euclaise/mathqa_programs huggingface dataset:
Problem: a certain roller coaster has 7 cars , and a passenger is equally likely to ride in any 1 of the 7 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 7 times , what is the probability that the passenger will ride in each of the 7 cars ?
Options: a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 720 / 16807 , e ) 1
Rationale: "if he is to ride 6 times and since he can choose any of the 6 cars each time , total number of ways is = 7 * 7 * 7 * 7 * 7 * 7 = 117649 now the number of ways if he is to choose a different car each time is = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 so the probability is = 5040 / 117649 = 720 / 16807 answer : d"
Answer: d
Python program:
a = math.factorial(7)
b = 1 / 7
c = b ** 7
d = a * c
Problem: what is the greatest of 3 consecutive integers whose sum is 18 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: "the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 18 ; = > 3 n = 15 ; = > n = 5 the greatest of the three numbers is therefore 5 + 2 = 7 answer : b"
Answer: b
Python program:
a = 18 - 3
b = a / 3
c = b + 2
Problem: a man can row his boat with the stream at 16 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 3 kmph , c ) 6 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 16 us = 4 s = ? s = ( 16 - 4 ) / 2 = 6 kmph answer : c"
Answer: c
Python program:
a = 16 - 4
b = a / 2
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 6.0 . 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 ) $ 1,800
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 6 $ then total value is 300 * 6.0 = 1800 . imo 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 * 6
j = i / 1000
Problem: a certain quantity of 45 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 45 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 45 ml and 25 ml is 20 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 20 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 10 % . therefore , 10 out of 20 is 1 / 2 and c is the answer ."
Answer: c
Python program:
a = 35 - 25
b = 45 - 35
c = a / b
d = c + 1 
e = 1/(d)
Problem: there are 16 bees in the hive , then 8 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 12 , d ) 24 , e ) 25
Rationale: 16 + 8 = 24 . answer is d .
Answer: d
Python program:
a = 16 + 8
Problem: let raj be 3 years older than ravi and hema be two years younger than ravi . raj is 3 times as old as rahul who is hema ’ s brother . the ratio of the ages of hema and her brother is 3 : 2 . find by how much percentage raj ’ s age is more than hema ’ s when raj will be 20 years old .
Options: a ) 33.33 , b ) 27.33 , c ) 28.38 , d ) 29.37 , e ) 28.31
Rationale: answer : 33.33
Answer: a
Python program:
a = 3 + 2 
b = 3 + 2 
c = 3 / 2
d = 3 - c
e = b / d
f = 3 * e
g = 3 + 2 
h = f - g
i = 3 + 2 
j = 3 / 2
k = 3 - j
l = i / k
m = 3 * l
n = 20 - m
o = h + n 
p = a / o
q = p * 100
Problem: the salaries of a and b together amount to $ 6000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 4500 , e ) $ 5200
Rationale: "let a ' s salary is x b ' s salary = 6000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 6000 - x ) x = $ 4500 answer is d"
Answer: d
Python program:
a = 100 - 85
b = 100 - 95
c = a / b
d = c + 1 
e = 6000 / d
f = 6000 - e
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 50 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 70
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 50 . thus , 3434 ( 90 + x ) = 50 + x or 270 + 3 x = 200 + 4 x or x = 70 answer : e"
Answer: e
Python program:
a = 90 - 50
b = 12 - 9
c = a / b
d = c * 12
e = d - 90
Problem: the diagonal of a rectangle is cm and its area is 20 sq . cm . the perimeter of the rectangle must be :
Options: a ) 18
b ) 77
c ) 625
d ) 276
e ) 191
Rationale: explanation : ( or ) { \ color { black } l ^ { 2 } + b ^ { 2 } = 41 } also , { \ color { black } ( l + b ) ^ { 2 } = l ^ { 2 } + b ^ { 2 } + 2 lb } = 41 + 40 = 81 ( l + b ) = 9 . perimeter = 2 ( l + b ) = 18 cm . answer : a ) 18
Answer: a
Python program:
a = 20 + 20 
b = 20 + 20 
c = b + 1 
d = a + c 
e = math.sqrt(d)
f = 2 * e
Problem: an empty fuel tank with a capacity of 214 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 106
Rationale: say there are a gallons of fuel a in the tank , then there would be 214 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 214 - a gallons of fuel b is 0.16 ( 214 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 214 - a ) = 30 - - > a = 106 . answer : e .
Answer: e
Python program:
a = 16 / 100
b = 214 * a
c = b - 30
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
Problem: if 27.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 638 , b ) 330 , c ) 550 , d ) 430 , e ) 880
Rationale: "students enrolled in biology are 27.5 % and therefore not enrolled are 72.5 % . so of 880 is 880 * . 225 = 638 answer is a 638"
Answer: a
Python program:
a = 880 / 100
b = 100 - 27
c = a * b
Problem: the ratio of local and international calls made by amy this week is 5 to 2 . if the ratio changes to 5 to 3 after amy makes 3 more international calls , how many local calls did amy make this week ?
Options: a ) 3 , b ) 5 , c ) 10 , d ) 15 , e ) 21
Rationale: the ratio of local and international calls made by amy this week is 5 to 2 let the current ratio be 5 x / 2 x the ratio changes to 5 to 3 after amy makes three more international calls 5 x / ( 2 x + 3 ) = 5 / 3 solving we get x = 3 initial ratio 15 : 6 ( 5 : 2 ) final ratio 15 : ( 6 + 3 ) = 15 : 9 = 5 : 3 so total number of local calls = 15 answer : d
Answer: d
Python program:
a = 3 - 2
b = 3 / a
c = b * 5
Problem: on a sum of money , the simple interest for 2 years is rs . 660 , while the compound interest is rs . 696.30 , the rate of interest being the same in both the cases . the rate of interest is :
Options: a ) 10 % , b ) 10.5 % , c ) 12 % , d ) none of these , e ) can not be determined
Rationale: "solution difference in c . i . and s . i . for 2 years = rs . ( 696.30 - 660 ) = rs . 36.30 . s . i . for one year = rs . 330 . ∴ s . i . on rs . 330 for 1 year = rs . 36.30 . ∴ rate ( 100 x 36.30 / 330 x 1 ) % = 11 % . answer d"
Answer: d
Python program:
a = 660 / 2
b = 696 - 30
c = 660 / 2
d = b - c
e = 100 * d
f = 660 / 2
g = e / f
Problem: what is the ratio between perimeters of two squares one having 4 times the diagonal then the other ?
Options: a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 4 : 1 , e ) 3 : 3
Rationale: "d = 4 d d = d a √ 2 = 4 d a √ 2 = d a = 4 d / √ 2 a = d / √ 2 = > 4 : 1 answer : d"
Answer: d
Python program:
a = 4 / 4
b = 4 / a
Problem: what is the distance covered by a train if it travels with a speed of 150 kmh for 8 hours ?
Options: a ) 1000 km , b ) 700 km , c ) 800 km , d ) 1400 km , e ) 1200 km
Rationale: "distance = time x speed distance = 150 x 8 = 1200 answer : e"
Answer: e
Python program:
a = 150 * 8
Problem: following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 12 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 . , c ) 16 . , d ) 14 . , e ) 14.5
Rationale: "price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 12 / 1.5 = 8 total price = 8 + 8 = 16 c is the answer"
Answer: c
Python program:
a = 10 * 100
b = 100 + 25 
c = a / b
d = 12 * 100
e = 100 + 50 
f = d / e
g = c + f
Problem: of the 120 passengers on flight 750 , 55 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 44 , b ) 48 , c ) 50 , d ) 52 , e ) 58
Rationale: number of passengers on flight = 120 number of female passengers = . 5 * 120 = 66 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 66 - 8 = 58 answer e
Answer: e
Python program:
a = 55 / 100
b = 120 * a
c = 10 / 100
d = 120 * c
e = 10 / 100
f = 120 * e
g = f / 3
h = d - g
i = b - h
Problem: if x ^ 2 + 1 / x ^ 2 = 9 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 72 , c ) 79 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = 9 andsquareboth sides : ( x ² + 1 / x ² ) ² = 81 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 81 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 81 simplify : x ⁴ + 1 / x ⁴ = 79 answer : c"
Answer: c
Python program:
a = 2 ** 2
b = a - 2
Problem: a certain no . when divided by 65 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 65 + 25 = 90 / 15 = 6 ( remainder ) c"
Answer: c
Python program:
a = 65 - 25
b = a - 4
c = b - 2
Problem: a , b and c started a partnership business by investing rs . 24000 , rs . 32000 , rs . 36000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 80000 , d ) 92000 , e ) 50000
Rationale: "a : b : c = 24000 : 32000 : 36000 = 6 : 8 : 9 let total profit = p then p ã — 9 / 23 = 36000 p = ( 36000 ã — 23 ) / 9 = 92000 answer is d ."
Answer: d
Python program:
a = 24000 / 36000
b = a * 36000
c = 32000 / 36000
d = c * 36000
e = b + d 
f = e + 36000
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 60 / kg . how much did a kg of coffee cost in june ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 60 = > x = 60 e"
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 20 / 100
d = c + 1 
e = b * d
f = 60 / e
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 300 meters . they next meet after sally has run 150 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 700 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 300 meters , thus second time she runs 2 * 300 = 600 meters . since second time ( when they run full circumference ) brenda runs 600 meters and sally runs 150 meters , thus the circumference is 600 + 150 = 750 meters . answer : d ."
Answer: d
Python program:
a = 2 * 300
b = a + 150
Problem: a person travels equal distances with speeds of 8 km / hr , 9 km / hr and 10 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 6 km , b ) 3 km , c ) 7 km , d ) 5 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 8 + x / 9 + x / 10 = 47 / 60 x / 3 = 47 / 60 = > x = 2.33 . total distance = 3 * 2.33 = 6.99 km . answer : c"
Answer: c
Python program:
a = 47 / const_60
b = 1 / 8
c = 1 / 9
d = b + c 
e = 1 / 10
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 127.05 , what is value of j ?
Options: a ) 300 , b ) 320 , c ) 370 , d ) 400 , e ) 450
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 127.05 here 127 is the quotient . given that remainder = 16 so , 127.05 = 127 + 16 / j so , j = 320 answer : b"
Answer: b
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 127 - 5
e = 16 / d
Problem: the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 5 years will be
Options: a ) 22 : 17 , b ) 9 : 11 , c ) 5 : 4 , d ) 4 : 5 , e ) 8 : 11
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 5 ) : ( 12 + 5 ) = 22 : 17 answer : a"
Answer: a
Python program:
a = 4 + 3 
b = 28 / a
c = 4 * b
d = c + 5 
e = 4 + 3 
f = 28 / e
g = 3 * f
h = g + 5 
i = d / h
Problem: there is an antique clock exhibition . so many clock are piled up with distinct numbers tagged with them . the person managing it hangs different clocks numbers periodically on the main wall . at 9 : 20 am , he hung the clock number 200 ; at 11 : 00 am , he hung the clock number 30 ; at 4 : 00 pm , he hung the clock number 240 . which numbered clock will he hang on the wall when the time is 7 : 30 pm ?
Options: a ) 313 , b ) 314 , c ) 315 , d ) 316 , e ) 317
Rationale: solution : he will hang clock number 315 at 7 : 30 pm . the person has been hanging the clock number which corresponds with the angle between the hour hand and the minute hand of the clock at that time . answer c
Answer: c
Python program:
a = 12 * 10
b = a * 3
c = 7 * 30
d = 4 + 1 
e = 30 / d
f = 12 * 10
g = f * 3
h = g / 12
i = e * h
j = c - i
k = b - j
Problem: the mean of 30 values was 150 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 148 , e ) none of the above
Rationale: "corrected mean = 150 × 30 − 135 + 165 / 30 = 4500 − 135 + 165 / 30 = 4530 / 30 = 151 answer a"
Answer: a
Python program:
a = 30 * 150
b = 165 - 135
c = a + b 
d = c / 30
Problem: machine a and machine b are each used to manufacture 550 sprockets . it takes machine a 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 5.5 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 550 qt = 500 for a : ( t + 10 ) ( q ) = 550 qt + 10 q = 550 500 + 10 q = 550 q = 5 so a can produce 5 / hour . then b can produce = 5 ( 1.1 ) = 5.5 / hour . a"
Answer: a
Python program:
a = 10 * 550
b = 100 + 10 
c = b / 100
d = a * c
e = 100 + 10 
f = e / 100
g = 550 * f
h = g - 550
i = d / h
j = 550 / i
Problem: a batch of cookies was divided amomg 4 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 5 / 8
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 4 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 4 ) = 5 / 12 x = 5 / 8 answer : e"
Answer: e
Python program:
a = 2 / 3
b = 1 - a
c = 2 / 3
d = 1 / 4
e = c - d
f = b + e
Problem: there are , in a certain league , 8 teams , and each team face another team for a total of 12 times . how many games are played in the season ?
Options: a ) 150 , b ) 121 , c ) 144 , d ) 180 , e ) 1200
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 144 option c ."
Answer: c
Python program:
a = 8 - 1
b = a * 12
c = 8 / 2
d = b * c
Problem: a man spends rs . 1700 per month on an average for the first 3 months , rs 1550 for next 4 months and rs . 1800 per month for the last 5 months and saves rs . 5200 a year . what is his average monthly income ?
Options: a ) 2025 , b ) 2125 , c ) 2225 , d ) 2325 , e ) 2425
Rationale: explanation : total expenditure for the first 3 months = 3 ã — 1700 = 5100 total expenditure for 4 months = 4 ã — 1550 = 6200 total expenditure for 5 months = 5 ã — 1800 = 9000 total expenditure and saving ( which is income for one year ) = 5100 + 6200 + 9000 + 5200 = rs . 25500 so , average monthly income = 25500 / 12 = rs . 2125 answer b
Answer: b
Python program:
a = 1700 * 3
b = 1550 * 4
c = a + b 
d = 1800 * 5
e = c + d 
f = e + 5200 
g = f / 12
Problem: 25 x 10 + 25 x 11 = ?
Options: a ) 725 , b ) 720 , c ) 600 , d ) 525 , e ) none of them
Rationale: "= 25 x ( 10 + 11 ) ( by distributive law ) = 25 x 21 = 525 answer is d"
Answer: d
Python program:
a = 10 ** 25
b = 25 * a
Problem: the average of 25 results is 45 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 740 , b ) 750 , c ) 690 , d ) 780 , e ) 708
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 45 or , x = 708 . answer : option e"
Answer: e
Python program:
a = 25 * 45
b = 12 * 17
c = a - b
d = 12 * 14
e = c - d
Problem: the sale price sarees listed for rs . 400 after successive discount is 20 % and 15 % is ?
Options: a ) 297 , b ) 272 , c ) 342 , d ) 762 , e ) 269
Rationale: "400 * ( 80 / 100 ) * ( 85 / 100 ) = 272 answer : b"
Answer: b
Python program:
a = 400 * 20
b = a / 100
c = 400 - b
d = 400 * 20
e = d / 100
f = 400 - e
g = f * 15
h = g / 100
i = c - h
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability q that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: the required probability q = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer .
Answer: d
Python program:
a = 3 * 5
b = 3 + 5 
c = 5 + 2 
d = b * c
e = d / 2
f = a / e
Problem: in what proportion must rice at rs 3.10 per kg be mixed with rice at rs 3.60 per kg , so that the mixture be worth rs 3.25 a kg ?
Options: a ) 3 / 5 , b ) 3 / 2 , c ) 5 / 3 , d ) 5 / 7 , e ) 7 / 3
Rationale: "c . p of 1 kg of cheaper rice = rs 3.10 c . p of 1 kg of expensive rice = rs 3.60 the mixture be worth for 1 kg = rs 3.25 by the alligation rule : quantity of cheaper rice / quantity of expensive rice = ( 3.6 - 3.25 ) / ( 3.25 - 3.10 ) = ( 0.35 ) / ( 0.15 ) = 7 / 3 e"
Answer: e
Python program:
a = 3 - 60
b = 3 - 25
c = a / b
Problem: of the families in city x in 1994 , 40 percent owned a personal computer . the number of families in city x owning a computer in 1998 was 30 percent greater than it was in 1994 , and the total number of families in city x was 4 percent greater in 1998 than it was in 1994 . what percent of the families in city x owned a personal computer in 1998 ?
Options: a ) 50 % , b ) 52 % , c ) 56 % , d ) 70 % , e ) 74 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40 number of families owning computer in 1998 = 40 * 130 / 100 = 52 number of families in 1998 = 104 the percentage = 52 / 104 * 100 = 50 % . answer : a"
Answer: a
Python program:
a = 30 + 100 
b = a * 40
c = b / 100
d = 100 + 4 
e = c / d
f = 100 * e
Problem: one - third less than 35 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 35 , d ) 42 , e ) 45
Rationale: lots of ways to tackle this . 35 % of 180 = 63 1 / 3 of 63 = 21 so , 1 / 3 less than 63 is equal to 63 - 21 = 42 answer : d
Answer: d
Python program:
a = 35 / 100
b = a * 180
c = 1 / 3
d = 35 / 100
e = d * 180
f = c * e
g = b - f
Problem: country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 420 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 214 million , b ) $ 1120 million , c ) $ 1144 million , d ) $ 1240 million , e ) $ 1080 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 420 mill / 2 month i . e . $ 210 mill / month difference / month = 210 - 120 = 90 difference / year = $ 90 mill * 12 = $ 1080 mill answer : e"
Answer: e
Python program:
a = 12 / 2
b = 420 * a
c = 1 * 44
d = b - c
Problem: a company produces 65000 bottles of water everyday . if a case can hold 13 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 13 number of cases required to hold 65000 bottles = 65000 / 13 = 5000 cases . so the answer is c = 5000"
Answer: c
Python program:
a = 65000 / 13
Problem: what will be the fraction of 5 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 5 * 1 / 100 = 1 / 20 . option a"
Answer: a
Python program:
a = 5 / 2
b = circle_area / (
Problem: operation # is defined as adding a randomly selected two digit multiple of 4 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 4 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Python program:
a = 10 + 3 
b = 4 + a 
c = b / 2