euclaise/mathqa_programs huggingface dataset:
Problem: in a particular state , 60 % of the counties received some rain on monday , and 55 % of the counties received some rain on tuesday . no rain fell either day in 25 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 12.5 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 67.5 %
Rationale: "60 + 55 + 25 = 140 % the number is 40 % above 100 % because 40 % of the counties were counted twice . the answer is b ."
Answer: b
Python program:
a = 60 + 55 
b = 100 - 25
c = a - b
Problem: triathlete dan runs along a 2 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 5 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 9 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: dan travels 4 miles round trip . running part : ( 2 / 10 = 1 / 5 * 60 = 12 minutes ) swimming part : ( 2 / 5 = 2 / 5 * 60 = 24 minutes ) 4 miles in ( 12 + 24 ) minutes 4 / 36 = 1 / 9 mile per minute answer : 1 / 9 mile per minute
Answer: a
Python program:
a = 2 + 2 
b = 2 / 5
c = b * const_60
d = 2 / 10
e = d * const_60
f = c + e 
g = a / f
Problem: what is the smallest number which when increased by 3 is divisible by 12 , 15 , 35 , and 40 ?
Options: a ) 837 , b ) 947 , c ) 1027 , d ) 1155 , e ) 1231
Rationale: "factor each of the numbers 8 , 15 , 35 , and 40 into primes : 12 = 2 * 2 * 3 ; 15 = 3 * 5 ; 35 = 5 * 7 ; 40 = 2 * 2 * 2 * 5 the smallest number divisible by all of them is thus 2 * 2 * 2 * 3 * 5 * 7 = 840 837 + 3 = 840 a"
Answer: a
Python program:
a = math.lcm(12, 15)
b = math.lcm(35, 40)
c = math.lcm(a, b)
d = c + 3
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number r of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "r = 7 is the correct answer . good solution buneul . b"
Answer: b
Python program:
a = 25 / 5
b = a + 2
Problem: if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 2 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 10 / 3 , d ) 2 , e ) 4
Rationale: "n = 2 d / 5 j = n / 2 = d / 5 the average of november and january is ( n + j ) / 2 = 3 d / 5 / 2 = 3 d / 10 d is 10 / 3 times the average of november and january . the answer is c ."
Answer: c
Python program:
a = 2 / 5
b = 2 / 5
c = 1 / 2
d = b * c
e = a + d 
f = e / 2
g = 1 / f
Problem: 7 people average age is 30 . youngest person age is 5 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 35 = 161 so average age would be 175 / 7 = 25 answer : c
Answer: c
Python program:
a = 30 * 7
b = 5 * 7
c = a - b
d = c / 7
Problem: the average age of applicants for a new job is 35 , with a standard deviation of 30 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 16 , c ) 31 , d ) 18 , e ) 34
Rationale: "minimum age = average - 1 standard deviation = 35 - 30 = 5 maximum age = average + 1 standard deviation = 35 + 30 = 35 maximum number of different ages of the applicants = 35 - 5 + 1 = 31 answer c"
Answer: c
Python program:
a = 35 + 30 
b = 35 - 30
c = a - b
d = c + 1
Problem: linda spent 3 / 5 of her savings on furniture and the rest on a tv . if the tv cost her $ 400 , what were her original savings ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 600 , d ) $ 1000 , e ) $ 800
Rationale: "if linda spent 3 / 5 of her savings on furnitute , the rest 5 / 5 - 3 / 5 = 2 / 5 on a tv but the tv cost her $ 400 . so 2 / 5 of her savings is $ 400 . so her original savings are 5 / 2 times $ 400 = $ 2000 / 2 = $ 1000 correct answer d"
Answer: d
Python program:
a = 3 / 5
b = 1 - a
c = 400 / b
Problem: a man buys an item at rs . 1300 and sells it at the loss of 20 percent . then what is the selling price of that item
Options: a ) rs . 660 , b ) rs . 760 , c ) rs . 860 , d ) rs . 1040 , e ) none of these
Rationale: explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 1300 = 80 / 100 * 1300 = 1040 option d
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 1300 * b
Problem: two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer w between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) w = 18 , e ) 20
Rationale: "since we are concerned with integers w between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Python program:
a = 3 * 2
b = a * 3
Problem: a sum of money lent out at s . i . amounts to rs . 850 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 440 , b ) s . 500 , c ) s . 540 , d ) s . 782 , e ) s . 840
Rationale: "s . i for 5 years = ( 1020 - 850 ) = rs . 170 . s . i . for 2 years = 170 / 5 * 2 = rs . 68 . principal = ( 850 - 68 ) = rs . 782 . answer : d"
Answer: d
Python program:
a = 1020 - 850
b = a / 5
c = b * 2
d = 850 - c
Problem: on dividing 15698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 154 , c ) 852 , d ) 176 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 15698 - 14 ) / 89 = 176 answer ( d )"
Answer: d
Python program:
a = 15698 - 14
b = a / 89
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 570 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 570 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 24500 answer : b"
Answer: b
Python program:
a = 8 / 100
b = 1 * 0
c = 570 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 1
i = math.floor(h)
Problem: income and expenditure of a person are in the ratio 4 : 3 . if the income of the person is rs . 20000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 5000
Rationale: "let the income and the expenditure of the person be rs . 4 x and rs . 3 x respectively . income , 4 x = 20000 = > x = 5000 savings = income - expenditure = 4 x - 3 x = x so , savings = rs . 5000 answer : e"
Answer: e
Python program:
a = 3 / 4
b = a * 20000
c = 20000 - b
Problem: given that 268 x 74 = 19832 , find the value of 2.68 x . 74 .
Options: a ) 1.9832 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9832 answer a
Answer: a
Python program:
a = 268 / 100
b = 74 / 100
c = a * b
Problem: the average age of 60 students in a class is 10 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 71 , b ) 65 , c ) 61 , d ) 45 , e ) 36
Rationale: "total age of 50 students = 60 * 10 = 600 total age of 51 persons = 61 * 11 = 671 age of teacher = 671 - 600 = 71 years answer is a"
Answer: a
Python program:
a = 60 * 10
b = a + 1 
c = b + 60 
d = 60 * 10
e = c - d
Problem: the ratio of investments of two partners p and q is 7 : 5.00001 and the ratio of their profits is 7.00001 : 10 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 28 , b ) 10 , c ) 288 , d ) 277 , e ) 211
Rationale: 7 * 5 : 5 * x = 7 : 10 x = 10 answer : b
Answer: b
Python program:
a = 7 / 5
b = 10 / 7
c = a * b
d = c * 5
Problem: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance traveled downstream in 15 minutes is :
Options: a ) 9.25 , b ) 5.25 , c ) 7.25 , d ) 6.25 , e ) 5.1
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 15 / 60 ) ) km = 6.25 km . answer : d"
Answer: d
Python program:
a = 15 / const_60
b = 20 + 5 
c = a * b
Problem: by selling 80 pens , a trader gains the cost of 20 pens . find his gain percentage ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 50 %
Rationale: "let the cp of each pen be rs . 1 . cp of 80 pens = rs . 80 profit = cost of 20 pens = rs . 20 profit % = 20 / 80 * 100 = 25 % answer : a"
Answer: a
Python program:
a = 20 / 80
b = a * 100
Problem: a salt manufacturing company produced a total of 1000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its average monthly production for that year ?
Options: a ) 1750 , b ) 2789 , c ) 2500 , d ) 1550 , e ) 2000
Rationale: total production of salt by the company in that year = 1000 + 1100 + 1200 + . . . . + 2100 = 18600 . average monthly production of salt for that year = 18600 / 12 = 1550 . answer : d
Answer: d
Python program:
a = 10 + 1 
b = 100 * a
c = 1000 + b 
d = 1000 + c 
e = d * 12
f = e / 2
g = f / 12
Problem: a batsman in his 11 th inning makes a score of 69 and their by increasing his average by 1 . what is his average after the 11 th inning ?
Options: a ) 58 , b ) 59 , c ) 68 , d ) 69 , e ) 78
Rationale: "10 x + 69 = 11 ( x + 1 ) x = 58 + 1 = 59 answer : b"
Answer: b
Python program:
a = 1 * 11
b = 69 - a
c = b + 1
Problem: john makes $ 40 a week from his job . he earns a raise andnow makes $ 55 a week . what is the % increase ?
Options: a ) 15 % , b ) 16.66 % , c ) 17.8 % , d ) 19 % , e ) 37.5 %
Rationale: "increase = ( 15 / 40 ) * 100 = 37.5 % . e"
Answer: e
Python program:
a = 55 - 40
b = a / 40
c = b * 100
Problem: if x and y are positive integers and y ≠ 1 , then xy ( y − 1 ) is
Options: a ) always even , b ) always odd , c ) odd only when x is odd , d ) even only when y is even , e ) odd only when xy is odd
Rationale: "expression is xy ( y - 1 ) . we can ignore x and only work with y . if y = even - > entire expression is even since anything multiplied by even is even if y = odd , y - 1 - > even - > entire expression is even since anything multiplied by even is even hence , entire expression will always be even . answer ( a ) ."
Answer: a
Python program:
a = 1 + 1
Problem: you collect baseball cards . suppose you start out with 13 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 15 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "solution start with 13 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 13 + 1 which is 7 , so you ' re left with 13 - 7 = 6 . peter takes 1 baseball card from you : 6 - 1 = 5 baseball cards . paul triples the number of baseball cards you have : 5 ã — 3 = 15 baseball cards . so you have 15 at the end . correct answer : a"
Answer: a
Python program:
a = 13 - 4
b = a - 4
c = b - 1
d = c * 3
Problem: the list price of an article is rs . 70 . a customer pays rs . 61.74 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 2 % , e ) 4 %
Rationale: "explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 61.74 x = 2 % option d"
Answer: d
Python program:
a = 10 / 100
b = 70 * a
c = 70 - b
d = c - 61
e = 10 / 100
f = 70 * e
g = 70 - f
h = d / g
i = h * 100
Problem: what is the smallest integer b for which 27 ^ b > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ b > 3 ^ 24 converting into the same bases : 27 ^ b > 27 ^ 8 therefore for the equation to hold true , b > 8 or b = 9 option c"
Answer: c
Python program:
a = 24 / 3
b = math.floor(a)
c = b + 1
Problem: the median annual household income in a certain community of 21 households is $ 50000 . if the mean r income of a household increases by 10 % per year over the next 2 years , what will the median income in the community be in 2 years ?
Options: a ) $ 50000 , b ) $ 60000 , c ) $ 60500 , d ) $ 65000 , e ) can not be determined
Rationale: answer is e , because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean r is increase by 10 % . it could be the case that small number of higher end incomes increased a little or many low end incomes increased - it can not be identified .
Answer: e
Python program:
a = 10 / 100
b = 1 + a 
c = b * 50000
Problem: the contents of a certain box consist of 80 apples and 30 oranges . how many oranges must be added to the box so that exactly 50 % of the pieces of fruit in the box will be apples ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 65
Rationale: "apple = ( apple + orange + x ) * 0.5 80 = ( 30 + 80 + x ) * 0.5 x = 50 answer : b"
Answer: b
Python program:
a = 80 + 30 
b = 50 / 100
c = 80 / b
d = a - c
Problem: the sum of the squares of three numbers is 125 , while the sum of their products taken two at a time is 50 . their sum is :
Options: a ) 15 , b ) 30 , c ) 40 , d ) 50 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 125 xy + yz + zx = 50 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 125 + ( 2 * 50 ) ( x + y + z ) ^ 2 = 225 so x + y + z = 15 answer : a"
Answer: a
Python program:
a = 125 - 50
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 125 - 50
f = e / 2
g = 125 - f
h = math.sqrt(g)
i = d + h
Problem: in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 3 , - 1 ) , ( 3 , 8 ) , ( 14 , 2 ) , ( 14 , - 5 ) ?
Options: a ) 76 , b ) 88 , c ) 100 , d ) 112 , e ) 124
Rationale: "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 9 + 7 ) × 11 = 88 . the answer is b ."
Answer: b
Python program:
a = 1 + 8 
b = 2 + 8 
c = a + b 
d = 14 - 3
e = c * d
f = e / 2
Problem: a man was engaged on a job for 30 days on the condition that he would get a wage of rs . 10 for the day he works , but he have to pay a fine of rs . 2 for each day of his absence . if he gets rs . 216 at the end , he was absent for work for . . . days .
Options: a ) 7 days , b ) 5 days , c ) 3 days , d ) 4 days , e ) 8 days
Rationale: the equation portraying the given problem is : 10 * x – 2 * ( 30 – x ) = 216 where x is the number of working days . solving this we get x = 23 number of days he was absent was 7 ( 30 - 23 ) days . answer : a
Answer: a
Python program:
a = 30 * 10
b = a - 216
c = 10 + 2 
d = b / c
Problem: if 9 ^ y = 3 ^ 16 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "9 ^ y = 3 ^ 2 y = 3 ^ 16 2 y = 16 y = 8 the answer is e ."
Answer: e
Python program:
a = 16 / 2
Problem: the average age of 3 boys is 15 years and their ages are in proportion 3 : 5 : 7 . what is the age in years of the eldest boy ?
Options: a ) 6 , b ) 9 , c ) 16 , d ) 4 , e ) 21
Rationale: 3 x + 5 x + 7 x = 45 x = 3 7 x = 21 answer : e
Answer: e
Python program:
a = 15 * 3
b = a / 15
c = 7 * b
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 19 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 10 , e ) 29 / 100
Rationale: "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 19 - 2 cmb = 100 b - cb - mb - 2 cmb = 29 hence the probability = 29 / 100 . e"
Answer: e
Python program:
a = 50 + 40 
b = a - 19
c = 100 - b
d = c / 100
Problem: a towel , when bleached , lost 30 % of its length and 15 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 40.5 % , c ) 44 % , d ) 54 % , e ) 64 %
Rationale: "percentage change in area = ( − 30 − 15 + ( 30 × 15 ) / 100 ) % = − 40.5 % i . e . , area is decreased by 40.5 % answer : b"
Answer: b
Python program:
a = 100 * 100
b = 100 - 30
c = 100 - 15
d = b * c
e = a - d
f = e / 100
Problem: if a , b and c together can finish a piece of work in 4 days . a alone in 12 days and b in 24 days , then c alone can do it in ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: c = 1 / 4 - 1 / 12 – 1 / 24 = 1 / 8 = > 8 days ' answer : c
Answer: c
Python program:
a = 1 / 12
b = const_0_25 - a
c = 1 / 24
d = b - c
e = 1 / d
Problem: at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 15 of which were white and 15 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 20 % , b ) 25 % , c ) 62.5 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 15 short - stemmed pink = 15 = > short - stemmed red = 10 15 / p = 10 / r = > r = 2 r / 3 so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + 2 r / 3 + 20 = 120 = > 5 r = 300 and r = 60 long stemmed r = 60 - 10 = 50 so long stemmed red / r = 50 / 80 = 62.5 % answer - c"
Answer: c
Python program:
a = 120 / 3
b = 120 - a
c = 120 / 3
d = c - 15
e = d - 15
f = b * e
g = 120 / 3
h = g - 15
i = h - 15
j = 15 + i 
k = f / j
l = 120 / 3
m = 120 - l
n = k / m
o = n * 100
Problem: the average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 120 kg , b ) 130 kg , c ) 137 kg , d ) 190 kg , e ) none
Rationale: "solution total weight increased = ( 10 x 7.2 ) kg = 72 kg . weight of new person = ( 65 + 72 ) kg = 137 kg . answer c"
Answer: c
Python program:
a = 10 * 7
b = 65 + a
Problem: a fold density is 19 times greater than the water and for copper it is 9 times . at what ratio you can mix gold and copper to get 15 times denser than water . ?
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 5 , d ) 3 : 8 , e ) 3 : 7
Rationale: suppose x units of gold are mixed with y units of copper to make ( x + y ) units of alloy which is 15 times denser than water . then 19 * x + 9 * y = 15 * ( x + y ) = > 19 * x - 15 * x = 15 * y - 9 * y = > 4 * x = 6 * y = > x / y = 3 / 2 so gold and copper should be mixed respectively in the ratio of 3 : 2 answer : b
Answer: b
Python program:
a = 15 - 9
b = 19 - 15
c = a / b
Problem: r is the set of positive even integers less than 50 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) three , d ) five , e ) seven
Rationale: "squares < 50 { 1 , 4,9 , 16,25 , 36,49 } s = { 1,4 , 16,36 } r = { 2 , . . . . . 48 } hence c ."
Answer: c
Python program:
a = 4 - 1
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 45 , what is the total amount ?
Options: a ) 115 , b ) 116 , c ) 195 , d ) 118 , e ) 119
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 45 39 - - - ? = > 195 answer : c"
Answer: c
Python program:
a = 100 / 45
b = a * 45
c = 50 / 45
d = c * 45
e = b + d 
f = e + 45
Problem: a jar contains a mixture of two liquids acid ( nitric acid ) and base ( ammonium chloride ) in the ratio 4 : 1 . when 10 litres of the mixture is taken out and 10 litres of liquid base is poured into the jar , the ratio becomes 2 : 3 . how many litres of liquid acid was contained in the jar ?
Options: a ) 14 lts , b ) 18 lts , c ) 20 lts , d ) 16 lts , e ) 26 lts
Rationale: % age of liquid base in the original mixture = 1 / 5 x 100 = 20 % in the final mixture % of the liquid base = 3 / 5 x 100 = 60 % now using the rule of allegation hence reduced quantity of the first mixture and the quantity of mixture b which is to be added are the same . total mixture = 10 + 10 = 20 liters and quantity of liquid a = 20 / 5 x 4 = 16 lts answer : d
Answer: d
Python program:
a = 10 + 10 
b = a * 4
c = 1 + 4 
d = b / c
Problem: if x + y = 4 , x - y = 36 , for integers of x and y , x = ?
Options: a ) 20 , b ) 15 , c ) 25 , d ) 13 , e ) 42
Rationale: "x + y = 4 x - y = 36 2 x = 40 x = 20 answer is a"
Answer: a
Python program:
a = 4 + 36 
b = a / 2
Problem: if c is 25 % of a and 15 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 125 % , e ) 250 %
Rationale: "answer = d 25 a / 100 = 20 b / 100 b = 25 a / 20 = 125 a / 100 = 125 %"
Answer: d
Python program:
a = 25 / 100
b = 15 / 100
c = a / b
d = c * 100
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 864 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 864 - 640 = 224 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 224 / 28 = 56 / 7 = 8 total hrs = 40 + 8 = 48 answer d 48"
Answer: d
Python program:
a = 16 * 40
b = 864 - a
c = 100 + 75 
d = 16 * c
e = d / 100
f = b / e
g = 40 + f
Problem: praveen starts business with rs . 3500 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) rs . 7500 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) rs . 6000
Rationale: "let hari ’ s capital be rs . x . then , 3500 * 12 / 7 x = 2 / 3 = > 14 x = 126000 = > x = 9000 . answer : d"
Answer: d
Python program:
a = 5 / 12
b = 1 - a
c = 3500 / b
d = 2 / 3
e = c / d