euclaise/mathqa_programs huggingface dataset:
Problem: if 20 liters of chemical x are added to 80 liters of a mixture that is 30 % chemical x and 70 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 32 % , b ) 35 % , c ) 38 % , d ) 41 % , e ) 44 %
Rationale: "the amount of chemical x in the solution is 20 + 0.3 ( 80 ) = 44 liters . 44 liters / 100 liters = 44 % the answer is e ."
Answer: e
Python program:
a = 30 / 100
b = a * 80
c = 20 + b
Problem: the present population of a town is 60000 . the population increases annually at 10 % . find the population after 3 years .
Options: a ) 86000 , b ) 79860 , c ) 76300 , d ) 82900 , e ) none of these
Rationale: explanation : solution : the required population is 60000 ( 1 + 10 / 100 ) ^ 3 = 60000 * 110 / 100 * 110 / 100 * 110 / 100 = 79860 answer : b
Answer: b
Python program:
a = 10 + 100 
b = 10 + 100 
c = 10 + 100 
d = 60000 * c
e = d / 100
f = b * e
g = f / 100
h = a * g
i = h / 100
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 4 more than 1 / 4 of the fine and peter paid $ 4 less than 1 / 3 of the fine , leaving pay $ 5 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 30 , b ) $ 25 , c ) $ 35 , d ) $ 40 , e ) $ 45
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 4 ] + [ ( 1 / 3 ) f – 4 ] + [ ( 1 / 2 ) f – 5 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 5 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 60 12 f = 13 f – 60 – f = – 60 f = 60 well , if the fine cost $ 60 , then sam paid the part not covered by joe or peter . half the fine is $ 30 , and sam paid $ 5 less than this : $ 25 . answer = b"
Answer: b
Python program:
a = 1 / 2
b = 1 / 4
c = 1 / 3
d = b + c 
e = a + d 
f = e * 5
g = f + 5 
h = g * 2
i = h + 10
Problem: the total car population in a chennai is 900 out of which 500 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red
Options: a ) 20.5 % , b ) 22.5 % , c ) 21.5 % , d ) 10.5 % , e ) 32.5 %
Rationale: "total honda brand red cars = 90 / 100 * 500 = 450 total red cars = 60 / 100 * 900 = 540 no . of non - honda cars = 900 - 500 = 400 no . of non - honda red cars = 540 - 450 = 90 % of non - honda red cars = 90 / 400 * 100 = 22.5 % answer : b"
Answer: b
Python program:
a = 12 + 12 
b = 90 * 1
c = b + 3 
d = 90 * 1
e = c - d
f = e / 2
g = a - f
Problem: find the least number of 5 digits which is exactly divisible by 12 , 15 and 18 ?
Options: a ) 1080 , b ) 10080 , c ) 10025 , d ) 11080 , e ) 12080
Rationale: lcm = 180 180 ) 10000 ( 55 9900 - - - - - - - - - 100 10000 + 180 - 100 = 10080 answer : b
Answer: b
Python program:
a = 4 * 2
b = 12 * 4
c = a + b 
d = math.lcm(12, 15)
e = math.lcm(d, 18)
f = c * e
Problem: a certain sum amount to $ 1400 in 2 yrs and $ 2000 in 5 years on certain fixed simple interest . in how many yrs would the amount be $ 1640 had it been put at the rate of interest compounded annually ?
Options: a ) 4.5 , b ) 3.5 , c ) 3 , d ) 2 , e ) 1.5
Rationale: we can form equations as following : initial amount = p , total amount after interest = t , interest per year = i t = p + i given t 1 = p + 2 i = 1400 t 2 = p + 5 i = 2000 from this we get , p = 1000 i = 200 $ now we know that simple interest is < compound interest ( ci = si only after 1 st year if ci is compounded annually ) consider simple interest - after 1 st yer it is 200 $ , after 2 nd years it is 400 $ and after 3 rd year it is 600 $ . to get a 240 $ compound interest the duration have to be > 1 year and < 2 years . only option fitting : option e .
Answer: e
Python program:
a = 1640 - 1400
b = 2000 - 1400
c = 5 - 2
d = b / c
e = a / d
f = 2 / 5
g = 1 / 10
h = f - g
i = e + h
Problem: the h . c . f . of two numbers is 15 and their l . c . m . is 620 . if one of the numbers is 375 , then the other is :
Options: a ) 36.6 , b ) 42.8 , c ) 28.4 , d ) 11.6 , e ) 24.8
Rationale: "other number = ( 15 x 620 ) / 375 = 24.8 . answer : e"
Answer: e
Python program:
a = 15 * 375
Problem: from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn .
Options: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 3 , e ) none of these
Rationale: "explanation : total number of cases = 52 total face cards = 16 [ favourable cases ] so probability = 16 / 52 = 4 / 13 option a"
Answer: a
Python program:
a = 4 * 3
b = a / 52
Problem: what is 92 % of 3 / 5 ?
Options: a ) 0.552 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.69
Rationale: "92 % * ( 3 / 5 ) = 0.92 * 0.6 = 0.552 answer : a"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 92 * n
p = o / 100
Problem: if 9 a - b = 10 b + 80 = - 12 b - 2 a , what is the value of 2 a + 22 b ?
Options: a ) - 4 , b ) - 2 , c ) - 80 , d ) 2 , e ) 4
Rationale: "this implies 9 a - b = 10 b + 80 , 9 a - b = - 12 b - 2 a , 10 b + 80 = - 12 b - 2 a manipulating the second equation gives us 10 b + 80 = - 12 b - 2 a = = > 2 a + 22 b = - 80 answer is c"
Answer: c
Python program:
a = 80 / 2
b = a * 2
c = negate * (
Problem: a can do a work in 24 days and b can do it in 8 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 10 days , c ) 6 days , d ) 8 days , e ) 7 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 24 b ' s 1 day ' s work = 1 / 8 they work together = 1 / 24 + 1 / 8 = 6 days answer : option c"
Answer: c
Python program:
a = 1 / 8
b = 1 / 24
c = a - b
d = 1 / c
Problem: the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is :
Options: a ) 25 years , b ) 35 years , c ) 45 years , d ) 55 years , e ) 75 years
Rationale: "solution let their ages be x year and ( x + 10 ) years respectively . then , ( x + 10 ) - 15 = 2 ( x - 15 ) ⇔ x - 5 = 2 x - 30 ⇔ x = 25 . ∴ present age of the elder person = ( x + 10 ) = 35 years . answer b"
Answer: b
Python program:
a = 3 + 2 
b = 10 - a
c = 10 - b
d = 3 + 2 
e = 10 - d
f = e * 2
g = c + f
Problem: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 65 marks . how many sums did sandy get correct ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 65 5 x = 125 x = 25 the answer is d ."
Answer: d
Python program:
a = 2 * 30
b = a + 65 
c = 2 + 3 
d = b / c
Problem: a person distributed 20 % of his income to his 3 children each . he deposited 25 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) a ) 452000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 400000 , e ) e ) 652000
Rationale: "3 children got = 3 * 20 % = 60 % wife got = 25 % orphan house = 5 % total = 60 + 25 + 5 = 90 % remaining = 100 - 90 = 10 % 10 % = 40000 100 % = 40000 * 100 / 10 = $ 400000 answer is d"
Answer: d
Python program:
a = 20 * 3
b = a + 25 
c = b + 5 
d = 100 - c
e = 40000 / d
f = e * 100
Problem: the average weight of 4 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 71 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 4 × 1.5 = 6 kg so the weight of new person = 65 + 6 = 71 kg answer a"
Answer: a
Python program:
a = 4 * 1
b = 65 + a
Problem: convert 0.38 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 17 / 50 , d ) 19 / 50 , e ) none
Rationale: "answer 0.38 = 38 / 100 = 19 / 50 correct option : d"
Answer: d
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 0
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) rs . 20 , b ) rs . 60 . , c ) rs . 40 , d ) rs . 30 , e ) rs . 90
Rationale: ( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : b
Answer: b
Python program:
a = 17 - 5
b = 720 / a
Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 5 times , what is the probability that it will land on either side all 5 times ?
Options: a ) 1 / 5 , b ) 1 / 10 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32
Rationale: "must be either 5 heads or 5 tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 1 / 32 + 1 / 32 = 1 / 16 answer : d"
Answer: d
Python program:
a = 2 ** 4
b = 1 / a
Problem: the average of 10 numbers is 210 . the average of first 5 numbers is 40 and the average of last 4 numbers is 200 . what is the middle number ?
Options: a ) a ) 200 , b ) b ) 2000 , c ) c ) 800 , d ) d ) 2100 , e ) e ) 1100
Rationale: the total of ten numbers = 10 x 210 = 2100 the total of first 5 and last 4 numbers is = 5 x 40 + 4 x 200 = 1000 so , the middle number is ( 2100 - 1000 ) = 1100 e
Answer: e
Python program:
a = 210 * 10
b = 5 * 40
c = a - b
d = 4 * 200
e = c - d
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 10 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 36.55 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.9 = $ 14 - - > x = $ 15.55 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 15.55 + 21 = $ 36.55 . answer : a ."
Answer: a
Python program:
a = 40 / 100
b = 35 * a
c = b + 35
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 240 . their h . c . f is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 240 x = 4 the numbers are 3 * 4 , 4 * 4 , 5 * 4 hence required h . c . f . = 4 answer is c"
Answer: c
Python program:
a = 3 * 5
b = a * 100
c = 4 * 5
d = b + c
Problem: a cistern is normally filled in 14 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 88 , c ) 40 , d ) 99 , e ) 112
Rationale: "1 / 14 - 1 / x = 1 / 16 x = 112 answer : e"
Answer: e
Python program:
a = 1 / 14
b = 14 + 2 
c = 1 / b
d = a - c
e = 1/(d)
Problem: the overall age of x and y is 15 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19
Rationale: b 15 ( x + y ) â € “ ( y + z ) = 15 x â € “ z = 15
Answer: b
Python program:
a = 15 / 1
Problem: sachin is younger than rahul by 5 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 15.5
Rationale: "if rahul age is x , then sachin age is x - 5 , so ( x - 5 ) / x = 7 / 9 = > 9 x - 45 = 7 x = > 2 x = 45 = > x = 22.5 so sachin age is 22.5 - 7 = 15.5 answer : e"
Answer: e
Python program:
a = 9 - 7
b = 5 / a
c = b * 7
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 42 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 , b ) 27 , c ) 50 , d ) 99 , e ) 12
Rationale: "relative speed = 42 + 30 = 72 km / hr . 72 * 5 / 18 = 20 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 20 = 50 sec . answer : c"
Answer: c
Python program:
a = 42 + 30
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 128 and $ 140 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 640 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: "$ 128 for 2 years = $ 64 per year . extra $ 12 yearned with the compound interest is the percent yearned on percent . so , $ 12 is yearned on $ 64 , which means that the interest = 5 % . this on the other hand means that half of the savings = 64 * 5 = $ 320 . twice of that = $ 640 . answer : a ."
Answer: a
Python program:
a = 140 - 128
b = 2 * a
c = b / 128
d = 128 / c
Problem: every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 2 / 5 of the juniors is equal to 1 / 3 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 3 / 20 , b ) 1 / 3 , c ) 5 / 12 , d ) 12 / 17 , e ) 5 / 11
Rationale: "let total number of juniors = j total number of seniors = s ( 2 / 5 ) j = ( 1 / 3 ) s = > s = 6 / 5 j total number of students = j + s = ( 11 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 11 / 5 ) j ] = 5 / 11 answer e"
Answer: e
Python program:
a = 5 * 1
b = 5 * 5
c = 3 + b 
d = a / c
Problem: dominos charges $ 6.25 for a veg pizza of std size that costs a total of $ 2.85 to make . pizza hut charges $ 5.80 for a similar pizza that costs $ 1.80 to make . if dominos sells 2000 pizzas , how many must pizza hut sell to make at least as much in total gross profit as its competitor does ?
Options: a ) 858 , b ) 1875 , c ) 14667 , d ) 63840 , e ) 146667
Rationale: dominos : profit / pizza = 6.25 - 2.85 = 3.75 : no of pizza = 2000 : gross profit = 2000 * 3.75 = 7500 pizza hut : profit / pizza = 4 : gross profit = 7500 : no of cups = 7500 / 4 = 1875 answer b
Answer: b
Python program:
a = 6 - 25
b = a * 2000
c = 5 - 8
d = b / c
e = d + 100
Problem: a certain company reported that the revenue on sales increased 20 % from 2000 to 2003 , and increased 40 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 17 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 120 and and in 2005 140 , so from 2003 to 2005 it increased by ( 140 - 120 ) / 120 = 20 / 120 = 17 % answer : e ."
Answer: e
Python program:
a = 40 / 100
b = 1 + a 
c = 20 / 100
d = 1 + c 
e = b - d
f = 20 / 100
g = 1 + f 
h = e / g
i = h * 100
Problem: the average height of 30 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?
Options: a ) 174.5 , b ) 173.5 , c ) 172.5 , d ) 171.5 , e ) 170.5
Rationale: "the total height was 15 cm too much . the average height should be reduced by 15 cm / 30 = 0.5 cm the answer is a ."
Answer: a
Python program:
a = 30 * 175
b = 151 - 136
c = a - b
d = c / 30
Problem: how many integers are between 2 and 57 / 7 , inclusive ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: "57 / 7 = 8 . xx we are not concerned about the exact value of 57 / 7 as we just need the integers . the different integers between 2 and 57 / 7 would be 2,3 , 4 , 5 , 6 , 7 , 8 . total number of integers = 7 option b"
Answer: b
Python program:
a = 57 / 7
b = a - 2
c = b + 1
Problem: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 130 mangoes .
Options: a ) 360 , b ) 380 , c ) 400 , d ) 406 , e ) 433
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 130 mangoes = 130 * 3.33 = 433 . answer e"
Answer: e
Python program:
a = 1 / 10
b = 1 - a
c = 360 / b
d = c - 360
e = d / 12
f = e * 130
Problem: if 3 a – 2 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 5 , 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 . . b"
Answer: b
Python program:
a = 32 - 5
b = a - 5
c = b - 2
d = c - 2
e = d - 1
f = e - 3
g = f - 1
h = g + 2 
i = h - 3
j = i - 5
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 1000 , what is the least possible value of n ?
Options: a ) 12 , b ) 11 , c ) 14 , d ) 13 , e ) 15
Rationale: 1000 = 2 * 2 * 2 * 5 * 5 * 5 , so we need 3 factors of 2 and 3 factors of 5 . therefore , the smallest value of n is 15 , so the answer is e .
Answer: e
Python program:
a = 1000 / 2
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 2 . in the subsequent n games , the ratio of the team ´ s wins to losses was 1 : 4 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 20 , b ) 9 : 23 , c ) 11 : 27 , d ) 23 : 54 , e ) 31 : 77
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 3 * 4 / 9 + 1 / 5 * 5 / 9 = 4 / 27 + 3 / 27 = 7 / 27 losses = 1 - 7 / 27 = 20 / 27 the ratio of wins to losses is 7 : 20 . the answer is a ."
Answer: a
Python program:
a = 1 + 1 
b = 3 + 0 
c = a / b
Problem: in an it company , there are a total of 120 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 75
Rationale: "you could pick 70 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 75 . e"
Answer: e
Python program:
a = 80 - 120
b = 50 - 35
c = a + b
Problem: a and b can do a piece of work in 6 days , b and c in 8 days , c and a in 12 days . how long will c take to do it ?
Options: a ) 48 days , b ) 55 days , c ) 24 days , d ) 33 days , e ) 40 days
Rationale: "2 c = 1 / 8 + 1 / 12 – 1 / 6 = 1 / 24 c = 1 / 48 = > 48 days answer : a"
Answer: a
Python program:
a = 6 * 3
b = 6 * 3
c = b / 12
d = 6 * 3
e = d / 6
f = 6 * 3
g = f / 8
h = e + g 
i = c + h 
j = i / 2
k = 6 * 3
l = k / 6
m = j - l
n = a / m
Problem: john can row at 5 kmph and still water . he takes 5 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 28 km , b ) 12 km , c ) 16 km , d ) 30 km , e ) 20 km
Rationale: let the distance between a and b be x km . total time = x / ( 5 + 1 ) + x / ( 5 - 1 ) = 5 = > x / 6 + x / 4 = 4 = > ( 2 x + 3 x ) / 12 = 5 = > x = 12 km . answer : b
Answer: b
Python program:
a = 5 + 1 
b = 1 / a
c = 5 - 1
d = 1 / c
e = b + d 
f = 5 / e
Problem: a semicircle has a radius of 12 . what is the approximate perimeter of the semicircle ?
Options: a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 12 + 2 * 12 which is about 62 . the answer is b ."
Answer: b
Python program:
a = circumface / (
b = a + 2
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 64 , find the sum of money ?
Options: a ) 328 , b ) 262 , c ) 72 , d ) 205 , e ) 267
Rationale: a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 64 41 - - - - ? = > rs . 328 answer : a
Answer: a
Python program:
a = 64 / 40
b = 100 + 65 
c = b + 40 
d = a * c
Problem: sonika bought a v . c . r . at the list price of 18,400 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 19,872 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,400 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,400 = 8 ⁄ 100 × 18400 = 1472 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,400 + 1472 = 19,872 . answer a"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = b + 8 
d = c * 100
e = 1 + 4 
f = e * 2
g = d * f
h = 1 + 4 
i = h * 100
j = g + i 
k = 100 + 8 
l = j * k
m = l / 100
n = 1 + 4 
o = n * 100
p = o * 2
q = m / p
r = math.floor(q)
Problem: if x is equal to the sum of the integers from 60 to 80 , inclusive , and y is the number of even integers from 60 to 80 , inclusive , what is the value of x + y ?
Options: a ) 1361 , b ) 1481 , c ) 1601 , d ) 1721 , e ) 1841
Rationale: "x = 60 + 61 + . . . + 80 = 21 ( 70 ) = 1470 y = 11 x + y = 1481 the answer is b ."
Answer: b
Python program:
a = 60 + 80 
b = a / 2
c = 80 - 60
d = c + 1 
e = b * d
f = 80 - 60
g = f / 2
h = g + 1 
i = e + h
Problem: a mixture contains alcohol and water in the ratio 2 : 5 . if 10 liters of water is added to the mixture , the ratio becomes 2 : 7 . find the quality of alcohol in the given mixture .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: let the quantity of alcohol and water be 2 x and 5 x 2 x / ( 5 x + 10 ) = 2 / 7 20 x = 4 ( 3 x + 5 ) x = 5 quantity of alcohol = 2 * 5 = 10 liters . answer is b
Answer: b
Python program:
a = 10 * 1
Problem: in the biology lab of ` ` jefferson ' ' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10800 petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000
Rationale: 5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c
Answer: c
Python program:
a = 10 ** 6
b = a * 5
c = b / 10800
Problem: if x is 11 percent greater than 80 , then x =
Options: a ) 88.8 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "11 % of 80 = ( 80 * 0.11 ) = 8.8 11 % greater than 80 = 80 + 8.8 = 88.8 answer is clearly a ."
Answer: a
Python program:
a = 11 / 100
b = a * 80
c = 80 + b
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1628 ?
Options: a ) s . 109 , b ) s . 108 , c ) s . 110 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1628 74 x = 1628 = > x = 22 5 x = 110 rs . answer : c"
Answer: c
Python program:
a = 6 * 3
b = 9 * 4
c = a + b 
d = 4 * 5
e = c + d 
f = 1628 / e
g = 5 * f