euclaise/mathqa_programs huggingface dataset:
Problem: in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 215,000 , b ) 216,000 , c ) 217,000 , d ) 218,000 , e ) 219,000
Rationale: this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 2 = 5 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 5 = 216,000 . hence b .
Answer: b
Python program:
a = 7 - 2
b = a * 3600
c = b * 12
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36.00001 sec . the length of each train is ?
Options: a ) 50 , b ) 99 , c ) 77 , d ) 26 , e ) 23
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 36 = 25 / 9 = > x = 50 . answer : a"
Answer: a
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = 36 * 1
e = d / 2
Problem: two numbers n and 14 have lcm = 56 and gcf = 10 . find n .
Options: a ) 24 , b ) 40 , c ) 44 , d ) 54 , e ) 64
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 14 × n = 56 × 10 n = 56 × 10 / 14 = 40 correct answer b"
Answer: b
Python program:
a = 56 * 10
b = a / 14
Problem: how many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 4 percent sugar solution ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the amount that needs to be evaporated . 0.02 ( 50 ) = 0.04 ( 50 - x ) 0.04 x = 2 - 1 x = 1 / 0.04 = 25 liters the answer is b ."
Answer: b
Python program:
a = 50 / 100
b = a * 4
c = 50 - b
Problem: a batsman scored 60 runs which included 2 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 30 % , b ) 33.33 % , c ) 40 % , d ) 60 % , e ) 50 %
Rationale: "explanation : number of runs made by running = 60 - ( 2 x 4 + 2 x 6 ) = 60 - ( 20 ) = 20 now , we need to calculate 20 is what percent of 60 . = > 20 / 60 * 100 = 33.33 % option b"
Answer: b
Python program:
a = 2 * 2
b = 2 * 2
c = a + b 
d = 60 - c
e = d / 60
f = e * 100
Problem: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 5 people to do 5 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: 3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 5 people can do 5 / 3 of the work in one day . 5 people can do 5 times the work in 3 days . the answer is c .
Answer: c
Python program:
a = 5 / 5
b = 3 * a
Problem: tom opened a shop investing rs . 500 . jose joined him 2 months later , investing rs . 350 . they earned a profit of rs . 1720 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 80 , b ) 20 , c ) 30 , d ) 41 , e ) 15
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 1720 = 80 a"
Answer: a
Python program:
a = 2 * 3
b = 2 * a
c = 500 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 350 * f
h = 2 * 3
i = 2 * h
j = 500 * i
k = g + j 
l = c / k
m = 1 - l
n = 1720 * m
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 8748 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 94.50 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 8748 ⇔ 12 x 2 = 8748 ⇔ x 2 = 729 ⇔ x = 27 . so , length = 81 m and breadth = 108 m . perimeter = [ 2 ( 81 + 108 ) ] m = 378 m . ∴ cost of fencing = rs . ( 0.25 × 378 ) = rs . 94.50 . answer d"
Answer: d
Python program:
a = 3 * 4
b = 8748 / a
c = math.sqrt(b)
d = 3 * c
e = 3 * 4
f = 8748 / e
g = math.sqrt(f)
h = 4 * g
i = rectangle_perimeter * (
j = i / 25
Problem: the angle between the minute hand and the hour hand of a clock when the time is 4.20 , is :
Options: a ) 10 d , b ) 0 d , c ) 15 d , d ) 5 d , e ) 20 d
Rationale: "angle traced hr 13 / 3 = ( 360 / 12 * 13 / 3 ) = 130 traced by min hand 20 min = ( 360 / 60 * 20 ) = 120 req = ( 130 - 120 ) = 10 d answer a"
Answer: a
Python program:
a = 3 * 4
b = 3 * 4
c = b - 1
d = a / c
e = 4 + 1 
f = 3 * 4
g = f - 1
h = e * g
i = d * h
j = const_60 / 2
k = i - j
l = 3 * 4
m = l - 1
n = k * m
o = n / 2
Problem: the positive numbers w , x , y , and z are such that x is 40 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 23.2 - answer d"
Answer: d
Python program:
a = 40 + 100 
b = a / 100
c = 40 + 100 
d = c / 100
e = b * d
f = 100 - 40
g = f / 100
h = e * g
i = h - 1
j = 100 * i
Problem: if 10 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 40 days , d ) 48 days , e ) 50 days
Rationale: "10 * 80 = 20 * x x = 40 days answer : c"
Answer: c
Python program:
a = 10 * 80
b = a / 20
Problem: a trader sells 60 meters of cloth for rs . 8400 at the profit of rs . 12 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 128 , b ) 140 , c ) 123 , d ) 110 , e ) 150
Rationale: "sp of 1 m of cloth = 8400 / 60 = rs . 140 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 140 - rs . 12 = rs . 128 . answer : a"
Answer: a
Python program:
a = 8400 / 60
b = a - 12
Problem: 48 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 26 , c ) 42 , d ) 27 , e ) 21
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 48 = 21 answer : e"
Answer: e
Python program:
a = 4 + 3 
b = 4 + 3 
c = b + 2 
d = a / c
e = d * 48
f = e / 2
Problem: a car covers a distance of 624 km in 6 â ½ hours . find its speed ?
Options: a ) 104 , b ) 190 , c ) 109 , d ) 278 , e ) 211
Rationale: explanation : 624 / 6 = 104 kmph answer : c
Answer: c
Python program:
a = 624 / 6
Problem: when average age of 23 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 22 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 23 numbers = 0 . sum of 23 numbers ( 0 x 23 ) = 0 . it is quite possible that 22 of these numbers may be positive and if their sum is a then 23 rd number is ( - a ) answer is 22 ( b )"
Answer: b
Python program:
a = 23 - 1
Problem: if 2 : 9 : : x : 18 , then find the value of x
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "explanation : treat 2 : 9 as 2 / 9 and x : 18 as x / 18 , treat : : as = so we get 2 / 9 = x / 18 = > 9 x = 36 = > x = 4 option c"
Answer: c
Python program:
a = 9 * 2
b = a + 9 
c = b / 18
Problem: during the first two weeks of january , the total rainfall in springdale was 35 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 21 inches
Rationale: total rainfall in 2 weeks = 35 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 35 inches x = 14 and 1.5 x = 21 rainfall during second week = 21 inches option e
Answer: e
Python program:
a = 1 + 1 
b = 1 / 5
c = 35 * b
Problem: if you roll one fair 6 - sided die , what is the probability that the number is even or less than 3 ?
Options: a ) 2 / 3 , b ) 1 / 2 , c ) 3 / 4 , d ) 5 / 6 , e ) 1 / 3
Rationale: the numbers which satisfy the conditions are 1 , 2 , 4 , and 6 . the probability is 4 / 6 = 2 / 3 the answer is a .
Answer: a
Python program:
a = 3 / 6
b = 1 / 6
c = a + b
Problem: a fifth of arun â € ™ s marks in mathematics exceed a third of his marks in english by 20 . if he got 260 marks in two subjects together how many marks did he got in english ?
Options: a ) 12080 , b ) 18060 , c ) 20060 , d ) 20040 , e ) none of them
Rationale: let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 5 ) x - ( 1 / 3 ) y = 20 3 x - 5 y = 300 â € ¦ â € ¦ > ( 1 ) x + y = 260 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 200 and y = 60 answer is c .
Answer: c
Python program:
a = 260 * 20
b = a * 2
c = b * 2
Problem: in a colony of 70 residents , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of education to uneducated persons is 8 : 27 , then find the ratio of the number of educated and uneducated men in the colony ?
Options: a ) 1 : 7 , b ) 1 : 1 , c ) 1 : 2 , d ) 1 : 9 , e ) 1 : 3
Rationale: "number of men in the colony = 4 / 7 ( 70 ) = 40 number of women in the colony = 3 / 7 ( 70 ) = 30 number of educated women in the colony = 1 / 5 ( 30 ) = 6 number of uneducated women in the colony = 4 / 5 ( 30 ) = 24 number of educated persons in the colony = 8 / 35 ( 70 ) = 16 as 6 females are educated , remaining 10 educated persons must be men . number of uneducated men in the colony = 40 - 10 = 30 number of educated men and uneducated men are in the ratio 10 : 30 = > 1 : 3 answer : e"
Answer: e
Python program:
a = 8 + 27 
b = 70 / a
c = b * 8
d = 4 + 3 
e = 70 / d
f = e * 3
g = 1 + 4 
h = f / g
i = c - h
j = 8 + 27 
k = 70 / j
l = k * 27
m = 4 + 3 
n = 70 / m
o = n * 3
p = 1 + 4 
q = o / p
r = q * 4
s = l - r
t = i / s
Problem: 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?
Options: a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 62
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 4 40 + 10 + 4 - 7 = 47 like apple answer : a"
Answer: a
Python program:
a = 40 - 3
b = a + 7 
c = 10 - 7
d = b + c
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 50,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 30000 , b ) 60000 , c ) 50000 , d ) 90000 , e ) 70000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 150000 - x ) respectively . then , ( 1 / 3 ) x = ( 1 / 2 ) ( 150000 - x ) ( x / 3 ) + ( x / 2 ) = 75000 5 x / 6 = 75000 x = 75000 x 6 / 5 = 90000 savings in public provident fund = rs . ( 150000 - 90000 ) = rs . 60000 answer is b ."
Answer: b
Python program:
a = 100 * 10
b = a * 100
c = 100 * 10
d = c * 100
e = 2 * 100
f = e * 100
g = d - f
h = b + g 
i = 3 / 2
j = i + 1 
k = 1 / j
l = h * k
Problem: a girl goes to her school from her house at a speed of 6 km / hr and returns at a speed of 4 km / hr . if she takes 10 hours in going and coming back , the distance between her school and house is
Options: a ) 12 kms , b ) 16 kms , c ) 20 kms , d ) 24 kms , e ) none of above
Rationale: let distance be d 10 = d / 4 + d / 6 answer : d
Answer: d
Python program:
a = 6 * 4
b = 10 * a
c = 6 + 4 
d = b / c
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 12 , what is the sum of the first 15 terms of the progression ?
Options: a ) 90 , b ) 80 , c ) 70 , d ) 60 , e ) 50
Rationale: "4 th term + 12 th term = 12 i . e . , ( a + 3 d ) + ( a + 11 d ) = 12 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 12 - - - - - - - - - - - - - - - from ( 1 ) = 90 answer : a"
Answer: a
Python program:
a = 15 / 2
b = a * 12
Problem: ( 51 + 52 + 53 + . . . + 100 ) = ?
Options: a ) 2525 , b ) 2975 , c ) 3225 , d ) 3775 , e ) 2753
Rationale: "explanation : this is an a . p . in which a = 51 , l = 100 and n = 50 . sum = n ( a + l ) = 50 x ( 51 + 100 ) = ( 25 x 151 ) = 3775 . 2 2 answer : d"
Answer: d
Python program:
a = 51 + 52 
b = a / 53
Problem: a car was driving at 50 km / h for 30 minutes , and then at 40 km / h for another 30 minutes . what was its average speed ?
Options: a ) 80 . , b ) 75 . , c ) 70 . , d ) 65 . , e ) 54 .
Rationale: "driving at 50 km / h for 30 minutes , distance covered = 50 * 1 / 2 = 25 km driving at 40 km / h for 30 minutes , distance covered = 40 * 1 / 2 = 20 km average speed = total distance / total time = 45 / 1 = 45 km / h answer : a"
Answer: a
Python program:
a = 30 + 30 
b = 30 / a
c = b * 50
d = 30 + 30 
e = 30 / d
f = e * 40
g = c + f 
h = 30 + 30 
i = h / const_60
j = g / i
Problem: a and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 11 : 00 a . m . ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 15 , e ) 3
Rationale: "sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour . hence , they cross each other 15 times before 11 : 00 a . m . answer d"
Answer: d
Python program:
a = 2 + 3 
b = 2 + 3 
c = a + b
Problem: a started a business with an investment of rs . 10000 and after 7 months b joined him investing rs . 12000 . if the profit at the end of a year is rs . 24000 , then the share of b is ?
Options: a ) 10000 , b ) 8000 , c ) 12000 , d ) 6000 , e ) 14000
Rationale: "ratio of investments of a and b is ( 10000 * 12 ) : ( 12000 * 5 ) = 2 : 1 total profit = rs . 24000 share of b = 1 / 3 ( 24000 ) = rs . 8000 answer : b"
Answer: b
Python program:
a = const_60 * 100
b = 24000 - a
Problem: in a certain pond , 30 fish were caught , tagged , and returned to the pond . a few days later , 30 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 750 , c ) 1250 , d ) 2500 , e ) 10 000
Rationale: "if x is total number of fish in the pond : 4 = 30 / x * 100 = > x = 750 so answer is b"
Answer: b
Python program:
a = 2 / 30
b = 30 / a
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 9 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 289 m , d ) 799 m , e ) 1000 m
Rationale: speed = 300 / 9 = 100 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 100 / 3 = > x = 1000 m . answer : e
Answer: e
Python program:
a = speed * (
b = a - 39
Problem: a and b ’ s salaries together amount to rs . 4,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a ’ s salary ?
Options: a ) 2777 , b ) 1500 , c ) 3000 , d ) 2776 , e ) 2881
Rationale: ( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 4000 4 b = 4000 = > b = 1000 a = 3000 answer c
Answer: c
Python program:
a = 2 + 3 
b = 4 * a
c = 2 * b
d = c * 100
e = 85 / 100
f = 1 - e
g = d * f
h = 95 / 100
i = 1 - h
j = 85 / 100
k = 1 - j
l = i + k 
m = g / l
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 324 different signs . if the company used 322 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 324 signs ?
Options: a ) 246 , b ) 248 , c ) 1292 , d ) 15,128 , e ) 30,256
Rationale: "# of 2 - letter codes possible from 324 different signs = 324 * 324 . # of 2 - letter codes possible from 322 different signs = 322 * 322 . the difference = 324 ^ 2 - 322 ^ 2 = ( 324 - 322 ) ( 324 + 322 ) = 1292 . answer : c ."
Answer: c
Python program:
a = 324 - 322
b = 322 * a
c = 324 - 322
d = b * c
Problem: the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 3.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 3.50 + 0.50 ( x − 2 ) = 3.50 + . 5 * 3 = 3.5 + 1.5 = 5 $ answer e
Answer: e
Python program:
a = 18 - 2
b = a / 4
c = b + 1 
d = c - 2
e = 0 * 5
f = 3 + 5
Problem: a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 4 t seconds , then what is the length of the platform ?
Options: a ) 0.5 l , b ) l , c ) 1.5 l , d ) 2 l , e ) 3 l
Rationale: "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 4 t ( l + p ) / ( l / t ) = 4 t p = 3 l the answer is e ."
Answer: e
Python program:
a = 4 - 1
Problem: the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 675 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "area = l * w = 3 w ^ 2 = 675 w ^ 2 = 225 w = 15 the answer is b ."
Answer: b
Python program:
a = 675 / 3
b = a / 3
c = b / 4
Problem: in feb mrs bil ' s earnings were 70 percent of the bil family ' s total income . in june mrs bil earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs bil ' s earnings were approximately what percent of the bil family ' s total income ?
Options: a ) 72 , b ) 34 , c ) 78 , d ) 37 , e ) 27
Rationale: lets say the family income is 100 in may , bil earned 70 family income is 30 in june , bil earned 10 % more than may , so it is ( 70 + 10 * 70 / 100 = 77 ) family income is same 30 in june bil ' s income percent is 77 * 100 / 107 ~ 72 ans is a
Answer: a
Python program:
a = 70 / 10
b = 70 + a 
c = 70 / 10
d = 100 + c 
e = b / d
f = e * 100
Problem: find the number of zeroes at the end of 50 !
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "calculate division by 5 and 25 50 / 5 = 10 50 / 25 = 2 total = 12 answer : c"
Answer: c
Python program:
a = 2 + 2
Problem: a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random form this box . the probability that at least one of these is defective is :
Options: a ) 8 / 19 , b ) 7 / 19 , c ) 10 / 19 , d ) 20 / 19 , e ) 22 / 19
Rationale: "p ( none is defective ) = 16 c 2 / 20 c 2 = 12 / 19 p ( at least one is defective ) = 1 - 12 / 19 = 7 / 19 answer b"
Answer: b
Python program:
a = 20 - 4
b = math.comb(a, 2)
c = math.comb(20, 2)
d = b / c
e = 1 - d
Problem: john and amanda stand at opposite ends of a straight road and start running towards each other at the same moment . their rates are randomly selected in advance so that john runs at a constant rate of 2 , 3 , 4 , or 5 miles per hour and amanda runs at a constant rate of 3 , 4 , 5 , 6 , or 7 miles per hour . what is the probability that john has traveled farther than amanda by the time they meet ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 20 , e ) 7 / 20
Rationale: john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 4 * 2 / 5 = 2 / 20 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 4 * 1 / 5 = 1 / 20 p ( john runs farther ) = 2 / 20 + 1 / 20 = 3 / 20 the answer is d .
Answer: d
Python program:
a = 4 * 5
b = 3 / a
Problem: john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 40,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 50000 , b ) 55000 , c ) 60000 , d ) 70000 , e ) 80804
Rationale: a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 40,000 ( 1 + 0.04 / 4 ) ^ 4 - 40,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 40,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 40,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 40,000 ( 1.0201 + 1 ) = 80804 . hence answer is e .
Answer: e
Python program:
a = 4 * 100
b = a * 100
c = 4 / 100
d = c / 4
e = 1 + d 
f = e ** 4
g = b * f
h = 4 * 100
i = h * 100
j = g - i
k = 2 / 100
l = k / 2
m = 1 + l 
n = m ** 2
o = n - 1
p = j / o
Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 14 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 10 and 7 , d ) 3 and 10 , e ) 8 and 5
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 14 cm 2 more than the first area . therefore a 1 + 14 = a 2 x ( x − 3 ) + 14 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 14 = x 2 + x − 2 x − 2 2 x = 16 x = 8 . so , the sides of the rectangle are 8 cm and ( 8 − 3 ) = 5 cm long . so answer is e ."
Answer: e
Python program:
a = 14 / 2
b = a + 1 
c = b - 3
Problem: if two positive numbers are in the ratio 1 / 10 : 1 / 7 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 42.8 % . , c ) 60 % . , d ) 68 % . , e ) 80 % .
Rationale: "given ratio = 1 / 10 : 1 / 7 = 7 : 10 let first number be 7 x and the second number be 10 x . the second number is more than first number by 3 x . required percentage = 3 x / 7 x * 100 = 42.8 % . answer : b"
Answer: b
Python program:
a = 1 / 7
b = a * 100
Problem: if 7125 ¸ 1.25 = 5700 < the value of 712.5 ÷ 12.5 is :
Options: a ) 5.7 , b ) 57 , c ) 570 , d ) 0.57 , e ) 0.057
Rationale: given 7125 / 1.25 = 5700 712.5 / 12.5 = 71.25 / 1.25 = 7125 * 1 / 1.25 * 100 = 5700 / 100 = 57 answer : b
Answer: b
Python program:
a = 712 / 5
Problem: how many of the positive factors of 33 are not factors of 45 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 33 - 1 , 3 , 11 , 33 , factors of 45 - 1 , 3 , 5 , 9 , 15 , 45 , comparing both , we have three factors of 33 which are not factors of 45 - 11 , 33 , the answer is c"
Answer: c
Python program:
a = 45 / 33
Problem: find the principle on a certain sum of money at 5 % per annum for 6 years if the amount being rs . 1120 ?
Options: a ) 862 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: 1120 = p [ 1 + ( 5 * 6 ) / 100 ] p = 862 answer : a
Answer: a
Python program:
a = 5 * 6
b = a / 100
c = 1 + b 
d = 1120 / c