euclaise/mathqa_programs huggingface dataset:
Problem: for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 902 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "we know that : x > 1 , y > 1 , and x + 3 y < 902 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest no all factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 1000 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 902 so , 3 y < 390 = = > y < 130 so , y can take any value which is less than 130 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . e"
Answer: e
Python program:
a = 4 + 3 
b = 4 + 4 
c = b + 1 
d = a + c
Problem: alice is now 10 years older than bob . if in 6 years alice will be twice as old as bob , how old will alice be in 5 years ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: a = b + 10 so b = a - 10 . a + 6 = 2 ( b + 6 ) . a + 6 = 2 ( a - 10 + 6 ) . a + 6 = 2 a - 8 . a = 14 . in 5 years , alice will be 19 years old . the answer is a .
Answer: a
Python program:
a = 10 * 2
b = a + 5 
c = b - 6
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 2,800 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 8,400 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 30 % , b ) 35 % , c ) 25 % , d ) 40 % , e ) 50 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 2800 : 8400 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : c"
Answer: c
Python program:
a = 2 * 800
b = 2 * 1000
c = b + 100 
d = c + 2 
e = a / d
Problem: thabo owns exactly 180 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 180 3 x + 60 + x = 180 x = 30 answer ( c . )"
Answer: c
Python program:
a = 180 + 20 
b = a / 4
c = b - 20
Problem: a school has 7 maths 6 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: total subjects = 7 + 6 + 5 = 18 max subjects by 1 teacher = 3 so , min of teachers required = 18 / 3 = 6 answer : c
Answer: c
Python program:
a = 7 + 6 
b = a + 5 
c = b / 3
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 10 per sq m ?
Options: a ) 6350 , b ) 7357 , c ) 6328 , d ) 6750 , e ) 7560
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 10 = rs . 6750 answer : d"
Answer: d
Python program:
a = 2 * 5
b = 75 + a 
c = 2 * 5
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.36 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.48 , d ) 44 , e ) 48
Rationale: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 36 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 36 = 48 cents . answer : e ."
Answer: e
Python program:
a = 1 / 2
b = 8 / a
c = b / 12
d = 0 * 36
e = c * d
Problem: at a certain high school , the senior class is twice the size of the junior class . if 3 / 8 of the seniors and 1 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 4
Rationale: "start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 3 / 8 ) * 200 = 75 and ( 1 / 4 ) * 100 = 25 . 75 + 25 = 100 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 100 total students in japanese , so 100 students in japanese / 300 total students equals 1 / 3 of the students in both classes that study japanese . answer : d"
Answer: d
Python program:
a = 8 + 4 
b = 4 / a
Problem: in a school with 604 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 150 , b ) 151 , c ) 250 , d ) 350 , e ) none
Rationale: "sol . let the number of grils be x . then , number of boys = ( 600 - x ) . then , ( 11 3 / 4 × 604 ) ⇔ 11 x + 12 ( 604 - x ) ⇔ x = 7248 - 7097 ⇔ 151 . answer b"
Answer: b
Python program:
a = 12 * 604
b = 9 / 12
c = 11 + b 
d = c * 604
e = a - d
Problem: when the price of an article was reduced by 20 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 44 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 20 % , the new price is 0.8 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.8 p ) ( 1.8 n ) = 1.44 np , which is 1.44 times the old revenue , so is 44 % greater . answer : a"
Answer: a
Python program:
a = 80 + 100 
b = 100 - 20
c = a * b
d = c / 100
e = d - 100
Problem: a 110 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 35 , b ) 20 , c ) 47 , d ) 36 , e ) 31
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 110 = 31 answer : e"
Answer: e
Python program:
a = 2 / 5
b = a + 1 
c = 110 / b
d = 110 - c
Problem: sachin is younger than rahul by 8 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 24.5 , c ) 26 , d ) 27 , e ) 28
Rationale: "if rahul age is x , then sachin age is x - 8 , so ( x - 8 ) / x = 7 / 9 = > 9 x - 72 = 7 x = > 2 x = 72 = > x = 36 so sachin age is 36 - 8 = 28 answer : e"
Answer: e
Python program:
a = 9 - 7
b = 8 / a
c = b * 7
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length
Options: a ) 12 , b ) 12.1 , c ) 13 , d ) 14 , e ) 15
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 20 = 12.1 sec . answer : option b"
Answer: b
Python program:
a = 110 + 132 
b = 72 * const_0_2778
c = a / b
Problem: a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 25 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 44 % , b ) 40 % , c ) 50 % , d ) 56.25 % , e ) 36.25 %
Rationale: "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 25 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.25 . so his profit is $ 6.25 - $ 4 = $ 2.25 and his profit percent is ( 2.25 / 4 ) * 100 = 56.25 % answer : - d"
Answer: d
Python program:
a = 100 + 25 
b = 100 - 20
c = a / b
d = c - 1
e = d * 100
Problem: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 90 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: ( 110 mph + 90 mph ) / 2 = 100 mph correct answer is : d
Answer: d
Python program:
a = 110 + 90 
b = a / 2
Problem: in 30 years , a will be twice as old as b was 30 years ago . if a is now 5 years older than b , the present age of b is ?
Options: a ) 85 yrs , b ) 95 yrs , c ) 93 yrs , d ) 82 yrs , e ) 90 yrs
Rationale: "let b ' s present age = x years then a ' s present age = x + 5 years x + 5 + 30 = 2 ( x - 30 ) x + 35 = 2 x - 60 x = 95 years answer is b"
Answer: b
Python program:
a = 2 * 30
b = a + 30 
c = b + 5
Problem: a jogger running at 9 kmph along side a railway track is 280 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 40 sec , c ) 36 sec , d ) 72 sec , e ) none of these
Rationale: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 280 + 120 ) m = 400 m . ∴ time taken = ( 400 ⁄ 10 ) sec = 40 sec . answer b"
Answer: b
Python program:
a = 280 + 120 
b = a / 1000
c = 45 - 9
d = b / c
e = d * const_60
f = e * const_60
Problem: an escalator moves towards the top level at the rate of 7 ft . sec and its length is 180 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 5 sec , b ) 25 sec , c ) 20 sec , d ) 15 sec , e ) 10 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 180 / ( 7 + 2 ) = 20 sec answer : c"
Answer: c
Python program:
a = 7 + 2 
b = 180 / a
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1000 resolutions ?
Options: a ) 1077 m , b ) 804 m , c ) 978 m , d ) 1048 m , e ) 878 v
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1000 resolutions . = 1000 * 2 * 22 / 7 * 22.4 = 104800 cm = 1408 m answer : d"
Answer: d
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 * 1000
i = h / 100
Problem: a garrison of 2000 men has provisions for 60 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1500 , b ) 1893 , c ) 1979 , d ) 1900 , e ) 1278
Rationale: "2000 - - - - 60 2000 - - - - 45 x - - - - - 20 x * 20 = 2000 * 45 x = 4500 2000 - - - - - - - 1500 answer : a"
Answer: a
Python program:
a = 2000 * 60
b = 2000 * 15
c = a - b
d = c / 20
e = d - 2000
Problem: anil grows tomatoes in his backyard which is in the shape of a square . each tomato takes 1 cm 2 in his backyard . this year , he has been able to grow 131 more tomatoes than last year . the shape of the backyard remained a square . how many tomatoes did anil produce this year ?
Options: a ) 4225
b ) 4096
c ) 4356
d ) insufficient data
e ) none of these
Rationale: detailed solution let the area of backyard be x 2 this year and y 2 last year ∴ x 2 - y 2 = 131 = ) ( x + y ) ( x - y ) = 131 now , 131 is a prime number ( a unique one too . check out its properties on google ) . also , always identify the prime number given in a question . might be helpful in cracking the solution . = ) ( x + y ) ( x - y ) = 131 x 1 = ) x + y = 131 x - y = 1 = ) 2 x = 132 = ) x = 66 and y = 65 ∴ number of tomatoes produced this year = 662 = 4356 correct choice ( c )
Answer: c
Python program:
a = 131 + 1 
b = a / 2
c = b ** 2
Problem: when asked what the time is , a person answered that the amount of time left is 1 / 5 of the time already completed . what is the time .
Options: a ) 2 , b ) 9 , c ) 3 , d ) 8 , e ) 6
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 15 x ⇒ x = 2024 − x = 15 x ⇒ x = 20 time is 8 pm answer : d"
Answer: d
Python program:
a = 1 * 12
b = 1 * 12
c = 1 / 5
d = c + 1 
e = b / d
f = a - e
Problem: a sum of money at simple interest amounts to rs . 1717 in 1 year and to rs . 1734 in 2 years . the sum is :
Options: a ) rs . 1200 , b ) rs . 1690 , c ) rs . 1600 , d ) rs . 1700 , e ) rs . 1500
Rationale: "s . i . for 1 year = rs . ( 1734 - 1717 ) = rs . 17 . principal = rs . ( 1717 - 17 ) = rs . 1700 . answer : option d"
Answer: d
Python program:
a = 1734 - 1717
b = a * 1
c = b / 2
d = 1717 - c
Problem: if remainder is 8 , quotient is 43 and dividend is 997 then what is divisor ?
Options: a ) 21 , b ) 20 , c ) 23 , d ) 27 , e ) 31
Rationale: we know dividend = divisor * quotient + remainder = = = > 997 = divisor * 43 + 8 = = = = = > 989 / 43 = divisor = = = > divisor = 23 ans - c
Answer: c
Python program:
a = 997 - 8
b = a / 43
Problem: victor gets 80 % marks in examinations . if these are 240 marks , find the maximum marks .
Options: a ) 334 , b ) 300 , c ) 376 , d ) 288 , e ) 271
Rationale: "let the maximum marks be m then 80 % of m = 240 ⇒ 80 / 100 × m = 240 ⇒ m = ( 240 × 100 ) / 80 ⇒ m = 24000 / 80 ⇒ m = 300 therefore , maximum marks in the examinations are 300 answer : b"
Answer: b
Python program:
a = 80 / 100
b = 240 / a
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 10800 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 105.00 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 10800 ⇔ 12 x 2 = 10800 ⇔ x 2 = 900 ⇔ x = 30 . so , length = 90 m and breadth = 120 m . perimeter = [ 2 ( 90 + 120 ) ] m = 420 m . ∴ cost of fencing = rs . ( 0.25 × 420 ) = rs . 105.00 . answer d"
Answer: d
Python program:
a = 3 * 4
b = 10800 / a
c = math.sqrt(b)
d = 3 * c
e = 3 * 4
f = 10800 / e
g = math.sqrt(f)
h = 4 * g
i = rectangle_perimeter * (
j = i / 25
Problem: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 60 , what is the greatest possible value of q minus r ?
Options: a ) 52 , b ) 54 , c ) 55 , d ) 56 , e ) 58
Rationale: "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 60 . the greatest multiple of 9 which is less than 60 is 54 . the answer is b ."
Answer: b
Python program:
a = 10 - 1
b = reminder * (
Problem: there were 35 students in a hostel . due to the admission of 7 new students the expenses of the mess were increased by rs . 84 per day while the average expenditure per head diminished by re 1 . what was the original expenditure of the mess ?
Options: a ) rs 450 , b ) rs 920 , c ) rs 550 , d ) rs . 630 , e ) none of these
Rationale: explanation : let the original average expenditure be rs . x then , 42 ( x - 1 ) - 35 x = 84 ? 7 x = 126 ? x = 18 therefore original expenditure = rs . ( 35 18 ) = rs . 630 . answer : d
Answer: d
Python program:
a = 35 + 7 
b = 84 + a 
c = b / 7
d = c * 35
Problem: 27 is a perfect cube . when x is added to the prime factor of 27 , the result is also a perfect cube . what is x ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: "27 is 3 * 3 * 3 a 3 + 1 = 4 , 4 = 2 * 2 b 3 + 3 = 6 , 6 = 2 * 3 c 3 + 5 = 8 , 8 = 2 * 2 * 2 d 3 + 7 = 10 , 10 = 2 * 5 e 3 + 11 = 14 , 14 = 2 * 7 c is the only addition that gives a perfect cube ."
Answer: c
Python program:
a = 27 - 3
b = a / 3
Problem: a 480 m long train is running at a speed of 55 km / hr . it crossed a platform of length 620 m in ?
Options: a ) 41.1 sec , b ) 72 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 480 m + 620 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 1100 m time = distance / speed = 1100 x 18 / ( 5 x 55 ) = 72 sec ans is : b"
Answer: b
Python program:
a = 480 + 620 
b = 55 * const_0_2778
c = a / b
Problem: if the sum and difference of two numbers are 15 and 10 respectively , then the difference of their square is :
Options: a ) 12 , b ) 150 , c ) 160 , d ) 180 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 15 and x - y = 10 x 2 - y 2 = ( x + y ) ( x - y ) = 15 * 10 = 150 . answer : b"
Answer: b
Python program:
a = 15 + 10 
b = a / 2
c = b ** 2
d = 15 + 10 
e = d / 2
f = 15 - e
g = f ** 2
h = c - g
Problem: a batsman scored 100 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 40 % , c ) 45 ( 5 / 11 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 100 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 100 - 60 = 40 required % = ( 40 / 100 ) × 100 = 40 % answer : option b"
Answer: b
Python program:
a = 3 * 8
b = 8 * 3
c = a + b 
d = 100 - c
e = d / 100
f = e * 100
Problem: a shopkeeper sold an article at $ 100 with 45 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 72 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 145 = $ 69 ( approximately ) answer is e"
Answer: e
Python program:
a = 100 + 45 
b = 100 / a
c = 100 * b
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . two hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 3 miles per hour and walt ' s 4 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "in the first 2 hours lionel at the rate of 3 miles per hour covered distance = rate * time = 3 * 2 = 6 miles . so , the distance between him and walt was 48 - 6 = 42 miles when walt left his house . now , their combined rate to cover this distance was 3 + 4 = 7 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 42 / 7 = 6 hours . total time that lionel was walking is 2 + 6 = 8 hours , which means that he covered in that time interval distance = rate * time = 3 * 8 = 24 miles . answer : d ."
Answer: d
Python program:
a = 3 * 3
b = 48 - a
c = 4 + 3 
d = b / c
e = d + 3 
f = 3 * e
Problem: the difference between the local value and the face value of 6 in the numeral 85475641 is
Options: a ) 459 , b ) 954 , c ) 594 , d ) 584 , e ) 458
Rationale: "explanation : ( local value of 6 ) - ( face value of 6 ) = ( 600 - 6 ) = 594 c )"
Answer: c
Python program:
a = 6 * 1000
b = a - 6
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 17 % , then the cost price of the article is :
Options: a ) 500 , b ) 334 , c ) 555 , d ) 664 , e ) 526
Rationale: 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 117 = rs . 526 answer : option e
Answer: e
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 17 
g = e / f
Problem: 28 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 13.25 , b ) 38.25 , c ) 33.25 , d ) 12.25 , e ) 31.25
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 28 = 12.25 answer : d"
Answer: d
Python program:
a = 4 + 3 
b = 4 + 3 
c = b + 2 
d = a / c
e = d * 28
f = e / 2
Problem: a 35 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 10 , b ) 20 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 35 = 10 answer : a"
Answer: a
Python program:
a = 2 / 5
b = a + 1 
c = 35 / b
d = 35 - c
Problem: car a is 30 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 4.5 , c ) 4.75 , d ) 3.75 , e ) 3.5
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 30 miles and drive 8 miles ahead so to drive 38 miles it ' ll need 38 / 8 = 3.5 hours . answer : c"
Answer: c
Python program:
a = 30 + 8 
b = 58 - 50
c = a / b
Problem: if a car went the first third of the distance at 80 kmh , the second third at 18 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 34 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 720 ( this number is convenient because it is divisible by 80 , 18 and 48 ) so : 720 = 80 * t 1 = 9 hrs 720 = 18 * t 2 = 40 hrs 720 = 48 * t 3 = 15 hrs t = t 1 + t 2 + t 3 = 64 hrs d = rt ( 720 * 3 ) = r * 64 r = 33.75 answer : a"
Answer: a
Python program:
a = 1 / 80
b = 1 / 18
c = a + b 
d = 1 / 48
e = c + d 
f = 3 / e
Problem: in a group of ducks and cows , the total number of legs are 22 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 22 = > 2 x = 22 = > x = 11 a"
Answer: a
Python program:
a = 22 / 2
Problem: how long does a train 110 meters long running at the rate of 36 km / hr take to cross a bridge 132 meters in length ?
Options: a ) 24.2 sec , b ) 30.6 sec , c ) 32.6 sec , d ) 28.1 sec , e ) 20.4 sec
Rationale: "distance = length of train + length of bridge = 110 + 132 = 242 speed = 36 km / hr = 36 * 5 / 18 = 10 m / s required time = 242 / 10 = 24.2 seconds answer is a"
Answer: a
Python program:
a = 110 + 132 
b = 36 * const_0_2778
c = a / b
Problem: a certain airline ' s fleet consisted of 100 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "let x be the number of years . 4 x > 100 - 3 x 7 x > 100 x > 14 + 2 / 7 the answer is b ."
Answer: b
Python program:
a = 3 + 4 
b = 100 / a