euclaise/mathqa_programs huggingface dataset:
Problem: last year sandy saved 6 % of her annual salary . this year , she made 10 % more money than last year , and she saved 9 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 140 % , b ) 152 % , c ) 165 % , d ) 176 % , e ) 190 %
Rationale: let last year ' s salary be x . last year , sandy save 0.06 x this year , sandy saved 0.09 * 1.1 x = 0.099 x 0.099 x / 0.06 x = 99 / 60 = 1.65 = 165 % the answer is c .
Answer: c
Python program:
a = 9 / 100
b = 100 + 10 
c = a * b
d = 6 * 100
e = d / 100
f = c / e
g = f * 100
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 170 . what is the share of rahul ?
Options: a ) $ 68 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 170 * 2 / 5 = $ 68 answer is a"
Answer: a
Python program:
a = 3 + 2 
b = 2 / a
c = b * 170
Problem: the ratio between sumit ' s and prakash ' s age at present is 2 : 3 . sumit is 6 years younger than prakash . the ratio of sumit ' s age to prakash ' s age after 6 years will be :
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 3 : 8 , e ) none
Rationale: explanation : let their ages be 2 x and 3 x years . 3 x - 2 x = 6 or x = 6 sumit ' s age = 12 years , prakash ' s age = 24 years ratio of their ages = 18 : 24 = 3 : 4 . correct option : c
Answer: c
Python program:
a = 6 * 2
b = a + 6 
c = 6 * 2
d = c + 6 
e = d + 6 
f = b / e
Problem: if a person walks at 12 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 100 km , c ) 60 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 12 12 x = 10 x + 200 2 x = 200 x = 100 km . answer : b"
Answer: b
Python program:
a = 12 - 10
b = 20 / a
c = 10 * b
Problem: cara leaves her home and walks toward don ' s house . two hours later , don leaves his home and walks toward cara ' s house . the distance between their homes is 45 kilometers , cara ' s walking speed is 6 km / h , and don ' s walking speed is 5 km / h . how many kilometers will cara walk before she meets don ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: cara walks 12 km in the first two hours so there are 33 km remaining . when don starts walking , they complete a total of 11 km per hour . they will meet three hours after don starts walking . since cara walks for 5 hours , she walks 30 km . the answer is e .
Answer: e
Python program:
a = 6 * 2
b = 6 * 2
c = 45 - b
d = 6 + 5 
e = c / d
f = 6 * e
g = a + f
Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 3 / 4 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and curved
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8
Rationale: good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 3 / 4 of the garden is green , so , since all the flowers must be either green or yellow , we know that 1 / 4 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( curved ) = 1 / 4 * 1 / 2 = 1 / 8 , or a .
Answer: a
Python program:
a = 3 / 4
b = 1 - a
c = 1 / 2
d = b * c
Problem: 10 / 21 of 3 / 5 of a number is greater than 4 / 7 of 1 / 5 of the same number by 36 . what is half of that number ?
Options: a ) 105 , b ) 180 , c ) 210 , d ) 240 , e ) 315
Rationale: "let no . be x 10 / 21 * 3 / 5 * x - 4 / 7 * 1 / 5 * x = 8 by further solving 30 x / 105 - 4 x / 35 = 36 18 x / 105 = 36 x = 210 we have to find x / 2 = 210 / 2 = 105 answer : a"
Answer: a
Python program:
a = 4 / 0
b = 5 / 5
c = a * b
d = 2 / 0
e = 10 / 7
f = d * e
g = c - f
h = 36 / g
i = h / 1
Problem: the speed of a bus increases by 2 km after every one hour . if the distance travelling in the first one hour was 35 km . what was the total distance travelled in 12 hours ?
Options: a ) 233 , b ) 552 , c ) 376 , d ) 287 , e ) 166
Rationale: given that distance travelled in 1 st hour = 35 km and speed of the bus increases by 2 km after every one hour hence distance travelled in 2 nd hour = 37 km hence distance travelled in 3 rd hour = 39 km . . . total distance travelled = [ 35 + 37 + 39 + . . . ( 12 terms ) ] this is an arithmetic progression ( ap ) with first term , a = 35 , number of terms , n = 12 and common difference , d = 2 . the sequence a , ( a + d ) , ( a + 2 d ) , ( a + 3 d ) , ( a + 4 d ) , . . . is called an arithmetic progression ( ap ) where a is the first term and d is the common difference of the ap sum of the first n terms of an arithmetic progression ( ap ) , sn = n 2 [ 2 a + ( n − 1 ) d ] where n = number of terms hence , [ 35 + 37 + 39 + . . . ( 12 terms ) ] = s 12 = 122 [ 2 × 35 + ( 12 − 1 ) 2 ] = 6 [ 70 + 22 ] = 6 × 92 = 552 hence the total distance travelled = 552 km answer : b
Answer: b
Python program:
a = 12 - 1
b = a * 2
c = 35 + b 
d = 35 + c 
e = 12 / 2
f = d * e
Problem: a tailor trims 11 feet from opposite edges of a square piece of cloth , and 7 feet from the other two edges . if 84 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "let the original side of the square be x . ( x - 22 ) * ( x - 14 ) = 84 = 6 * 14 x = 28 the answer is c ."
Answer: c
Python program:
a = 2 * 11
b = 2 * 3
c = a + b 
d = 2 * 7
e = 2 * 11
f = d * e
g = 84 - f
h = 11 * g
i = 2 * 11
j = 2 * 7
k = i + j 
l = k ** 2
m = h + l 
n = math.sqrt(m)
o = c + n 
p = o / 2
Problem: an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq . m ?
Options: a ) rs . 4082.40 , b ) rs . 1024.21 , c ) rs . 2810.6 , d ) rs . 3214 , e ) none of these
Rationale: explanation : length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 x 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer is a
Answer: a
Python program:
a = 6 * 1
b = 100 + 40 
c = b / 100
d = a * c
e = 100 + 25 
f = e / 100
g = 6 * f
h = d * g
i = h * 45
Problem: in a office work is distribute between p persons . if 1 / 7 members are absent then work increased for each person is ?
Options: a ) 13.67 % , b ) 14.67 % , c ) 15.67 % , d ) 16.67 % , e ) 17.67 %
Rationale: "let total % of work is 100 % total person = p 1 / 7 person are absent of total person . so absent person is 1 / 7 p ie p / 7 . left person is , p - p / 7 = 6 p / 7 . p person do the work 100 % 1 person do the work 100 * p % 6 p / 7 person do the work ( 100 * p * 7 ) / 6 p % = 116.67 % work increased for each person is = ( 116.67 - 100 ) % = 16.67 % answer : d"
Answer: d
Python program:
a = 100 * 7
b = 7 - 1
c = a / b
d = c - 100
Problem: a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 20000 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1600 / 20 × 10 ) = 20000 answer : c"
Answer: c
Python program:
a = 25 * 100
b = 16 * 100
c = a * b
d = 20 * 10
e = c / d
Problem: in a school of 700 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 173 , b ) 126 , c ) 153 , d ) 143 , e ) 133
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 700 * 18 / 100 = 126 answer : b"
Answer: b
Python program:
a = 44 + 28 
b = a + 10 
c = 100 - b
d = 700 * c
e = d / 100
Problem: a shop keeper marked 30 % above the cost price and offered 20 % discount then find it ' s net profit ?
Options: a ) 2 % , b ) 2.5 % , c ) 3.7 % , d ) 4.6 % , e ) 5 %
Rationale: "net profit = 30 - 20 + ( 30 * ( - 25 ) / 100 ) = 2.5 % answer is b"
Answer: b
Python program:
a = 100 + 30 
b = 100 + 30 
c = b * 20
d = c / 100
e = a - d
f = e - 100
Problem: the speed of a car is 100 km in the first hour and 80 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 88 , d ) 54 , e ) 90
Rationale: "s = ( 100 + 80 ) / 2 = 90 kmph answer : e"
Answer: e
Python program:
a = 100 + 80 
b = a / 2
Problem: the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 60 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 95 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 60 ) / 10 avg = 100 - 5 = 95 answer is c"
Answer: c
Python program:
a = 100 * 10
b = a - 60
c = b + 10 
d = c / 10
Problem: there are 300 seniors at morse high school , and 50 % of them have cars . of the remaining grades ( freshmen , sophomores , and juniors ) , only 10 % of them have cars . if 20 % of all the students at morse have cars , how many students are in the 3 lower grades ?
Options: a ) 600 , b ) 900 , c ) 1200 , d ) 1350 , e ) 1500
Rationale: let x be the number of students in the lower three grades . 0.1 x + 150 = 0.2 ( x + 300 ) 0.1 x = 900 x = 900 the answer is b .
Answer: b
Python program:
a = 300 * 50
b = 300 * 20
c = a - b
d = 20 - 10
e = c / d
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 9.95 each . one day , she bought 20 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 199 , d ) $ 171.6 , e ) $ 190
Rationale: $ 9.95 * 20 = $ 199 . answer is c .
Answer: c
Python program:
a = 20 * 9
b = math.floor(a)
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 90 km / hr . what is the length of the platform ?
Options: a ) 229 , b ) 240 , c ) 400 , d ) 277 , e ) 221
Rationale: "speed = 90 * 5 / 18 = 25 m / sec . length of the train = 25 * 20 = 500 m . let the length of the platform be x m . then , ( x + 500 ) / 36 = 25 = > x = 400 m . answer : c"
Answer: c
Python program:
a = 90 * const_0_2778
b = 20 * a
Problem: in a mixed college 160 students are there in one class . out of this 160 students 5 / 8 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 5 / 8 = 100 total boys : 160 - 100 = 60 answer is b"
Answer: b
Python program:
a = 160 / 8
b = a * 3
Problem: a ferry can transport 85 tons of vehicles . automobiles range in weight from 1,800 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 23 , b ) 41 , c ) 48 , d ) 90 , e ) 86
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1800 pounds here since , 1 ton = 2000 pounds 85 tons will be 170,000 pounds from the answer choices : let max number of vehicles be 86 total weight will be = 90 * 1800 = 162000 pounds , which is lesser than the maximum weight allowed . ans : d"
Answer: d
Python program:
a = 85 * 2
b = a * 1000
c = 1000 + 100 
d = c + 100 
e = d + 100 
f = e + 100 
g = f + 100 
h = g + 100 
i = b / h
Problem: if 10 gallons of grape juice are added to 50 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 50 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 50 × 0.10 = 5 gallons of grape juice . 50 × 0.90 = 45 gallons of other components . if we add 10 gallons of grape juice , we will end up with 15 gallons of grape juice and 45 gallons of other components , and we will have a total of 60 gallons of the mixture . so 15 / 60 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 25 / 100 = 25 % . the correct answer is choice ( b )"
Answer: b
Python program:
a = 10 / 100
b = a * 50
c = b + 10 
d = 50 + 10 
e = c / d
f = e * 100
Problem: an artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent . if paint previously accounted for 4 times as much of the expense of painting as did canvas , by what percent did the total cost for paint and canvas decrease ?
Options: a ) 40 % , b ) 44 % , c ) 50 % , d ) 56 % , e ) 60 %
Rationale: paint : canvas cost is 4 : 1 . so , paint accounts for 80 % of cost and canvas accounts for 20 % . canvas , after decrease by 40 % will be ( 100 - 40 ) % of 20 % = > 60 % of 20 % = > 12 % of original paint , after decrease by 60 % will be ( 100 - 60 ) % of 80 % = > 40 % of 80 % = > 32 % of original new cost as a % of old cost = 32 + 12 = 44 % of original . so , overall cost saving = 100 - 44 = 56 % therefore , ( d )
Answer: d
Python program:
a = 40 / 100
b = a * 4
c = 60 / 100
d = b + c 
e = 4 + 1 
f = d / e
g = 1 - f
h = g * 100
Problem: a man can row upstream at 55 kmph and downstream at 65 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 70 , c ) 60 , d ) 80 , e ) 24
Rationale: "us = 55 ds = 65 m = ( 55 + 65 ) / 2 = 60 answer : c"
Answer: c
Python program:
a = 55 + 65 
b = a / 2
Problem: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 60 paise per sq . metre
Options: a ) s 510 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 60 = 51000 p in rs = 51000 / 100 = rs 510 answer : a"
Answer: a
Python program:
a = 110 * 65
b = 2 * 5
c = 110 - b
d = 2 * 5
e = 65 - d
f = c * e
g = a - f
h = g * 60
i = h / 100
Problem: a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 40 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 ∗ 2 / 25 = 40 seconds option c"
Answer: c
Python program:
a = 360 + 140 
b = 45 * 1000
c = b / 3600
d = a / c
Problem: in some quantity of ghee , 60 % is pure ghee and 40 % is vanaspati . if 10 kg of pure ghee is added , then the strength of vanaspati ghee becomes 20 % . the original quantity was :
Options: a ) 10 , b ) 27 , c ) 87 , d ) 23 , e ) 93
Rationale: "explanation : let the original quantity be x kg . vanaspati ghee in x kg = ( 40 x / 100 ) kg = ( 2 x / 5 ) kg . now , ( 2 x / 5 ) / ( x + 10 ) = 20 / 100 < = > 2 x / ( 5 x + 50 ) = 1 / 5 < = > 5 x = 50 < = > x = 10 . answer : a ) 10 kg"
Answer: a
Python program:
a = 20 * 10
b = 40 - 20
c = a / b
Problem: evaluate 926 + 9.026 + 0.926 + 9.0026
Options: a ) 944.9755 , b ) 944.9655 , c ) 944.9565 , d ) 946.9565 , e ) 944.9546
Rationale: "926 + 9.026 + 0.926 + 9.0026 = 944.9546 option e"
Answer: e
Python program:
a = 9 / 26
b = 926 / a
Problem: what is the units digit of the expression 17 ^ 7 - 2 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 7 , e ) 9
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 17 ^ 7 = 3 3 - 2 = 1 answer a"
Answer: a
Python program:
a = 4 + 3 
b = a + 2
Problem: if v is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of v ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: v = 30 ! 8 v = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 out of these 30 , 27 , 24 , 21 , 18 , 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2 , 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 so we have a total of 14 three ' s . . . therefore the maximum value of k can be 14 ( c )
Answer: c
Python program:
a = 30 / 3
b = 3 ** 2
c = 30 / b
d = math.floor(c)
e = a + d 
f = 3 ** 3
g = 30 / f
h = math.floor(g)
i = e + h
Problem: find the side of the largest possible square slabs which can be paved on the floor of a room 2 m 50 cm long and 1 m 50 cm broad . also find the number of such slabs to pave the floor .
Options: a ) 25 , 20 , b ) 30 , 15 , c ) 50 , 15 , d ) none of these , e ) 75,35
Rationale: explanation : hcf ( 250 , 150 ) = 50 cm the number slabs = 250 * 150 / 50 * 50 = 15 answer : c
Answer: c
Python program:
a = 2 + 3 
b = 2 * 3
c = a * b
Problem: a train speeds past a pole in 25 seconds and a platform 200 m long in 30 seconds . its length is :
Options: a ) 1200 m , b ) 2000 m , c ) 1500 m , d ) 1000 m , e ) 4000 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 25 = > y = x / 25 x + 200 / 30 = x / 25 x = 1000 m . answer : option d"
Answer: d
Python program:
a = 2 - 1
b = 200 * a
Problem: two cubes have their volumes in the ratio 1 : 27 . find the ratio of their surface areas .
Options: a ) 1 : 9
b ) 2 : 9
c ) 3 : 9
d ) 5 : 9
e ) none of them
Rationale: let their edges be a and b . then , = a ^ 3 / b ^ 3 = 1 / 27 ( or ) ( a / b ) ^ 3 = ( 1 / 3 ) 3 ( or ) ( a / b ) = ( 1 / 3 ) . therefore , ratio of their surface area = 6 a ^ 2 / 6 b ^ 2 = a ^ 2 / b ^ 2 = ( a / b ) ^ 2 = 1 / 9 , i . e . 1 : 9 . answer is a .
Answer: a
Python program:
a = 1 / 27
b = 1/(3)
c = a ** b
d = c ** 2
Problem: one fourth of a solution that was 14 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 24 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.14 + 25 * x = 100 * 0.16 - - > x = 0.22 . answer : c ."
Answer: c
Python program:
a = 16 / 100
b = a * 4
c = 14 / 100
d = c * 4
e = 14 / 100
f = d - e
g = b - f
h = g * 100
Problem: a certain fraction has the same ratio to 1 / 18 , as 2 / 5 does to 2 / 9 . what is this certain fraction ?
Options: a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 10 , d ) 1 / 12 , e ) 1 / 15
Rationale: "x / ( 1 / 18 ) = ( 2 / 5 ) / ( 2 / 9 ) x = 2 * 9 * 1 / 18 * 5 * 2 = 1 / 10 the answer is c ."
Answer: c
Python program:
a = 1 / 18
Problem: how many odd numbers between 10 and 2000 are the squares of integers ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 43 which includes 20 numbers . the answer is e ."
Answer: e
Python program:
a = 10 + 4
Problem: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score e for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean e = 74 . answer : a ."
Answer: a
Python program:
a = 58 * 3
b = 98 * 2
c = a + b 
d = 2 + 3 
e = c / d
Problem: walking at the rate of 3 kmph a man cover certain distance in 3 hr 20 min . running at a speed of 9 kmph the man will cover the same distance in .
Options: a ) 45 min , b ) 50 min , c ) 40 min , d ) 48 min , e ) 54 min
Rationale: "distance = speed * time 3 * 10 / 3 = 10 km new speed = 9 kmph therefore time = d / s = 10 / 9 = 54 min answer : e ."
Answer: e
Python program:
a = 20 / const_60
b = 3 + a 
c = 3 * b
d = c / 9
e = d * const_60
Problem: what percent is 25 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2.5 % , e ) 3 %
Rationale: "1 kg = 1000 gm 25 / 1000 × 100 = 2500 / 1000 = 5 / 2 = 2.5 % d )"
Answer: d
Python program:
a = 25 / 1
b = a * 100
Problem: an airplane covers 50 miles in 1 / 5 hours . how many miles can the airplane cover in 5 hours ?
Options: a ) 800 , b ) 600 , c ) 1250 , d ) 950 , e ) 1000
Rationale: divide 5 by 1 / 5 = 5 ÷ 1 / 5 = 5 / 1 ÷ 1 / 5 = 5 / 1 * 5 / 1 = 25 . then , multiply 50 by 25 to get 1250 in 5 hours , the airplane will cover 1250 miles answer is c .
Answer: c
Python program:
a = 50 * 5
b = a * 5
Problem: evaluate 35 / . 07
Options: a ) 400 , b ) 500 , c ) 505 , d ) none of these , e ) 506
Rationale: "explanation : 35 / . 07 = 3500 / 7 = 500 option b"
Answer: b
Python program:
a = 7 / 35
b = 100 / 0
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 19.7 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 26 % , c ) 30 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 19.70 let marked price be rs . x . then , 95 / 100 x = 119.70 x = 11970 / 95 = rs . 126 now , s . p . = rs . 126 , c . p . = rs . 100 profit % = 26 % . answer : b"
Answer: b
Python program:
a = 100 + 19 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: 0.003 x 0.2 = ?
Options: a ) 0.0006 , b ) 0.006 , c ) 0.06 , d ) 0.6 , e ) 6.0
Rationale: "3 x 2 = 6 . sum of decimal places = 4 0.003 x 0.2 = 0.0006 answer : option a"
Answer: a
Python program:
a = 0 / 3
b = a * 100
Problem: a candidate who gets 30 % of the marks fails by 60 marks . but another candidate who gets 45 % marks gets 30 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 240 marks , c ) 280 marks , d ) 371 marks , e ) 827 marks
Rationale: "30 % - - - - - - - - - - - - 60 45 % - - - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 90 30 % - - - - - - - - - - - - - - 180 180 + 60 = 240 marks answer : b"
Answer: b
Python program:
a = 60 + 30 
b = 45 / 100
c = 30 / 100
d = b - c
e = a / d
f = 30 / 100
g = e * f
h = g + 60
Problem: in may , the groundskeeper at spring lake golf club built a circular green with an area of 80 π square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 160 π , b ) 320 π , c ) 400 π , d ) 540 π , e ) 640 π
Rationale: "area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 80 π ) = 320 π the answer is b ."
Answer: b
Python program:
a = math.sqrt(80)
b = a * 2
c = b ** 2
d = c * math.pi
Problem: 80 pie square inches of material of negligible thickness are required to construct a 1 / 16 scale model of a cylindrical barrel . if the diameter of the base of the barrel is 160 inches , then what is the volume of the barrel , to the nearest cubic foot ?
Options: a ) 2 pie
b ) 11 pie
c ) 178 pie
d ) 711 pie
e ) 1280 pie
Rationale: radius of barrel , r = 80 radius of model , r = 80 / 16 = 5 surface area of the model = 2 ∗ pi ∗ r ( r + h ) = 80 ∗ pi which gives h = 3 and h = 3 ∗ 16 = 48 so , volume of the barrel = pi ∗ r 2 ∗ h = pi ∗ ( 80 ) 2 ∗ ( 48 ) in cubic inches converting in cubic ft results : volume = pi ∗ ( 80 ) 2 ∗ ( 48 ) / ( 12 ) 3 = 178 pi cubic ft approximately answer [ c ]
Answer: c
Python program:
a = 160 / 2
b = 80 / 2
c = 80 / 16
d = b / c
e = 80 / 16
f = d - e
g = f * 16
h = volume_cylinder / (
i = 10 + 2 
j = i ** 3
k = math.floor(h, j)