euclaise/mathqa_programs huggingface dataset:
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 20 miles per gallon , and from town b to town c , the car averaged 24 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 40 , b ) 30 , c ) 42 , d ) 33 , e ) 35
Rationale: "step 1 ) took lcm of 20 and 24 . . came as 120 . step 2 ) 120 distance between b to c . . . do 120 / 24 hence 5 gallons used step 3 ) twice distance . . hence 120 * 2 = 240 . . . do as above . . 240 / 20 = 7 gallons used step 4 ) total gallons . . 5 + 7 = 12 gallons step ) total miles = 120 + 240 = 360 miles hence . . average of whole journey = 360 / 12 which comes to 30 answer : b"
Answer: b
Python program:
a = 24 * 10
b = 24 * 10
c = b / 2
d = a + c 
e = 24 * 10
f = e / 20
g = 24 * 10
h = g / 2
i = h / 24
j = f + i 
k = d / j
Problem: a bowl of fruit contains 10 apples and 23 oranges . how many oranges must be removed so that 50 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 13 , c ) 14 , d ) 17 , e ) 20
Rationale: "number of apples = 10 number of oranges = 23 let number of oranges that must be removed so that 50 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 10 + ( 23 - x ) = 33 - x 10 / ( 33 - x ) = 5 / 10 = > 20 = 33 - x = > x = 13 answer b"
Answer: b
Python program:
a = 10 + 23 
b = 50 / 100
c = a * b
d = c - 10
e = 50 / 100
f = d / e
Problem: given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 5 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 5 is 6 + 5 = 11 . answer : e ."
Answer: e
Python program:
a = 3 + 3 
b = a + 5
Problem: if a / x = 1 / 3 and a / y = 1 / 4 , then ( x + y ) =
Options: a ) 2 a , b ) a / 2 , c ) 6 a , d ) 7 a , e ) 9 a
Rationale: ratio 1 : 3 a = x ratio 2 : 4 a = y x + y = 7 a answer is d
Answer: d
Python program:
a = 4 + 3
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 70 units . if today ' s production of 90 units raises the average to 75 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 3
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 70 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 70 n + 90 = 75 * ( n + 1 ) - - > n = 3 . answer : e ."
Answer: e
Python program:
a = 90 - 70
b = 75 - 70
c = a / b
d = c - 1
Problem: a is twice as good a work man as b and together they finish the work in 6 days . in how many days a alone can finish the work ?
Options: a ) 3 , b ) 9 , c ) 7 , d ) 2 , e ) 6
Rationale: "wc = 2 : 1 2 x + x = 1 / 6 = > x = 1 / 18 2 x = 1 / 9 a can do the work in 9 days . answer : b"
Answer: b
Python program:
a = 1/(6)
b = 2 + 1 
c = a / b
d = 1/(c)
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is five times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 45 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 15 : 2 = > for 15 soap , salt = 2 = > for 2 soap , salt = ( 2 / 15 ) * 2 = 4 / 15 so , water : soap : salt = 3 : 2 : 4 / 15 = 45 : 30 : 4 after open container , water : soap : salt = 22.5 : 30 : 4 so , water : salt = 22.5 : 4 = 45 : 8 e"
Answer: e
Python program:
a = 2 * 3
b = a * 3
c = 2 * 2
d = c * 2
e = b / d
Problem: if a @ b = a * b ^ ( 1 / 2 ) then 4 @ 9 = ? self made
Options: a ) 2 , b ) 12 , c ) 3 , d ) 8 , e ) 4
Rationale: 4 * ( 9 ) ^ 1 / 2 = 4 * 3 = 12 b is the answer
Answer: b
Python program:
a = 1 / 2
b = 9 ** a
c = 4 * b
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 25 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 979923 , c ) 980241 , d ) 1178125 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 25 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1178125 d"
Answer: d
Python program:
a = 25 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1000000 * h
Problem: the difference between simple interest and compound interest of a certain sum of money at 20 % per annum for 2 years is $ 48 . then the sum is
Options: a ) $ 600 , b ) $ 1000 , c ) $ 1200 , d ) $ 1500 , e ) $ 2000
Rationale: "20 % of ( year 1 interest ) = 20 % of ( 20 % of principal ) = 48 principal = $ 1200 answer ( c )"
Answer: c
Python program:
a = 2 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 20
f = e - 20
g = 20 * 2
h = g / 100
i = f - h
Problem: the equal amounts of money are deposited in two banks each at 15 % per annum for 3.5 years and 5 years respectively . if the difference between their interests is rs . 144 , find the each sum ?
Options: a ) 640 , b ) 500 , c ) 3000 , d ) 1000 , e ) 2000
Rationale: ( p * 5 * 15 ) / 100 - ( p * 3.5 * 15 ) / 100 = 144 75 p / 100 â € “ 52.5 p / 100 = 144 22.5 p = 144 * 100 = > p = rs . 640 answer a
Answer: a
Python program:
a = 15 * 5
b = 15 * 3
c = a - b
d = c / 100
e = 144 / d
Problem: the number of stamps that p and q had were in the ratio of 5 : 3 respectively . after p gave q 10 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 9 : 7 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 90
Rationale: "p started with 5 k stamps and q started with 3 k stamps . ( 5 k - 10 ) / ( 3 k + 10 ) = 9 / 7 35 k - 27 k = 160 k = 20 p has 5 ( 20 ) - 10 = 90 stamps and q has 3 ( 20 ) + 10 = 70 stamps . the answer is a ."
Answer: a
Python program:
a = 10 * 9
b = 10 * 7
c = a + b 
d = 9 + 7 
e = c / d
Problem: if y is the smallest positive integer such that 31,360 multiplied by y is the square of an integer , then y must be
Options: a ) 21 , b ) 10 , c ) 61 , d ) 72 , e ) 14
Rationale: "31360 = 8 * 8 * 7 * 7 * 5 * 2 , so we need one 5 and one 2 to make it a square of a number . so 5 * 2 = 10 ans : b"
Answer: b
Python program:
a = 2 + 3 
b = a * 2
Problem: solution y is 30 percent liquid x and 70 percent water . if 3 kilograms of water evaporate from 8 kilograms of solution y and 3 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 35 % , b ) 37 % , c ) 41.3 % , d ) 42 % , e ) 45 %
Rationale: in 8 kilograms of solution y there are 0.3 * 8 = 2.4 kilograms of solution x ; after 3 kilograms of water are replaced by 3 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 3 = 0.9 kilograms of solution x are added , so in the new solution of 8 kilograms there are 2.4 + 0.9 = 3.3 kilograms of solution x , which is 3.3 / 8 * 100 = 41.3 % of this new solution . answer : c .
Answer: c
Python program:
a = 30 / 100
b = 8 * a
c = 30 / 100
d = 3 * c
e = b + d 
f = 30 / 100
g = 8 * f
h = 30 / 100
i = 3 * h
j = g + i 
k = 70 / 100
l = 8 * k
m = l - 3
n = 70 / 100
o = 3 * n
p = m + o 
q = j + p 
r = e / q
s = 100 * r
Problem: a train 480 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 22 kmph , b ) 108 kmph , c ) 54 kmph , d ) 71 kmph , e ) 88 kmph
Rationale: "s = 480 / 16 * 18 / 5 = 108 kmph answer : b"
Answer: b
Python program:
a = 480 / 16
b = const_3_6 * a
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr . find the time taken by the boat to go 80 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 80 km downstream = ( 80 / 17 ) hrs = 4 hrs 42 minutes . answer e"
Answer: e
Python program:
a = 13 + 4 
b = 80 / a
Problem: a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 187 , b ) 279 , c ) 280 , d ) 285 , e ) 262
Rationale: "since the month begins with a sunday , so there will be five sundays in the month . required average = [ ( 510 * 5 ) + ( 240 * 25 ) ] / 30 = 8550 / 30 = 285 . answer : d"
Answer: d
Python program:
a = 4 + 1 
b = a * 510
c = 4 + 1 
d = 4 + 1 
e = c * d
f = e * 240
g = b + f 
h = g / 30
Problem: the sum of present age of abe and the age before 7 years is 35 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 35 2 x - 7 = 35 2 x = 35 + 7 x = 42 / 2 x = 21 z = x + 7 = 21 + 7 = 28 answer : d
Answer: d
Python program:
a = 35 + 7 
b = a / 2
c = b + 7
Problem: the two lines y = x and x = - 6 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the point of intersection is ( - 6 , - 6 ) . the triangle has a base of length 6 and a height of 6 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 6 * 6 = 18 the answer is d ."
Answer: d
Python program:
a = 6 * 6
b = a / 2
Problem: what distance will be covered by a bus moving at 36 kmph in 30 seconds ?
Options: a ) 287 , b ) 600 , c ) 289 , d ) 300 , e ) 207
Rationale: "36 kmph = 36 * 5 / 18 = 10 mps d = speed * time = 10 * 30 = 300 m . answer : d"
Answer: d
Python program:
a = 36 * const_0_2778
b = a * 30
Problem: if 2.5 of a number is equal to 0.75 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 10 , d ) 20 : 3 , e ) 30 : 7
Rationale: "2.5 a = 0.75 b - > a / b = 0.75 / 2.5 = 75 / 250 = 3 / 10 : . a : b = 3 : 10 answer : c"
Answer: c
Python program:
a = 0 * 75
b = 2 * 5
c = a / b
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.5 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 13 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.5 weight of the new student = ( 30 * 27.5 – 29 * 28 ) = 825 - 812 = 13 answer : d"
Answer: d
Python program:
a = 29 + 1 
b = a * 27
c = 29 * 28
d = b - c
Problem: if 4 tic equals 3 tacs and 6 tacs equal 4 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 3 / 10 , e ) 2 / 1
Rationale: "4 tic = 3 * tac and 6 * tac = 4 * toc ; 24 * tic = 18 * tac and 18 * tac = 12 * toc - - > 24 * tic = 12 * toc - - > tic / toc = 24 / 12 = 2 / 1 . answer : e ."
Answer: e
Python program:
a = 4 / 4
b = 3 / 4
c = a + b
Problem: the speed of a boat in still water is 30 kmph . what is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time ?
Options: a ) 11 kmph , b ) 10 kmph , c ) 12 kmph , d ) 16 kmph , e ) 15 kmph
Rationale: x = the speed of the stream ( 30 + x ) / ( 30 - x ) = 2 / 1 30 + x = 60 - 2 x 3 x = 30 x = 10 km / hour if the speed of the stream is 10 km / hour , then the ' downstream ' speed of the boat is 30 + 10 = 40 km / hour and the ' upstream ' speed of the boat is 30 - 10 = 20 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 40 = 80 km downstream and 2 x 20 = 40 km / hour upstream . answer : b
Answer: b
Python program:
a = 1 + 2 
b = 30 / a
Problem: after getting 2 successive discounts , a shirt with a list price of rs 150 is available at rs 105 . if the second discount is 12.55 , find the first discount .
Options: a ) 22 % , b ) 18 % , c ) 24 % , d ) 17 % , e ) 20 %
Rationale: "let the first discount be x % then , 87.5 % of ( 100 - x ) % of 150 = 105 = 87.5 / 100 * ( 100 - x ) / 100 * 450 = 150 = > 105 = > 100 - x = ( 105 * 100 * 100 ) / ( 150 * 87.5 ) = 80 x = ( 100 - 80 ) = 20 first discount = 20 % answer is e ."
Answer: e
Python program:
a = 105 * 100
b = 100 - 12
c = a / b
d = 150 - c
e = d * 100
f = e / 150
Problem: a rectangular plot measuring 60 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 44 m
b ) 66 m
c ) 26 m
d ) 56 m
e ) 25 m
Rationale: perimeter of the plot = 2 ( 60 + 50 ) = 220 m no of poles = 220 / 5 = 44 m answer : a
Answer: a
Python program:
a = 60 + 50 
b = a * 2
c = b / 5
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 15 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15 - 2 * 1.5 = 12 . answer : d .
Answer: d
Python program:
a = 2 * 1
b = 15 - a
Problem: in how many years will a sum of money doubles itself at 12 % per annum on simple interest ?
Options: a ) 15 % , b ) 20 % , c ) 10 % , d ) 8 % , e ) 22 %
Rationale: "p = ( p * 12 * r ) / 100 r = 8 % answer : d"
Answer: d
Python program:
a = 100 / 12
Problem: 20 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 278 , c ) 800 , d ) 1600 , e ) 121
Rationale: "( 20 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 5 x = 320 x = 1600 answer : d"
Answer: d
Python program:
a = 650 * 20
b = a / 100
c = b + 190 
d = c * 100
e = d / 20
Problem: it will take 18 days for cameron to complete a certain task alone . he worked for 9 days before she was joined by sandra . both of them completed the remaining task in 3 and half days . how many days will it take both of them to complete the entire job ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9
Rationale: explanation : cameron and sandra completed half work in 3.5 days = > they can complete whole work in 7 days answer : option b
Answer: b
Python program:
a = 1 / 2
b = 3 + a 
c = 9 / 18
d = b / c
Problem: if greg buys 5 shirts , 4 trousers and 2 ties , the total cost is $ 80 . if greg buys 7 shirts , 4 trousers and 2 ties , the total cost is $ 70 . how much will it cost him to buy 2 trousers , 3 shirts and 1 ties ?
Options: a ) $ 37.5 , b ) $ 64 , c ) $ 75 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 5 x + 4 y + 2 z = 80 7 x + 4 y + 2 z = 70 adding both the equations = 12 x + 8 y + 4 z = 150 3 x + 2 y + 1 z = 37.5 ans a"
Answer: a
Python program:
a = 70 + 80 
b = a / 2
Problem: what is the sum of all the numbers between 1 and 16 , inclusive ?
Options: a ) 190 , b ) 200 , c ) 185 , d ) 166 , e ) 213
Rationale: "all you have to do is add 1 + 2 + 3 + 4 . . . + 14 + 15 + 16 , which is 190 . final answer : a"
Answer: a
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 1 
t = 2 + 4 
u = s + t
Problem: ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 20 % if no discount was offered ?
Options: a ) 19200 , b ) 17606 , c ) 17604 , d ) 17600 , e ) 117601
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 20 % if no discount was offered = 16000 * 120 / 100 = rs . 19200 . answer : a"
Answer: a
Python program:
a = 100 + 20 
b = 12500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: the distance between delhi and mathura is 100 kms . a starts from delhi with a speed of 50 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 45 kmph at 8 p . m . from delhi . when will they meet ?
Options: a ) 11 , b ) 77 , c ) 8 3 / 4 , d ) 8 1 / 2 , e ) 8
Rationale: "d = 100 – 50 = 50 rs = 45 + 50 = 95 t = 90 / 45 = 0.5 hours 8 a . m . + 0.5 = 8 1 / 2 a . m . . answer : d"
Answer: d
Python program:
a = 50 + 45 
b = 100 / a
c = 8 + b
Problem: the length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively . find how many minimum number of square tiles would be required to cover it completely ?
Options: a ) 375
b ) 2570
c ) 2800
d ) 3315
e ) none of these
Rationale: explanation : since we require minimum number of square tiles , the size of the tile is given as the h . c . f . of two sides of the room . the h . c . f . of 1625 cm & 1275 cm . is 25 cm . hence , we get , required number = ( 1625 * 1275 ) / ( 25 * 25 ) = 3315 answer : d
Answer: d
Python program:
a = 16 * 25
b = 12 * 75
c = rectangle_area / (
Problem: a man can row upstream at 25 kmph and downstream at 37 kmph , and then find the speed of the man in still water ?
Options: a ) 86 , b ) 67 , c ) 31 , d ) 15 , e ) 17
Rationale: "us = 25 ds = 37 m = ( 37 + 25 ) / 2 = 31 answer : c"
Answer: c
Python program:
a = 25 + 37 
b = a / 2
Problem: walking at 50 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 24 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "speed is inversly proprtional to time walking at 50 % of speed meand 1 / 2 s takes 2 t . it takes 24 minutes extra to cover the distance . then 2 t = t + 24 t = 24 . option a is correct"
Answer: a
Python program:
a = 50 / 100
b = 1 / a
c = b - 1
d = 24 / c
Problem: 80 % of the population of a village is 32000 . the total population of the village is ?
Options: a ) 40000 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312
Rationale: "x * ( 80 / 100 ) = 32000 x = 400 * 100 x = 40000 answer : a"
Answer: a
Python program:
a = 100 / 80
b = a * 32000
Problem: a number x is 4 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 75 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 4 . then y = 1 is less than x = 4 by ( 4 - 1 ) / 4 * 100 = 3 / 4 * 100 = 75 % . answer : b ."
Answer: b
Python program:
a = 4 - 1
b = a / 4
c = b * 100
Problem: a trader has 1600 kg of sugar . he sells a part at 8 % profit and the rest at 12 % profit . if he gains 11 % on the whole , find the quantity sold at 12 % ?
Options: a ) 1000 , b ) 1200 , c ) 1400 , d ) 1450 , e ) 1500
Rationale: by rule of alligation , % profit by selling part 1 % profit by selling part 2 8 12 net % profit 11 12 - 11 = 1 11 - 8 = 3 = > quantity of part 1 : quantity of part 2 = 1 : 3 given that total quantity = 1600 kg hence , quantity of part 2 ( quantity sold at 12 % profit ) = 1600 × 3 4 = 1200 b )
Answer: b
Python program:
a = 1600 * 11
b = 1600 * 8
c = a - b
d = 12 - 8
e = c / d
Problem: john spent 40 percent of his earning last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did john have left over ?
Options: a ) 30 % , b ) 32 % , c ) 45 % , d ) 68 % , e ) 70 %
Rationale: say john ' s earning last month was $ 100 . john spent 40 percent of his earning last month on rent - - > $ 40 on rent ; 30 percent less than what he spent on rent to purchase a new dishwasher - - > $ 40 * 0.7 = $ 28 on the dishwasher . left over amount 100 - ( 40 + 28 ) = $ 32 . answer : b .
Answer: b
Python program:
a = 100 - 30
b = a / 100
c = 40 / 100
d = 100 * c
e = b * d
f = 40 / 100
g = 100 * f
h = e + g 
i = 100 - h
Problem: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 4 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 5 women + 4 children ) ' s 1 day work = ( 5 / 10 + 4 / 140 ) = 1 / 10 5 women and 4 children will complete the work in 10 days . e"
Answer: e
Python program:
a = 10 * 7
b = 5 / a
c = 10 * 14
d = 10 / c
e = b + d 
f = 1/(e)
Problem: lloyd normally works 7.5 hours per day and earns $ 4.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 2.0 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 47.25 , c ) $ 60.75 , d ) $ 54.00 , e ) $ 70.00
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.5 + 3 * 4.5 * 2.0 = 60.75 answer c"
Answer: c
Python program:
a = 7 * 5
b = 10 - 5
c = b * 2
d = c * 4
e = a + d
Problem: on a certain road , 20 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 20 % of them exceeded the speed limit and received the ticket , i . e . x / 5 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = x / 5 or y / x = 1 / 4 or y / x * 100 = 1 / 4 * 100 = 25 % d"
Answer: d
Python program:
a = 100 - 20
b = 20 / a
c = b * 100
Problem: if the remainder is 16 when the integer n is divided by 30 , what is the remainder when 2 n is divided by 15 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: n = 30 k + 16 2 n = 2 ( 30 k + 16 ) = 4 k * 15 + 32 = 4 k * 15 + 2 * 15 + 2 = 15 j + 2 the answer is b .
Answer: b
Python program:
a = 16 * 2
b = a - 30
Problem: to apply for the position of photographer at a local magazine , a photographer needs to include 4 or 5 photos in an envelope accompanying the application . if the photographer has pre - selected 7 photos representative of her work , how many choices does she have to provide the photos for the magazine ?
Options: a ) 48 , b ) 50 , c ) 52 , d ) 54 , e ) 56
Rationale: 7 c 4 + 7 c 5 = 35 + 21 = 56 the answer is e .
Answer: e
Python program:
a = math.factorial(7)
b = math.factorial(5)
c = a / b
d = 7 * 2
e = c + d
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 30 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 76 , c ) 28 , d ) 66 , e ) 11
Rationale: explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 30 / 5 = 6 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 6 = 66 secs . answer : d
Answer: d
Python program:
a = 6 - 1
b = 30 / a
c = 12 - 1
d = b * c
Problem: john purchased some shirts and trousers for $ 1100 . he paid $ 550 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 11
Rationale: "given that the total purchase of two items cost 1100 . so the average purchase of one item will cost 1100 / 2 = 550 . its given as total shirt cost 100 $ less . hence total shirt cost = 550 - 275 and total trouser cost = 300 + 275 5 shirts = 275 $ = = > one shirt = 55 $ one trouser = 55 + 20 = 75 $ total trousers = 825 / 75 = 11 . e"
Answer: e
Python program:
a = 20 + 20 
b = 5 * a
c = 1100 - b
d = 20 + 20 
e = d + 20 
f = c / e