euclaise/mathqa_programs huggingface dataset:
Problem: a reduction of 21 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.66 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 2.1
Rationale: "100 * ( 21 / 100 ) = 21 - - - 10 ? - - - 1 = > rs . 2.1 100 - - - 79 ? - - - 2.1 = > rs . 2.66 answer : a"
Answer: a
Python program:
a = 21 / 100
b = a * 100
c = b / 10
d = 21 / 100
e = d * 100
f = c / e
g = f * 100
Problem: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 500 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 500 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 1000 n = 10 satisfies this . a"
Answer: a
Python program:
a = 1 / 500
b = 1000 * a
Problem: what is the least number should be added to 1156 , so the sum of the number is completely divisible by 25 ?
Options: a ) 19 , b ) 2 , c ) 5 , d ) 6 , e ) 8
Rationale: "( 1156 / 25 ) gives remainder 6 6 + 19 = 25 , so we need to add 19 answer : a"
Answer: a
Python program:
a = 1156 / 25
b = math.floor(a)
c = b + 1 
d = c * 25
e = d - 1156
Problem: the youngest of 4 children has siblings who are 4 , 5 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: x + ( x + 4 ) + ( x + 5 ) + ( x + 7 ) = 84 4 x + 16 = 84 4 x = 68 x = 17 the answer is d .
Answer: d
Python program:
a = 4 * 21
b = 4 + 5 
c = b + 7 
d = a - c
e = d / 4
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 500 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3999 , b ) 7799 , c ) 2500 , d ) 2772 , e ) 6250
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 500 b capital = 37500 * 1 / 6 = 6250 . answer : e"
Answer: e
Python program:
a = 500 * 100
b = a / 2
Problem: in a kilometer race , a beats b by 50 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 50 sec , b ) 190 sec , c ) 287 sec , d ) 74 sec , e ) 697 sec
Rationale: "explanation : time taken by b run 1000 meters = ( 1000 * 10 ) / 50 = 200 sec . time taken by a = 200 - 10 = 190 sec . answer b"
Answer: b
Python program:
a = 1 * 1000
b = 50 / 10
c = a / b
d = c - 10
Problem: two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 6 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 8 1 / 8 km , d ) 9 km , e ) 5 km
Rationale: rs = 5 ¾ - 4 ½ = 1 ¼ t = 6 ½ h . d = 5 / 4 * 13 / 2 = 65 / 8 = 8 1 / 8 km answer : c
Answer: c
Python program:
a = 1 / 2
b = 6 + a 
c = 3 / 4
d = 5 + c 
e = 1 / 2
f = 4 + e 
g = d - f
h = b * g
i = h + 2
Problem: the average of 8 numbers is 25 , that of the first 2 is 20 and of the next 3 is 26 . the sixth number is less than the seventh by 4 , and less than the eighth by 6 . the last number is
Options: a ) 30 , b ) 32 , c ) 40 , d ) 36 , e ) 38
Rationale: explanation : sum of all the numbers = 25 * 8 = 200 sum of first two numbers = 40 sum of next three numbers ( i . e . , 3 rd , 4 th and 5 th ) = 78 so , sum of first five numbers = 118 and sum of 6 th , 7 th and 8 th number = 82 assuming sixth number to be x , we get 7 th number = x + 4 and 8 th number = x + 6 . so , x + ( x + 4 ) + ( x + 6 ) = 82 = > x = 24 . hence , last number ( 8 th number ) = 30 . answer : a
Answer: a
Python program:
a = 25 * 8
b = 2 * 20
c = 3 * 26
d = b + c 
e = a - d
f = e + 8 
g = f / 3
Problem: 18 : 12 seconds : : ? : 6 minutes
Options: a ) 10 , b ) 9 , c ) 20 , d ) 25 , e ) 30
Rationale: 18 * 6 = 12 * x x = 9 answer : b
Answer: b
Python program:
a = 18 / 12
b = 6 * a
Problem: a ship going at the speed of 18 km / hr crosses a light house in 20 seconds . what is the length of the train ?
Options: a ) 120 , b ) 150 , c ) 100 , d ) 240 , e ) 200
Rationale: speed = ( 18 x 5 / 18 ) = 5 m / sec . length of the train = ( speed x time ) . length of the train = 5 x 20 m = 100 m . answer : c
Answer: c
Python program:
a = 18 * const_0_2778
b = a * 20
Problem: matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days peter stops and peter completes the remaining work in 10 days . in how many days matt complete the work separately .
Options: a ) 28 , b ) 27 , c ) 26 , d ) 25 , e ) 29
Rationale: together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 10 < = > x = 10 / ( 8 / 20 ) = 25 d
Answer: d
Python program:
a = 1 / 20
b = 12 * a
c = 1 - b
d = 10 / c
Problem: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 7 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 7 , e ) e ) 16
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"
Answer: d
Python program:
a = 7 * 1
Problem: a number is increased by 30 % and then decreased by 30 % . find the net increase or decrease per cent .
Options: a ) 9 % , b ) 8 % , c ) 7 % , d ) 3 % , e ) 6 %
Rationale: "let the number be 100 . increase in the number = 30 % = 30 % of 100 = ( 30 / 100 ã — 100 ) = 30 therefore , increased number = 100 + 30 = 130 this number is decreased by 30 % therefore , decrease in number = 30 % of 130 = ( 30 / 100 ã — 130 ) = 3900 / 100 = 39 therefore , new number = 130 - 39 = 91 thus , net decreases = 100 - 91 = 9 hence , net percentage decrease = ( 9 / 100 ã — 100 ) % = ( 900 / 100 ) % = 9 % answer : a"
Answer: a
Python program:
a = 30 + 100 
b = 100 - 30
c = a * b
d = c / 100
Problem: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 27 , find the value of ab .
Options: a ) 5 , b ) 9 , c ) 4 , d ) 10 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 27 - 9 = 18 ab = 9 . answer is b ."
Answer: b
Python program:
a = 3 ** 2
b = 27 - a
c = b / 2
Problem: a man can row his boat with the stream at 19 km / h and against the stream in 11 km / h . the man ' s rate is ?
Options: a ) 4 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 19 us = 11 s = ? s = ( 19 - 11 ) / 2 = 4 kmph answer : a"
Answer: a
Python program:
a = 19 - 11
b = a / 2
Problem: kamal ' s salary was decreased by 50 % and subsequently increased by 30 % . how much percent does he lose ?
Options: a ) 30 % , b ) 37 % , c ) 65 % , d ) 35 % , e ) 45 %
Rationale: explanation : solution : let original salary = rs . 100 . new final salary = 130 % of ( 50 % of rs . 100 ) = rs . ( 130 / 100 * 50 / 100 * 100 ) = rs . 65 . . ' . decrease = 35 % answer : d
Answer: d
Python program:
a = 50 / 100
b = 30 / 100
c = b + 1 
d = a * c
e = 1 - d
f = e * 100
Problem: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 10 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 9 / 10 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: "x * 6 / 100 * 1 + ( 20000 - x ) * 10 / 100 * 1 = 1440 6 x - 8 x = 144000 - 200000 = > - 2 x = - 4000 = > x = 2000 so 18000 / 20000 = 9 / 10 answer - b"
Answer: b
Python program:
a = 1 + 4 
b = 2 * a
c = 100 * b
d = 4 * 100
e = c + d 
f = 1 + 4 
g = 2 * f
h = 4 * g
i = e + h 
j = i / 20
k = j / 10
l = k + 10 
m = l - 6
n = m / 20
Problem: the ratio of a to b to c is 2 to 3 to 4 , and a , b , c are positive integers . if the average ( arithmetic mean ) of the 3 numbers is 42 , what is the value of a ?
Options: a ) 24 , b ) 25 , c ) 28 , d ) 30 , e ) 32
Rationale: let a = 2 k , b = 3 k , and c = 4 k . a + b + c = 2 k + 3 k + 4 k = 9 k since the average is 42 : 9 k / 3 = 42 3 k = 42 k = 14 then a = 28 . the answer is c .
Answer: c
Python program:
a = 42 * 3
b = 2 + 3 
c = b + 4 
d = a / c
e = d * 2
Problem: what is the dividend . divisor 18 , the quotient is 9 and the remainder is 4
Options: a ) a ) 166 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158
Rationale: "d = d * q + r d = 18 * 9 + 4 d = 166 answer : a"
Answer: a
Python program:
a = 18 * 9
b = a + 4
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 174 votes . find the total number of valid votes ?
Options: a ) 435 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 174 = > 4 x / 10 = 174 = > 4 x = 1740 = > x = 435 . answer : a"
Answer: a
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 174 / c
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1320 cm is ?
Options: a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 1320 = > x = 15 answer : a"
Answer: a
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 14
h = 1320 / g
Problem: a train 125 m long passes a man , running at 8 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 37 km / hr , b ) 53 km / hr , c ) 36 km / hr , d ) 26 km / hr , e ) 87 km / hr
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 8 = 45 = > x = 53 km / hr . answer : b"
Answer: b
Python program:
a = 8 * const_0_2778
b = a * 8
c = 125 - b
d = c / 8
e = d / const_0_2778
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 4 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 3 : 1 , d ) 1 : 5 , e ) 1 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 2 + 7 / 2 = 6 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6 : 2 = 3 : 1 . answer : c"
Answer: c
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 4 - g
i = 87 * 5
j = i / 100
k = 4 - j
l = h + k 
m = e / l
Problem: the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 880 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 14 + 8 ) = 880 d = 80 the answer is d ."
Answer: d
Python program:
a = 14 + 8 
b = a / 2
c = 880 / b
Problem: 1 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.02775 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 1 / 36 = . 02 something answer ( b )
Answer: b
Python program:
a = 1 / 0
b = 1 / 0
c = a + b 
d = 1/(c)
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 162 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.8 , e ) 2.22
Rationale: "speed = 162 * 5 / 18 = 45 m / sec time taken = 100 / 45 = 2.22 sec . answer : e"
Answer: e
Python program:
a = 162 * const_0_2778
b = 100 / a
Problem: which number need to add to 956734 to get a number exactly divisible by 412 ?
Options: a ) 345 , b ) 342 , c ) 343 , d ) 342 , e ) 341
Rationale: "956734 / 412 = 2322 and reminder = 70 . 412 - 70 = 342 so , the next number divisible by 412 is 342 places in front of 956734 which means 342 + 956734 = 957076 342 should be added to 956734 b"
Answer: b
Python program:
a = 956734 / 412
b = math.floor(a)
c = b + 1 
d = 956734 / 412
e = c - d
f = 412 * e
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 40 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 2000 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 40 minutes = 15 / 18 * 40 * 60 = 2000 m answer is c"
Answer: c
Python program:
a = 15 * 1000
b = a / const_60
c = b * 40
Problem: a circular wheel radius is 1.75 m . for covering 11 k . m how much time it revolve ?
Options: a ) 10
b ) 100
c ) 1000
d ) 10000
e ) 50
Rationale: distance traveled in 1 round = perimeter = { 2 * 22 / 7 * 175 / 100 } m = 11 m total no . of revolution in covering 11 km = 11000 / 11 = 1000 answer c
Answer: c
Python program:
a = 11 * 1000
b = a / circumface
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b"
Answer: b
Python program:
a = 1 / 12
b = a * 3
c = 1 / 30
d = c / 2
e = b / d
f = e * 2
Problem: 0.0006688 / 0.0000150 x 19.85 = ?
Options: a ) 850 , b ) 900 , c ) 950 , d ) 1000 , e ) 2000
Rationale: "explanation : ? = 6688 / 150 x 19.85 = 45 x 20 = 900 answer : option b"
Answer: b
Python program:
a = 0 / 6688
Problem: find the highest value of ' a ' so that 365 a 24 is divisible by 8 .
Options: a ) 9 , b ) 8 , c ) 0 , d ) 2 , e ) 1
Rationale: "explanation : given , number is divisible by 8 only if ' a 24 ' is divisible by 8 . . : highest value of a is ' 8 ' . answer : option b"
Answer: b
Python program:
a = math.lcm(100, 8)
b = math.gcd(100, 8)
c = a * b
d = c / 100
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 70 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 40 , e ) 25
Rationale: "12 * 70 = 840 840 % 21 = 40 answer : d"
Answer: d
Python program:
a = 12 * 70
b = a / 21
Problem: last year a certain bond price with a face value of 5000 yielded 6 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4615 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: interest = 0.06 * 5000 = 0.065 * selling price - - > selling price = 0.06 * 5000 / 0.065 - - > selling price = ~ 4,615 answer : a .
Answer: a
Python program:
a = 6 / 100
b = 5000 * a
c = 6 / 5
d = b / c
Problem: if 5 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 8 , b ) 6 , c ) 7 , d ) 10 , e ) 9
Rationale: "5 ( log 2 ^ 2 * 5 ^ 2 ) = x 5 log ( 5 * 2 ) ^ 2 = x 5 * 2 log ( 5 * 2 ) = x 10 log 10 = x log 10 base 10 = 1 so 10 * 1 = x x = 10 answer : d"
Answer: d
Python program:
a = 5 ** 2
b = 4 * a
c = b ** 5
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 58 %
Options: a ) 18.75 , b ) 19.75 , c ) 26.89 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 58 / 100 = 50.40 so x = 26.89 answer : c"
Answer: c
Python program:
a = 100 / 58
b = 60 * 84
c = b / 100
d = a * c
e = d - 60
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 14 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 14 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 14 x = 14 answer : b"
Answer: b
Python program:
a = 7 / 5
b = 14 / 7
c = a * b
d = c * 5
Problem: the population of a town is 7500 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9300 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7500 ã — 100 / 90 ã — 100 / 90 = 9259 a )"
Answer: a
Python program:
a = 10 / 100
b = 7500 * a
c = 7500 - b
d = 10 / 100
e = 7500 * d
f = 7500 - e
g = 10 / 100
h = f * g
i = c - h
Problem: a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 7 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 880 , b ) $ 1050 , c ) $ 1280 , d ) $ 1460 , e ) $ 1640
Rationale: "the total surface area is 2 ( 2 * 3 + 3 * 7 + 2 * 7 ) = 82 square feet the total cost is 82 * $ 20 = $ 1640 the answer is e ."
Answer: e
Python program:
a = surface_rectangular_prism * (
Problem: how many of the positive factors of 24 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 8 , 12 and 24 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 4 answer d"
Answer: d
Python program:
a = 16 / 24
Problem: a company pays 12.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 18 , d ) 19 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 12.5 * 50 ) / 100 = rs . 6.25 rs . 25 is income on an investment of rs . 100 rs . 6.25 is income on an investment of rs . ( 6.25 * 100 ) / 25 = rs . 25 answer : a"
Answer: a
Python program:
a = 12 * 5
b = a / 100
c = b * 100
d = c / 25
Problem: a box contains 10 tablets of medicine a and 13 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "the worst case scenario will be if we remove all 13 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 13 + 2 = 15 tablets . answer : b ."
Answer: b
Python program:
a = 13 + 2
Problem: what is the smallest number which , when increased by 7 , is divisible by 7 , 8 , and 24 ?
Options: a ) 154 , b ) 161 , c ) 168 , d ) 175 , e ) 182
Rationale: "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 7 = 161 . the answer is b ."
Answer: b
Python program:
a = math.lcm(24, 8)
b = a - 7
Problem: find the simple interest on rs . 73,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8125 , d ) 9125 , e ) none of them
Rationale: "p = rs . 73000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 73,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9125 answer is d ."
Answer: d
Python program:
a = 2 * 3
b = a * 100
c = b * 100
d = 3 * 3
e = d * 100
f = 3 + 2 
g = f * 2
h = e * g
i = c + h 
j = 16 * 3
k = j + 2 
l = k / 3
m = i * l
n = 3 * 3
o = 2 * 3
p = 2 * o
q = n / p
r = m * q
s = 1 / 100
t = r * s
Problem: find large number from below question the difference of 2 no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1245 , b ) 1430 , c ) 1540 , d ) 1600 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Python program:
a = 2 - 6
b = 1365 - 1
c = a / b
d = c * 1365
Problem: calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes at 13 km / hr downstream and 4 km / hr upstream .
Options: a ) 4.5 kmph , b ) 9.5 kmph , c ) 7.5 kmph , d ) 8.5 kmph , e ) 5.5 kmph
Rationale: "speed in still water = ( 13 + 4 ) 1 / 2 kmph = 8.5 kmph . answer : d"
Answer: d
Python program:
a = 13 + 4 
b = a / 2
Problem: two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 7 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 7 / 4 , b ) 4 / 3 , c ) 15 / 4 , d ) 10 / 3 , e ) 64 / 21
Rationale: rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 7 combined = 13 / 42 work done in 2 days = 13 / 21 work left = 8 / 21 rate * time = work left 1 / 8 * time = 8 / 21 time = 64 / 21 e
Answer: e
Python program:
a = 4 + 2 
b = 1 / a
c = 1 / 7
d = b + c 
e = d * 2
f = 1 - e
g = 1 / 7
h = f / g
i = max(h)
Problem: car dealership x , the total profit from sales increased by 10 percent over the previous years , while the number of cars sold decreased by 10 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 23 % , e ) 25 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.1 x / 0.9 y = 11 / 9 ( x / y ) increase in profit per car = ( ( 2 / 9 ) ( x / y ) ) / ( x / y ) * 100 = 22.22 % answer = c"
Answer: c
Python program:
a = 100 + 10 
b = 10 - 3
c = a / b
d = 100 / 10
e = c - d
f = 100 / 10
g = e / f
h = g * 100
Problem: of 70 players on a football team , 28 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 56 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 28 rest = 70 - 28 = 42 left handed = 42 / 3 = 14 right handed = 28 if all thrower are right handed then total right handed is 28 + 28 = 56 so a . 56 is the right answer"
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 28
d = b * c
e = d + 28