euclaise/mathqa_programs huggingface dataset:
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 81 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 81 , e ) 40
Rationale: let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 81 ( x - y ) - - > x + y = 81 . answer : d .
Answer: d
Python program:
a = math.floor(81)
Problem: how much is it cost $ 0.50 each tire for 8 tires ?
Options: a ) $ 3.00 , b ) $ 9.00 , c ) $ 2.00 , d ) $ 4.00 , e ) $ 7.00
Rationale: d . $ 4.00
Answer: d
Python program:
a = 8 * 0
Problem: it takes avery 4 hours to build a brick wall while tom can do it in 2 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 20 , b ) 40 , c ) 30 , d ) 50 , e ) 60
Rationale: "avery takes 4 hours tom takes 2 hours efficiency of avery is 1 / 4 units / hr efficiency of tom is 1 / 2 units / hr combined efficiency of tom and avery is 1 / 4 + 1 / 2 = 3 / 4 units / hr since they worked for 1 hour they completed 3 / 4 units of work and 1 / 4 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 4 / 1 / 2 hours = > 1 / 2 * 60 = 30 minutes . . . answer will be ( c )"
Answer: c
Python program:
a = 1 / 4
b = 1 / 2
c = a + b 
d = 1 - c
e = 1 / 2
f = d / e
g = f * const_60
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 4 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 90 m , d ) 180 m , e ) none
Rationale: solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 4 ) m = 90 m . answer c
Answer: c
Python program:
a = 36 + 45 
b = a * const_0_2778
c = b * 4
Problem: set x consists of 15 integers and has median of 20 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 60 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 40 , 40 , 40 , 50 , 60 this is possible . hence it is the greatest such number . answer ( d )"
Answer: d
Python program:
a = 20 + 20
Problem: if x / 2 years ago roger was 18 years old and x / 2 years from now he will be 4 x years old , how old will he be 5 x years from now ?
Options: a ) 32 , b ) 35 , c ) 30 , d ) 51 , e ) 28
Rationale: "assume the current age = a a - x / 2 = 18 ( i ) a + x / 2 = 4 x or a = 7 x / 2 ( ii ) putting the value of a from ( ii ) in ( i ) 7 x / 2 - x / 2 = 18 or 6 x / 2 = 18 therefore x = 6 and a = 21 5 x years from now , age will be 21 + 5 * 6 = 51 option d"
Answer: d
Python program:
a = 2 * 5
b = a * 2
c = 18 - 1
d = c / 2
e = b - d
Problem: a small college reduced its faculty by approximately 23 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 253 , b ) 208 , c ) 224 , d ) 254 , e ) 302
Rationale: "if x is the original number of faculty members , then after 23 % reduction in faculty members number is . 77 x but we are given . 77 x = 195 x = 253 so the original number of faculty members is 253 correct answer - a"
Answer: a
Python program:
a = 100 - 23
b = a / 100
c = 195 / b
Problem: a bakery has 6 employees . it pays annual salaries of $ 15,000 to each of 2 employees , $ 17,000 to 1 employee , and $ 18,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 16,200 , b ) $ 16,500 , c ) $ 16,800 , d ) $ 17,000 , e ) $ 17,400
Rationale: "average = 2 ( 15000 ) + ( 17000 ) + 3 ( 18000 ) / 6 = $ 16,833 the answer is c ."
Answer: c
Python program:
a = 10 + 10 
b = a + 1 
c = b + 1 
d = c * 3
e = 10 + 10 
f = e - 1
g = f * 2
h = d + g 
i = 10 + 10 
j = i + 1 
k = h + j 
l = k / 6
Problem: the current birth rate per certain number of people is 32 , whereas corresponding death rate is 11 per same number of people . if the net growth rate in terms of population increase is 2.1 percent , find number of persons . ( initally )
Options: a ) 1000 , b ) 10000 , c ) 100 , d ) 2000 , e ) 20000
Rationale: sol . net growth on x = ( 32 - 11 ) = 21 . net growth on 100 = ( 21 / x ã — 100 ) % = 2.1 % . then x = 1000 answer : a
Answer: a
Python program:
a = 32 - 11
b = a / 2
c = 100 * b
Problem: if a lends rs . 4000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 112.5 , b ) 122.5 , c ) 132.5 , d ) 114.5 , e ) 180
Rationale: "( 4000 * 1.5 * 3 ) / 100 = > 180 answer : e"
Answer: e
Python program:
a = 4000 * 11
b = a * 3
c = b / 100
d = 4000 * 10
e = d * 3
f = e / 100
g = c - f
Problem: if x is less than y by 35 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 53.85 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 35 % ) = > 35 / ( 100 - 35 ) * 100 = 53.85 % answer : d"
Answer: d
Python program:
a = 100 - 35
b = 100 / a
c = b - 1
d = c * 100
Problem: two numbers are in the ratio of 3 : 8 . if 24 be subtracted from each , they are in the ratio of 4 : 9 . find the numbers ?
Options: a ) 60,89 , b ) 60,88 , c ) - 27 , - 128 , d ) 60,84 , e ) - 72 , - 192
Rationale: "( 3 x - 24 ) : ( 8 x - 24 ) = 4 : 9 x = - 24 = > - 72 , - 192 answer : e"
Answer: e
Python program:
a = 3 * 24
Problem: if 3 tic equals 6 tacs and 2 tacs equal 7 tocs , what is the ratio of one tic to one toc ?
Options: a ) 7 / 1 , b ) 6 / 5 , c ) 5 / 6 , d ) 3 / 10 , e ) 1 / 15
Rationale: "3 tic = 6 * tac and 2 * tac = 7 * toc ; 6 * tic = 12 * tac and 12 * tac = 42 * toc - - > 6 * tic = 42 * toc - - > tic / toc = 42 / 6 = 7 / 1 . answer : a ."
Answer: a
Python program:
a = 7 / 3
b = 6 / 3
c = a + b
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 60 % of the total ?
Options: a ) 858 . , b ) 545 . , c ) 618 . , d ) 644 . , e ) 666 .
Rationale: "answer is a : 858 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 60 % of total is 515 , so 100 % is approx . 858 ."
Answer: a
Python program:
a = 226 + 423
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.3 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) 7 kg
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.3 weight of the new student = ( 30 * 27.3 – 29 * 28 ) = 819 - 812 = 7 answer : e"
Answer: e
Python program:
a = 29 + 1 
b = a * 27
c = 29 * 28
d = b - c
Problem: a train 225 m long passes a man , running at 10 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 81 , b ) 90 , c ) 91 , d ) 85 , e ) 96
Rationale: "speed of the train relative to man = 225 / 10 m / sec = 45 / 2 m / sec . = 45 / 2 x 18 / 5 km / hr = 81 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 10 = 81 = 91 km / hr . answer : c"
Answer: c
Python program:
a = 10 * const_0_2778
b = a * 10
c = 225 - b
d = c / 10
e = d / const_0_2778
Problem: how many positive integers less than 100 are neither multiples of 4 or 5 .
Options: a ) a ) 30 , b ) b ) 60 , c ) c ) 32 , d ) d ) 33 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 4 till 100 = 100 / 4 = 25 2 ) multiples of 5 till 100 = 100 / 5 = 20 add the two 25 + 20 = 45 ; subtract common terms that are multiple of both 4 and 5 . . lcm of 4 and 5 = 20 multiples of 20 till 100 = 100 / 20 = 5 = so total multiples of 4 and 5 = 45 - 5 = 40 ans = 100 - 40 = 60 b"
Answer: b
Python program:
a = 4 + 4 
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the present ratio of students to teachers at a certain school is 30 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "lets say t = 10 - - - > s = 300 - - - > 350 / 15 = a bit less than 25 ( a and b will only make this ratio lesser , eliminate a and b ) go for t = 12 - - > s = 30 * 12 = 360 - - - > 360 + 50 / 12 + 5 = less than 25 . either you can now go further with t = 15 or mark e as the answer . check : t = 15 - - - > s = 30 * 15 = 450 - - - > 450 + 50 / 20 = 25 . answer : e"
Answer: e
Python program:
a = 30 + 25 
b = a / 25
Problem: a train is 360 meter long is running at a speed of 60 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 27 seconds , b ) 29 seconds , c ) 40 seconds , d ) 30 seconds , e ) 12 seconds
Rationale: "speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 3 / 50 ) = 30 seconds answer : d"
Answer: d
Python program:
a = 360 + 140 
b = 60 * 1000
c = b / 3600
d = a / c
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 64 more for rs . 40 . what is the reduced price / dozen ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "sol . lie purchases 6 a bananas mere for 4096 of rs 40 or , rs 16 . reduced price per do 3 a"
Answer: a
Python program:
a = 40 / 100
b = 40 * a
c = b / 64
d = 12 * c
Problem: a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.4 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 240 , e ) e . 200
Rationale: "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.4 = 240 answer : d"
Answer: d
Python program:
a = 15 * 12
b = a * 10
c = b / 100
d = c / 100
e = d / 100
f = 1 / 8
g = 0 * 4
Problem: excluding stoppages , the speed of a bus is 48 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 5 , b ) 4.15 , c ) 4.25 , d ) 5.5 , e ) none of these
Rationale: "due to stoppages , it covers 314 km less . time taken to cover 3 km = ( ( 3 / 48 ) ã — 60 ) = 4.15 min . option ( b ) is correct"
Answer: b
Python program:
a = 48 - 45
b = a / 48
c = const_60 * b
Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 60 people were made to stand in a column , how many columns could be formed ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "16 * 30 = 60 * n n = 8 the answer is b ."
Answer: b
Python program:
a = 60 / 16
b = 30 / a
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 2 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 65 , b ) 63 , c ) 52 , d ) 60 , e ) 68
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 2 w = 120 = > w = 60 answer d"
Answer: d
Python program:
a = rectangle_area / (
Problem: a man took loan from a bank at the rate of 12 % p . a . s . i . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 15002 , b ) 15001 , c ) 15000 , d ) 15007 , e ) 15009
Rationale: principal = ( 100 * 5400 ) / ( 12 * 3 ) = rs . 15000 . answer : c
Answer: c
Python program:
a = 5400 * 100
b = a / 3
c = b / 12
Problem: a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variables costs averaging $ 8 per item . if the manufacturer ’ s selling price per item is $ 12 , how many items the manufacturer produce and sell to earn an annual profit of $ 140,000 ?
Options: a ) 2,858 , b ) 8,667 , c ) 21,429 , d ) 35,000 , e ) 67,500
Rationale: "let the items manufactured or sold bex 130000 + 8 x = 12 x - 140000 4 x = 270000 x = 67500 ans : e"
Answer: e
Python program:
a = 3 + 8 
b = a + 12 
c = 100 ** 2
d = b * c
e = 12 - 8
f = d / e
g = 4 * 2
h = f / g
i = h * 3
j = i / 1000
Problem: how many numbers between 100 and 714 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 15 , e ) 99
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 714 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 714 : 714 / 42 = 17 hence , 42 * 14 = 714 is the last number divisible by 42 within 714 hence , total numbers divisible by 2 , 3 , 7 together are ( 17 â € “ 2 ) = 15 answer : d"
Answer: d
Python program:
a = 2 * 3
b = a * 7
c = 714 / b
d = 2 * 3
e = d * 7
f = 100 / e
g = c - f
Problem: how many paying stones , each measuring 3 m * 2 m are required to pave a rectangular court yard 60 m long and 14 m board ?
Options: a ) 99 , b ) 140 , c ) 26 , d ) 17 , e ) 12
Rationale: "60 * 14 = 3 * 2 * x = > x = 140 answer : b"
Answer: b
Python program:
a = rectangle_area / (
Problem: if a light flashes every 6 seconds , how many times will it flash in 1 / 2 of an hour ?
Options: a ) 301 times , b ) 351 times , c ) 401 times , d ) 451 times , e ) 481 times
Rationale: "in 1 / 2 of an hour there are 30 * 60 = 1800 seconds the number of 6 - second intervals = 1800 / 6 = 300 after the first flash , there will be 300 more flashes for a total of 301 . the answer is a ."
Answer: a
Python program:
a = 3600 / 4
b = a * 3
c = b / 6
Problem: the average runs scored by a batsman in 30 matches is 40 . in the next 10 matches the batsman scored an average of 13 runs . find his average in all the 30 matches ?
Options: a ) 24.3 , b ) 25.3 , c ) 26.3 , d ) 28.3 , e ) 34.5
Rationale: "total score of the batsman in 30 matches = 600 . total score of the batsman in the next 10 matches = 130 . total score of the batsman in the 30 matches = 730 . average score of the batsman = 730 / 30 = 24.3 . answer : a"
Answer: a
Python program:
a = 40 * 30
b = 13 * 10
c = a + b 
d = 30 + 10 
e = c / d
Problem: a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 36 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let x be the wholesale price . then 1.8 x = 36 and x = 36 / 1.8 = 20 . to achieve a 100 % markup , the price needs to be $ 40 . the retailer needs to increase the price by $ 4 more . the answer is b .
Answer: b
Python program:
a = 80 / 100
b = 1 + a 
c = 36 / b
d = c * 2
e = d - 36
Problem: in the city of san durango , 60 people own cats , dogs , or rabbits . if 30 people owned cats , 40 owned dogs , 16 owned rabbits , and 12 owned exactly two of the 3 types of pet , how many people owned all 3 ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 7 , e ) 32
Rationale: you are considering a case when cat dogs and rabbit are not exactly equal to 12 . the solution shall be 60 = 30 + 40 + 16 - 12 - 2 x and hence x shall be 7 . answer d
Answer: d
Python program:
a = 30 + 40 
b = a + 16 
c = b - 12
d = c - 60
e = d / 2
Problem: a certain company ’ s profit in 1996 was 17 percent greater than its profit in 1995 , and its profit in 1997 was 25 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 35 % , e ) 46.25 %
Rationale: "profit in 1995 - 100 profit in 1996 - 117 % increae profit in 1997 in comparison to 1995 = 17 + 117 * 25 % = 46.25 correct option : e"
Answer: e
Python program:
a = 25 / 100
b = a + 1 
c = 17 / 100
d = 1 + c 
e = b * d
f = e - 1
g = f * 100
Problem: a can give b 80 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 130.12 , b ) 130.43 , c ) 130.22 , d ) 111.0 , e ) 111.12
Rationale: a runs 1000 m while b runs 920 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 920 = 869.56 m b can give c = 1000 - 869.56 = 130.43 m . answer : b
Answer: b
Python program:
a = 100 * 10
b = 100 * 10
c = 100 * 10
d = c - 200
e = b * d
f = 100 * 10
g = f - 80
h = e / g
i = a - h
Problem: 30 square stone slabs of equal size were needed to cover a floor area of 58.8 sq . m . find the length of each stone slab ?
Options: a ) 140 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 58.8 / 30 m 2 = 1.96 m 2 length of each slab √ 1.96 = 1.4 m = 140 cm"
Answer: a
Python program:
a = 58 / 8
b = math.sqrt(a)
c = b * 100
Problem: nhai employs 100 men to build a highway of 2 km in 50 days working 8 hours a day . if in 25 days they completed 1 / 3 part of work . than how many more emploies should nhai hire to finish it in time working 10 hours a day
Options: a ) 60 , b ) 70 , c ) 80 , d ) 50 , e ) 40
Rationale: "( m 1 * d 1 * h 1 ) / w 1 = ( m 2 * d 2 * h 2 ) / w 2 ( 100 * 25 * 8 ) / ( 1 / 3 ) = ( ( 100 + a ) * 25 * 10 ) ) / ( 2 / 3 ) 160 = 100 + a a = 60 answer : a"
Answer: a
Python program:
a = 100 * 25
b = a * 8
c = 2 * b
d = 25 * 10
e = c / d
f = e - 100
Problem: the average of first four prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "23 + 29 + 31 + 37 = 120 / 4 = 30 answer : c"
Answer: c
Python program:
a = 20 + 1
Problem: jar x is 1 / 4 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 / 2 , e ) 2 / 3
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 4 + p / 4 = p / 2 the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = 1 / 4
c = 1 / 4
d = b * c
e = a + d
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 40 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 612 kms , d ) 752 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 40 + 42 + 44 + . . . . . upto 12 terms ) this is an a . p with first term , a = 40 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 40 + { 12 - 1 ) x 2 ] = 6 ( 102 ) = 612 kms . answer : c"
Answer: c
Python program:
a = 2 * 40
b = 12 - 1
c = b * 2
d = a + c 
e = 12 / 2
f = d * e
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 60 per square m ?
Options: a ) rs . 50000 , b ) rs . 52000 , c ) rs . 57000 , d ) rs . 60000 , e ) rs . 67000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 60 * 950 = rs . 57000 c"
Answer: c
Python program:
a = 20 * 15
b = a * 2
c = b * 60
d = 20 * 5
e = d * 2
f = e * 60
g = c + f 
h = 15 * 5
i = h * 2
j = i * 60
k = g + j
Problem: a small island country of 5000 people has an emigration and immigration statistic per 500 persons of 50.4 and 15.4 respectively . how long will it take for the population to be half of its current number .
Options: a ) 6.8 , b ) 8.5 , c ) 6.1 , d ) 9.1 , e ) 7.14
Rationale: annual decrease is ( 500 + 15.4 - 50.4 ) * 10 = 4650 hence every year there is a decrease of 350 for the population to become half 2500 must emigrate therefore 2500 / 350 = 133.3 correct option is e ) 7.14
Answer: e
Python program:
a = 5000 / 2
b = 50 - 4
c = 5000 / 500
d = b * c
e = a / d
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.9 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 66 ) = 1178 kgs actual average weight is 1178 / 20 = 58.9 kgs c"
Answer: c
Python program:
a = 58 * 4
b = 66 - 56
c = a + b 
d = c / 20
Problem: in a certain store , the profit is 320 % of the cost . if the cost increases by 40 % but the selling price remains constant , approximately what percentage of the selling price is the profit
Options: a ) 67 % , b ) 80 % , c ) 90 % , d ) 100 % , e ) none of above
Rationale: explanation : let c . p . = rs . 100 . then , profit = rs . 320 , s . p . = rs . 420 . new c . p . = 140 % of rs . 100 = rs . 140 new s . p . = rs . 420 . profit = rs . ( 420 - 140 ) = rs . 280 required percentage = ( 280 / 420 ) * 100 = 66.67 % ( approx ) = 67 % answer : a
Answer: a
Python program:
a = 100 + 320 
b = 100 + 40 
c = a - b
d = 100 + 320 
e = c / d
f = e * 100
Problem: if the perimeter of a rectangular garden is 480 m , its length when its breadth is 100 m is ?
Options: a ) 299 m , b ) 140 m , c ) 200 m , d ) 167 m , e ) 128 m
Rationale: "2 ( l + 100 ) = 480 = > l = 140 m answer : b"
Answer: b
Python program:
a = 480 / 2
b = a - 100
Problem: a family pays $ 800 per year for an insurance plan that pays 60 percent of the first $ 1000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,600 , e ) $ 2,000
Rationale: assuming the medical expenses are $ 1000 or more , the family pays $ 800 + $ 400 = $ 1200 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 600 when the medical expenses are $ 1600 . the answer is d .
Answer: d
Python program:
a = 1000 - 800
Problem: the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 10 and 15 . the larger of the two numbers is :
Options: a ) 350 , b ) 250 , c ) 450 , d ) 500 , e ) 620
Rationale: "explanation : clearly , the numbers are ( 30 x 10 ) and ( 30 x 15 ) . { \ color { blue } \ therefore } larger number = ( 30 x 15 ) = 450 . answer : c ) 450"
Answer: c
Python program:
a = 30 * 15