ?
Options: a ) 285 , b ) 277 , c ) 290 , d ) 662 , e ) 262
Rationale: "390 * ( 86 / 100 ) * ( 85 / 100 ) = 285 answer : a"
Answer: a
Python program:
a = 390 * 14
b = a / 100
c = 390 - b
d = 390 * 14
e = d / 100
f = 390 - e
g = f * 15
h = g / 100
i = c - h
Problem: with both inlets open , a water tank will be filled with water in 42 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 7,000 , b ) 10,500 , c ) 11,750 , d ) 12,000 , e ) 13,000
Rationale: "the work done by inlet a and b together in 1 min = 1 / 42 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 42 ) - ( 1 / 120 ) = 1 / 65 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 65 ) - ( 1 / 120 ) = 50 cubic meter = 7000 cubic meter answer : option a"
Answer: a
Python program:
a = const_60 / 42
b = 1/(2)
c = a - b
d = c / const_60
e = const_60 * 2
f = 1/(e)
g = d - f
h = 50 / g
i = h / 1000
Problem: if a rectangular billboard has an area of 91 square feet and a perimeter of 40 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 91 and a perimeter of 40 . 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 91 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . let ' s test answer b : 7 if . . . the shorter side = 7 . . . the area = 91 . . . . 91 / 7 = 13 = the longer side perimeter = 7 + 7 + 13 + 13 = 40 b"
Answer: b
Python program:
a = 40 / 2
b = 40 / 2
c = b ** 2
d = 4 * 91
e = c - d
f = math.sqrt(e)
g = a - f
h = g / 2
Problem: the ratio of the volumes of two cubes is 27 : 125 . what is the ratio of their total surface areas ?
Options: a ) 9 : 25 , b ) 9 : 35 , c ) 81 : 124 , d ) 81 : 126 , e ) 81 : 129
Rationale: "ratio of the sides = 3 √ 27 : 3 √ 125 = 3 : 5 ratio of surface areas = 3 ^ 2 : 5 ^ 2 = 9 : 25 answer : option a"
Answer: a
Python program:
a = 27 / 125
b = 1 / 3
c = a ** b
Problem: the ratio of the first and second class fares between two stations is 3 : 1 and that of the number of passengers travelling between the two stations by the first and the second class is 1 : 50 . if in a day , rs . 1 , 325 are collected from the passengers travelling between the two stations , then the amount collected from the second class from the second class passengers is
Options: a ) 1,250 , b ) 1,000 , c ) 850 , d ) 750 , e ) 350
Rationale: explanation : let the fares be 3 x and x respectively for the first and second class . suppose in a day passengers travelling between the two stations be 1 and 50 . then by given condition , 3 x × 1 + x × 50 = 1,325 = > x = 25 the amount collected from second class = 25 × 50 = rs . 1250 answer : a
Answer: a
Python program:
a = 1 * 1
Problem: find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm ?
Options: a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 90 cm 2
Rationale: "1 / 2 * 20 ( 5 + 4 ) = 90 cm 2 answer : e"
Answer: e
Python program:
a = 1 / 2
b = 4 + 5 
c = a * b
d = c * 20
Problem: a club wants to mix 20 pounds of candy worth $ 10.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 20 * 10 + 5 * w ) / ( 20 + w ) = > 120 + 6 w = 200 + 5 w = > w = 80 answer e"
Answer: e
Python program:
a = 20 * 10
b = 6 * 0
c = a - b
Problem: the reciprocal of the hcf and lcm of two are 1 / 12 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 166
Rationale: "reciprocal of the hcf and lcm of two are 1 / 12 and 1 / 312 so , hcf = 12 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 12 * 312 / 24 = 156 answer : d"
Answer: d
Python program:
a = 12 * 312
b = a / 24
Problem: a can do a piece of work 20 days . b can do work in 35 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16.32 days , c ) 12.72 days , d ) 17 days , e ) 18 days
Rationale: "lcm = 140 , ratio = 20 : 35 = 4 : 7 no of days = 140 / ( 4 + 7 ) = 90 / 5 = 12.72 days answer : c"
Answer: c
Python program:
a = 1 / 20
b = 1 / 35
c = a + b 
d = 1 / c
Problem: the sale price shirts listed for rs . 1000 after successive discount is 15 % and 2 % is ?
Options: a ) 338 , b ) 823 , c ) 833 , d ) 337 , e ) 733
Rationale: "1000 * ( 85 / 100 ) * ( 98 / 100 ) = 833 answer : c"
Answer: c
Python program:
a = 1000 * 15
b = a / 100
c = 2 * 1000
d = c / 100
e = b + d 
f = 1000 - e
Problem: what is the ratio of 4 / 7 to the product 3 * ( 7 / 3 ) ?
Options: a ) 4 : 49 , b ) 1 : 3 , c ) 3 : 21 , d ) 1 : 7 , e ) 3 : 49
Rationale: "4 / 7 / 21 / 3 = 4 / 49 . . . imo option a ."
Answer: a
Python program:
a = 4 / const_60
Problem: exactly 5 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 92 % , e ) 90 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 5 % of all reporters reporters covering politics / all reporters = 5 / 70 = 1 / 14 reporters not covering politics / all reporters = 13 / 14 = 92 % = d"
Answer: d
Python program:
a = 100 - 30
b = 5 / a
c = 1 - b
d = c * 100
Problem: kanul spent $ 35000 in buying raw materials , $ 40000 in buying machinery and 20 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 87952 , b ) $ 93750 , c ) $ 89542 , d ) $ 95820 , e ) $ 84256
Rationale: "let the total amount be x then , ( 100 - 20 ) % of x = 35000 + 40000 80 % of x = 75000 80 x / 100 = 75000 x = $ 93750 answer is b"
Answer: b
Python program:
a = 35000 + 40000 
b = 20 / 100
c = 1 - b
d = a / c
Problem: the total age of a and b is 18 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 15 , d ) 18 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 18 a - c = 18 answer is d"
Answer: d
Python program:
a = 18 * 1
Problem: the sector of a circle has radius of 21 cm and central angle 150 o . find its perimeter ?
Options: a ) 91.5 , b ) 91.4 , c ) 97 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 150 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 55 + 42 = 97 cm answer : c"
Answer: c
Python program:
a = 21 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 21