euclaise/mathqa_programs huggingface dataset:
Problem: a grocery shop has a sale of rs . 6235 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 5191 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6235 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6235 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 33809 + x = 39000 = > x = 39000 − 33809 = 5191 answer : d"
Answer: d
Python program:
a = 5 + 1 
b = 6500 * a
c = 6235 + 6927 
d = 6855 + c 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: a train 225 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 86 , b ) 50 , c ) 12 , d ) 13 , e ) 67
Rationale: "speed of the train relative to man = ( 225 / 10 ) m / sec = ( 45 / 2 ) m / sec . [ ( 45 / 2 ) * ( 18 / 5 ) ] km / hr = 81 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 81 = = > x = 86 km / hr . answer : option a"
Answer: a
Python program:
a = 5 * const_0_2778
b = a * 5
c = 225 - b
d = c / 5
e = d / const_0_2778
Problem: 0.0006688 / 0.0000120 x 17.05 = ?
Options: a ) 450.1 , b ) 910.1 , c ) 930.1 , d ) 920.1 , e ) 950.1
Rationale: "explanation : ? = 0.0006688 / 0.0000120 x 17.05 = 950.1 answer : option e"
Answer: e
Python program:
a = 0 / 6688
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 45 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 15 , e ) 14
Rationale: initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 45 + q = > q = 15 answer : d
Answer: d
Python program:
a = 10 * 3
b = 45 - a
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 75 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 30 , b ) 35 , c ) 25 , d ) 40 , e ) 45
Rationale: "assume total distance = 100 miles time taken for 75 miles = 75 / 75 = 1 hour time taken for the rest of the 25 miles = 25 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 25 / v hence v = 25 mph answer : c"
Answer: c
Python program:
a = 50 + 75 
b = a - 75
c = 50 + 75 
d = c / 50
e = 75 / 75
f = d - e
g = b / f
Problem: if 20 men can build a wall 66 metres long in 15 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 151.36 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 15 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 15 * 20 ) = 151.36 mtrs answer : a"
Answer: a
Python program:
a = 86 * 8
b = 20 * 15
c = a / b
d = 66 * c
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "we are given that orangeade is made on day 1 with an equal amount of water and orange juice . we can set this information up into a ratio using a variable multiplier : w : oj = x : x thus , orangeade quantity = amount of water + amount of oj = x + x = 2 x we are next given that orangeade on day 2 was made by mixing the same amount of orange juice with twice the amount of water . we can set this information up into a ratio using a variable multiplier : w : oj = 2 x : x thus , orangeade quantity = amount of water + amount of oj = 2 x + x = 3 x we also know that all orangeade made was sold and that the revenue on both days was the same . we can therefore set up the following equation : day 1 revenue = day 2 revenue that is , ( quantity sold day 1 ) ( price per glass day 1 ) = ( quantity sold day 2 ) ( price per glass day 2 ) let a be the amount of orangeade a glass can hold , then quantity sold day 1 = the number of glasses of orangeade sold on day 1 = 2 x / a similarly , quantity sold day 2 = the number of glasses of orangeade sold on day 2 = 3 x / a we also know that the price per glass on day 1 = $ 0.6 but we don ’ t know the price per glass on day 2 , so let ’ s label it as variable p . we now have : ( 2 x / a ) ( 0.6 ) = ( 3 x / a ) ( p ) multiplying both sides by a , we have : ( 2 x ) ( 0.6 ) = ( 3 x ) ( p ) 1.2 x = 3 xp 1.2 = 3 p p = 0.4 thus , each glass of orangeade was sold for $ 0.40 on day 2 . answer d ."
Answer: d
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many r hours will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many r hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."
Answer: a
Python program:
a = 1 / 12
b = 1 / 30
c = a - b
d = 1/(c)
e = 1 / 7
f = 1 / 12
g = e - f
h = 1/(g)
i = d + h
Problem: the number 1254 is divisible by which number ?
Options: a ) 8 , b ) 7 , c ) 4 , d ) 5 , e ) 6
Rationale: last 3 digit can not divisible by 8 so , reject option a 1254 is not divisible by 7 last number is not 0 or 5 , so neglect 4 is not divide 1254 divisibility rule of 6 is a number divisible both by 3 and 2 . 1254 attains both divisible . so the number is divisible by 6 option e
Answer: e
Python program:
a = 100 + 100 
b = 10 - 1
c = a + b 
d = 1254 / c
Problem: what is the cost of leveling the field in the form of parallelogram at the rate of rs . 40 / 10 sq . metre , whose base & perpendicular distance from the other side being 24 m & 34 m respectively ?
Options: a ) s . 600 , b ) s . 630 , c ) s . 640 , d ) s . 648 , e ) s . 816
Rationale: "area of the parallelogram = length of the base * perpendicular height = 24 * 34 = 816 m . total cost of levelling = rs . 816 e"
Answer: e
Python program:
a = 24 * 34
b = 40 / 10
c = a * b
Problem: a certain no . when divided by 35 leaves aremainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) c
Answer: c
Python program:
a = 35 - 25
b = a - 4
c = b - 2
Problem: on a certain road , 40 % 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 ) 22 % , e ) 50 %
Rationale: "suppose there are x motorists . 40 % of them exceeded the speed limit and received the ticket , i . e . 2 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 = 2 x / 5 or y / x = 1 / 2 or y / x * 100 = 1 / 2 * 100 = 50 % e"
Answer: e
Python program:
a = 100 - 20
b = 40 / a
c = b * 100
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 56 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 280 , b ) $ 800 , c ) $ 892 , d ) $ 1,108 , e ) $ 1,200
Rationale: "( a ) $ 280 ( b ) $ 800 ( c ) $ 892 ( d ) $ 1,108 ( e ) $ 1,200 y = 2000 - x . 1 x - . 08 ( 2000 - x ) = 56 . - 160 + . 18 x = 56 x = 1200 and y = 800 answer : b"
Answer: b
Python program:
a = 100 * 10
b = a * 2
c = 10 * 8
d = c * 2
e = d + 56 
f = 10 / 100
g = 8 / 100
h = f + g 
i = e / h
j = b - i
Problem: if a mixture is 1 ⁄ 2 alcohol by volume and 3 ⁄ 2 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 3 ⁄ 7 , b ) 4 ⁄ 7 , c ) 3 ⁄ 4 , d ) 4 ⁄ 3 , e ) 7 ⁄ 4
Rationale: "should be a sub - 600 level q . . volume = { 1 / 2 } / { 3 / 2 } = 1 / 3 c"
Answer: c
Python program:
a = 2 / 0
b = 3 / 2
c = a / b
Problem: a number when divided by 342 gives a remainder 38 , what remainder will be obtained by dividing the same number 21 ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 2 , e ) 3
Rationale: "explanation : 342 + 38 = 380 / 21 = 2 ( remainder ) answer : d"
Answer: d
Python program:
a = 21 * 2
b = 38 - a
Problem: at the beginning of 1992 , maria ' s stock portfolio was worth $ 600000 . during 1992 , the portfolio ' s value increased by 95 % . during the next year , the portfolio increased its worth by only 5 % . what was maria ' s portfolio worth , in dollars , by the end of 1993 ?
Options: a ) 1 , 180000 , b ) 1 , 200000 , c ) 1 , 200300 , d ) 1 , 228500 , e ) 1 , 330,000
Rationale: by the end of 1992 , the port folio worth is 1.95 * ( $ 600 k ) by 1993 , the portfolio is 1.05 * ( 1.95 * $ 600 k ) = $ 1 , 228,500 answer : d
Answer: d
Python program:
a = 600000 / 3
Problem: amit and ananthu can do a work in 15 days and 45 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 28 days , b ) 30 days , c ) 33 days , d ) 35 days , e ) 39 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 45 ananthu can do work in = 4 / 5 * 45 = 36 days so total days = 36 + 3 = 39 days answer : e"
Answer: e
Python program:
a = 1/(15)
b = a * 3
c = 1 - b
d = 1/(45)
e = c / d
f = e + 3
Problem: a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 5 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 20 : 25 , c ) 1 : 5 , d ) 2 : 5 , e ) 4 : 6
Rationale: "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 5 - - > x ( a - b ) = 5 . since 5 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 5 . the above implies that either x = 1 and a - b = 5 or x = 5 and a - b = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13 . for the original question only option which fits is e , 4 : 5 . cats = 5 * 4 = 20 and dogs = 5 * 5 = 25 . answer : b ."
Answer: b
Python program:
a = 5 * 4
b = 5 * 4
c = b + 5 
d = a / c
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of w is less than the square root of w . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "w 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Python program:
a = 2 * 3
b = 100 - 10
c = a + b
Problem: 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is
Options: a ) 24 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "solution let the two parts be ( 54 - x ) and x . then , 10 ( 54 - x ) + 22 x = 780 = 12 x = 240 ‹ = › x = 20 . therefore bigger part = ( 54 - x ) = 34 . answer d"
Answer: d
Python program:
a = 54 * 10
b = 780 - a
c = 22 - 10
d = b / c
e = 54 - d
Problem: a work which could be finished in 9 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "explanation : x - - - - - - - 9 ( x + 10 ) - - - - 6 x * 9 = ( x + 10 ) 6 x = 20 answer : b"
Answer: b
Python program:
a = 3 * 2
b = a * 10
c = 3 * 2
d = 9 - c
e = b / d
Problem: if the compound interest on a certain sum of money for 6 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 1800 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 6 yrs = ( 3000 x 10 x 6 ) / 100 = 1800 / - answer : c ."
Answer: c
Python program:
a = 3 * 0
b = a * 10
c = b * 10
d = c * 6
e = d / 100
Problem: a bicycle wheel has a diameter of 0.66 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 448 , c ) 1408 , d ) 482 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.66 m ) = 482.5 . hence 482 complete revolutions . answer d"
Answer: d
Python program:
a = 1000 * 1
b = 3 * 4
c = b + 2 
d = 4 * 2
e = d + 2 
f = e ** 2
g = c / f
h = 3 + g 
i = h * 0
j = a / i
Problem: a sum of money amounts to rs . 9800 after 5 years and rs . 12015 after 8 years at the same rate of simple interest . the rate of interest per annum is ?
Options: a ) 12.05 % , b ) 5 % , c ) 13.05 % , d ) 22.05 % , e ) 18.05 %
Rationale: s . i . for 3 years = ( 12015 - 9800 ) = rs . 2215 s . i . for 5 years = rs . 2215 / 3 * 5 = rs . 3691 . principal = ( 9800 - 3675 ) = rs . 6108 hence , rate = ( 100 * 3691 ) / ( 6125 * 5 ) = 12.05 % answer : a
Answer: a
Python program:
a = 12015 - 9800
b = 9800 * 8
c = 5 * 12015
d = b - c
e = a / d
f = e * 100
Problem: how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 51 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: a + b / ab = 2 / 3 3 = 1 * 3 or 3 * 1 a + b in both case = 4 correct 0 answer : e
Answer: e
Python program:
a = 34 / 51
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 8 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 27 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : d ."
Answer: d
Python program:
a = 3 ** 3
b = a - 1
Problem: the average age of one class strength 32 students is 16 yrs . if the staff ' s age is also included , the average increases by one year . find the age of the staff
Options: a ) 50 , b ) 52 , c ) 49 , d ) 32 , e ) 35
Rationale: total age of students = > 32 × 16 = 512 yrs total age inclusive staff = 33 × ( 16 + 1 ) = 561 = > staff ' s age 561 - 512 = 49 yrs answer c
Answer: c
Python program:
a = 32 + 1 
b = 16 + 1 
c = a * b
d = 32 * 16
e = c - d
Problem: the area of a rectangular plot is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the plot ?
Options: a ) 14 m , b ) 20 m , c ) 18 m , d ) 12 m , e ) 15 m
Rationale: "lb = 460 m 2 let breath = b l = b * ( 100 + 15 ) / 100 = 115 b / 100 from these 115 b / 100 * b = 460 b 2 = 46000 / 115 = 400 b = root of 400 = 20 m answer b"
Answer: b
Python program:
a = 15 / 100
b = 1 - a
c = 460 / b
d = math.sqrt(c)
Problem: a man purchased 5 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 250 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: "explanation : 10 * 150 = 1500 5 * 100 + 5 * 150 = 1250 1500 – 1250 = 250 a"
Answer: a
Python program:
a = 10 * 150
b = 5 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 8 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 4 days ?
Options: a ) 30 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: 5 machines do x units in 8 days we have x / 8 = > rate of the 5 machines we know that we need to have 3 x units in 4 days therefore , we need to get to 3 x / 4 rate of the machines . rate of one machine is x / 8 * 1 / 5 = x / 40 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 4 days . 3 x / 4 work needs to be done by machines that work at x / 40 rate . let ' s assign a constant y for the number of machines : ( x / 40 ) * y = 3 x / 4 y = 3 x / 4 * 40 / x cancel 4 with 40 , and x with x and get - > 30 . answer choice a
Answer: a
Python program:
a = 5 * 3
b = 8 / 4
c = a * b
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 2,2 ) , ( 8,2 ) , ( 3,5 ) , ( 9,5 ) ?
Options: a ) 18 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 52 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 8 - 2 = 6 unit delta y will give us the dimension of the other side of parallelogram = 5 - 2 = 3 unit area of parallelogram = 6 * 3 = 18 answer is a"
Answer: a
Python program:
a = 3 + 2
Problem: on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 10 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 600 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,000
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 10 % . 10 x = 200 = > x = 2000 answer e"
Answer: e
Python program:
a = 60 - 40
b = 10 * a
c = 10 / 100
d = b / c
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 50 %
Options: a ) 40.8 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 50 / 100 = 50.40 so x = 40.8 answer : a"
Answer: a
Python program:
a = 100 / 50
b = 60 * 84
c = b / 100
d = a * c
e = d - 60
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much q does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) q = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Python program:
a = 3 / 96
b = a / 2
c = 1 + b 
d = c ** 4
e = 10000 * d
Problem: machine p and machine q are each used to manufacture 440 sprockets . it takes machine p 10 hours longer to produce 440 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 440 / x = 440 / 1.1 x + 10 1.1 ( 440 ) = 440 + 11 x 11 x = 44 x = 4 the answer is b ."
Answer: b
Python program:
a = 10 / 100
b = a + 1 
c = 440 / b
d = 440 - c
e = d / 10
Problem: a retailer buys 100 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 110 , b ) 175 , c ) 212 , d ) 218 , e ) 220
Rationale: "let the market price of each pen be $ 1 then , cost price of 100 pens = $ 36 selling price of 100 pens = 99 % of $ 100 = $ 99 profit % = ( ( 63 * 100 ) / 36 ) % = 175 % answer b"
Answer: b
Python program:
a = 1 / 100
b = 1 - a
c = 36 / 100
d = b - c
e = 36 / 100
f = d / e
g = 100 * f
Problem: 3 litre of water is added to 11 litre of a solution containing 42 % of alcohol in the water . the percentage of alcohol in the new mixture is ?
Options: a ) 30 % , b ) 33 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: we have a 11 litre solution containing 42 % of alcohol in the water . = > quantity of alcohol in the solution = 11 × 42 100 = 11 × 42100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 11 + 3 = 14 percentage of alcohol in the new solution = 11 × 42 100 14 × 100 = 11 × 4210014 × 100 = 11 × 3 100 = 33 % b )
Answer: b
Python program:
a = 11 * 42
b = a / 100
c = 3 + 11 
d = b / c
e = d * 100
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red card is drawn ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 26 , d ) 1 / 13 , e ) 5 / 13
Rationale: "the total number of cards is 52 . the number of red cards is 26 . p ( red card ) = 26 / 52 = 1 / 2 the answer is a ."
Answer: a
Python program:
a = 4 * 3
b = a / 52
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 26 , b ) 95 , c ) 90 , d ) 42 , e ) 22
Rationale: "sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 10 = rs . 95 answer : b"
Answer: b
Python program:
a = 8925 / 85
b = a - 10
Problem: a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 375
Rationale: max no . of crates = 5 . max weight = 120 kg max . weight carried = 5 * 120 = 600 kg = c
Answer: c
Python program:
a = 5 * 120
Problem: a student completes a 3 part exam as follows . the student completes sections a in 24 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 7 : 8 , b ) 6 : 7 , c ) 5 : 6 , d ) 4 : 5 , e ) 3 : 4
Rationale: the time spent on section b and section c is 18 minutes each . the ratio of c to a is 18 : 24 = 3 : 4 the answer is e .
Answer: e
Python program:
a = 3 / 4
Problem: the average of first 3 prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50
Rationale: 23 + 29 + 31 = 83 / 3 = 27.7 answer : d
Answer: d
Python program:
a = 20 + 3 
b = 20 + 3 
c = b + 4 
d = c + 2 
e = a + d 
f = 20 + 3 
g = f + 4 
h = g + 2 
i = h + 2 
j = e + i 
k = j / 3
Problem: a reduction of 44 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.3 , b ) 8.3 , c ) 7.3 , d ) 3.3 , e ) 1.3
Rationale: "explanation : 40 * ( 44 / 100 ) = 17.6 - - - 64 ? - - - 12 = > rs . 3.30 answer : d"
Answer: d
Python program:
a = 44 / 100
b = 44 * a
c = b / 64
d = 12 * c