euclaise/mathqa_programs huggingface dataset:
Problem: how many multiples of 10 are there between 11 and 1001 ?
Options: a ) 98 , b ) 99 , c ) 100 , d ) 97 , e ) 95
Rationale: "10 * 2 = 20 10 * 100 = 1000 total multiples = ( 100 - 2 ) + 1 = 99 answer b"
Answer: b
Python program:
a = 1001 - 11
b = a / 10
c = b + 1
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "rom the beginning ; initially milk to water is 12 l : 8 l remove half 6 - 4 add 10 l milk 16 - 4 remove half 8 - 2 add 10 l milk 18 - 2 18 : 2 = 9 : 1 answer : b"
Answer: b
Python program:
a = 3 + 2 
b = 3 / a
c = 20 - 10
d = b * c
e = d + 10 
f = e / 20
g = 20 - 10
h = f * g
i = h + 10 
j = 3 + 2 
k = 2 / j
l = 20 - 10
m = k * l
n = m / 20
o = 20 - 10
p = n * o
q = i / p
Problem: 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days x do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time x = 3 days to finish the task imo a"
Answer: a
Python program:
a = 6 * 8
b = 3 * 6
c = a - b
d = 6 + 4 
e = c / d
Problem: if an investor puts $ 600 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 661.50 , b ) $ 663.50 , c ) $ 665.50 , d ) $ 667.50 , e ) $ 669.50
Rationale: "1.05 * 1.05 * 600 = $ 661.50 the answer is a ."
Answer: a
Python program:
a = 10 / 2
b = a / 100
c = 1 + b 
d = c ** 2
e = 600 * d
Problem: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 6 is
Options: a ) 3 , b ) 7 , c ) 21 , d ) 189 , e ) 198
Rationale: in that case , the sophie prime numbers greater than 6 are 7 , 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be d
Answer: d
Python program:
a = 6 - 1
b = 2 + 1 
c = a + b 
d = 2 + 1 
e = c + d 
f = e - 10
g = 6 - 1
h = 2 + 1 
i = g + h 
j = 2 * i
k = j + 1 
l = k - 10
m = f * l
n = 2 + 1 
o = m * n
p = 6 - 1
q = 2 + 1 
r = p + q 
s = 2 + 1 
t = r + s 
u = 2 + 1 
v = t + u 
w = 2 * v
x = w + 1 
y = 2 * 10
z = x - y
A = o * z
Problem: the difference of two numbers is 1335 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 264
Rationale: "let the smaller number be x . then larger number = ( x + 1335 ) . x + 1335 = 6 x + 15 5 x = 1320 x = 264 smaller number = 264 . answer e"
Answer: e
Python program:
a = 1335 + 15 
b = 6 - 1
c = a / b
Problem: dawson has to secure 30 % marks to clear his exam of class 8 th . he got 30 marks and failed by 36 marks . what is the maximum marks ?
Options: a ) 180 , b ) 190 , c ) 200 , d ) 210 , e ) 220
Rationale: e 220 to pass the exam ravish needs 30 + 36 = 66 marks . = > ( 66 / 30 ) * 100 = 220
Answer: e
Python program:
a = 30 + 36 
b = a * 100
c = b / 30
Problem: if the price of a book is first decreased by 15 % and then increased by 10 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 6.5 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . decreased by 15 % = 85 then increased 10 % on rs 85 = 85 + 8.5 = 93.5 net change in price = 100 - 93.5 = 6.5 answer : c"
Answer: c
Python program:
a = 100 * 15
b = a / 100
c = 100 - b
d = c / 100
e = 100 * 10
f = e / 100
g = 100 + f 
h = g / 100
i = d * h
j = i * 100
k = 100 - j
Problem: a warehouse is labeling computer inventory with 5 - digit codes . each code is to consist of 4 digits between the numbers 0 and 9 . the manager is debating whether to allow any 5 - digit codes to have leading zero ' s before a non - zero number is used . if not allowed , then numbers like 0025 cannot be used . the manager wants to measure the magnitude of the number of 5 - digit code possibilities that are lost if he disallows the use of leading zero ' s . how many such codes would be lost ?
Options: a ) 981 , b ) 1000 , c ) 1011 , d ) 10000 , e ) 1110
Rationale: the number of codes possible if leading zero is allowed = 10 * 10 * 10 * 10 * 10 = 10 ^ 5 the number of codes possible if leading zero is not allowed = 9 * 10 * 10 * 10 * 10 = 9 * 10 ^ 4 the difference = 10 ^ 5 - 9 * 10 ^ 4 = 10 ^ 4 ( 10 - 9 ) = 10 ^ 4 . answer : d . similar questions to practice : hope it helps .
Answer: d
Python program:
a = 10 ** 5
b = 10 ** 4
c = 9 * b
d = a - c
Problem: tim and é lan are 90 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 45 miles . , d ) 60 miles . , e ) 65 miles .
Rationale: "in 1 st hour : relative speed of the two will be 10 + 5 = 15 miles / hour . as they move towards each other , the distance between them reduces by 15 miles . distance left between them : 90 - 15 = 75 miles . in 2 nd hour : speed of tim : 20 mph , that of elan : 10 mph . relative speed of the two will be 20 + 10 = 30 miles / hour . as they move towards each other , the distance between them reduces by 30 miles . distance left between them : 75 - 30 = 45 miles . in 3 rd hour : speed of tim : 40 mph , that of elan : 20 mph . relative speed of the two will be 40 + 20 = 60 miles / hour . now in order to cover the remaining distance of 45 miles . they will take : ( 45 / 60 ) hrs . = ( 3 / 4 ) hour . distance travelled by tim ? in first hour : 1 hour * ( 10 miles per hour ) = 10 miles in second hour : 1 hour * ( 20 miles per hour ) = 20 miles in third hour : ( 3 / 4 ) hour * ( 40 miles per hour ) = 30 miles total distance travelled : 10 + 20 + 30 = 60 miles . d is the answer"
Answer: d
Python program:
a = 5 + 10 
b = 10 / a
c = b * 90
Problem: every year an amount increases by 1 / 9 th of itself . how much will it be after two years if its present value is rs . 64000 ?
Options: a ) 81000 , b ) 81007 , c ) 81008 , d ) 79012.3 , e ) 81022
Rationale: "64000 * 10 / 9 * 10 / 9 = 79012.3 answer : d"
Answer: d
Python program:
a = 1 / 9
b = a * 64000
c = 64000 + b 
d = 1 / 9
e = 1 / 9
f = e * 64000
g = 64000 + f 
h = d * g
i = c + h
Problem: if c is 20 % of a and 10 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 200 %
Rationale: answer = e 20 a / 100 = 10 b / 100 b = 20 a / 10 = 200 a / 100 = 200 %
Answer: e
Python program:
a = 20 / 100
b = 10 / 100
c = a / b
d = c * 100
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 3600 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 4500 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 3600 5 - - - ? = > 4500 answer : b"
Answer: b
Python program:
a = 12 - 7
b = 7 - 3
c = 3600 / b
d = a * c
Problem: the area of a triangle will be when a = 1 m , b = 2 m , c = 5 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1
Rationale: s = ( 1 + 2 + 5 ) / 2 = 4 answer : c
Answer: c
Python program:
a = 1 + 2 
b = a + 5 
c = b / 2
Problem: a and b can do a work in 25 days and 10 days respectively . a starts the work and b joins him after 2 days . in how many days can they complete the remaining work ?
Options: a ) 4.28 days , b ) 4.38 days , c ) 5.28 days , d ) 6.28 days , e ) 2.28 days
Rationale: "work done by a in 2 days = 2 / 5 remaining work = 3 / 5 work done by both a and b in one day = 1 / 25 + 1 / 10 = 7 / 50 remaining work = 3 / 5 * 50 / 7 = 4.28 days . answer : a"
Answer: a
Python program:
a = 1/(10)
b = 1/(25)
c = a + b 
d = 1/(c)
e = d + 25 
f = e - 3
Problem: a grocery store priced a gallon of milk at 25 % above the wholesale price of $ 4 . if a customer comes in with a coupon for 5 % off milk , how much does that customer pay ?
Options: a ) $ 4.95 , b ) $ 4.75 , c ) $ 5.05 , d ) $ 4.50 , e ) $ 5.25
Rationale: wholesale cost of milk = $ 4 milk was priced at 25 % above $ 4 = $ 5 % discount given by coupon = 5 % customer paid = . 95 * 5 = $ 4.75 answer b
Answer: b
Python program:
a = 25 / 100
b = a + 1 
c = b * 4
d = c / 100
e = d * 5
f = 5 - e
Problem: a number is doubled and 9 is added . if resultant is trebled , it becomes 81 . what is that number
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 81 = > 2 x + 9 = 27 = > x = 9 answer : option a"
Answer: a
Python program:
a = 3 * 9
b = 81 - a
c = 3 * 2
d = b / c
Problem: what is the average of odd numbers from 1 to 79 ?
Options: a ) 30 , b ) 25 , c ) 35 , d ) 40 , e ) 45
Rationale: "sum of n odd natural number is given by , sum of n odd natural numbers = n * n average of n odd natural numbers is given by , = ( n * n ) / n = n . here , n = number of terms = ( 79 + 1 ) / 2 = 40 . so , required average = 40 . answer : d"
Answer: d
Python program:
a = 1 + 1 
b = 1 * a
c = b / 2
d = c / 1
e = d * 79
Problem: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 120000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4800 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 120000 p = rs . [ ( 24 * 4 * 4 * 120000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 46080000 / 9600 ) = > p = rs . 4800 answer : d"
Answer: d
Python program:
a = 24 * 4
b = a * 4
c = b * 120000
d = 10 * 16
e = d * 6
f = e * 10
g = c / f
Problem: in an exam ashley secured 332 marks . if she secured 83 % makes , find the maximum marks
Options: a ) 133 , b ) 376 , c ) 377 , d ) 400 , e ) 377
Rationale: let the maximum marks be m . ashley ’ s marks = 83 % of m ashley secured 332 marks therefore , 83 % of m = 332 ⇒ 83 / 100 × m = 332 ⇒ m = ( 332 × 100 ) / 83 ⇒ m = 33200 / 83 ⇒ m = 400 therefore , ashley got 332 marks out of 400 marks . answer : d
Answer: d
Python program:
a = 83 / 100
b = 332 / a
Problem: a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 24 years , e ) none of these
Rationale: "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years = > ( x + 24 ) + 2 = 2 ( x + 2 ) = > x + 26 = 2 x + 4 so , x = 22 option c"
Answer: c
Python program:
a = 2 * 2
b = a - 2
c = 24 - b
d = 2 - 1
e = c / d
Problem: if 3 x = 8 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 2 z , c ) 11 z / 24 , d ) 3 z / 5 , e ) z / 9
Rationale: "3 x = 8 y = z x = z / 3 and y = z / 8 x + y = z / 3 + z / 8 = 11 z / 24 answer is c"
Answer: c
Python program:
a = 3 * 100
b = a / 2
c = b - 2
d = 3 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: a train requires 10 seconds to pass a pole while it requires 35 seconds to cross a stationary train which is 500 mtrs long . find the speed of the train .
Options: a ) 68 kmph , b ) 70 kmph , c ) 72 kmph , d ) 60 kmph , e ) 50 kmph
Rationale: "in 10 s the train crosses the pole and in 35 sec the train crosses one more stationary train in 25 sec the train travels a distance of 500 mtrs speed = 500 / 25 = 20 m / s = 20 ( 3600 / 1000 ) = 20 * 18 / 5 = 72 kmph answer : c"
Answer: c
Python program:
a = 35 - 10
b = 500 / a
c = b * const_3_6
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 12000 x 7 ) + 6000 ( x - 7 ) 2000 x = 42000 x = 21 . answer b"
Answer: b
Python program:
a = 12000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: the radius of a wheel is 22.6 cm . what is the distance covered by the wheel in making 750 resolutions ?
Options: a ) 754 m , b ) 704 m , c ) 1055.04 m , d ) 1058.04 m , e ) 204 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 750 resolutions . = 750 * 2 * 22 / 7 * 22.6 = 105504 cm = 1055.04 m answer : c"
Answer: c
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 750
i = h / 100
Problem: car z travels 45 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 360 , c ) 400 , d ) 408.3 , e ) 440
Rationale: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 45 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 36 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 36 miles / gallon * 10 gallons = 360 miles . answer b ."
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = b * 45
d = c * 10
Problem: evaluate : log 3 27
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "solution log 3 27 = n = 3 n = 27 = 33 n ‹ = › 3 . answer a"
Answer: a
Python program:
a = 27 / 3
b = 3 / a
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 140 m length ?
Options: a ) 82.1 sec . , b ) 12.5 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 140 = 250 m . required time = 250 / 20 = 12.5 sec . answer : b"
Answer: b
Python program:
a = 110 + 140 
b = 72 * const_0_2778
c = a / b
Problem: the average of 12 result is 55 . average of the first 6 of them is 42 and that of the last 6 is 48 . find the 8 th result ?
Options: a ) 35 , b ) 564 , c ) 526 , d ) 48 , e ) 50
Rationale: "sum of all the 12 results = 12 * 55 = 660 sum of the first 6 of them = 6 * 42 = 252 sum of the last 6 of them = 6 * 48 = 288 so , the 8 th number = 600 + 252 - 288 = 564 . b"
Answer: b
Python program:
a = 6 * 42
b = 6 * 48
c = a + b 
d = 12 * 55
e = c - d
Problem: 15 % of 75 is the same as vx % of 450 . find x .
Options: a ) 1 , b ) 2.5 , c ) 3 , d ) 4 , e ) 5
Rationale: 15 % of 75 = 11.25 450 * x / 100 = 11.25 x = 2.5 answer : b
Answer: b
Python program:
a = 15 * 75
b = a / 450
Problem: a fill pipe can fill 1 / 2 of cistern in 25 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 10 min , b ) 15 min , c ) 20 min , d ) 25 min , e ) 30 min
Rationale: "required time = 25 * 2 * 1 / 2 = 25 minutes answer is d"
Answer: d
Python program:
a = 25 / 1
Problem: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 520 ?
Options: a ) 259 , b ) 498 , c ) 676 , d ) 823 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 520 y = 2 x + 2 518 = 2 x x = 259 answer : a . 259"
Answer: a
Python program:
a = 520 - 2
b = a / 2
Problem: if 15 % of 40 is greater than 25 % of a number by 2 , the number is
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "explanation : 15 / 100 * 40 - 25 / 100 * x = 2 or x / 4 = 4 so x = 16 option b"
Answer: b
Python program:
a = 15 / 100
b = a * 40
c = b - 2
d = 25 / 100
e = c / d
Problem: john purchased 1325 large bottles at $ 1.89 per bottle and 750 small bottles at $ 1.38 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.63 , b ) $ 1.71 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.76
Rationale: "( 1325 * 1.89 + 750 * 1.38 ) / ( 1325 + 750 ) = ~ 1.71 option ( b )"
Answer: b
Python program:
a = 1325 * 1
b = 750 * 1
c = a + b 
d = 1325 + 750 
e = c / d
Problem: find the smallest number of six digits exactly divisible by 25 , 35,45 and 15 .
Options: a ) 100555 , b ) 100775 , c ) 100885 , d ) 100995 , e ) 100665
Rationale: "smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 â € “ 800 ) = 100775 . answer is b ."
Answer: b
Python program:
a = 100 * 100
b = 10 * a
c = b - 100
d = c + 35
Problem: the moon revolves around the earth at a speed of approximately 1.05 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,780 , e ) 3,672
Rationale: moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.05 * 3600 = 3780 kilometers per hour . option d is correct
Answer: d
Python program:
a = 1 * 5
Problem: the speed of a car is 100 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 80 , d ) 54 , e ) 15
Rationale: "s = ( 100 + 60 ) / 2 = 80 kmph answer : c"
Answer: c
Python program:
a = 100 + 60 
b = a / 2
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 1446 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 32200 , b ) 41897 , c ) 58799 , d ) 60000 , e ) 62782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 1446 p = 60000 answer : d"
Answer: d
Python program:
a = 20 + 1 
b = 20 + 1 
c = a * b
d = 20 + 1 
e = c + d
Problem: a man buys a cycle for rs . 2000 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) 1800 , b ) 1420 , c ) 1430 , d ) 1440 , e ) 1540
Rationale: "s . p . = 90 % of rs . 2000 = 90 / 100 x 2000 = rs . 1800 answer : a"
Answer: a
Python program:
a = 100 - 10
b = a * 2000
c = b / 100
Problem: a runs twice as fast as b and gives b a start of 71 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 150 m . , d ) 142 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 71 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 71 m is 71 / 1 = 71 m so the total time taken by a and b to reach = 2 * 71 = 142 m answer : d"
Answer: d
Python program:
a = 71 * 2
Problem: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of b .
Options: a ) 240 , b ) 288 , c ) 277 , d ) 390 , e ) 361
Rationale: "( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 13 / 21 * 630 = 390 answer : d"
Answer: d
Python program:
a = 3000 * 8
b = 3000 - 1000
c = 12 - 8
d = b * c
e = a + d 
f = 4000 * 8
g = 4000 + 1000 
h = 12 - 8
i = g * h
j = f + i 
k = e + j 
l = 630 / k
m = 3000 * 8
n = 3000 - 1000
o = 12 - 8
p = n * o
q = m + p 
r = l * q
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 500 , find the original price per kg ?
Options: a ) s . 12.7 , b ) s . 12.4 , c ) s . 12.5 , d ) s . 12.1 , e ) s . 12.9
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 500 - - - 80 ? - - - 2 = > rs . 12.5 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a * 500
c = b / 10
d = 20 / 100
e = d * 500
f = c / e
g = f * 100
Problem: evaluate : 59 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 51 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 59 - 12 * 3 * 2 = 59 - 8 = 51 correct answer b"
Answer: b
Python program:
a = 12 * 3
b = a * 2
c = 59 - b
Problem: the average age of a class of 20 students is 22 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 42 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 22 , average would not have changed . since average increased by 2 , age of the teacher = 19 + 22 × 1 = 44 answer : e"
Answer: e
Python program:
a = 20 + 2 
b = 22 + 2 
c = a * b
d = 20 * 22
e = c - d
Problem: the length of a rectangle is 18 cm and its breadth is 10 cm . when the length is increased to 25 cm , what will be the breadth of the rectangle if the area remains the same ?
Options: a ) 7 cm
b ) 7.1 cm
c ) 7.2 cm
d ) 7.3 cm
e ) none of these
Rationale: solution let the breadth be b . then , ⇒ 25 b = 18 × 10 ⇒ b = ( 18 x 10 / 25 ) cm = 7.2 cm answer c
Answer: c
Python program:
a = 18 * 10
b = a / 25
Problem: a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 540 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 63
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 540 / 9 = 60 , so the median is also 60 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 63 . option e ."
Answer: e
Python program:
a = 540 / 9
b = a + 3
Problem: walking at 70 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 56
Rationale: "speed is inversly proprtional to time walking at 70 % of speed meand 7 / 10 s takes 10 / 7 t . it takes 24 minutes extra to cover the distance . then 10 / 7 t = t + 24 10 t = 7 t + 168 3 t = 168 t = 56 . option e is correct"
Answer: e
Python program:
a = 70 / 100
b = 1 / a
c = b - 1
d = 24 / c
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 40 % profit ?
Options: a ) 220 , b ) 230 , c ) 960 , d ) 780 , e ) 896
Rationale: "c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 140 % of rs . 640 = 140 / 100 * 640 = rs . 896 . e"
Answer: e
Python program:
a = 832 - 448
b = a / 2
c = 832 - b
d = 40 / 100
e = 1 + d 
f = c * e
Problem: two employees x and y are paid a total of rs . 880 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 880 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 880 â ‡ ’ y [ 12 / 10 + 1 ] = 880 â ‡ ’ 22 y / 10 = 880 â ‡ ’ 22 y = 8800 â ‡ ’ y = 8800 / 22 = 800 / 2 = rs . 400 e )"
Answer: e
Python program:
a = 1 + 4 
b = a * 2
c = 880 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g