euclaise/mathqa_programs huggingface dataset:
Problem: the speed of a car is 98 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 75 kmph , c ) 87 kmph , d ) 79 kmph , e ) 86 kmph
Rationale: "s = ( 98 + 60 ) / 2 = 79 kmph answer : d"
Answer: d
Python program:
a = 98 + 60 
b = a / 2
Problem: what is the least whole number that should be added to 625573 if it is to be divisible by 3 ?
Options: a ) 6 , b ) 1 , c ) 4 , d ) 3 , e ) 2
Rationale: a number is divisible by 3 if the sum of the digits is divisible by 3 . . here , 6 + 2 + 5 + 5 + 7 + 3 = 28 , the next multiple of 3 is 30 . 2 must be added to 625574 to make it divisible by 3 e
Answer: e
Python program:
a = 625573 - 1
b = a + 3 
c = b - 625573
Problem: what least number must be subtracted from 2000 to get a number exactly divisible by 17 ?
Options: a ) 9 , b ) 8 , c ) 5 , d ) 11 , e ) 15
Rationale: "on dividing 2000 by 17 , we get 11 as remainder . required number to be subtracted = 11 answer d"
Answer: d
Python program:
a = 2000 / 17
b = math.floor(a)
c = b * 17
d = 2000 - c
Problem: how many 7 in between 1 to 120 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78,79 , 87,97 , 107,117 22 7 ' s between 1 to 120 answer : c"
Answer: c
Python program:
a = 7 * 1
b = 120 / a
Problem: in 1990 the budgets for projects q and v were $ 620,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: "let the no of years it takes is x . 620 + 30 x = 780 - 10 x - - > 40 x = 160 and x = 4 . thus , it happens in 1994 . c ."
Answer: c
Python program:
a = 2 * 3
b = 10 * a
c = 1990 + b
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 162.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 35 , c ) $ 31 , d ) $ 41 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 162.5 subtracting the first equation from the second gives us b + 3 s = 42.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 35 . in any case , there is no necessity to know each item ' s price , just the sum . answer : b"
Answer: b
Python program:
a = 162 - 50
b = 120 + a 
c = 162 - 50
d = c * 3
e = b - d
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day at 1 mile faster than 2 nd day for same hours . how many miles in total did she walk ?
Options: a ) 63 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: "first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 5 hours - 25 miles total 18 + 20 + 25 = 63 answer : option a ."
Answer: a
Python program:
a = 3 + 1 
b = 18 / 3
c = b - 1
d = a * c
e = 18 + d 
f = 18 / 3
g = 3 + 1 
h = f * g
i = e + h
Problem: simplify : ( 4 + 3 ) + ( 8 - 3 - 1 )
Options: a ) - 11 , b ) – 12 , c ) 11 , d ) 12 , e ) 10
Rationale: solution : ( 4 + 3 ) + ( 8 - 3 - 1 ) = 7 + ( 8 - 3 - 1 ) = 7 + 8 - 3 - 1 = 15 - 1 = 11 answer : ( c )
Answer: c
Python program:
a = 4 + 3 
b = 8 - 3
c = b - 1
d = a + c
Problem: a train running at the speed of 56 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 140 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 56 * ( 5 / 18 ) m / sec = 140 / 9 m / sec length of train ( distance ) = speed * time ( 140 / 9 ) * 9 = 140 meter answer : a"
Answer: a
Python program:
a = 56 * 1000
b = a / 3600
c = b * 9
Problem: how many 9 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 123454321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 90000
Rationale: take the task of building palindromes and break it intostages . stage 1 : select the 9 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 8 th , 7 th , 6 th , 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 9 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 90000 ways ) answer : e
Answer: e
Python program:
a = 9 * 10
b = a * 10
c = b * 10
d = c * 10
Problem: when sold at a 60 % discount , a sweater nets the merchant a 20 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 66.67 % , d ) 80 % , e ) 100 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 60 % of 100 = 40 . . profit = 20 % . . therefore the wholesale purchase cost = x . . . . 1.2 x = 40 or x = 33.33 . . . marked price was 100 so . . . so answer is 66.67 % . . c"
Answer: c
Python program:
a = 100 - 60
b = 20 / 100
c = 1 + b 
d = a / c
e = 100 - d
Problem: jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 56,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 28,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 56,000 i . e . rs . 28,000 answer : a"
Answer: a
Python program:
a = 4 * 2
b = 2 + 3 
c = b * 2
d = a * c
e = d * 100
f = 2 + 3 
g = f * 100
h = g * 100
i = e + h 
j = 2 + 3 
k = j * 2
l = k / 2
m = 4 * 3
n = l / m
o = i * n
Problem: a start walking from a place at a uniform speed of 3 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 3.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 3 + 5 / 9 = 3.55 answer b"
Answer: b
Python program:
a = const_60 + 48 
b = a / const_60
c = 1 / b
d = c + 3
Problem: find the 25 % of rs . 600 .
Options: a ) s . 150 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60
Rationale: "explanation : 25 % of 600 = > 25 / 100 * 600 = rs . 150 answer : a"
Answer: a
Python program:
a = 25 / 100
b = 600 * a
Problem: ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 60900 . what is his profit percent ?
Options: a ) 10.7 % , b ) 19 % , c ) 18 % , d ) 14 % , e ) 16 %
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 60900 profit ( % ) = ( 60900 - 55000 ) / 55000 * 100 = 10.7 % answer : a"
Answer: a
Python program:
a = 42000 + 13000 
b = 60900 - a
c = 42000 + 13000 
d = b / c
e = d * 100
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 10 - meter platform and caught it after it had traveled 29.65 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 10 + 10 + 5 + 2.5 + 1.25 + 0.6 + 0.3 ans b"
Answer: b
Python program:
a = 10 / 2
b = a / 2
Problem: if the length of the sides of two cubes are in the ratio 2 : 1 , what is the ratio of their total surface area ?
Options: a ) 2 : 1 , b ) 3 : 1 , c ) 4 : 1 , d ) 6 : 1 , e ) 8 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 2 x ) ^ 2 = 24 x ^ 2 . the ratio of surface areas is 4 : 1 . the answer is c ."
Answer: c
Python program:
a = 2 * 2
Problem: a question paper has 2 parts , a & b , each containing 5 questions . if a student has to choose 3 from part a & 4 from part b , in how many ways can he choose the questions ?
Options: a ) 50 , b ) 100 , c ) 152 , d ) 150 , e ) 55
Rationale: "there 3 questions in part a out of which 4 question can be chosen as = 5 c 3 . similarly , 5 questions can be chosen from 10 questions of part b as = 5 c 4 . hence , total number of ways , = 5 c 3 * 5 c 4 = [ 5 ! / ( 2 ! 3 ! ) ] * [ 5 ! / ( 4 ! * 1 ) ] = { 10 } * { 5 * 4 ! / ( 4 ! ) } = 10 * 5 = 50 . a"
Answer: a
Python program:
a = math.comb(5, 3)
b = math.comb(5, 4)
c = a * b
d = c / 5
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 42 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2500 km , e ) 3150 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 42 = 30 x = 3150 km answer is e"
Answer: e
Python program:
a = 30 * 42
Problem: what is the speed of the stream if a canoe rows upstream at 8 km / hr and downstream at 12 km / hr
Options: a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 1.9 kmph
Rationale: "sol . speed of stream = 1 / 2 ( 12 - 8 ) kmph = 2 kmph . answer d"
Answer: d
Python program:
a = 12 - 8
b = a / 2
Problem: obra drove 150 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 %
b ) 12.5 %
c ) 18.75 %
d ) 25 %
e ) 31.25 %
Rationale: area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 150 π / 480 π = 31.25 % hence , answer is e .
Answer: e
Python program:
a = circumface / (
b = a * 150
c = b * 3
d = c - 2
e = d - 4
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 305 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 610 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 305 ) = 2 + 2 ( extra ) = > 2 x - 610 = x = > x = 610 . answer : b"
Answer: b
Python program:
a = 305 * 2
Problem: at a florist shop on a certain day , all corsages sold for either $ 20 or $ 30 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 10 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1000
Rationale: "let , no . of corsages @ $ 20 = x , no . of corsages @ $ 30 = y and revenue = r so , 20 x + 30 y = r . . . . . . . . . ( 1 ) now , given the situation , 20 ( x + 8 ) + 30 ( y - 8 ) = r - . 1 r = > 20 x + 160 + 30 y - 240 = . 9 r = > 20 x + 30 y = . 9 r + 80 . . . . . . . . . . . . ( 2 ) so , r = . 9 r + 80 = > r = 800 the answer is d ."
Answer: d
Python program:
a = 20 * 8
b = 30 * 8
c = a - b
d = negate / (
e = 10 / 100
f = d - e
Problem: two pots are in side - by - side . one pot , which is 20 inches tall , casts a shadow that is 10 inches long . the other pot is 40 inches tall . compute , in inches , the length of the shadow that the taller pot casts .
Options: a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20
Rationale: the ratio of shadow to height is constant , so if x is the length of the shadow , then 20 / 10 = 40 / x and x = 20 . correct answer e
Answer: e
Python program:
a = 10 / 20
b = a * 40
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 19000 , then find his savings ?
Options: a ) 3800 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 19000 = > x = 3800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3800 . answer : a"
Answer: a
Python program:
a = 4 / 5
b = a * 19000
c = 19000 - b
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 7.0 = ?
Options: a ) - 0.61 , b ) 1.0 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 0.61 answer a
Answer: a
Python program:
a = 1 * 9
b = negate - (
c = 2 * 6
d = b / c
Problem: if 9 a - b = 10 b + 60 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 8 , b ) - 4 , c ) 0 , d ) 4 , e ) 8
Rationale: "( i ) 9 a - 11 b = 60 ( ii ) 2 a + 22 b = - 60 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."
Answer: c
Python program:
a = 60 / 2
b = a * 2
c = negate * (
Problem: in a fuel station the service costs $ 2.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 462 $
Rationale: 12 * 2.75 + 0.65 * 12 * 55 = 462 hence - e
Answer: e
Python program:
a = 0 * 65
b = a * 12
Problem: find 20 % of 240
Options: a ) 96 , b ) 94 , c ) 86 , d ) 74 , e ) 48
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 20 % of 240 20 / 100 × 240 = 48 answer : e"
Answer: e
Python program:
a = 20 / 240
Problem: if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 12 . what is the value of f ( 6 ) ?
Options: a ) 1 , b ) 0 , c ) - 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 12 then f ( 5 ) = 12 - 5 = 7 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 7 - 6 = 1 . answer : a . questions on funtions to practice :"
Answer: a
Python program:
a = 1 + 4 
b = 12 - a
c = b - 6
Problem: if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 12.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 318 , b ) $ 289 , c ) $ 282 , d ) $ 274 , e ) $ 286
Rationale: total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 12 = 16 * 12 = 192 $ total charge = 126 + 192 = 318 $ answer a
Answer: a
Python program:
a = 3 + 4 
b = 18 * a
c = 3 + 4 
d = 23 - c
e = 12 * d
f = b + e
Problem: when a number is divided by 3 & then multiply by 12 the answer is 9 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 2.25 , d ) 5.7 , e ) 6.5
Rationale: "if $ x $ is the number , x / 3 * 12 = 9 = > 4 x = 9 = > x = 2.25 c"
Answer: c
Python program:
a = 9 / 12
b = a * 3
Problem: juan and his five friends will sit on six fixed seats around a circular table . if juan must sit on the seat closest to the window and jamal must sit next to juan , in how many can juan and his five friends sit ?
Options: a ) 20
b ) 24
c ) 48
d ) 72
e ) 120
Rationale: j = juan , f = jamal since j is always fixed , set j , set f relative to j , then see how many options there are : j f 4 3 2 1 = 24 or f j 4 3 2 1 = 24 24 + 24 = 48 … c answer : c
Answer: c
Python program:
a = math.factorial(4)
b = a * 2
Problem: lucia ' s sells kale at x dollar per pound for the first 20 pounds and . 8 x for every subsequent pound . amby ' s price is x per pound for the first 14 pounds and . 9 x for subsequent pounds . what is the minimum number of pounds over 15 for which lucia ' s becomes an equal or better deal ?
Options: a ) 24 , b ) 26 , c ) 25 , d ) 27 , e ) 28
Rationale: for amy ' s deal to be better , the cost has to be less or equal to lucia ' s assuming ' n ' is the number of pounds of kale , the equation is 20 x + ( n - 20 ) ( 0.8 x ) < = 14 x + ( n - 14 ) ( 0.9 x ) resolve it : = = > 20 x + 0.8 nx - 16 x < = 14 x + 0.9 nx - 12.6 x = = > 2.6 x < = 0.1 nx = = > 26 x < = nx = = > x ( n - 26 ) > = 0 as x can not be 0 , = = > n - 26 > = 0 = = > n > = 26 so the minimum value is 26 ' b ' would be the correct answer
Answer: b
Python program:
a = 8 / 10
b = 20 * a
c = 20 - b
d = 9 / 10
e = 14 * d
f = 14 - e
g = c - f
h = 1 / 10
i = g / h
Problem: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 1 . what is the value of 7 y – x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y - 3 = x 7 y - x = 3 the answer is c ."
Answer: c
Python program:
a = 2 * 4
b = a - 1
c = 6 * 3
d = 2 * 11
e = c - d
f = b / e
g = 7 * f
h = 2 * 4
i = h - 1
j = 6 * 3
k = 2 * 11
l = j - k
m = i / l
n = 11 * m
o = n + 4 
p = g - o
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 140800 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 140800 = 1 * 5 ^ 2 * 8 ^ 3 * 11 the factors of 8 must come from the purple point value , so there are 3 purple chips . the answer is c .
Answer: c
Python program:
a = 5 - 2
Problem: evaluate 49 / . 07
Options: a ) 400 , b ) 500 , c ) 700 , d ) none of these , e ) 506
Rationale: "explanation : 49 / . 07 = 4900 / 7 = 700 option c"
Answer: c
Python program:
a = 7 / 49
b = 100 / 0
Problem: an employee ’ s annual salary was increased 30 % . if her old annual salary equals $ 30,000 , what was the new salary ?
Options: a ) $ 28,000 , b ) $ 25,000 , c ) $ 20,000 , d ) $ 35,000 , e ) $ 39,000
Rationale: "old annual salary = $ 30,000 salary increase = 30 % . original salary = $ 30,000 * 30 / 100 = $ 9000 new salary = $ 30,000 + $ 9000 = $ 39,000 hence e ."
Answer: e
Python program:
a = 100 - 10
b = a * 1000
c = 100 - 10
d = c * 1000
e = const_0_25 * 100
f = e * 1000
g = d - f
h = b / g
i = h - 1
j = i * 100
Problem: 1 , 3,5 , 7,9 , . . . . 50 find term of sequnce
Options: a ) 1000 , b ) 1200 , c ) 1300 , d ) 1800 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Python program:
a = negate - (
Problem: david deposited $ 5000 to open a new savings account that earned 6 percent annual interest , compounded semi - annually . if there were no other transactions in the account , what the amount of money in david account one year after the account was opened ?
Options: a ) $ 5306 , b ) $ 6120 , c ) $ 5136 , d ) $ 5405 , e ) $ 5500
Rationale: approach # 1 : 6 percent annual interest compounded semi - annually - - > 3 % in 6 moths . for the first 6 moths interest was 3 % of $ 5000 , so $ 150 ; for the next 6 moths interest was 3 % of $ 5000 , plus 3 % earned on previous interest of $ 150 , so $ 150 + $ 6 = $ 156 ; total interest for one year was $ 150 + $ 156 = $ 306 , hence balance after one year was $ 5000 + $ 306 = $ 5306 . answer : a .
Answer: a
Python program:
a = 5000 * 6
b = a / 100
c = 5000 + b
Problem: ( 1000 ) 7 ÷ ( 10 ) 17 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: explanation : = ( 103 ) 7 / ( 10 ) 17 = ( 10 ) 21 / ( 10 ) 17 = 10 ( 4 ) = 10000 option d
Answer: d
Python program:
a = 1000 * 10
Problem: how many multiples of 3 are there between 100 and 300 ( both are inclusive ) ?
Options: a ) 67.6 , b ) 1.58 , c ) 2.47 , d ) 3.54 , e ) 6.51
Rationale: "the answer is ( 300 - 100 ) / 3 + 1 = 67.6 answer is a"
Answer: a
Python program:
a = 300 - 100
b = a / 3
c = b + 1
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 50 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 50 , b ) 15 / 50 , c ) 8 / 50 , d ) 3 / 50 , e ) 7 / 50
Rationale: let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 } n ( x ) = 15 , n ( s ) = 50 hence , the required probability is 15 / 50 . answer : b
Answer: b
Python program:
a = 3 * 5
b = a / 50
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 10 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 1.250 kg , e ) none of these
Rationale: "the weight of non - water in 10 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 10 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 1.25 answer : d"
Answer: d
Python program:
a = 100 - 90
b = a * 10
c = b / 100
d = 100 - 20
e = c / d
f = e * 100
Problem: two trains , a and b , started simultaneously from opposite ends of a 200 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 200 - mile trip in 10 hours ; train b , traveling at a constant rate , completed the 200 - mile trip in 6 hours . how many miles had train a traveled when it met train b ?
Options: a ) 70 , b ) 75 , c ) 87.5 , d ) 90 , e ) 92.5
Rationale: "as the ratio of the rates of a and b is 6 to 10 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 6 / ( 6 + 10 ) = 6 / 16 of 200 miles : 200 * 6 / 16 = 75 miles . answer : b ."
Answer: b
Python program:
a = 10 + 6 
b = 6 / a
c = b * 200
Problem: a mixture of 200 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 11 liters , b ) 11.2 liters , c ) 12.5 liters , d ) 13.78 liters , e ) 13.33 liters
Rationale: "number of liters of water in 200 liters of the mixture = 20 % of 120 = 20 / 100 * 200 = 40 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 40 + p ) and total volume of mixture is ( 200 + p ) . ( 40 + p ) = 25 / 100 * ( 200 + p ) 160 + 4 p = 200 + p p = 13.33 liters . answer : e"
Answer: e
Python program:
a = 25 / 100
b = a * 200
c = 20 / 100
d = c * 200
e = b - d
f = 25 / 100
g = 1 - f
h = e / g