euclaise/mathqa_programs huggingface dataset:
Problem: if a is an integer greater than 6 but less than 17 and b is an integer greater than 3 but less than 29 , what is the range of a / b ?
Options: a ) 15 / 4 , b ) 13 / 2 , c ) 9 / 7 , d ) 1 / 5 , e ) 7 / 6
Rationale: "the way to approach this problem is 6 < a < 17 and 3 < b < 29 minimum possible value of a is 7 and maximum is 16 minimum possible value of b is 4 and maximum is 28 range = max a / min b - min a / max b ( highest - lowest ) 16 / 4 - 7 / 28 = 15 / 4 hence a"
Answer: a
Python program:
a = 17 - 1
b = 3 + 1 
c = a / b
d = 6 + 1 
e = 29 - 1
f = d / e
g = c - f
Problem: increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 56.25
Rationale: "soln : - x * 1.25 * 1.25 = 1.5625 x so there is a net increase of 56.25 % . answer e ."
Answer: e
Python program:
a = 25 / 100
b = a + 1 
c = 25 / 100
d = c + 1 
e = b * d
f = e - 1
g = f * 100
Problem: ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 61900 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 18 , d ) 99 , e ) 12.5
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 61900 profit ( % ) = ( 61900 - 55000 ) / 55000 * 100 = 12.5 % answer : e"
Answer: e
Python program:
a = 42000 + 13000 
b = 61900 - a
c = 42000 + 13000 
d = b / c
e = d * 100
Problem: increasing the original price of an article by 5 percent and then increasing the new price by 5 percent is equivalent to increasing the original price by
Options: a ) 10.25 % , b ) 12.5 % , c ) 14.75 % , d ) 15.15 % , e ) 16.25 %
Rationale: "1.05 * 1.05 * x = 1.1025 * x the answer is a ."
Answer: a
Python program:
a = 5 / 100
b = 1 + a 
c = 5 / 100
d = 1 + c 
e = b * d
f = e - 1
g = 100 * f
Problem: there are 1200 jelly beans divided between two jars , jar x and jar y . if there are 400 fewer jelly beans in jar x than 3 times the number of beans in jar y , how many beans are in jar x ?
Options: a ) 650 , b ) 700 , c ) 750 , d ) 800 , e ) 850
Rationale: x + y = 1200 so y = 1200 - x x = 3 y - 400 x = 3 ( 1200 - x ) - 400 4 x = 3200 x = 800 the answer is d .
Answer: d
Python program:
a = 1200 + 400 
b = a / 4
c = 1200 - b
Problem: if x is 20 percent more than y and y is 70 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 36 % , e ) 60 %
Rationale: z = 100 ; y = 30 so x = 36 x as % of z = 36 / 100 * 100 = > 36 % answer will be ( d )
Answer: d
Python program:
a = 20 / 100
b = 1 + a 
c = 100 - 70
d = b * c
Problem: how many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language ?
Options: a ) 321 , b ) 65 , c ) 120 , d ) 100 , e ) 80
Rationale: 1 million distinct 3 digit initials are needed . let the number of required alphabets in the language be ‘ n ’ . therefore , using ‘ n ’ alphabets we can form n * n * n = n 3 distinct 3 digit initials . note distinct initials is different from initials where the digits are different . for instance , aaa and bbb are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different . this n 3 different initials = 1 million i . e . n 3 = 106 ( 1 million = 106 ) = > n 3 = ( 102 ) 3 = > n = 102 = 100 hence , the language needs to have a minimum of 100 alphabets to achieve the objective . ans : d
Answer: d
Python program:
a = 1 * 1000
b = a * 1000
c = 10 * 1000
d = b / c
Problem: a train covers a distance of 12 km in 10 min . if it takes 8 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 100 , b ) 110 , c ) 160 , d ) 130 , e ) 140
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 8 = 160 m . answer : option c"
Answer: c
Python program:
a = 12 / 10
b = a - 8
c = 12 / b
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 11 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 14 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 11 k waiters . 14 k = 11 k + 12 k = 4 there are 12 cooks . the answer is d ."
Answer: d
Python program:
a = 12 / 14
b = 12 / 14
c = a * b
Problem: bruce purchased 8 kg of grapes at the rate of 70 per kg and 11 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1165 , c ) c ) 1055 , d ) d ) 1065 , e ) e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 11 kg of mangoes = 55 × 11 = 605 . total cost he has to pay = 560 + 605 = 1165 b"
Answer: b
Python program:
a = 8 * 70
b = 11 * 55
c = a + b
Problem: a 56 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 8 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 5.6 assume x gallons of water are added . 5.6 / 56 + x = 8 / 100 560 = 8 x + 448 8 x = 112 x = 14 correct option : d"
Answer: d
Python program:
a = 10 - 8
b = 56 * a
c = b / 8
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 120 more than a :
Options: a ) 2348 , b ) 3480 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 120 total earning = \ inline \ frac { 58 xy } { 100 } = 3480 answer : b ) rs . 3480"
Answer: b
Python program:
a = 3 * 6
b = 4 * 5
c = a + b 
d = 5 * 4
e = c + d 
f = 4 * 5
g = 3 * 6
h = f - g
i = 120 / h
j = e * i
Problem: if log 2 = 0.3010 and log 3 = 0.4771 , the value of log 5 ( 512 )
Options: a ) 3.876 , b ) 2.967 , c ) 2.87 , d ) 3.912 , e ) 1.9
Rationale: "log 5 ( 512 ) = log ( 512 ) / log 5 = log 2 ^ 9 / log ( 10 / 2 ) = 9 log 2 / ( log 10 - log 2 ) = ( 9 x 0.3010 ) / ( 1 - 0.3010 ) = 2.709 / 0.699 = 2709 / 699 = 3.876 answer is a ."
Answer: a
Python program:
a = 0 / 3010
b = 0 * 3010
Problem: what is the smallest positive integer x such that 507 + x is the cube of a positive integer ?
Options: a ) 15 , b ) 5 , c ) 50 , d ) 2 , e ) 4
Rationale: "given 507 + x is a perfect cube so we will take 512 = 8 * 8 * 8 507 + x = 512 x = 512 - 507 = 5 correct option is b"
Answer: b
Python program:
a = 3 + 4
Problem: a train which has 440 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 56 sec , b ) 44 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 440 / ( ( 45 - 9 ) ( 5 / 18 ) = 440 / 36 * ( 5 / 18 ) = 440 / 10 = 44 sec answer : b"
Answer: b
Python program:
a = 45 / const_3_6
b = 9 / 2
c = b / const_3_6
d = a - c
e = 440 / d
Problem: two numbers have a h . c . f of 16 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2560 / 16 = 160 . answer : c"
Answer: c
Python program:
a = 2560 / 16
Problem: what is the tens digit of 36 ^ 4 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 20 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 6 ( dont actually calculate full values ) and answer is c : 5"
Answer: c
Python program:
a = 4 + 1 
b = 36 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 38 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 38 % of 1100 ) + ( 32 % of 900 ) = 418 + 288 = 706 failed = 2000 - 706 = 1294 failed % = [ ( 1294 / 2000 ) x 100 ] % = 64.7 % . answer : b"
Answer: b
Python program:
a = 100 * 10
b = 2 * a
c = 38 / 100
d = 100 * 10
e = 2 * d
f = e - 900
g = c * f
h = b - g
i = 32 / 100
j = i * 900
k = h - j
l = 100 * 10
m = 2 * l
n = k / m
o = n * 100
Problem: an article is bought for rs . 600 and sold for rs . 450 , find the loss percent ?
Options: a ) 16 % , b ) 18 % , c ) 19 % , d ) 20 % , e ) 25 %
Rationale: "600 - - - - 150 100 - - - - ? = > 16 2 / 3 % answer : e"
Answer: e
Python program:
a = 450 * 100
b = a / 600
c = 100 - b
Problem: 0.003 * 0.5 = ?
Options: a ) 0.00015 , b ) 0.0015 , c ) 0.015 , d ) 0.15 , e ) none of these
Rationale: "explanation : 3 * 5 = 15 . sum of decimal places = 4 . 0.003 * 0.5 = 0.0015 = 0.0015 answer b"
Answer: b
Python program:
a = 0 / 3
b = a * 100
Problem: a man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 8 kmph , d ) 1 kmph , e ) 2 kmph
Rationale: explanation : speed of the boat downstream = speed of the boat upstream \ small \ therefore the speed of the stream = answer : a
Answer: a
Python program:
a = 60 / 3
b = 30 / 3
c = a - b
d = c / 2
Problem: the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 10 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 100 , d ) $ 120 , e ) $ 140
Rationale: "3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 10 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 10 ) = $ 60 . the answer is a ."
Answer: a
Python program:
a = 5 / 3
b = 3 / 2
c = a - b
d = 10 / c
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 600 inclusive ?
Options: a ) 190 , b ) 195 , c ) 305 , d ) 205 , e ) 210
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 600 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 60 ( 10 ) = 600 so we know that there are 60 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 600 = 610 20 + 590 = 610 30 + 580 = 610 etc . since there are 60 total terms , this pattern will create 30 ' pairs ' of 610 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 30 ) ( 610 ) / ( 60 ) = 305 final answer : c"
Answer: c
Python program:
a = 10 + 600 
b = 600 - 10
c = b / 10
d = c + 1 
e = a * d
f = e / 2
g = 600 - 10
h = g / 10
i = h + 1 
j = f / i
Problem: a $ 74.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: "listed selling price of chair = 74.95 $ discounted selling price of chair = 59.95 $ discount = 74.95 - 59.95 = 15 $ % decrease in price of chair = ( 15 / 74.95 ) * 100 % = 20 % approx answer b"
Answer: b
Python program:
a = 74 - 95
b = a / 74
c = b * 100
Problem: if rs . 595 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 420 , b ) s . 360 , c ) s . 389 , d ) s . 368 , e ) s . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 595 * 2 / 17 = rs . 70 b ' s share = 595 * 3 / 17 = rs . 105 c ' s share = 595 * 12 / 17 = rs . 420 . answer : a"
Answer: a
Python program:
a = 2 / 3
b = 1 / 4
c = a * b
d = 1 / 4
e = c + d 
f = e + 1 
g = 595 / f
Problem: a part - time employee ’ s hourly wage was increased by 50 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 15 % , c ) 25 % , d ) 33 % , e ) 50 %
Rationale: let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 50 % wage increase , the employee makes $ 1.50 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.50 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.50 to get : new # of hours = 100 / 1.50 ≈ 67 hours so , the number of hours decreases from 100 hours to ( approximately ) 67 hours . this represents a 33 % decrease ( approximately ) . answer : d
Answer: d
Python program:
a = 50 / 100
b = 50 + 100 
c = b / 100
d = a / c
e = d * 100
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 3 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 5 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 3 ) / ( 10 - 5 ) = 2 / 5 so they should be mixed in the ratio 2 : 5 answer - a"
Answer: a
Python program:
a = 5 - 3
b = 10 - 5
c = a / b
Problem: the q train leaves station a moving at a constant speed , and passes by stations b and c , in this order . it takes the q train 7 hours to reach station b , and 5 additional hours to reach station c . the distance between stations a and b is m kilometers longer than the distance between stations b and c . what is the distance between stations a and c in terms of m ?
Options: a ) 1.8 m , b ) 6 m , c ) 7 m , d ) 9 m , e ) 12 m
Rationale: the reason it is failing for you is that you chose incorrect numbers . if the question says it q took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b
Answer: b
Python program:
a = 5 / 7
b = 1 - a
c = 2 / b
d = c - 1
Problem: what is the area of a square field whose sides have a length of 12 meters ?
Options: a ) 225 sq m , b ) 126 sq m , c ) 144 sq m , d ) 267 sq m , e ) 231 sq m
Rationale: "12 * 12 = 144 sq m the answer is c ."
Answer: c
Python program:
a = square_area / (
Problem: if 4 a – 2 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . d"
Answer: d
Python program:
a = 32 - 4
b = a - 4
c = b - 2
d = c - 2
e = d - 1
f = e - 4
g = f - 1
h = g + 2 
i = h - 4
j = i - 4
Problem: a room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 107 , b ) 117 , c ) 127 , d ) 137 , e ) 147
Rationale: "let us calculate both the length and width of the room in centimeters . length = 6 meters and 24 centimeters = 624 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 624 and 432 = 48 thus , the number of square tiles required = ( 624 x 432 ) / ( 48 x 48 ) = 13 x 9 = 117 answer : b"
Answer: b
Python program:
a = 6 * 100
b = a + 24 
c = 4 * 100
d = c + 32 
e = b * d
f = 6 * 100
g = f + 24 
h = 4 * 100
i = h + 32 
j = math.gcd(g, i)
k = 6 * 100
l = k + 24 
m = 4 * 100
n = m + 32 
o = math.gcd(l, n)
p = j * o
q = e / p
Problem: how many integers are between 8 and 122 / 7 , inclusive ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 16
Rationale: 122 / 7 = 17 . xx we are not concerned about the exact value of 122 / 7 as we just need the integers . the different integers between 8 and 122 / 7 would be 8 , 9 , 10 , 11 , 12,13 , 14,15 , 16,17 total number of integers = 10 option b
Answer: b
Python program:
a = 122 / 7
b = a - 8
c = b + 1
Problem: there are 60 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 37 , c ) 42 , d ) 53 , e ) 64
Rationale: "x + ( x - 14 ) = 60 - - > x = 37 . answer : b ."
Answer: b
Python program:
a = 60 + 14 
b = a / 2
Problem: a man sitting in a train which is traveling at 50 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 50 ) kmph = 62 kmph . answer : c .
Answer: c
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 50
Problem: the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of the remainingplayers is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 18 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c"
Answer: c
Python program:
a = 26 + 3 
b = a + 26 
c = 11 - 2
d = b - c
e = 11 - 2
f = 11 - e
g = d / f
Problem: the true discount on a bill of rs . 2160 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2160 td = rs . 360 pw = f - td = 2160 - 360 = rs . 1800 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 1800 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 1800 × 2160 = 15 × 2160 = rs . 432 answer : option a"
Answer: a
Python program:
a = 2160 - 360
b = 360 / a
c = b * 2160
Problem: if the cost price is 82 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 22 % , c ) 13 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 82 profit = $ 18 profit % = 18 / 82 * 100 = 25 / 6 = 22 % approximately answer is b"
Answer: b
Python program:
a = 100 - 82
b = a / 82
c = b * 100
Problem: the average of first six prime numbers which are between 50 and 90 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 64 , e ) 67
Rationale: "explanation : first six prime numbers which are between 50 and 90 = 53 , 59 , 61 , 67 , 71 , 73 average = ( 53 + 59 + 61 + 67 + 71 + 73 ) / 6 = 64 answer : d"
Answer: d
Python program:
a = 50 + 1
Problem: if 0.5 % of a = 85 paise , then the value of a is ?
Options: a ) rs . 170 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 85 / 100 ∴ a = rs . ( 85 / 0.5 ) = rs . 170 correct option : a"
Answer: a
Python program:
a = 85 / 0
Problem: suganya and suriya are partners in a business . suganya invests rs . 15,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 31,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 18,040 , d ) rs . 7015.56 , e ) none
Rationale: "solution ratio of their shares = ( 15000 ã — 8 ) : ( 42000 ã — 10 ) = 2 : 7 . suganya ' s share = rs . ( 31570 ã — 2 / 9 ) = rs . 7015.56 answer d"
Answer: d
Python program:
a = const_0_25 * 100
b = a * 10
Problem: find the compound interest on $ 1200 for 5 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 1786 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 5 = $ 2986 ci = $ 1786 answer is c"
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = b ** 5
d = 1200 * c
e = d - 1200
Problem: a person want to give his money of $ 15800 to his 4 children a , b , c , d in the ratio 5 : 9 : 6 : 5 . what is the a + c share ?
Options: a ) $ 4000 , b ) $ 2890 , c ) $ 3005 , d ) $ 6952 , e ) $ 6003
Rationale: "a ' s share = 15800 * 5 / 25 = $ 3160 c ' s share = 15800 * 6 / 25 = $ 3792 a + c = $ 6952 answer is d"
Answer: d
Python program:
a = 5 + 3 
b = a + 6 
c = 3 / 0
d = c * 15800
Problem: a certain class of students is being divided into teams . the class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 12 24 so , lets find the least common multiple of 12 24 , ie 24 so our answer is ( a ) 24"
Answer: a
Python program:
a = math.lcm(12, 24)
Problem: a group of 6 children and 10 adults are going to the zoo . child tickets cost $ 10 , and adult tickets cost $ 16 . how much will the zoo tickets cost in all ?
Options: a ) $ 220 , b ) $ 340 , c ) $ 150 , d ) $ 100 , e ) $ 120
Rationale: step 1 : find the cost of the children ' s tickets . 6 × $ 10 = $ 60 step 2 : find the cost of the adults ' tickets . 10 × $ 16 = $ 160 step 3 : find the total cost . $ 60 + $ 160 = $ 220 the zoo tickets will cost $ 220 . answer is a .
Answer: a
Python program:
a = 6 * 10
b = 10 * 16
c = a + b
Problem: the price of rice falls by 40 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 40 % , new price for 20 kg rice , = ( 100 - 40 % of 100 ) = 60 new price of rice = 60 / 20 = rs . 3 per kg . rice can bought now at = 100 / 3 = 33.33 kg . answer : option e"
Answer: e
Python program:
a = 100 - 40
b = a / 20
c = 100 / b