euclaise/mathqa_programs huggingface dataset:
Problem: workers at a campaign office have 1000 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 300 , b ) 800 , c ) 1100 , d ) 600 , e ) 1900
Rationale: "( 1 / 5 ) * 1000 = 200 remaining = 1000 - 200 = 800 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 800 = 200 remaining now = 800 - 200 = 600 answer : option d"
Answer: d
Python program:
a = 1000 / 5
b = 1000 - a
c = 1000 / 5
d = 1000 - c
e = d / 4
f = b - e
Problem: a cycle is bought for rs . 1000 and sold for rs . 1080 , find the gain percent ?
Options: a ) 11 , b ) 20 , c ) 12 , d ) 40 , e ) 8
Rationale: "1000 - - - - 80 100 - - - - ? = > 8 % answer : e"
Answer: e
Python program:
a = 1080 - 1000
b = a / 1000
c = b * 100
Problem: a corporation paid $ 7 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 100 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 100 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 114 % , d ) 23 % , e ) 43 %
Rationale: "difference in ratios = ( 30 / 100 ) - ( 7 / 50 ) = ( 8 / 50 ) % change = ( change ( 8 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 114 % answer - c"
Answer: c
Python program:
a = 30 + 7 
b = a / 100
c = 7 / 50
d = b - c
e = 7 / 50
f = d / e
g = f * 100
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 2 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 2 , c ) 12 , d ) 14 , e ) 15
Rationale: - > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 2 ^ 2 - 2 = 2 . thus , the answer is b .
Answer: b
Python program:
a = 2 ** 2
b = a - 2
Problem: the ratio of two quantities is 5 : 8 . if each of the quantities is increased by 10 , what is the ratio of the new quantities ?
Options: a ) 5 : 8 , b ) 50 : 78 , c ) 2 : 3 , d ) it can not be determined from the information given . , e ) 6 : 7
Rationale: since the ratio is 5 : 8 we can put the quantities as 5 k and 8 k . moreover increasing quantities implies that the quantities become 5 k + 10 and 8 k + 10 . so the ratio is ( 5 k + 10 ) : ( 8 k + 10 ) . the ratio value depend on the value of k . so it can not be determined from the information given . the answer is d
Answer: d
Python program:
a = 5 + 10 
b = 8 + 10 
c = a / b
Problem: in the x - y plane , point ( x , y ) is a lattice point if both x and y are integers . a square has a center at ( 0 , 0 ) and side = 4 . some points , such as the center ( 0 , 0 ) , are inside the square , but a point such as ( 0 , 2 ) is on the square but not in the square . how many lattice points are in the square ?
Options: a ) 10 , b ) 9 , c ) 8 , d ) 5 , e ) 12
Rationale: the lattice points that are in the square , that lie on the x and y axes , are ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , ( 0 , - 1 ) , and ( - 1 , 0 ) . the lattice points in the square and not on the x and y axes are ( 1 , 1 ) , ( - 1 , 1 ) , ( 1 , - 1 ) , and ( - 1 , - 1 ) . there are a total of 9 lattice points in the square . answer : b
Answer: b
Python program:
a = 4 * 2
b = a + 1
Problem: a boy is travelling from his home to school at 5 km / hr and reached 5 min late . next day he travelled at 10 km / hr and reached 10 min early . distance between home and school ?
Options: a ) 2.5 km , b ) 3 km , c ) 4 km , d ) 5.6 km , e ) 6.5 km
Rationale: "let the distance be x t 1 = x / 5 hr t 2 = x / 10 hr difference in time = 5 + 10 = 15 = 1 / 4 hr x / 5 - x / 10 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer is a"
Answer: a
Python program:
a = 5 / const_60
b = 10 / const_60
c = a + b 
d = 1 / 10
e = c / d
Problem: a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 168 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 168 / 21 = 8 hours option e"
Answer: e
Python program:
a = 16 + 5 
b = 168 / a
Problem: a cube of side one meter length is cut into small cubes of side 10 cm each . how many such small cubes can be obtained ?
Options: a ) 1898 , b ) 1098 , c ) 1000 , d ) 2008 , e ) 1082
Rationale: along one edge , the number of small cubes that can be cut = 100 / 10 = 10 along each edge 10 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 10 * 10 * 10 = 1000 answer : c
Answer: c
Python program:
a = 10 ** 2
b = a ** 3
c = 10 ** 3
d = b / c
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 62.5 , d ) 82.5 , e ) 65.9
Rationale: "e $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 90 / 100 ) = 59.375 mp = 65.9 e"
Answer: e
Python program:
a = 100 + 25 
b = 47 * 50
c = b / 100
d = 100 - 10
e = c / d
f = e * 100
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 8 rows or 6 rows or 4 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 60 , c ) 24 , d ) 76 , e ) 21
Rationale: "explanation : the least number of trees that are required = lcm ( 8 , 6,4 ) = 24 . answer : c"
Answer: c
Python program:
a = 4 * 6
b = a * 8
c = b / 2
Problem: if the sides of a triangle are 78 cm , 72 cm and 30 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 765 cm 2 , c ) 1080 cm 2 , d ) 197 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 78 cm , 72 cm and 30 cm is right angled , where the hypotenuse is 78 cm . area of the triangle = 1 / 2 * 72 * 30 = 1080 cm 2 answer : c"
Answer: c
Python program:
a = 72 * 30
b = a / 2
Problem: if 60 % of a number is equal to one half of another number , what is the ratio of first number to the second number ?
Options: a ) 4 : 5 , b ) 5 : 6 , c ) 6 : 5 , d ) 5 : 4 , e ) 2 : 5
Rationale: "let 60 % of a = 1 / 2 b . then , 60 a / 100 = 1 b / 2 = > 3 a / 5 = 1 b / 2 a / b = ( 1 / 2 * 5 / 3 ) = 5 / 6 a : b = 5 : 6 . answer : b"
Answer: b
Python program:
a = 1 / 4
b = 60 / 100
c = a / b
Problem: it takes avery 2 hours to build a brick wall while tom can do it in 5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 25 minutes . , b ) 30 minutes . , c ) 40 minutes . , d ) 1 hour and 30 minutes , e ) 1 hour and 20 minutes
Rationale: "avery ' s efficiency is 100 / 2 = 50 % tom ' s = 100 / 5 = 20 % they worked together for 1 hour and finished 70 % of the job remaining = 30 % tom will complete 20 % in 60 minutes , and 10 % in 60 * 10 / 20 minutes = 30 minutes time taken by tom to finish the remaining on his own = 60 + 30 = 90 minutes answer : d"
Answer: d
Python program:
a = 1 / 2
b = 1 / 5
c = a + b 
d = 1 - c
e = 1 / 5
f = d / e
g = f * const_60
Problem: an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 3 / 5 % , then the amount invested at 11 % was ?
Options: a ) 23777 , b ) 30000 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 48 / 5 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 960000 x = 70000 sum invested at 9 % = rs . 70000 sum invested at 11 % = rs . ( 100000 - 70000 ) = rs . 30000 . answer : b"
Answer: b
Python program:
a = 3 / 5
b = 9 + a 
c = b / 100
d = 100000 * c
e = 9 / 100
f = 100000 * e
g = d - f
h = 11 / 100
i = 9 / 100
j = h - i
k = g / j
Problem: find the numbers which are in the ratio 3 : 2 : 2 such that the sum of the first and the second added to the difference of the third and the second is 20 ?
Options: a ) 12 , 8,8 , b ) 4 , 4,22 , c ) 9 , 3,32 , d ) 9 , 6,12 , e ) 9 , 2,23
Rationale: "let the numbers be a , b and c . a : b : c = 3 : 2 : 2 given , ( a + b ) + ( c - b ) = 20 = > a + c = 20 = > 3 x + 2 x = 20 = > x = 4 a , b , c are 3 x , 2 x , 2 x a , b , c are 12 , 8 , 8 . answer : a"
Answer: a
Python program:
a = 4 * 0
b = a / 3
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 170 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 247 , b ) s . 248 , c ) s . 240 , d ) s . 229 , e ) s . 212
Rationale: "given that sp = rs . 170 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 170 ) / 85 = 20 * 6 = rs . 200 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 200 * 120 ) / 100 = rs . 240 answer : c"
Answer: c
Python program:
a = 15 / 100
b = 1 - a
c = 170 / b
d = 15 / 100
e = 1 - d
f = 170 / e
g = 20 / 100
h = f * g
i = c + h
Problem: mary ' s income is 50 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 90 % , e ) 64 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 90 ( 50 percent more than tim ' s income ) . thus , mary ' s income ( 90 ) is 90 % of juan ' s income ( 100 ) . answer : d ."
Answer: d
Python program:
a = 40 / 100
b = 1 - a
c = 50 / 100
d = 1 + c 
e = b * d
f = e * 100
Problem: peter invests a sum of money and gets back an amount of $ 800 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 653 , b ) 664 , c ) 698 , d ) 744 , e ) 700
Rationale: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 800 = 54 interest earned for 3 years = 54 * 3 = 162 amount invested = 815 - 162 = 653 answer : a"
Answer: a
Python program:
a = 854 - 800
b = 4 / 100
c = 3 / 100
d = b - c
e = a / d
f = 3 / 100
g = e * f
h = 800 - g
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 200 resolutions .
Options: a ) 271.34 m , b ) 281.34 m , c ) 291.34 m , d ) 301.34 m , e ) 311.34 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 200 resolutions . = 200 * 2 * 22 / 7 * 22.4 = 28134 cm = 281.34 m answer : b"
Answer: b
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 200
i = h / 100
Problem: what is the value of 3 x ^ 2 − 1.8 x + 0.6 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0.6 , c ) 0.3 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.6 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.6 = 0 + 0.6 = 0.6 answer : b"
Answer: b
Python program:
a = 3 ** 2
b = 1 ** 8
c = a - b
d = c / 1000
e = d / 1000
f = e * 3
g = 3 ** 2
h = 1 ** 8
i = g - h
j = i / 1000
k = j / 1000
l = f - k
Problem: mr . hernandez , who was a resident of state x for only 12 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 4 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 720 , c ) $ 600 , d ) $ 300 , e ) $ 60
Rationale: "total tax for the year = 22,500 x 4 % = 900 as stated annual tax is prorated as per the duration of stay . prorated tax = 900 ( 12 / 12 ) = 900 answer a"
Answer: a
Python program:
a = 4 * 100
b = a * 100
c = 100 * const_0_25
d = c * 100
e = b + d 
f = e / 100
g = f * 4
h = g * 12
i = 3 * 4
j = h / i
Problem: the sum of digits of a two digit number is 12 , the difference between the digits is 6 . find the number
Options: a ) 85 , b ) 93 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 12 , x - y = 6 adding these 2 x = 18 = > x = 9 , y = 3 . thus the number is 93 answer b"
Answer: b
Python program:
a = 12 + 6 
b = a / 2
c = b * 12
d = 12 + 6 
e = d / 2
f = 12 - e
g = c + f
Problem: how many 4 - digit numbers can be formed from the digits 0,2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and if the repetition is not allowed ?
Options: a ) 200 , b ) 240 , c ) 300 , d ) 360 , e ) 120
Rationale: "since , each desired number is divisible by 5 , so we must have either 0 or 5 at the unit place . so , the tens place can now be filled by any of the remaining 6 digits ( 2 , 3 , 6 , 7 , 9 , 0 or 5 ) the hundreds place can now be filled by any of the remaining 5 digits therefore the 3 - digit no can be formed by ( 4 * 5 * 6 * 2 ) = 240 ways ans - b"
Answer: b
Python program:
a = 5 * 4
Problem: if 8 workers can build 8 cars in 8 days , then how many days would it take 7 workers to build 7 cars ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 7 workers can build 7 / 8 car per day . the time required to build 7 cars is 7 / ( 7 / 8 ) = 8 days the answer is c ."
Answer: c
Python program:
a = 8 * 8
b = a / 8
c = 7 / 7
d = b * c
Problem: the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 45 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 450 ft , d ) 900 ft , e ) 1000 ft
Rationale: "point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 45 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 10 . sub x = 10 either in ( x + 5 ) * 30 or in x * 45 to get the distance , which is 450 . so the correct choice is c ."
Answer: c
Python program:
a = 10 / 2
b = 30 * a
c = b / 3
d = 10 / 2
e = c + d 
f = 30 * e
Problem: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1242 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1242 or 9 x = 1242 or x = 138 . required number = 138 . answer : e"
Answer: e
Python program:
a = 43 - 34
b = 1242 / a
Problem: in an election , candidate a got 85 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 340000 , c ) 347000 , d ) 356000 , e ) 404600
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 85 % therefore , the number of valid votes polled in favour of candidate a = 85 % of 476000 = 85 / 100 × 476000 = 40460000 / 100 = 404600 e )"
Answer: e
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 85 / 100
e = c * d
Problem: find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 306.09 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01
Rationale: "a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"
Answer: c
Python program:
a = 4 / 100
b = 1 + a 
c = 3 / 2
d = b ** c
e = 5000 * d
f = e - 5000
Problem: a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price . if the retailer decreases the retail price by 20 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 26 , b ) 37.5 , c ) 42 , d ) 44 , e ) 50
Rationale: "answer : d = 44 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 80 % increase makes retail price = 180 . now 20 % decrease - > ( 1 - 20 / 100 ) * 180 = 144 . now compared to the wholesale price of 100 , 44 % increase is what will have the same effect as increasing the wholesale price ."
Answer: d
Python program:
a = 80 / 100
b = 1 + a 
c = 20 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: the slant height of a cone is 22 cm and radius of the base is 7 cm , find the curved surface of the cone ?
Options: a ) 426 , b ) 284 , c ) 483 , d ) 256 , e ) 428
Rationale: "π * 22 * 7 = 483 answer : c"
Answer: c
Python program:
a = math.pi * 7
b = a * 22
Problem: one night 40 percent of the female officers on a police force were on duty . if 240 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 300 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 240 number of female officers on duty on that night = 240 / 2 = 120 ( 40 / 100 ) * f = 120 = > f = 300 answer b"
Answer: b
Python program:
a = 240 / 2
b = 40 / 100
c = a / b
Problem: there are 4 red shoes & 6 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 2 , d ) 2 / 15 , e ) 2 / 16
Rationale: "taking 4 red shoe the probablity is 4 c 2 from 10 shoes probablity of taking 2 red shoe is 4 c 2 / 10 c 2 = 2 / 15 answer : d"
Answer: d
Python program:
a = math.comb(4, 2)
b = 4 + 6 
c = math.comb(b, 2)
d = a / c
Problem: how much water should be added to 14 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 27 liters , c ) 26 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 14 + x ) ) ) 2 = 5 % * ( 14 + x ) - - - - - - - - > x = 26 ans c"
Answer: c
Python program:
a = 2 * 100
b = 75 / 100
c = b * 20
d = 20 - c
e = a / d
f = e - 14
Problem: a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 8 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 25
Rationale: on the way down , the rate is 1.5 * 8 = 12 miles per day . the distance of the route down the mountain is 2 * 12 = 24 miles . the answer is d .
Answer: d
Python program:
a = 8 * 2
b = 3 / 2
c = a * b
Problem: what is the 20 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 2 nd , 4 th , 6 th , . . . ) to the right of the decimal point is alternating by 2 , 0 , 7 thus 20 th digit is 2 . answer : b ."
Answer: b
Python program:
a = 1 / 37
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6.6 . the true discount is
Options: a ) rs . 72 , b ) rs . 36 , c ) rs . 55 , d ) rs . 50 , e ) none
Rationale: solution t . d = [ b . g x 100 / r x t ] = rs . ( 6.6 x 100 / 12 x 1 ) = rs . 55 . answer c
Answer: c
Python program:
a = 12 / 100
b = 6 / 6
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 92 . find the number of students who wrote the exam .
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 55
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 92 ( x - 5 ) 80 x - ( 5 * 20 ) = 92 ( x - 5 ) 360 = 12 x = > x = 30 answer : c"
Answer: c
Python program:
a = 92 * 5
b = 5 * 20
c = a - b
d = 92 - 80
e = c / d
Problem: if x is to be chosen at random from the integers between 1 to 6 , inclusive , and y is to be chosen at random from the integers between 7 and 10 , inclusive , what is the probability that x + y will be even ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 6 * 2 / 4 = 1 / 4 p ( x and y are both odd ) = 3 / 6 * 2 / 4 = 1 / 4 p ( x + y is even ) = 1 / 4 + 1 / 4 = 1 / 2 the answer is a ."
Answer: a
Python program:
a = 2 * 2
b = 3 * 2
c = a + b 
d = 6 - 1
e = 6 * d
f = c / e
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 7.5 $ then total value is 300 * 7.5 = 2250 . answer : option e is correct answer . ."
Answer: e
Python program:
a = 3 * 100
b = 8 * 10
c = a + b 
d = c + 4 
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 7
j = i / 1000
Problem: a bowl was filled with 10 ounces of water , and 0.08 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 40 % , d ) 4 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 08 * 50 = . 08 * 100 / 2 = 8 / 2 = 4 percent of the original amount of water evaporated during this period = ( 4 / 10 ) * 100 % = 40 % answer c"
Answer: c
Python program:
a = 50 * 0
b = a / 10
c = b * 100
Problem: machine a and machine b are each used to manufacture 440 sprockets . it takes machine a 10 hours longer to produce 440 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 2
Rationale: "machine b : takes x hours to produce 440 sprockets machine a : takes ( x + 10 ) hours to produce 440 sprockets machine b : in 1 hour , b makes 440 / x sprockets machine a : in 1 hour , a makes 440 / ( x + 10 ) sprockets equating : 1.1 ( 440 / ( x + 10 ) ) = 440 / x 484 / ( x + 10 ) = 440 / x 484 x = 440 x + 4400 44 x = 4400 x = 100 a makes 440 / ( 110 ) = 4 sprockets per hour answer : c"
Answer: c
Python program:
a = 10 * 440
b = 100 + 10 
c = b / 100
d = a * c
e = 100 + 10 
f = e / 100
g = 440 * f
h = g - 440
i = d / h
j = 440 / i
Problem: two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 42 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 72 sec , b ) 132 sec , c ) 192 sec , d ) 252 sec , e ) none
Rationale: "solution relative speed = ( 42 - 40 ) kmph = 2 kmph = ( 2 x 5 / 18 ) m / sec = ( 10 / 18 ) m / sec time taken = ( 350 x 18 / 10 ) sec = 630 sec . answer e"
Answer: e
Python program:
a = 200 + 150 
b = a / 1000
c = 42 - 40
d = b / c
e = 3600 * d