euclaise/mathqa_programs huggingface dataset:
Problem: the population of a town increased from 1 , 75000 to 2 , 97500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) 7 %
Rationale: solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 ã — 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e
Answer: e
Python program:
a = 1000 * 100
b = a * 2
c = b + 97500 
d = 1000 * 100
e = d + 75000 
f = c - e
g = f / 10
h = 1000 * 100
i = h + 75000 
j = g / i
k = j * 100
Problem: the workforce of company x is 40 % female . the company hired 20 additional male workers , and as a result , the percent of female workers dropped to 50 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 480 , b ) 500 , c ) 520 , d ) 460 , e ) 440
Rationale: "let x be the total worker then 0.4 x = female worker and 0.6 x is male worker then 20 male worker added 04 x / ( 0.6 x + 20 ) = 50 / 100 or 40 x = 50 * ( 0.6 x + 100 ) = 30 x + 5000 or 10 x = 5000 , x = 500 total worker = 500 + 20 = 520 c"
Answer: c
Python program:
a = 50 / 100
b = a * 20
c = 40 / 100
d = 50 / 100
e = c - d
f = b / e
g = f + 20
Problem: the ratio of kamla and nisha is 6 : 5 and the sum of their ages is 44 . what will be the ratio of their ages after 8 years .
Options: a ) 5 : 6 , b ) 7 : 8 , c ) 8 : 7 , d ) 12 : 11 , e ) 14 : 13
Rationale: answer : let age of kamla is 6 x and age of nisha is 5 x . then , 6 x + 5 x = 4411 x = 44 , x = 4 after 8 year the ratio of their ages = 6 x + 8 / 5 x + 8 = 8 : 7 answer c
Answer: c
Python program:
a = 6 + 1 
b = 8 / a
Problem: two identical cubes if one of them is painted pink on its 4 side and blue on the remaining two side then how many faces painted pink to other cube so that probability of getting cube is 1 / 3 when we roll both the cube .
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: 0 faces should be painted pink i . e all faces blue answer : a
Answer: a
Python program:
a = 1 / 3
b = 4 / 6
c = a / b
d = c * 6
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 25 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 11.79 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 25 = 9 * 12 / 5 = 21.6 time difference = 11.79 ans : a"
Answer: a
Python program:
a = 55 + 9 
b = a - 1
c = 9 / 25
d = 9 / 55
e = c - d
f = b * e
g = max(f)
Problem: the cost price of a radio is rs . 2400 and it was sold for rs . 1980 , find the loss % ?
Options: a ) 17 % , b ) 12 % , c ) 22 % , d ) 24 % , e ) 21
Rationale: "2400 - - - - 420 100 - - - - ? = > 17 % answer : a"
Answer: a
Python program:
a = 2400 - 1980
b = a / 2400
c = b * 100
Problem: a couple spent $ 132 in total while dining out and paid this amount using a credit card . the $ 132 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 100 , b ) $ 104 , c ) $ 108 , d ) $ 112 , e ) $ 116
Rationale: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 132 x = 100 the correct answer is a ."
Answer: a
Python program:
a = 132 * 100
b = 100 + 20 
c = a / b
d = c * 100
e = 100 + 10 
f = d / e
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 14000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 28 , b ) 19 , c ) 22 , d ) 20 , e ) 21
Rationale: "let the total number of workers be x . then , 8000 x = ( 14000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 56000 = x = 28 . answer : a"
Answer: a
Python program:
a = 14000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 52 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 10 , b ) 36 , c ) 38 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 6 ) ( b + 6 ) = m + 52 - - - - - - - - - > ( l + 6 ) ( b + 6 ) - 52 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 6 ) ( b + 6 ) - 52 lb + 2 l + 2 b + 4 = lb + 6 l + 6 b + 36 - 52 simplify 4 l + 4 b = 20 - - - - - - > 2 ( l + b ) = 10 ( check eq ( 1 ) ) answer is a"
Answer: a
Python program:
a = 3 * 2
b = a ** 2
c = 1 * 2
d = c ** 2
e = b - d
f = 52 - e
g = f / 2
Problem: uncle bruce is baking chocolate chip cookies . he has 50 ounces of dough ( with no chocolate ) and 40 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 30 % chocolate ?
Options: a ) 22.86 , b ) 23.86 , c ) 25 , d ) 26 , e ) 27
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 70 % * total = 40 = > ( 7 / 10 ) total = 40 = > total = 400 / 7 = > total = 57.14 oz , from there , you must find 30 % of the total 57.14 oz of the mixture . 30 % * total = > ( 3 / 10 ) ( 57.14 ) = 17.14 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 40 - 17.14 = 22.86 oz chocolate left over . answer : a"
Answer: a
Python program:
a = 30 / 100
b = a * 30
Problem: in arun ' s opinion , his weight is greater than 61 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 64 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 62.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: let arun ' s weight be x kg . according to arun , 61 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 64 . the values satisfying all the above conditions are 62 and 63 . required average = ( 62 + 63 ) / 2 = 62.5 kg answer : b
Answer: b
Python program:
a = 61 + 1 
b = 64 + a 
c = b / 2
Problem: a and b together have $ 1210 . if of a ' s amount is equal to of b ' s amount , how much amount does b have ?
Options: a ) $ 400 , b ) $ 489 , c ) $ 484 , d ) $ 365 , e ) % 342
Rationale: ( 4 / 15 ) a = ( 2 / 5 ) b = > a = ( ( 2 / 5 ) * ( 15 / 4 ) ) b = > a = ( 3 / 2 ) b = > a / b = 3 / 2 a : b = 3 : 2 b ' s share = rs . ( 1210 * ( 2 / 5 ) ) = $ 484 option c
Answer: c
Python program:
a = 1210 * 2
b = a * 2
c = b / 10
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 20 % ?
Options: a ) 20 % , b ) 28 % , c ) 60 % , d ) 26 % , e ) 30 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 80 2 / 3 sp 1 = 80 sp 1 = 120 100 - - - 20 = > 20 % answer : a"
Answer: a
Python program:
a = 100 - 20
b = 2 / 3
c = a / b
d = c - 100
Problem: what is the minimum value of | x - 4 | + | x + 6 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 6 | > = 0 - - > minimum occurs at x = - 6 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 6 - - > result = 10 + 0 + 11 = 21 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 10 + 1 = 11 x = 5 - - > result = 1 + 11 + 0 = 12 x = 6 - - > result = 2 + 12 + 1 = 15 so minimum value of the expression occurs at x = 4 and the resultant value = 11 answer : e
Answer: e
Python program:
a = 6 + 5
Problem: how many five - digit numbers that do not contain the digits 4 or 7 are there ?
Options: a ) 44648 , b ) 27844 , c ) 28642 , d ) 16864 , e ) 32458
Rationale: "we can have 7 digits ( 1 , 2,3 , 5,6 , 8,9 ) for the first place ( ten thousand ' s place ) . and similarly 8 digits for thousand ' s , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 5,6 , 8,9 ) so in total 7 * 8 * 8 * 8 * 8 = 28672 hence c"
Answer: c
Python program:
a = 10 * 10
b = 10 - 1
c = a * b
d = c * 7
Problem: the larger interior angle of a parallelogram is 90 ° more than its smaller interior angle . what is the measure of the smaller interior angle of the parallelogram ?
Options: a ) 90 ° , b ) 75 ° , c ) 60 ° , d ) 45 ° , e ) 30 °
Rationale: let smaller be x , larger becomes x + 90 . . . total of all angles = 360 so 4 x + 180 = 360 and x = 45 answer : d
Answer: d
Python program:
a = 90 / 2
Problem: a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a bridge of 800 meter length ?
Options: a ) 72 seconds , b ) 27 seconds , c ) 40 seconds , d ) 128 seconds , e ) 18 seconds
Rationale: "speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 150 / 9 m / sec total distance = 400 + 800 = 1200 meter time = distance / speed = 1200 * ( 9 / 150 ) = 72 seconds answer : a"
Answer: a
Python program:
a = 400 + 800 
b = 60 * 1000
c = b / 3600
d = a / c
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 200 per month . what is his monthly salary ?
Options: a ) rs . 5000 , b ) rs . 25000 , c ) rs . 7500 , d ) rs . 8500 , e ) rs . 9500
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 – 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 200 = > 5000 answer : a"
Answer: a
Python program:
a = 200 * 100
b = 100 - 20
c = 100 - 20
d = 20 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g
Problem: the average height of 20 students is 20 cm and the average height of 11 students is 20 cm . what is the average height of the 31 students ?
Options: a ) 40 cm , b ) 20 cm , c ) 30 cm , d ) 25 cm , e ) 35 cm
Rationale: the total height of the 31 students = ( 20 * 20 ) + ( 11 * 20 ) = 400 + 220 = 620 cm the required average height = 620 / 31 = 20 cm answer : b
Answer: b
Python program:
a = 20 * 20
b = 11 * 20
c = a + b 
d = c / 31
Problem: a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , two - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of lefthanded players who were not at practice ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were left - handed - - > 6 * 2 / 3 = 4 were left - handed and 2 right - handed . the number of right - handed players who were not at practice that day is 9 - 2 = 7 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 7 / 5 . answer : d
Answer: d
Python program:
a = 1 / 2
b = 2 / 3
c = 1 - b
d = 2 / 3
e = 1 - d
f = 2 / 3
g = e * f
h = c - g
i = a - h
j = 1 / 2
k = 2 / 3
l = 1 - k
m = 2 / 3
n = l * m
o = j - n
p = i / o
Problem: excluding the stoppages , the speed of a bus is 64 km / hr and including the stoppages the speed o the bus is 48 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 28 , e ) 91
Rationale: answer : b ) 15 minutes
Answer: b
Python program:
a = 48 / 64
b = a * const_60
c = const_60 - b
Problem: what amount does an investor receive if the investor invests $ 3000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 3420 , b ) $ 3630 , c ) $ 3870 , d ) $ 4040 , e ) $ 4220
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 5000 = 1.21 * 5000 = 3630 the answer is b ."
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 3000 * c
Problem: a fruit seller sells mangoes at the rate of rs . 12 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.82 , b ) rs 9.82 , c ) rs 10.82 , d ) rs 14.82 , e ) none of these
Rationale: "explanation : 85 : 12 = 105 : x x = ( 12 × 105 / 85 ) = rs 14.82 option d"
Answer: d
Python program:
a = 100 + 5 
b = 12 * a
c = 100 - 15
d = b / c
Problem: a sells a bicycle to b and makes a profit of 35 % . b sells the same bicycle to c at a profit of 45 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 115
Rationale: "explanation : let cp be 100 a sells at 35 % profit so sp = 135 b sells at 45 % profit = 135 x ( 1 + 45 / 100 ) = 195.75 cp sp 100 - - - 195.75 x - - - 225 cp = 225 x 100 / 195.75 = 114.94 answer : e"
Answer: e
Python program:
a = 100 + 45 
b = a / 100
c = 225 / b
d = 35 + 100 
e = d / 100
f = c / e
Problem: how many zeros does 10 ! end with ?
Options: a ) 10 , b ) 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "according to above 10 ! has 10 / 5 = 2 = 2 trailing zeros . answer : e"
Answer: e
Python program:
a = 4 + 1 
b = 10 / a
c = 4 + 1 
d = 10 - c
e = 4 + 1 
f = e ** 2
g = d / f
h = b + g 
i = 4 + 1 
j = 10 - i
k = 4 + 1 
l = k ** 3
m = j / l
n = h + m
Problem: find the value of y from ( 12 ) ^ 2 x 6 ^ 4 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 432
Rationale: 432 e
Answer: e
Python program:
a = 12 ** 2
b = 6 ** 4
c = a * b
d = c / 432
Problem: find the simple interest on rs . 5000 at 6 % per annum for the period from 5 th feb to 19 th april , 2015 .
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 60 , d ) rs . 70 , e ) none of these
Rationale: "explanation : given : 1 ) principal = rs . 5000 2 ) rate of interest = 6 % 3 ) time = 5 th feb to 19 th april , 2015 first find the time period 5 th feb to 19 th april , 2015 feb = 28 – 5 = 23 days march = 31 days april = 19 days total days = 23 + 31 + 19 = 73 days convert days into years , by dividing it by 365 time = 73 / 365 = 1 / 5 simple interest = ( p × r × t ) / 100 = [ 5000 × 6 × ( 1 / 5 ) ] / 100 = rs . 60 simple interest = rs . 60 answer is c"
Answer: c
Python program:
a = 5 * 19
b = a * 100
c = b * 100
d = 19 * 19
e = d * 100
f = 19 + 5 
g = f * 5
h = e * g
i = c + h 
j = 6 * 19
k = j + 5 
l = k / 19
m = i * l
n = 19 * 19
o = 5 * 19
p = 5 * o
q = n / p
r = m * q
s = 1 / 100
t = r * s
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 36 km / hr . what is the length of the platform ?
Options: a ) 160 , b ) 240 , c ) 288 , d ) 277 , e ) 221
Rationale: "speed = 36 * 5 / 18 = 10 m / sec . length of the train = 10 * 20 = 200 m . let the length of the platform be x m . then , ( x + 200 ) / 36 = 10 = > x = 160 m . answer : a"
Answer: a
Python program:
a = 36 * const_0_2778
b = 20 * a
Problem: car a runs at the speed of 42 km / hr & reaches its destination in 6 hr . car b runs at the speed of 52 km / h & reaches its destination in 9 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 7 : 13 , c ) 13 : 7 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 42 × 6 = 252 km distance travelled by car b = 52 × 9 = 468 km ratio = 252 / 468 = 7 : 13 b"
Answer: b
Python program:
a = 42 * 6
b = 52 * 9
c = a / b
Problem: the speed of a car is 90 km in the first hour and 55 km in the second hour . what is the average speed of the car ?
Options: a ) 72.5 kmph , b ) 75 kmph , c ) 87 kmph , d ) 56 kmph , e ) 86 kmph
Rationale: "s = ( 90 + 55 ) / 2 = 72.5 kmph answer : a"
Answer: a
Python program:
a = 90 + 55 
b = a / 2
Problem: by selling 15 pencils for a rupee a man loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "75 % - - - 15 125 % - - - ? 75 / 125 * 15 = 9 answer : b"
Answer: b
Python program:
a = 100 + 25 
b = 100 - 25
c = 1 / b
d = a * c
e = 1 / d
f = e * 15
Problem: a certain machine produces 850 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 7 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 142,800 , e ) 168,000
Rationale: "since 7 days consist of 24 * 7 hours the total hours of a week is 168 hours . since every hour the machine produces 850 units of product p the total product during 168 hours is 850 * 168 = 142,800 . correct option : d"
Answer: d
Python program:
a = 4 * 10
Problem: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 5 per metre approximately
Options: a ) 4457 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 7429
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 5 ) = rs . 7429 . answer : option e"
Answer: e
Python program:
a = 17 / 56
b = math.sqrt(a)
c = b * 100
d = circumface * (
Problem: a contractor undertakes to built a walls in 50 days . he employs 70 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 105 , b ) 30 , c ) 35 , d ) 20 , e ) none of these
Rationale: "70 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 70 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 70 × 25 × 0.6 / 25 × 0.4 = 105 men answera"
Answer: a
Python program:
a = 100 - 40
b = a / 100
c = 70 * b
d = 4 / 10
e = c / d
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 answer , e ) 95
Rationale: "the square roots of all numbers from answer choices are between 9 and 10 , so the product of primes of the number we are looking should be less then 9 , so this number should have only 2 - s , only 3 - s , only 5 - s , or only 2 - s and 3 - s as its primes . only 96 satisfies this . answer : d ."
Answer: d
Python program:
a = 2 * 3
b = 100 - 10
c = a + b
Problem: in how many no . between 10 and 40 exactly two of the digits is 4 ?
Options: a ) 10 , b ) 15 , c ) 35 , d ) 1 , e ) 45
Rationale: "it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even ae are large to have correct choice . ans : d"
Answer: d
Python program:
a = 40 / 10
b = a / 4
Problem: 10 people went to a hotel for combine dinner party 8 of them spent rs . 10 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 110 , c ) 1492 , d ) 1496 , e ) none of these
Rationale: "solution : let average expenditure of 10 people be x . then , 10 x = 8 * 10 + 2 * ( x + 4 ) ; or , 10 x = 10 * 10 + 2 x + 8 ; or , x = 11 ; so , total money spent = 11 * 10 = rs . 110 . answer : option b"
Answer: b
Python program:
a = 8 * 10
b = 10 - 8
c = b * 4
d = a + c 
e = 10 - 8
f = 10 - e
g = d / f
h = g * 10
Problem: a carpenter worked alone for 1 day on a job that would take him 6 more days to finish . he and another carpenter completed the job in 5 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 4.5 , b ) 7.5 , c ) 9.5 , d ) 17.5 , e ) 24.5
Rationale: a carpenter worked only 1 day on something that takes him 6 more days . means ; carpenter finishes his work in 7 days . let his buddy finish the same task in x days . respective rates per day : 1 / 7 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 7 per day . second one worked for 5 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 7 + 5 * 1 / x = 1 5 x + 35 = 7 x 2 x = 35 x = 17.5 days . ans : d
Answer: d
Python program:
a = 1 + 6 
b = 5 * a
c = b / 2
Problem: find the least number of five digits which is exactly divisible by 12 and 18 ?
Options: a ) a ) 1080 , b ) b ) 10080 , c ) c ) 10025 , d ) d ) 11080 , e ) e ) 12080
Rationale: "the smallest five digit numbers are 10025 , 10080,11080 10025 is not divisible by 12 10080 is divisible by both 12 and 18 answer : b"
Answer: b
Python program:
a = 10 * 1000
b = a - 1
c = b / 18
d = c + 1 
e = math.floor(d)
f = e * 18
g = f / 4
h = g / 100
i = h + 2
Problem: how many odd prime numbers are there less than 75 ?
Options: a ) 20 , b ) 1 , c ) 2 , d ) 16 , e ) 17
Rationale: "odd prime number less than 75 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 there is 20 the odd prime number answer is a"
Answer: a
Python program:
a = 75 - 100
b = a + 4
Problem: a is twice as good a workman as b and they took 7 days together to do the work b alone can do it in .
Options: a ) 23 days , b ) 25 days , c ) 21 days , d ) 26 days , e ) 29 days
Rationale: "c 21 days wc = 2 : 1 2 x + x = 1 / 7 x = 1 / 21 = > 21 days"
Answer: c
Python program:
a = 2 + 1 
b = 7 * a
c = b / 2
d = c * 2
Problem: if x is a positive integer with fewer than 3 digits , what is the probability that c x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability c that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Python program:
a = 100 / 4
b = a * 2
c = 100 / 5
d = c * 2
e = b + d 
f = e - 4
g = 100 - 1
h = f / g
Problem: if the cost price of 65 chocolates is equal to the selling price of 50 chocolates , the gain percent is :
Options: a ) 35 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 33 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 50 chocolates = rs . 50 ; s . p . of 50 chocolates = rs . 65 . . ' . gain % = 15 * 100 / 50 = 30 % answer : d"
Answer: d
Python program:
a = 65 - 50
b = 50 / a
c = 100 / b
Problem: a train , 155 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 155 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 155 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 155 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 155 + x = > 45 ã — 10 ã — 10 / 12 = 155 + x = > 15 ã — 10 ã — 10 / 4 = 155 + x = > 15 ã — 25 = 155 + x = 375 = > x = 375 - 155 = 220 answer : option d"
Answer: d
Python program:
a = 45 * const_0_2778
b = a * 30
c = b - 155