euclaise/mathqa_programs huggingface dataset:
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 65000 , then the share of b is ?
Options: a ) a ) 30000 , b ) b ) 34000 , c ) c ) 34098 , d ) d ) 33007 , e ) e ) 44098
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 65000 share of b = 6 / 13 ( 65000 ) = rs . 30000 answer : a"
Answer: a
Python program:
a = const_60 * 100
b = 65000 - a
Problem: if the radius of a circle is decreased 10 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 19 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.9 * old radius so new area = ( 0.9 ) ^ 2 old area = > 0.81 of old area = > 81 % old area ans : b"
Answer: b
Python program:
a = 10 / 100
b = a ** 2
c = b * 100
d = 100 - c
Problem: average age of students of an adult school is 44 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 180 , c ) 360 , d ) 240 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 44 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 60 so , required no . of students after joining the new students = x + 120 = 180 answer : b"
Answer: b
Python program:
a = 32 + 4 
b = a * 120
c = 120 * 32
d = b - c
e = 32 + 4 
f = 44 - e
g = d / f
h = g * 4
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 2 . find his average after 17 th inning .
Options: a ) 36 , b ) 39 , c ) 42 , d ) 45 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 2 ) . ∴ 16 ( x – 2 ) + 87 = 17 x or x = ( 87 – 32 ) = 55 . answer e"
Answer: e
Python program:
a = 17 * 2
b = 87 - a
c = b + 2
Problem: 24 oz of juice p and 25 oz of juice v are mixed to make smothies a and y . the ratio of p to v in smothie a is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie a ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: the ratio of p to v in smothie x is 4 is to 1 and that in y is 1 is to 5 . p 1 + p 2 = 24 v 1 + v 2 = 25 p 1 = 4 v 1 p 2 = v 2 / 5 4 v 1 + v 2 / 5 = 24 v 1 + v 2 = 25 4 v 2 - v 2 / 5 = 76 19 v 2 / 5 = 76 = > v 2 = 20 = > v 1 = 5 = > p 1 = 20 answer - d
Answer: d
Python program:
a = 24 * 5
b = a - 25
c = 1 / 4
d = 5 - c
e = b / d
Problem: during a certain season , a team won 60 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 50 , e ) 105
Rationale: "we are first given that a team won 60 percent of its first 100 games . this means the team won 0.6 x 100 = 60 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 60 + 0.5 t – 50 = 0.7 t 10 = 0.2 t 100 = 2 t 50 = t answer is d ."
Answer: d
Python program:
a = 60 - 70
b = 70 / 100
c = 50 / 100
d = b - c
e = a / d
f = 100 + e
Problem: in a certain pond , 20 fish were caught , tagged , and returned to the pond . a few days later , 20 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 ) 625 , c ) 1250 , d ) 2500 , e ) 500
Rationale: "if x is total number of fish in the pond : 4 = 20 / x * 100 = > x = 500 so answer is e"
Answer: e
Python program:
a = 2 / 20
b = 20 / a
Problem: a certain bus driver is paid a regular rate of $ 18 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 18 = 720 excess = 976 - 720 = 252 for extra hours = . 75 ( 18 ) = 13.5 + 18 = 31.5 number of extra hrs = 252 / 31.5 = 8 total hrs = 40 + 8 = 48 answer d 48"
Answer: d
Python program:
a = 18 * 40
b = 976 - a
c = 100 + 75 
d = 18 * c
e = d / 100
f = b / e
g = 40 + f
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 75 % profit on the first article and 75 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 768 , c ) 276 , d ) 750 , e ) 279
Rationale: "profit on first article = 75 % of 1000 = 750 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : d"
Answer: d
Python program:
a = 100 - 75
b = 100 / a
c = b * 1000
d = 100 + 75 
e = 100 / d
f = e * 1000
g = c + f 
h = 1000 + 1000 
i = g - h
j = i * 100
k = 100 - 75
l = 100 / k
m = l * 1000
n = 100 + 75 
o = 100 / n
p = o * 1000
q = m + p 
r = j / q
s = r * 100
Problem: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 50 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 13 , b ) 33 , c ) 50 , d ) 51 , e ) 52
Rationale: "the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . it means there is no effect of change in volume of water to the costing of the solution so a solution of 1 liter of spirit and 2 liters of water will cost 50 cents answer = 50 answer : c"
Answer: c
Python program:
a = 1 + 2 
b = 1 / a
c = 50 * b
d = 1 + 2 
e = c * d
Problem: in a company of 180 employees , 110 are females . a total of 90 employees have advanced degrees and the rest have a college degree only . if 35 employees are males with a college degree only , how many employees are females with advanced degrees ?
Options: a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 70
Rationale: "the number of males is 180 - 110 = 70 . the number of males with advanced degrees is 70 - 35 = 35 . the number of females with advanced degrees is 90 - 35 = 55 . the answer is b ."
Answer: b
Python program:
a = 180 - 110
b = a - 35
c = 90 - b
Problem: how many positive integers less than 8,000 are there in which the sum of the digits equals 5 ?
Options: a ) 57 , b ) 56 , c ) 55 , d ) 54 , e ) 53
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . b"
Answer: b
Python program:
a = 4 + 5 
b = a - 1
c = math.factorial(b)
d = math.factorial(5)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: c and d started a business by investing rs . 1000 / - and rs . 1500 / - respectively . find the d ’ s share out of a total profit of rs . 500 :
Options: a ) 400 , b ) 300 , c ) 200 , d ) 100 , e ) 150
Rationale: c = rs . 1000 / - d = rs . 1500 / - c share 2 parts & d share 3 parts total 5 parts - - - - - > rs . 500 / - - - - - > 1 part - - - - - - - > rs . 100 / - d share = 3 parts - - - - - > rs . 300 / - d
Answer: d
Python program:
a = 1000 / 500
b = 1500 / 500
c = a + b 
d = 500 / c
Problem: a train 400 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 56 , c ) 29 , d ) 27 , e ) 21
Rationale: "s = ( 400 + 300 ) / 45 = 700 / 45 * 18 / 5 = 56 answer : b"
Answer: b
Python program:
a = 400 + 300 
b = a / 1000
c = 45 / 3600
d = b / c
Problem: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 70 , what is the greatest possible value of q minus r ?
Options: a ) 63 , b ) 64 , c ) 65 , d ) 66 , e ) 67
Rationale: "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 70 . the greatest multiple of 9 which is less than 70 is 63 . the answer is a ."
Answer: a
Python program:
a = 10 - 1
b = reminder * (
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 7 liters of forest green to change it to verdant green ?
Options: a ) 5 / 3 , b ) 2 / 7 , c ) 7 / 3 , d ) 1 / 7 , e ) 1 / 4
Rationale: 7 liter of forset green have 4 liter of blue and 3 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 4 / ( 3 + x ) = ¾ 9 + 3 x = 16 = > x = 7 / 3 answer : c
Answer: c
Python program:
a = 4 / 3
b = a * 4
c = b - 3
Problem: the sum of three consecutive multiples of 3 is 90 . what is the largest number ?
Options: a ) 30 , b ) 33 , c ) 36 , d ) 39 , e ) 42
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 90 9 x = 81 x = 9 largest number = 3 x + 6 = 33 answer : b"
Answer: b
Python program:
a = 3 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 3 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 3 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 3 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: what will be the difference between simple and compound interest @ 25 % per annum on a sum of $ 3600 after 2 years ?
Options: a ) $ 150 , b ) $ 220 , c ) $ 225 , d ) $ 182 , e ) $ 189
Rationale: "s . i . = 3600 * 25 * 2 / 100 = $ 1800 c . i . = 3600 * ( 1 + 25 / 100 ) ^ 2 - 3600 = $ 2025 difference = 2025 - 1800 = $ 225 answer is c"
Answer: c
Python program:
a = 25 / 100
b = a + 1 
c = b ** 2
d = 3600 * c
e = d - 3600
f = 25 / 100
g = 3600 * f
h = g * 2
i = e - h
Problem: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 8 people to do 8 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 8 , e ) 11
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 8 people can do 8 / 3 of the work in one day . 8 people can do 8 times the work in 3 days . the answer is c ."
Answer: c
Python program:
a = 8 / 8
b = 3 * a
Problem: a is half good a work man as b and together they finish a job in 32 days . in how many days working alone b finish the job ?
Options: a ) 98 days , b ) 21 days , c ) 48 days , d ) 18 days , e ) 19 days
Rationale: "wc = 1 : 2 2 x + x = 1 / 32 = > x = 1 / 96 2 x = 1 / 96 = > 48 days answer : c"
Answer: c
Python program:
a = 3 / 2
b = 32 * a
Problem: the measurement of a rectangular box with lid is 25 cmx 24 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 2302 , c ) 2304 , d ) 8640 , e ) 964
Rationale: "d = 24 , r = 12 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 12 * 12 * 12 = 2304 π cm 3 answer : c"
Answer: c
Python program:
a = 4 / 3
b = 3 ** 3
c = a * b
Problem: if the sides of a square are multiplied by 10 , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 1 %
b ) 10 %
c ) 100 %
d ) 500 %
e ) 1000 %
Rationale: let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 10 x , so the area is 100 x ^ 2 . the area of the original square is 1 / 100 = 1 % times the area of the new square . the answer is a .
Answer: a
Python program:
a = 10 * 10
b = a / 100
Problem: machine t takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine t to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of t is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and t reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of t . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Python program:
a = 3 * 2
b = 2 * a
Problem: seller selling an apple for rs . 16 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 17 , d ) 18 , e ) 20
Rationale: "sp = 16 loss = cp 17 loss = cp − sp = cp − 16 ⇒ cp 17 = cp − 16 ⇒ 16 cp 17 = 16 ⇒ cp 17 = 1 ⇒ cp = 17 c"
Answer: c
Python program:
a = 16 + 1
Problem: what is the smallest number which when increased by 3 is divisible by 9 , 70 , 25 and 21 ?
Options: a ) 2927 , b ) 3147 , c ) 3387 , d ) 3567 , e ) 3797
Rationale: "when increased by 3 , the number must include at least 2 * 3 ^ 2 * 5 ^ 2 * 7 = 3150 the answer is b ."
Answer: b
Python program:
a = math.lcm(9, 70)
b = math.lcm(25, 21)
c = math.lcm(a, b)
d = c + 3
Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 8 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 8 = 42 42 / 12 = 3.5 feet answer : e"
Answer: e
Python program:
a = 2 + 10 
b = a * 2
c = b + 10 
d = c + 8 
e = 2 + 10 
f = d / e
Problem: an employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9 , b ) 13 , c ) 16 , d ) 20 , e ) 25
Rationale: let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.25 x now we need to find number of hours worked so that x * y = 1.25 x * z i . e z = 4 / 5 y % decrease = ( y - 4 / 5 y ) / y * 100 = 100 / 5 = 20 % . thus my answer is d
Answer: d
Python program:
a = 25 + 100 
b = a / 100
c = 100 / b
d = 100 - c
Problem: 45 men working 8 hours per day dig 40 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "( 45 * 8 ) / 40 = ( x * 6 ) / 50 = > x = 75 75 – 45 = 30 answer : c"
Answer: c
Python program:
a = 45 * 8
b = a / 40
c = b * 50
d = c / 6
e = d - 45
Problem: there are 150 ' zeroes ' and 151 ' ones ' written on a black board . a step involves choosing 3 digits and replacing them with a single digit . if all the 3 digits are identical , they are replaced with the same digit . otherwise , the digit that appears twice replaces the 3 chosen digits . what is the minimum number of steps after which there will be no zero written on the blackboard ?
Options: a ) 11 , b ) 37 , c ) 36 , d ) 76 , e ) 33
Rationale: if we strike out 3 zeros , we are in effect reducing two zeroes . so we need 74 steps to reduce 148 zeroes . there are 2 zeroes and 151 ones left now . the remaining zeroes can be reduced in 2 steps . hence the answer is 76 . answer : d
Answer: d
Python program:
a = 150 / 2
b = a + 1
Problem: a and b complete a work in 9 days . a alone can do it in 18 days . if both together can do the work in how many days ?
Options: a ) 6 days , b ) 8 days , c ) 5 days , d ) 7 days , e ) 15 days
Rationale: "1 / 9 + 1 / 18 = 1 / 6 6 / 1 = 6 days answer : a"
Answer: a
Python program:
a = 1/(9)
b = 1/(18)
c = a + b 
d = 1/(c)
Problem: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 5 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 146
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 5 % so total man = 150 * . 95 = 142.5 women will be = 175 - 142.5 = 32.5 so population after two years = [ 135 ^ 2 + 32.5 ^ 2 ] ^ . 5 = 146.15 = 146 so population after two year = 146 answer : e"
Answer: e
Python program:
a = 1 / 5
b = 1 - a
c = b * 150
d = c ** 2
e = 150 ** 2
f = 90 ** 2
g = e + f 
h = 1 / 2
i = g ** h
j = 1 / 5
k = 1 - j
l = k * 150
m = i - l
n = m ** 2
o = d + n 
p = 1 / 2
q = o ** p
Problem: if an object travels 200 feet in 4 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 36 , b ) 34 , c ) 356 , d ) 12 , e ) 45
Rationale: 1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 200 feet in 4 sec then it travels 200 / 4 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 50 feet in 1 hour = 180000 feet in 1 hr = 180000 / 5280 miles in 1 hour = 18000 / 528 miles / hr ~ 34 miles / hr answer - b
Answer: b
Python program:
a = 200 / 5280
b = 1 / 3600
c = 4 * b
d = a / c
Problem: a cube of side 3 meter length is cut into small cubes of side 15 cm each . how many such small cubes can be obtained ?
Options: a ) 8078 , b ) 1040 , c ) 1058 , d ) 1021 , e ) 8000
Rationale: "along one edge , the number of small cubes that can be cut = 300 / 15 = 20 along each edge 20 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 20 * 20 * 20 = 8000 answer : e"
Answer: e
Python program:
a = 3 ** 2
b = a ** 3
c = 3 ** 3
d = b / c
Problem: a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of 4 walls , the volume of the hall is :
Options: a ) 3348 , b ) 3898 , c ) 1200 , d ) 2881 , e ) 7881
Rationale: answer : c ) 1200
Answer: c
Python program:
a = 15 * 12
b = 15 + 12 
c = a / b
d = 15 * 12
e = c * d
Problem: if the sides of a triangle are 30 cm , 28 cm and 12 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 168 cm 2
Rationale: "the triangle with sides 30 cm , 28 cm and 12 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 12 = 168 cm 2 answer : e"
Answer: e
Python program:
a = 28 * 12
b = a / 2
Problem: the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 45 , b ) 65 , c ) 75 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 3 = 71 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 – 316 = 4 a = e + 4 = 71 + 4 = 75 c"
Answer: c
Python program:
a = 80 * 4
b = 79 * 4
c = 80 * 4
d = 84 * 3
e = c - d
f = 3 + e 
g = b - f
h = a - g
Problem: if the price of a certain computer increased 30 percent from d dollars to 377 dollars , then 2 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 580
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 377 ( given ) i . e . d = 377 / 1.3 = $ 290 i . e . 2 d = 2 * 290 = 580 answer : option e"
Answer: e
Python program:
a = 100 + 30 
b = a / 100
c = 377 / b
d = c * 2
Problem: you have been given a physical balance and 7 weights of 52 , 50 , 48 , 44 , 45 , 46 , and 78 kgs . . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 183 kgs . ?
Options: a ) 178 , b ) 180 , c ) 181 , d ) 182 , e ) 183
Rationale: "balance = 52 + 50 + 48 + 44 + 45 + 46 + 78 - 183 answer : e"
Answer: e
Python program:
a = 50 + 48 
b = a + 44 
c = b + 46
Problem: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 615 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "difference in c . i . and s . i for 2 years = $ 615 - $ 600 = $ 15 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 15 rate = ( 100 * 15 ) / ( 300 ) = 5 % the answer is b ."
Answer: b
Python program:
a = 615 - 600
b = 100 * a
c = 600 / 2
d = b / c
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 2000 and b rs . 3000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4416 , e ) 7291
Rationale: "2 : 3 = > 2 : 3 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 2 / 5 = 3456 + 960 = 4416 answer : d"
Answer: d
Python program:
a = 10 / 100
b = 1 - a
c = 9600 * b
d = 2000 + 3000 
e = 3000 / d
f = c * e
g = 9600 - f
Problem: annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 35 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 35 minutes , sam rides 7 km so sam will be 5 km ahead . it will take annie 100 minutes to catch sam . the answer is e ."
Answer: e
Python program:
a = 15 - 12
b = 40 / const_60
c = a * b
d = 12 / c
e = 15 - 12
f = 40 / const_60
g = e * f
h = d - g
i = 15 - 12
j = h / i
k = j * const_60
Problem: find the unknown term 8 , 86 , x , - 4 , - 12
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: 8 , 86 , x , - 4 , - 12 i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - 6 = - 4 - 4 - 8 = - 12 answer : a
Answer: a
Python program:
a = 12 / 4
b = a - 1
Problem: if a train , travelling at a speed of 360 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 381 m , b ) 112 m , c ) 500 m , d ) 125 m , e ) 433 m
Rationale: "c c = 360 * 5 / 18 * 5 = 500 m"
Answer: c
Python program:
a = 360 * const_0_2778
b = a * 5