euclaise/mathqa_programs huggingface dataset:
Problem: a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyence . if he has rs . 1400 left with him , find his expenditure on food and conveyence .
Options: a ) 800 , b ) 900 , c ) 100 , d ) 700 , e ) 500
Rationale: "let the salary be x , therefore house rent = 2 x / 5 , food = 3 x / 10 , conveyence = x / 8 . it is given that left over salary is 1400 / - so , x - ( 2 x / 5 + 3 x / 10 + x / 10 ) = 1400 by solving x = 8000 expenditure on food = 3200 and conveyence = 1000 answer : c"
Answer: c
Python program:
a = 2 / 5
b = 3 / 10
c = a + b 
d = 1 / 8
e = c + d 
f = 1 - e
g = 1400 / f
h = 3 / 10
i = g * h
j = 2 / 5
k = 3 / 10
l = j + k 
m = 1 / 8
n = l + m 
o = 1 - n
p = 1400 / o
q = 1 / 8
r = p * q
s = i + r
Problem: there are 17 students in a certain class . on the day the test was given , taqeesha was absent . the other 16 students took the test , and their average was 77 . the next day , taqeesha took the test , and with her grade included , the new average is 78 . what is taqeesha ’ s grade on the test ?
Options: a ) 78 , b ) 80 , c ) 87 , d ) 91 , e ) 94
Rationale: explanations 1 ) the average of the first 16 students is 77 . this means , the sum of these 16 scores is sum = ( average ) * ( number of scores ) = 77 * 16 = 1232 once taqeesha takes her test , the average of all 17 scores is 78 . this means , the sum of these 17 scores is : sum = ( average ) * ( number of scores ) = 78 * 17 = 1326 once we had the sum of the 16 scores , all we had to do was add taqeesha ’ s score to that total to get the sum of all 17 . therefore , the difference in these two sums is taqeesha ’ s score . 1326 – 1232 = 94 . answer : e .
Answer: e
Python program:
a = 78 + 16
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 15 percent . the enrollment on january 1 , 1993 , was 60 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 52
Rationale: "1.15 x = 60 - - > 23 / 20 * x = 60 - - > x = 60 * 20 / 23 = 1200 / 23 = ~ 52 . answer : e ."
Answer: e
Python program:
a = 100 + 15 
b = 100 / a
c = b * 60
Problem: a reduction of 30 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "800 * ( 30 / 100 ) = 240 - - - - 5 ? - - - - 1 = > rs . 48 answer : c"
Answer: c
Python program:
a = 800 * 30
b = a / 100
c = b / 5
Problem: a , b , c and d are 4 consecutive numbers . if the sum of a and dis 109 , what is the product of b and c ?
Options: a ) 2652 , b ) 2578 , c ) 2970 , d ) 3354 , e ) 4234
Rationale: c 2970 here d = a + 3 a + a + 3 = 109 2 a = 106 a = 53 so , numbers are 53 , 54 , 55 and 56 ∴ b × c = 54 × 55 = 2970
Answer: c
Python program:
a = 4 - 1
b = 109 - a
c = b / 2
d = c + 1 
e = 4 - 1
f = 109 - e
g = f / 2
h = g + 1 
i = h + 1 
j = d * i
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent q ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . q = [ ( 2 - 1 ) / 1 ] * 100 % = 100 %"
Answer: c
Python program:
a = 100 - 80
b = a - 10
c = 10 / b
d = c * 100
Problem: a student traveled 25 percent of the distance of the trip alone , continued another 40 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
Rationale: "let x be the total length of the trip . 0.25 x + 40 miles + 0.5 x = x 40 miles = 0.25 x x = 160 miles the answer is c ."
Answer: c
Python program:
a = 1/(25)
b = 1 - a
c = 1 / 2
d = b - c
e = 40 / d
Problem: of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 4 times the fraction of first - year students who have declared a major , what fraction of all the students in the dormitory are second - year students who have not declared a major ?
Options: a ) 1 / 15 , b ) 4 / 5 , c ) 4 / 15 , d ) 1 / 5 , e ) 2 / 5
Rationale: tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 4 ( 1 / 5 ( x / 2 ) ) = 2 / 5 ( x ) - - - > non major = x / 2 - 2 / 5 ( x ) = 1 / 5 ( x ) hence 1 / 5 d
Answer: d
Python program:
a = 4 / 5
b = 1 - a
Problem: if the personal income tax rate is lowered from 42 % to 28 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 34500 ?
Options: a ) $ 3500 , b ) $ 5000 , c ) $ 4830 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 42 - 28 ) % of 34500 = 4830 . answer : c"
Answer: c
Python program:
a = 34500 / 100
b = 42 - 28
c = a * b
Problem: solve the equation for x : 5 x - 14 + 3 x = 4 + 9 - x
Options: a ) 4 , b ) 5 , c ) 7 , d ) 9 , e ) 3
Rationale: "e 3 8 x + x = 13 + 14 9 x = 27 = > x = 3"
Answer: e
Python program:
a = 14 + 4 
b = 5 + 5 
c = a / b
Problem: the positive integers a and b leave remainders of 2 and 3 , respectively , when divided by 6 . a > b . what is the remainder when a – b is divided by 6 ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 2 , e ) 1
Rationale: let ' s test out some values of m and n that satisfy the given information . a leaves are remainder of 2 when divided by 6 so , a could equal 8 b leaves are remainder of 3 when divided by 6 so , b could equal 3 what is the remainder when a – b is divided by 6 ? so , a - b = 8 - 3 = 5 , and when we divide 5 by 6 , we get 0 with remainder 5 answer : c
Answer: c
Python program:
a = reminder + (
Problem: john left home and drove at the rate of 35 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 35 * 2 + 3 * 55 = 235 miles . answer a"
Answer: a
Python program:
a = 35 * 2
b = 3 * 55
c = a + b
Problem: a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 70 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 180
Rationale: "70 % is 30 % - points above 40 % and 10 % - points below 80 % . thus the ratio of ` ` the first 30 games ' ' to ` ` remaining games ' ' is 1 : 3 . so the team played a total of 30 + 90 = 120 games . the answer is c ."
Answer: c
Python program:
a = 40 / 100
b = 30 * a
c = 80 / 100
d = 70 / 100
e = c - d
f = b / e
Problem: mangoes , oranges and apples in a fruit shop are in the ratio of 10 : 2 : 3 . if there are 120 mangoes , the number of apples in the shop is : .
Options: a ) 36 , b ) 42 , c ) 72 , d ) 400 , e ) 56
Rationale: explanation : let mangoes = 10 x , oranges = 2 x & apples = 3 x . now , 10 x = 120 hence x = 12 . number of apples = 3 x = 36 . answer : a
Answer: a
Python program:
a = 120 / 10
b = a * 3
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 9 more than the average of 10 , 70 , and what number ?
Options: a ) 15 , b ) 25 , c ) 35 , d ) 13 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 9 = 31 sum of second list = 31 * 3 = 93 therefore the number = 93 - 80 = 13 answer : d"
Answer: d
Python program:
a = 20 + 40 
b = a + 60 
c = 9 * 3
d = c + 10 
e = d + 70 
f = b - e
Problem: if 4 xz + yw = 3 and xw + yz = 6 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 15 . , d ) 16 , e ) 18 .
Rationale: "expand this to get : ( 2 x + y ) ( 2 z + w ) = 4 xz + 2 xw + 2 yz + yw = 4 xz + yw + 2 xw + 2 yz [ i rearranged the terms ] = 3 + 2 xw + 2 yz [ replaced 4 xz + yw with 3 ] = 3 + 2 ( xw + yz ) factored out a 2 = 3 + 2 ( 6 ) = 3 + 12 = 15 answer : c"
Answer: c
Python program:
a = 6 * 2
b = 4 + 0
Problem: the sum of three consecutive even numbers is 42 . find the middle number of the three ?
Options: a ) 14 , b ) 66 , c ) 88 , d ) 99 , e ) 12
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 42 6 p = 42 = > p = 7 . the middle number is : 2 p = 14 . answer : a"
Answer: a
Python program:
a = 42 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 42 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 42 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 42 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "say may income = 100 l ' s income = 60 and rest of the family = 40 in june l ' s income = 60 * 120 / 100 = 72 so 72 / 72 + 40 = 64 % answer : a"
Answer: a
Python program:
a = 100 + 20 
b = 100 + 20 
c = b + 100 
d = a / c
e = d * 100
Problem: two cars start at the same time from opposite ends of a highway that is 105 miles long . one car is riding at 15 mph and the second car is riding at 20 mph . how long after they begin will they meet ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 20 + 15 = 35 mph total distance to be covered = 105 miles . time taken would be : 105 miles / 35 mph = 3 hours c is the answer ."
Answer: c
Python program:
a = 15 + 20 
b = 105 / a
Problem: the sum of the ages of 5 children born at the intervals of 3 year each is 40 year . what is the age of the youngest child ?
Options: a ) 2 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 40 â ‡ ” 5 x = 10 â ‡ ” x = 2 . â ˆ ´ age of the youngest child = x = 2 years . answer a"
Answer: a
Python program:
a = 5 / 3
b = 40 / a
c = 5 - 1
d = c * 3
e = b - d
f = e / 3
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 6 students is 14 years and that of the other 9 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 6 + 16 * 8 ) ] = 13 years . answer : c"
Answer: c
Python program:
a = 15 * 15
b = 6 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: find the annual income derived by investing $ 6800 in 10 % stock at 136 .
Options: a ) 550 , b ) 500 , c ) 250 , d ) 300 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 10 . by investing $ 6800 , income obtained = $ [ ( 10 / 136 ) * 6800 ] = $ 500 . answer b ."
Answer: b
Python program:
a = 6800 * 10
b = a / 136
Problem: find the sum of first 32 natural numbers
Options: a ) 470 , b ) 468 , c ) 465 , d ) 463 , e ) 528
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 32 ( 32 + 1 ) / 2 = 32 ( 33 ) / 2 = 528 answer : option e"
Answer: e
Python program:
a = 32 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 32 / e
g = f / 2
h = 32 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 32 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: how many 4 digit numbers are there , if it is known that the first digit is odd , the second is even , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 380
Rationale: "4 options for the first digit : 1 , 3 , 5 , 7 , 9 ; 5 options for the second digit : 0 , 2 , 4 , 6 , 8 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 5 * 5 * 4 * 4 = 400 numbers with two 2 - s , 2 x 2 x 5 * 1 * 1 * 4 = 20 . thus there are 400 - 20 = 380 such numbers . answer : e ."
Answer: e
Python program:
a = 4 + 1 
b = 4 + 1 
c = a * b
d = 4 * 4
e = c * d
f = 4 + 1 
g = 4 + 1 
h = f * g
i = h * 4
j = e - i
Problem: there are 60 people and 3 clubs m , s , and z in a company . 16 people joined m , 18 people joined s and 11 people joined z . if the members of m did not join any other club , at most , how many people of the company did not join any club ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: answer e . key is ' atmost ' here . so 16 people joined m . 18 people joined s and 11 people joined z . to get maximum people who did not join any club , 11 people who joined z are among 18 people who joined s . so 18 + 16 = 34 60 - 34 = 26
Answer: e
Python program:
a = 60 - 16
b = a - 18
Problem: 3 * 14 + 3 * 15 + 3 * 18 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 152
Rationale: "3 * 14 + 3 * 15 + 3 * 18 + 11 = 42 + 45 + 54 + 11 = 152 the answer is e ."
Answer: e
Python program:
a = 3 * 14
b = 3 * 15
c = a + b 
d = 3 * 18
e = c + d 
f = e + 11
Problem: how many digits 2 ^ 10 has ?
Options: a ) 3 , b ) 35 , c ) 50 , d ) 99 , e ) 101
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 therefore 3 digits would be my best guess a"
Answer: a
Python program:
a = math.log(2)
b = math.log(10)
c = a / b
d = c * 10
e = 1 + d 
f = math.floor(e)
Problem: 550 − ( 104 ÷ 20.8 ) = ?
Options: a ) 545 , b ) 525 , c ) 535 , d ) 625 , e ) 105
Rationale: "explanation : = 550 − ( 104 / 208 x 10 ) = 550 − 5 = 545 option a"
Answer: a
Python program:
a = 104 / 20
b = 550 - a
Problem: what is the greatest prime factor of 4 ^ 6 - 1 ?
Options: a ) 13 , b ) 17 , c ) 19 , d ) 23 , e ) 29
Rationale: "4 ^ 6 - 1 = ( 4 ^ 3 - 1 ) ( 4 ^ 3 + 1 ) = 63 * 65 = 7 * 9 * 5 * 13 the answer is a ."
Answer: a
Python program:
a = 6 / 2
b = 4 / a
c = math.floor(b)
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 4 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 4 ( 1 - x ) p 12 xp = 4 p - 4 xp 16 xp = 4 p x = 1 / 4 the answer is b ."
Answer: b
Python program:
a = 12 / 4
b = a + 1 
c = 1/(b)
Problem: find the simple interest on rs . 620 for 10 months at 10 paisa per month ?
Options: a ) 277 , b ) 620 , c ) 640 , d ) 678 , e ) 121
Rationale: "i = ( 620 * 10 * 10 ) / 100 = 620 answer : b"
Answer: b
Python program:
a = 10 / 100
b = 620 * a
Problem: one pump drains one - half of a pond in 4 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "first pump drains 1 / 2 of the tank in 4 hours so 8 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 8 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 8 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 8 + 1 / a ) = 1 / 2 solving u get a = 8 / 7 = 1.1 hence answer is b"
Answer: b
Python program:
a = 4 * 2
b = 1 / a
c = 1 - b
d = 1 / c
Problem: if 0.60 : x : : 6 : 4 , then x is equal to
Options: a ) 0.1 , b ) 0.4 , c ) 0.82 , d ) 0.8 , e ) none
Rationale: "sol . ( x × 6 ) = ( 0.60 × 4 ) ⇒ x = 2.4 / 6 = 0.40 . answer b"
Answer: b
Python program:
a = 0 * 60
b = a / 6
Problem: in a small snack shop , the average ( arithmetic mean ) revenue was $ 400 per day over a 10 - day period . during this period , if the average daily revenue was $ 360 for the first 6 days , what was the average daily revenue for the last 4 days ?
Options: a ) $ 420 , b ) $ 440 , c ) $ 450 , d ) $ 460 , e ) $ 480
Rationale: the average revenue was $ 400 per day over a 10 - day period - - > total revenue over 10 - day period is 10 * $ 400 = $ 4000 ; the average daily revenue was $ 360 for the first 6 days - - > total revenue for the first 6 days is 6 * $ 360 = 2160 ; total revenue for the last 4 days is $ 4000 - 2160 = $ 1840 ; average daily revenue for the last 4 days is $ 1840 / 4 = $ 460 . answer : d .
Answer: d
Python program:
a = 400 * 10
b = 360 * 6
c = a - b
d = c / 4
Problem: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 50 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 101 ° f , b ) 108 ° f , c ) 116 ° f , d ) 122 ° f , e ) 127 ° f
Rationale: let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 50 ) / 5 + 32 = 122 ° f the answer is d .
Answer: d
Python program:
a = 212 - 32
b = a / 100
c = b * 50
d = c + 32
Problem: louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compunded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louie have to pay each month ?
Options: a ) 333 , b ) 383 , c ) 402 , d ) 433 , e ) 483
Rationale: let the monthly payment be xx . after the 1 st month there will be 1000 ∗ 1.1 − x dollars left to repay ; after the 2 nd month there will be ( 1000 ∗ 1.1 − x ) ∗ 1.1 − x = 1210 − 2.1 x dollars left to repay ; after the 3 rd month there should be 0 dollars left to repay : ( 1210 − 2.1 x ) ∗ 1.1 − x = 0 - - > 1331 = 3.31 x - - > x ≈ 402 x ≈ 402 answer : c .
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = 1000 * b
d = 10 / 100
e = 1 + d 
f = c * e
g = 10 / 100
h = 1 + g 
i = f * h
j = 10 / 100
k = 1 + j 
l = 1 + k 
m = 10 / 100
n = 1 + m 
o = l * n
p = 1 + o 
q = i / p
Problem: when positive integer n is divided by positive integer j , the remainder is 26 . if n / j = 150.40 , what is value of j ?
Options: a ) 75 , b ) 65 , c ) 60 , d ) 130 , e ) 30
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 150.40 here 150 the quotient . given that remainder = 26 so , 150.40 = 150 + 26 / j so , j = 65 answer : b"
Answer: b
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 150 - 40
e = 26 / d
Problem: kim has 9 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 18 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 11 / 5 , c ) 1 / 9 , d ) 1 / 17 , e ) 1 / 5
Rationale: "can be tackled in this way as well : probability of selecting any 1 out of 10 shoes = 18 / 18 = 1 probability of selecting the next shoe ( out of 18 available ) having the same color = 1 / 18 ( as after selecting the 1 st one , there is only 1 another shoe left with the same color ) . thus the total probability = 1 * 1 / 17 = 1 / 17 . d is the correct answer ."
Answer: d
Python program:
a = math.comb(18, 2)
b = 9 / a
Problem: rahim bought 4 pillows with the average cost of $ 5 . if rahim also buys the fifth pillow with the price of $ 10 , what is the average ( arithmetic mean ) price of those 5 pillows ?
Options: a ) $ 6 , b ) $ 5 , c ) $ 5.5 , d ) $ 6.5 , e ) $ 7
Rationale: 4 pillowss - > total cost = 4 * avg cost = 4 * 5 = 20 fifth pillow cost = 10 total cost for 5 pillows = 20 + 10 = 30 am = 30 / 5 = 6 hence a
Answer: a
Python program:
a = 4 * 5
b = a + 10 
c = b / 5
Problem: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total e of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) 6 : 4 : 3 : 13 - - - - > this means , the total number e must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."
Answer: a
Python program:
a = 3000 + 3
Problem: - 84 x 19 + 100 = ?
Options: a ) 2436 , b ) 2801 , c ) - 1496 , d ) - 2071 , e ) none of them
Rationale: "given exp . = - 84 x ( 20 - 1 ) + 100 = - ( 84 x 20 ) + 84 + 100 = - 1680 + 184 = - 1496 answer is c"
Answer: c
Python program:
a = 1 - 2
b = 84 * 19
c = b - 100
d = a * c
Problem: the length of a rectangle is halved , while its breadth is tripled . whatis the % change in area ?
Options: a ) 30 % , b ) 40 % , c ) 50 percent , d ) 60 % , e ) 70 %
Rationale: "let original length = x and original breadth new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Python program:
a = 1 / 2
b = 3 * a
c = b - 1
d = c / 1
e = d * 100
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 15 , what was the price before the first discount ?
Options: a ) $ 45.10 , b ) $ 34.31 , c ) $ 28.44 , d ) $ 26.66 , e ) $ 65.23
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 15 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 15 solve for x x = $ 26.66 correct answer d"
Answer: d
Python program:
a = 100 * 100
b = a * 15
c = 100 - 25
d = c * 100
e = 100 - 25
f = e * 25
g = d - f
h = b / g
Problem: the average of first six prime numbers which are between 20 and 60 is
Options: a ) 34 , b ) 42 , c ) 45.7 , d ) 57 , e ) 67
Rationale: "explanation : first six prime numbers which are between 20 and 60 = 23 , 29 , 31 , 37 , 41 , 43 average = ( 23 + 29 + 31 + 37 + 41 + 43 ) / 6 = 34 answer : a"
Answer: a
Python program:
a = 20 + 1
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %
Rationale: "in the first plot 20 % of 300 seeds germinated , so 0.20 x 300 = 60 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 60 + 70 = 130 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 130 / 500 ) x 100 % , or 26 % . answer : b ."
Answer: b
Python program:
a = 20 / 100
b = a * 300
c = 35 / 100
d = c * 200
e = b + d 
f = 300 + 200 
g = e / f
h = g * 100