euclaise/mathqa_programs huggingface dataset:
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 12 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 22 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 23.57 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 12 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 14 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 14 ) = 1 / 2 ( 22 / 7 ) ( 14 ) = 308 / 14 = 22 cm answer : a"
Answer: a
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: a motorcyclist goes from bombay to pune , a distance of 192 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 2 : 8 , b ) 1 : 2 , c ) 2 : 5 , d ) 6 : 9 , e ) 6 : 2
Rationale: b 1 : 2 t = 192 / 32 = 6 h t = 6 - 3 = 3 time ratio = 6 : 3 = 2 : 1 speed ratio = 1 : 2
Answer: b
Python program:
a = 192 / 32
b = 192 / a
c = 192 / 32
d = c - 3
e = 192 / d
f = b / e
Problem: a corporation paid $ 8 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 20 % , d ) 23 % , e ) 86 %
Rationale: "difference in ratios = ( 30 / 150 ) - ( 8 / 50 ) = ( 6 / 50 ) % change = ( change ( 6 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 86 % answer - e"
Answer: e
Python program:
a = 30 + 8 
b = a / 150
c = 8 / 50
d = b - c
e = 8 / 50
f = d / e
g = f * 100
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9 , 40 and 41 ?
Options: a ) 6 , b ) 4 , c ) 24.5 , d ) 20.5 , e ) 12.5
Rationale: "explanatory answer 9 , 40 and 41 is pythagorean triplet . so , the triangle is right angled . key property about right triangles in a right angled triangle , the radius of the circle that circumscribes the triangle is half the hypotenuse . in the given triangle , the hypotenuse = 41 . therefore , the radius of the circle that circumscribes the triangle = 41 / 2 = 20.5 units . choice d"
Answer: d
Python program:
a = triangle_area_three_edges / (
Problem: 70 , 75 , 80 , 85 , 90 , 105 , 105 , 130 , 130 , 130 the list shown consists of the times , in seconds , that it took each of 10 schoolchildren to run a distance of 400 on of meters . if the standard devastation of the 10 running times is 25.4 seconds , rounded to the nearest tenth of a second , how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times ?
Options: a ) one , b ) two , c ) three , d ) four , e ) five
Rationale: the most time consuming part in this question is to define the mean . under exam pressure and time pressure it is very easy to make mistake . it is easier to group numbers : 130 * 3 = 390 ; 105 * 2 = 210 ; 75 + 85 = 160 ; 70 + 80 = 150 ; 90 ; next stage combine results , again using more convenient ways to calculate : 390 + 210 = 600 ; 160 + 150 = 310 ; 90 . 600 + 310 + 90 = 1000 . since there are 10 numbers the mean is 100 . questions asks to find the quantity of numbers one sd below the mean , which is 100 - 25,4 = 74,6 . there are only two numbers below 74,6 . the answer is b
Answer: b
Python program:
a = 100 - 25
b = math.floor(a)
c = 75 - b
d = c + 1
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 400 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 410 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 20,000 . now , put the value of x = 4000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 4000 + 5 % of 4000 = 4200 . 2 nd year , amount = 4200 + 5 % of 4200 = 4410 . we can see after 2 years interest = 4410 - 4000 = 410 . hence , it satisfies the question . hence d is the correct answer"
Answer: d
Python program:
a = 400 / 2
b = a ** 2
c = 410 - 400
d = b / c
Problem: a cricket bat is sold for $ 900 , making a profit of $ 225 . the profit percentage would be
Options: a ) 24 % , b ) 25.5 % , c ) 33.33 % , d ) 36.3 % , e ) 40 %
Rationale: "225 / ( 900 - 225 ) = 33.33 % . answer : c"
Answer: c
Python program:
a = 900 - 225
b = 225 / a
c = b * 100
Problem: a part of certain sum of money is invested at 16 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 5 : 4 , b ) 1 : 4 , c ) 3 : 1 , d ) 3 : 5 , e ) 3 : 4
Rationale: "12 : 16 = 3 : 4 answer : e"
Answer: e
Python program:
a = 12 / 100
b = a * 16
Problem: reduce 4128 / 4386 to its lowest terms
Options: a ) 14 / 13 , b ) 13 / 17 , c ) 16 / 17 , d ) 13 / 18 , e ) none of these
Rationale: explanation : hcf of 4128 and 4386 4128 ) 4386 ( 1 4128 - - - - - 258 ) 4128 ( 16 4128 - - - - 0 hence hcf of 4128 and 4386 is 258 . 4128 / 258 = 16 4386 / 258 = 17 4128 / 4386 = 16 / 17 answer : option c
Answer: c
Python program:
a = 4128 / 2
b = a / 3
c = 4386 / 2
d = c / 3
e = b / d
Problem: a bag holds 2 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: probability of selecting first red marble = 2 / 5 probability of selecting second red marble without replacement = 1 / 4 final probability = 2 / 5 * 1 / 4 = 1 / 10 correct answer - a
Answer: a
Python program:
a = math.comb(2, 2)
b = 2 + 3 
c = math.comb(b, 2)
d = a / c
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 40 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 40 4 n < 33 n < 8 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 8 ) combining the two - 1.5 < n < 8.25 n = 1 to 8 ( 48 integers ) and n = - 1 and 0 so 10 integers . a"
Answer: a
Python program:
a = 40 - 7
b = a / 4
c = math.floor(b)
d = 1 - 7
e = d / 4
f = math.floor(e)
g = c - f
Problem: a contractor undertook to do a piece of work in 9 days . he employed certain number of laboures but 6 of them were absent from the very first day and the rest could finish the work in only 15 days . find the number of men originally employed .
Options: a ) 15 , b ) 6 , c ) 13 , d ) 9 , e ) none of these
Rationale: let the number of men originally employed be x . 9 x = 15 ( x – 6 ) or x = 15 answer a
Answer: a
Python program:
a = 15 * 6
b = 15 - 9
c = a / b
Problem: the average of 11 results is 42 , if the average of first 5 results is 49 and that of the last 7 is 52 . find the fifth result ?
Options: a ) 145 , b ) 146 , c ) 147 , d ) 148 , e ) 149
Rationale: 1 to 11 = 11 * 42 = 462 1 to 5 = 5 * 49 = 245 5 to 11 = 7 * 52 = 364 5 th = 245 + 364 – 462 = 147 answer : c
Answer: c
Python program:
a = 5 * 49
b = 7 * 52
c = a + b 
d = 11 * 42
e = c - d
Problem: a train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph , in 12 seconds . it also passes a railway platform in 45 seconds . the length of the platform is
Options: a ) 400 m , b ) 450 m , c ) 560 m , d ) 600 m , e ) 680 m
Rationale: length of the ist train = 2 x m and the length of the other train be x m ( 1 / 2 ) the relative speed of the train ( 48 + 42 ) = 90 kmph or 25 m / s time taken to cross one another = 12 s hence , 12 = 2 x + x / 25 solving , x = 100 m and 200 m now to determine the length of the platform 45 = 100 + length of the platform / speed of the ist train 45 = 100 + l / 240 / 18 ( 48 kmph = 240 / 118 m / s ) solving , we get l = 600 m answer : d
Answer: d
Python program:
a = 48 * const_0_2778
b = 45 * a
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 5 / 6 . answer : e ."
Answer: e
Python program:
a = 2 ** 2
b = math.comb(5, 2)
c = math.comb(2, 1)
d = b * c
e = a / d
Problem: if seven machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 45 , b ) 60 , c ) 75 , d ) 84 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 7 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 14 / 3 = 10 / 3 * x x = 7 / 5 hour so 84 minutes answer : d"
Answer: d
Python program:
a = 3 / 5
b = 3 / 4
c = b / 5
d = c / 30
e = d * 2
f = a / e
Problem: what is the % change in the area of a rectangle when its length increases by 60 % and its width decreases by 60 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 36 % decrease , d ) 1 % decrease , e ) insufficient data
Rationale: "( 16 / 10 ) * ( 4 / 10 ) = 64 / 100 of original area 64 / 100 is a 36 % decrease from 100 / 100 - > c"
Answer: c
Python program:
a = 100 + 60 
b = 100 - 60
c = a * b
d = c / 100
e = 100 - d
Problem: initially two cups of same volume are present with milk filled upto 3 / 5 th and 4 / 5 th of their volumes . water is then filled . then two mixtures are mixed . find the ratio of water to milk in the mixture
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Rationale: water content can b in 1 st and second is 2 / 5 and 1 / 5 total : 3 / 5 . the total milk content is 7 / 5 . the ratio is ( ( 3 / 5 ) / ( 7 / 5 ) ) = 3 / 7 . answer : c
Answer: c
Python program:
a = 4 / 5
b = 1 - a
c = 3 / 5
d = 1 - c
e = b + d 
f = 3 / 5
g = 4 / 5
h = f + g 
i = e / h
Problem: convert 600 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 965604 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 600 mile = 600 * 1609.34 = 965604 meters answer is c"
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 600
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 30 litres of tomato juice ?
Options: a ) 3.75 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 30 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 3.75 liters . answer : a"
Answer: a
Python program:
a = 100 - 90
b = a / 100
c = b * 30
d = 100 - 20
e = d / 100
f = c / e
Problem: if x < y < z and y - x > 3 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 3 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 3 , the least value for y - x must be 5 , the least value for x must be 2 , and , thus , the least possible value for y must be 7 ( y - 2 = 5 , y = 7 ) 2 < 7 < z , since z is odd , the least possible value for z is 9 z - x = 9 - 2 = 7 answer a"
Answer: a
Python program:
a = 3 + 2 
b = a + 2
Problem: if an amount of rs 42900 is distributed equally amongst 22 persons , how much amount would each person get ?
Options: a ) rs 1950 , b ) rs 2000 , c ) rs 745 , d ) rs 765 , e ) none
Rationale: required amount = 42900 / 22 = rs 1950 answer a
Answer: a
Python program:
a = 42900 / 22
Problem: six bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 50 minutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) 26
Rationale: "l . c . m of 2,4 , 6,8 , 10,12 is 120 . i . e after each 2 min they will toll together . so in 50 min they will toll 25 times . as they have initially tolled once , the answer will be 25 + 1 = 26 . answer : e"
Answer: e
Python program:
a = 2 + 3 
b = a * 2
c = b * 3
d = 2 * c
e = d * 2
f = e / 10
g = 10 / f
Problem: what least number must be subtracted from 9671 so that the remaining number is divisible by 5 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "on dividing 9671 by 5 , we get remainder = 1 . required number be subtracted = 1 answer : e"
Answer: e
Python program:
a = 9671 / 5
b = math.floor(a)
c = b * 5
d = 9671 - c
Problem: find the average of all prime numbers between 50 and 70
Options: a ) 90 , b ) 45 , c ) 60 , d ) 90 , e ) 26
Rationale: "prime numbers between 50 and 70 are 53 , 59 , 61 , 67 required average = ( 53 + 59 + 61 + 67 ) / 4 = 240 / 4 = 60 answer is c"
Answer: c
Python program:
a = 50 + 1 
b = 50 + 1 
c = b + 2 
d = a + c 
e = 70 - 50
f = 70 - 2
g = e + f 
h = d + g 
i = h / 50
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 70 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 x = 8 . age of the youngest child = x = 8 years . e )"
Answer: e
Python program:
a = 70 / 5
b = a - 3
c = b - 3
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 120 ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 120 4 n < 113 n < 28 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 28 ( 48 integers ) and n = - 1 and 0 so 30 integers . e is the answer"
Answer: e
Python program:
a = 120 - 7
b = a / 4
c = math.floor(b)
d = 1 - 7
e = d / 4
f = math.floor(e)
g = c - f
Problem: the average of thirteen numbers is 9 . the average of first 6 numbers is 5 and the average of last 6 numbers is 7 . what is the middle number ?
Options: a ) 47 , b ) 45 , c ) 25 , d ) 37 , e ) 44
Rationale: the total of thirteen numbers = 13 x 9 = 117 the total of first 6 and last 6 numbers is = 6 x 5 + 6 x 7 = 72 so , the middle number is ( 117 - 72 ) = 45 b
Answer: b
Python program:
a = 6 + 6 
b = a + 1 
c = b * 9
d = 6 * 5
e = 6 * 7
f = d + e 
g = c - f
Problem: two heavily loaded sixteen - wheeler transport trucks are 1025 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 130 , c ) 150 , d ) 320 , e ) 145
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 1025 - 90 = 935 k ratio of speeds 9 : 8 - > 935 / 17 = 55 truck a = 90 + 55 * 9 = 585 truck b = 55 * 8 = 440 delta = 145 km answer e"
Answer: e
Python program:
a = 1025 - 90
b = 90 + 80 
c = a / b
d = 90 - 80
e = c * d
f = 90 + e
Problem: find the sum of all 2 digit numbers divisible by 3 .
Options: a ) 1565 , b ) 1665 , c ) 1300 , d ) 1448 , e ) 1465
Rationale: "all 2 digit numbers divisible by 3 are 12,15 , 18,21 , … … … . . 99 this is an a . p with a = 12 , and d = 3 , let it contain n terms then , 12 + ( n – 1 ) * 3 = 99 , or n = ( 99 - 12 ) / 3 + 1 = 30 required sum = 30 / 2 * ( 12 + 99 ) = 15 * 111 = 1665 answer : b"
Answer: b
Python program:
a = 100 + 4 
b = 100 * 10
c = b - 3
d = a + c 
e = 100 * 10
f = e - 3
g = 100 + 4 
h = f - g
i = h / 3
j = i + 1 
k = j / 2
l = d * k
Problem: 2 , 3 , 6 , 0 , 10 , - 3 , 14 , ( . . . )
Options: a ) - 6 , b ) 8 , c ) - 2 , d ) 4 , e ) 10
Rationale: "there are two series 2 , 6 , 10 , 14 , . . . ( adding 4 ) 3 , 0 , - 3 , . . . ( subtracting 3 ) hence , next term is - 3 - 3 = - 6 answer is a"
Answer: a
Python program:
a = negate - (
Problem: a man can row downstream at the rate of 12 km / hr and upstream at 8 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 6,3 , c ) 9,3 , d ) 10,2 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 12 + 8 ) = 10 km / hr rate of current = 1 / 2 ( 12 - 8 ) = 2 km / hr answer : option d"
Answer: d
Python program:
a = 12 - 8
b = a / 2
Problem: the present population of a town is 1000 . population increase rate is 25 % p . a . find the population of town after 2 years ?
Options: a ) 1000 , b ) 2000 , c ) 1563 , d ) 2153 , e ) 1245
Rationale: "p = 1000 r = 25 % required population of town = p ( 1 + r / 100 ) ^ t = 1000 ( 1 + 25 / 100 ) ^ 2 = 1000 ( 5 / 4 ) ^ 2 = 1563 ( approximately ) answer is c"
Answer: c
Python program:
a = 1000 * 25
b = a / 100
c = 1000 + b
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 2.0 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1332 , c ) s . 999 , d ) s . 1085 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.0 = 1332 answer : b"
Answer: b
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 2
f = e * 3
Problem: two employees m and n are paid a total of $ 605 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 245 , b ) $ 255 , c ) $ 265 , d ) $ 275 , e ) $ 285
Rationale: "1.2 n + n = 605 2.2 n = 605 n = 275 the answer is d ."
Answer: d
Python program:
a = 120 / 100
b = a + 1 
c = 605 / b
Problem: the weight of 4 dogs is determined to be 25 pounds , 31 pounds , 35 pounds and 33 pounds respectively . the weight of a fifth dog is determined to be y pounds . if the average ( arithmetic mean ) weight of the first 4 dogs is the same as that of all 5 dogs what is the value of y ?
Options: a ) 31 , b ) 33 , c ) 35 , d ) 37 , e ) 39
Rationale: total weight of the 4 dogs = ( 25 + 31 + 35 + 33 ) = 124 avg = 124 / 4 = 31 total weight of 5 dogs = 124 + y or 4 ( 31 ) + y average of 5 dogs as per question = 31 equation : 4 ( 31 ) + y = 5 ( 31 ) , or y = 31 . choose a
Answer: a
Python program:
a = 25 + 31 
b = 35 + 33 
c = a + b 
d = c / 4
Problem: how many ounces of a 60 % salt solution must be added to 40 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 40 , c ) 50 , d ) 60.33 , e ) 70
Rationale: "let x = ounces of 60 % salt solution to be added . 2 * 40 + . 6 x = . 4 ( 40 + x ) x = 40 amswer b"
Answer: b
Python program:
a = 40 / 100
b = a * 40
c = 20 / 100
d = c * 40
e = b - d
f = 40 / 100
g = 20 / 100
h = f - g
i = e / h
Problem: car a runs at the speed of 50 km / hr and reaches its destination in 8 hours . car b runs at the speed of 60 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 13 : 7 , d ) 5 : 3 , e ) 6 : 11
Rationale: "car a travels 50 × 8 = 400 km car b travels 60 × 4 = 240 km the ratio is 400 : 240 = 40 : 24 = 5 : 3 the answer is d ."
Answer: d
Python program:
a = 50 * 8
b = 60 * 4
c = a / b
Problem: if the cost price of 50 articles is equal to the selling price of 46 articles , then the gain or loss percent is ?
Options: a ) 22 , b ) 65 , c ) 78 , d ) 33 , e ) 8.69
Rationale: given that , cost price of 50 article is equal to selling price of 46 articles . let cost price of one article = rs . 1 selling price of 46 articles = rs . 50 but cost price of 46 articles = rs . 46 therefore , the trader made profit . \ percentage of profit = 4 / 46 * 100 = 8.69 % answer : e
Answer: e
Python program:
a = 100 * 46
b = a / 50
c = 100 - b
d = 100 * 46
e = d / 50
f = c / e
g = 100 * f
Problem: johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 21 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 4 miles , c ) 6.5 miles , d ) 8 miles , e ) 10 miles
Rationale: "answer : c ) 6.5 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 21 / ( 5 + 21 ) = 6.5 m / hr the distance between schoolhome should be half of that . ie . 6.5 miles answer c"
Answer: c
Python program:
a = 1 / 5
b = 1 / 21
c = a + b 
d = 1 / c
e = d * const_1_6
Problem: if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 3 y ^ 2 = ?
Options: a ) 2 , b ) 48 , c ) 0 , d ) 10 , e ) 3
Rationale: 3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 3 y ^ 2 = 3 * 16 = 48 answer is b
Answer: b
Python program:
a = 40 + 20 
b = 3 + 2 
c = a / b
d = c * 3
e = 40 - d
f = e ** 2
g = 3 * f
Problem: how many distinct 3 digit number less than 10
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "000,001 , 002,003 , 004,005 , 006,007 , 008,009 . 10 distinct 3 digit numbers less than 10 . answer : c"
Answer: c
Python program:
a = 2 + 3
Problem: the average age of a group of persons going for picnic is 16 years . 20 new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is ?
Options: a ) 10 , b ) 20 , c ) 37 , d ) 26 , e ) 22
Rationale: let the initial number of persons be x . then , 16 x + 20 * 15 = 15.5 ( x + 20 ) < = > 0.5 x = 10 < = > x = 20 . answer : b
Answer: b
Python program:
a = 15 * 5
b = 15 * 20
c = a - b
d = 16 - 15
e = c / d
Problem: in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 2000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 20000 , b ) 25000 , c ) 24000 , d ) 23000 , e ) 22000
Rationale: "winner - looser 55 % - 45 % if 2000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 2,000 people compose 10 % of all voters , which means that the total number of votes is 20,000 . answer : a ."
Answer: a
Python program:
a = 10 / 100
b = 2000 / a
Problem: if 99 < x < 199 and 10 < y < 100 , then the product xy can not be equal to :
Options: a ) 19,104 , b ) 19,903 , c ) 19 , 356.732 , d ) 19,502 , e ) 19,880
Rationale: correct answer : ( b ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 99 * 10 . the largest value must be less than 199 * 100 . this means that 990 < xy < 19,900 . ( b ) is outside of this range , so it is not a possible product of xy .
Answer: b
Python program:
a = 100 + 1