euclaise/mathqa_programs huggingface dataset:
Problem: find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2
Options: a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 3 x 11 ^ 2 = 2 ^ 22 x 7 ^ 3 x 11 ^ 2 total number of prime factors = ( 22 + 3 + 2 ) = 27 . answer is d ."
Answer: d
Python program:
a = 2 * 11
b = a + 3 
c = b + 2
Problem: for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 7 of whom are females , by how much does the index for the females exceed the index for the males in the group ?
Options: a ) 0.05 , b ) 0.0625 , c ) 0.2 , d ) 0.3 , e ) 0.6
Rationale: "index for females = ( 20 - 7 ) / 20 = 13 / 20 = 0.65 index for males = ( 20 - 13 / 20 = 7 / 20 = 0.35 index for females exceeds males by 0.65 - 0.35 = 0.3 answer : d"
Answer: d
Python program:
a = 20 - 7
b = a / 20
c = 7 / 20
d = b - c
Problem: the sum of the squares of three numbers is 138 , while the sum of their products taken two at a time is 131 . their sum is :
Options: a ) 20 , b ) 98 , c ) 37 , d ) 26 , e ) 17
Rationale: "explanation : let the numbers be a , b and c . then , a 2 + b 2 + c 2 = 138 and ( ab + bc + ca ) = 131 ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) 138 + 2 * 131 = 400 ( a + b + c ) = â ˆ š 400 = 20 answer : a"
Answer: a
Python program:
a = 138 - 131
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 138 - 131
f = e / 2
g = 138 - f
h = math.sqrt(g)
i = d + h
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 14 % ?
Options: a ) 34.375 % , b ) 48 % , c ) 50.5 % , d ) 52 % , e ) 56 %
Rationale: "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 86 gain % = 22 / 64 * 100 = 34.375 % . answer : option a"
Answer: a
Python program:
a = 100 - 14
b = a / 64
c = b - 1
d = c * 100
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm
b ) 47.14 cm
c ) 84.92 cm
d ) 94.94 cm
e ) 23.57 cm
Rationale: let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : e
Answer: e
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students e in the class ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25
Rationale: the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
Answer: c
Python program:
a = 50000 / 20000
b = 50000 / 20000
c = b * 3
d = 100000 / 20000
e = c + d 
f = a + e
Problem: a car travels first 160 km at 64 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 71.13
Rationale: "car travels first 160 km at 64 km / hr time taken to travel first 160 km = distancespeed = 16064 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 16080 total distance traveled = 160 + 160 = 2 × 160 total time taken = 16064 + 16080 average speed = total distance traveledtotal time taken = 2 × 16016064 + 16080 = 2164 + 180 = 2 × 64 × 8080 + 64 = 2 × 64 × 80144 = 2 × 8 × 8018 = 6409 = 71.11 km / hr answer : a"
Answer: a
Python program:
a = 160 / 64
b = 160 / 80
c = a + b 
d = 1 / c
e = 320 * d
Problem: a prize of $ 800 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 200 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 340
Rationale: "total value of the prize = $ 800 number of people = 20 2 / 5 of 800 ( = $ 320 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 800 - 320 = $ 480 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 480 - 140 = $ 340 , hence e is the correct answer ."
Answer: e
Python program:
a = 800 * 2
b = a / 5
c = 800 - b
d = 20 * 3
e = d / 5
f = 20 - e
g = f - 1
h = g * 20
i = c - h
Problem: simple interest on a certain sum of money for 3 years at 10 % per annum is half the compound interest on rs . 6500 for 2 years at 14 % per annum . the sum placed on simple interest is
Options: a ) rs . 6500 , b ) rs . 1947.4 , c ) rs . 973.7 , d ) rs . 2000 , e ) none
Rationale: "solution c . i . = rs [ 6500 x ( 1 + 14 / 100 ) â ² - 6500 ] rs . ( 6500 x 114 / 100 x 114 / 100 - 6500 ) = rs . 1947.4 . sum = rs . [ 973.7 x 100 / 3 x 10 ] = rs . 3245.67 . answer e"
Answer: e
Python program:
a = 6500 * 14
b = a / 100
c = 6500 * 14
d = c / 100
e = 6500 + d 
f = e * 14
g = f / 100
h = b + g 
i = h / 2
j = i / 3
k = j * 100
l = k / 10
Problem: mary works in a restaurant a maximum of 50 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 300 , b ) 420 , c ) 460 , d ) 320 , e ) 400
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 30 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 30 ) = $ 300 . the total amount is $ 160 + $ 300 = $ 460 answer c 460 ."
Answer: c
Python program:
a = 50 * 8
b = 50 - 20
c = 25 / 100
d = 8 * c
e = b * d
f = a + e
Problem: an outlet pipe empties a tank which is full in 5 hours . if the inlet pipe is kept open , which lets water in at the rate of 4 litres / min then outlet pipe would take 3 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 3200 litres , c ) 12800 litres , d ) 11200 litres , e ) 13200 litres
Rationale: let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 4 * 60 = 240 liters / hour ; net outflow rate when both pipes operate would be x - 240 liters / hour . capacity of the tank = x * 5 hours = ( x - 240 ) * ( 5 + 3 ) hours 5 x = ( x - 240 ) * 8 - - > x = 640 - - > capacity = 5 x = 3200 liters . answer : b .
Answer: b
Python program:
a = 4 * const_60
b = 5 + 3 
c = a * b
d = c / 3
e = d * 5
Problem: you buy a piece of land with an area of â ˆ š 625 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 25
Rationale: "try filling the numbers into the answer y x y = find the closest to 625 . answer e"
Answer: e
Python program:
a = math.sqrt(625)
Problem: in a division sum , the remainder is 4 and the divisor is 2 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :
Options: a ) 72 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "diver = ( 4 * 3 ) + 2 = 14 2 * quotient = 14 quotient = 7 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 7 ) + 2 = 100 c"
Answer: c
Python program:
a = 4 * 3
b = a + 2 
c = 4 * 3
d = c + 2 
e = d / 2
f = b * e
g = f + 4
Problem: if the sum of two numbers is 42 and their product is 437 , then find the absolute difference between the numbers .
Options: a ) 2 , b ) 4 , c ) 3 , d ) 1 , e ) 0
Rationale: let the numbers be x and y . then , x + y = 42 and xy = 437 x - y = sqrt [ ( x + y ) 2 - 4 xy ] = sqrt [ ( 42 ) 2 - 4 x 437 ] = sqrt [ 1764 – 1748 ] = sqrt [ 16 ] = 4 . required difference = 4 . answer is b .
Answer: b
Python program:
a = 42 ** 2
b = 4 * 437
c = a - b
d = math.sqrt(c)
Problem: for dinner , cara ate 240 grams of bread which was 8 times as much bread as she ate for lunch , and 6 times as much bread as she ate for breakfast . how much bread did cara eat in total ?
Options: a ) 300 , b ) 310 , c ) 320 , d ) 330 , e ) 340
Rationale: for breakfast , cara ate 240 / 6 = 40 grams . for lunch , cara ate 240 / 8 = 30 grams . for dinner , cara ate 240 grams . the total is 40 + 30 + 240 = 310 grams . the answer is b .
Answer: b
Python program:
a = 240 / 8
b = 240 / 6
c = a + b 
d = 240 + c
Problem: a rectangular box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ?
Options: a ) 3 m
b ) 4 m
c ) 5 m
d ) 6 m
e ) 2 m
Rationale: total area of cross roads = 60 x + 40 x − x 2 but total area of the cross roads = 291 m 2 hence , 60 x + 40 x − x 2 = 291 ⇒ 100 x − x 2 = 291 ⇒ x 2 − 100 x + 291 = 0 ⇒ ( x − 97 ) ( x − 3 ) = 0 ⇒ x = 3 answer : a
Answer: a
Python program:
a = 100 ** 2
b = 60 * 40
c = b - 2109
d = c * 4
e = a - d
f = math.sqrt(e)
g = 100 - f
h = g / 2
Problem: if 50 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 50 % of a = 1 / 3 b then 50 a / 100 = 1 b / 3 a / 2 = b / 3 a / b = 2 / 3 a : b = 2 : 3 answer is e"
Answer: e
Python program:
a = 1 / 4
b = 50 / 100
c = a / b
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 180 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 50 %
Rationale: "answer : e 180 ° divided by 360 ° equals 0.5 , therefore the sector is equal to 50 % of the total"
Answer: e
Python program:
a = 3600 / 10
b = 180 / a
c = b * 100
Problem: the speed at which a man can row a boat in still water is 25 kmph . if he rows downstream , where the speed of current is 11 kmph , what time will he take to cover 80 metres ?
Options: a ) 18 seconds , b ) 27 seconds , c ) 26 seconds , d ) 12 seconds , e ) 8 seconds
Rationale: "speed of the boat downstream = 25 + 11 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 80 m = 80 / 10 = 8 seconds . answer : e"
Answer: e
Python program:
a = 25 + 11 
b = a * const_0_2778
c = 80 / b
Problem: for a particular american football game , the probability of a team ' s quarterback throwing a completed pass on each throw is 3 / 10 . what is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50 % .
Options: a ) 10 , b ) 5 , c ) 2 , d ) 3 , e ) 1
Rationale: rule of subtraction : p ( a ) = 1 - p ( a ' ) rule of multiplication : p ( a ∩ b ) = p ( a ) p ( b ) the probability that the quarterback throws a completed pass at least once in 2 throws is 1 - ( 7 / 10 ) ^ 2 = 1 - 49 / 100 = 51 / 100 > 50 % answer : c
Answer: c
Python program:
a = 50 / 100
b = 10 * a
c = b - 3
Problem: a and b can do a work in 8 hours and 12 hours respectively . a starts the work at 6 am and they work alternately for one hour each . when will the work be completed ?
Options: a ) 9.6 days , b ) 7.6 days , c ) 4 days , d ) 8.6 days , e ) 6.6 days
Rationale: work done by a and b in the first two hours , working alternately = first hour a + second hour b = 1 / 8 + 1 / 12 = 5 / 24 . total time required to complete the work = 2 * 24 / 5 = 9.6 days . answer : a
Answer: a
Python program:
a = 1/(8)
b = 1/(12)
c = a + b 
d = 1/(c)
e = d * 2
Problem: in a weight - lifting competition , the total weight of joe ' s two lifts was 1800 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 700
Rationale: this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1800 pounds . we sum the two variables to obtain : f + s = 1800 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 1800 3 f = 2100 f = 700 answer is e .
Answer: e
Python program:
a = 1800 + 300 
b = a / 3
Problem: a train covers a distance of 12 km in 10 min . if it takes 1 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 15 , e ) 45
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 1 = 20 m . answer : option b"
Answer: b
Python program:
a = 12 / 10
b = a - 1
c = 12 / b
Problem: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 330 grams of compound x ?
Options: a ) 54 , b ) 162 , c ) 250 , d ) 275 , e ) 322
Rationale: total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 330 gms of x have 330 * 10 / 12 = 275 gms of b and 330 - 275 = 55 gms of a . cross check : - a / b = 55 / 275 = 2 / 10 ( as given ) ans d
Answer: d
Python program:
a = 330 * 10
b = 2 + 10 
c = a / b
Problem: the average salary of all the workers in a workshop is rs . 9000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 14
Rationale: "let the total number of workers be x . then , 9000 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 3000 x = 42000 = x = 14 . answer : e"
Answer: e
Python program:
a = 12000 - 9000
b = 7 * a
c = 9000 - 6000
d = b / c
e = 7 + d
Problem: find the sum of first 30 natural numbers
Options: a ) 470 , b ) 468 , c ) 465 , d ) 463 , e ) 485
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) 2 = 30 ( 30 + 1 ) 2 = 30 ( 31 ) 2 = 465 answer : option c"
Answer: c
Python program:
a = 30 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 30 / e
g = f / 2
h = 30 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 30 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 3 : 1 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 4 : 3 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: "we have ratio in 5 : 3 : 1 and this is shifted to 2 : 4 : 3 ( c : s : t ) if we observe the ratio of the tobacco increased by 2 times ( 3 - 1 ) t = 1 / 9 * 1350 = 150 . since tobacco increased by 2 times . . we get 150 * 2 = 300 . answer d is the answer . ."
Answer: d
Python program:
a = 100 * 10
b = 3 * 100
c = a + b 
d = 5 * 10
e = c + d 
f = 5 + 3 
g = f + 3 
h = 5 / g
i = e * h
j = 100 * 10
k = 3 * 100
l = j + k 
m = 5 * 10
n = l + m 
o = 5 + 3 
p = o + 3 
q = 3 / p
r = n * q
s = i - r
Problem: the charge for a single room at hotel p is 70 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 100 % , b ) 120 % , c ) 150 % , d ) 200 % , e ) 300 %
Rationale: "p = 0.3 r = 0.9 g r = 0.9 g / 0.3 = 3 g thus r is 200 % greater than g . the answer is d ."
Answer: d
Python program:
a = 100 - 70
b = 100 - 10
c = a / b
d = c * 100
e = 100 - d
f = 100 - 70
g = 100 - 10
h = f / g
i = h * 100
j = e / i
k = j * 100
Problem: average of 10 matches is 34 , how many runs one should should score to increase his average by 4 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 88
Rationale: explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 34 ) = 418 - 340 = 78 answer : option c
Answer: c
Python program:
a = 34 + 4 
b = 10 + 1 
c = a * b
d = 10 * 34
e = c - d
Problem: what least number should be added to 1021 , so that the sum is completely divisible by 25 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 5
Rationale: "1021 ã · 25 = 40 with remainder = 21 21 + 4 = 25 . hence 4 should be added to 1021 so that the sum will be divisible by 25 answer : option a"
Answer: a
Python program:
a = 25 - reminder
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 0 vers to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.75 , d ) 7 , e ) none
Rationale: "sol . required run rate = 282 – ( 3.2 × 10 / 40 ) = 240 / 40 = 6.25 . answer a"
Answer: a
Python program:
a = 10 * 3
b = 0 - a
c = b / 40
Problem: how many positive integers less than 50 are multiples of 6 but not multiples of 8 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "the lcm of 6 and 8 is 24 . if x < 50 and x is divisible by 6 not by 8 - - > x is not divisible by 24 . from 1 - - > 50 , we have 2 numbers which is divisible by 24 : 24 , 48 . from 1 - - > 50 , we have ( 48 - 6 ) / 6 + 1 = 8 numbers divisible by 6 . therefore , our answer is 8 - 2 = 6 numbers . b"
Answer: b
Python program:
a = 4 + 6 
b = a - 1
c = math.factorial(b)
d = math.factorial(6)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a reduction of 10 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 41 , e ) s . 16
Rationale: "800 * ( 10 / 100 ) = 80 - - - - 5 ? - - - - 1 = > rs . 16 answer : e"
Answer: e
Python program:
a = 800 * 10
b = a / 100
c = b / 5
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 17000 , then find the annual income of a ?
Options: a ) rs . 571200 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these
Rationale: "b ' s monthly income = 17000 * 112 / 100 = rs . 19040 b ' s monthly income = 2 parts - - - - > rs . 19040 a ' s monthly income = 5 parts = 5 / 2 * 19040 = rs . 47600 a ' s annual income = rs . 47600 * 12 = rs . 571200 answer : a"
Answer: a
Python program:
a = 12 / 100
b = 1 + a 
c = 17000 * b
d = 5 / 2
e = c * d
f = e * 12
Problem: two pipes can fill a tank in 18 minutes and 30 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 11 , d ) 1 / 10 , e ) 1 / 12
Rationale: part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 30 - 1 / 45 = 1 / 15 so , the tank becomes full in 15 minutes . answer : a
Answer: a
Python program:
a = 1 / 18
b = 1 / 30
c = a + b 
d = 1 / 45
e = c - d
Problem: 17 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 154 , b ) 184 , c ) 240 , d ) 272 , e ) 306
Rationale: "2 * 17 c 2 = 2 * 136 = 272 the answer is d ."
Answer: d
Python program:
a = 17 - 1
b = 17 * a
Problem: if a farmer sells 5 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 20 more chickens , he will run out of feed 1 day earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 15 , b ) 20 , c ) 20 / 3 , d ) 25 , e ) 10
Rationale: "let x = total feed required for the planned period n = number of chicken t = total time of the planned feed x = nt 1 ) x = ( n - 5 ) * ( t + 4 ) 2 ) x = ( n + 20 ) * ( t - 1 ) equating 1 & 2 ( n - 5 ) * ( t + 4 ) = ( n + 20 ) * ( t - 1 ) 5 n = 25 t n = 5 t x = n * n / 5 substituting this value in 1 n * n / 5 = ( n - 5 ) * ( n / 5 + 4 ) 15 n = 100 n = 20 / 3 c"
Answer: c
Python program:
a = 2 + 4 
b = 1 * 4
c = a * b
Problem: what will be the reminder when ( 13 ^ 13 + 13 ) is divided by 14 ?
Options: a ) 16 , b ) 14 , c ) 12 , d ) 18 , e ) 21
Rationale: ( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 13 ^ 13 + 1 ) will be divisible by ( 13 + 1 ) ; ( 13 ^ 13 + 1 ) + 12 when divided by 14 will give 12 as remainder . correct option : c
Answer: c
Python program:
a = 13 ** 13
b = a + 13 
c = 13 ** 13
d = c + 13 
e = d / 14
f = math.floor(e)
g = 14 * f
h = b - g
Problem: two whole numbers whose sum is 40 can not be in the ratio
Options: a ) 4 : 10 , b ) 2 : 3 , c ) 1 : 3 , d ) 2 : 4 , e ) 3 : 5
Rationale: d ) 2 : 4
Answer: d
Python program:
a = 40 / 2
b = a - 10
c = b / 2
d = 40 / 2
e = d + 10 
f = c / e
Problem: the remainder when positive integer nn ( n > 1 n > 1 ) is divided by 25 is 1 and the remainder when nn is divided by 7 is also 1 . what is the least value of nn ?
Options: a ) 76 , b ) 101 , c ) 126 , d ) 151 , e ) 176
Rationale: we ' re asked to find the least number that gives us a remainder of 1 when divided by 25 and gives us a remainder of 1 when divided by 7 . you might notice , rather quickly , that all of the answers gives us a remainder when divided by 25 . . . 76 = 75 + 1 101 = 100 + 1 126 = 125 + 1 151 = 150 + 1 176 = 175 + 1 so the real question is ` ` which of these 5 is the least number that has a remainder of 1 when divided by 7 ? ' ' from here , you can just do the ` ` brute force ' ' math : a : 76 / 7 = 10 r 6 not a match b : 101 / 7 = 14 r 3 not a match c : 126 / 7 = 18 r 0 not a match d : 151 / 7 = 21 r 4 not a match none of these numbers ` ` fits ' ' the description , so the answer must be e . e : 176 / 7 = 25 r 1 ; answer : e
Answer: e
Python program:
a = 25 * 7