euclaise/mathqa_programs huggingface dataset:
Problem: jack spent 1 / 6 of his lifetime in adolescence . his facial hair started growing after 1 / 12 more of his life . he successfully married his girlfriend diana after 1 / 7 more of his life . their son was born after 5 years from then . the son lived just 1 / 2 of what jack lived . jack dies 4 years after his son died . how long did jack live ?
Options: a ) 75 , b ) 90 , c ) 45 , d ) 80 , e ) 84
Rationale: e 84 explanation : let us assume that jack lived for p years . p / 6 + p / 12 + p / 7 + 5 + p / 2 + 4 = x = > p = 84 . therefore , jack lived for 84 years .
Answer: e
Python program:
a = 5 + 4 
b = 1 / 6
c = 1 / 12
d = b + c 
e = 1 / 7
f = d + e 
g = 1 / 2
h = f + g 
i = 1 - h
j = a / i
Problem: if 7 a - 3 b = 10 b + 40 = - 12 b - 2 a , what is the value of 9 a + 9 b ?
Options: a ) - 5 , b ) - 3 , c ) 0 , d ) 3 , e ) 5
Rationale: ( i ) 7 a - 13 b = 40 ( ii ) 2 a + 22 b = - 40 adding ( i ) and ( ii ) : 9 a + 9 b = 0 the answer is c .
Answer: c
Python program:
a = const_0_33 / 1000
Problem: the price of a book is increased from $ 300 to $ 420 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 420 â € “ rs 300 = rs 120 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 120 300 ) * 100 = 40 % c"
Answer: c
Python program:
a = 420 - 300
b = a / 300
c = b * 100
Problem: a train 210 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 50 sec , c ) 44 sec , d ) 49 sec , e ) 28 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 210 + 140 = 350 m required time = 350 * 2 / 25 = 28 sec answer : e"
Answer: e
Python program:
a = 45 - 140
b = a * const_0_2778
c = 210 / b
Problem: the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 8 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2125
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 8 of that new total price : p = 1 / 8 * $ 3,000 = $ 375 . plug this value in the first equation : c + 375 = $ 2,500 - - > c = $ 2,125 . answer : e ."
Answer: e
Python program:
a = const_0_25 * 1000
b = a * 10
c = const_0_25 * 1000
d = c * 10
e = 500 + d 
f = e / 8
g = b - f
Problem: if x is equal to the sum of the integers from 10 to 30 , inclusive , and y is the number of even integers from 10 to 30 , inclusive , what is the value of x + y ?
Options: a ) 401 , b ) 411 , c ) 421 , d ) 431 , e ) 441
Rationale: "x = 10 + 11 + . . . + 30 = 21 ( 20 ) = 420 y = 11 x + y = 431 the answer is d ."
Answer: d
Python program:
a = 10 + 30 
b = a / 2
c = 30 - 10
d = c + 1 
e = b * d
f = 30 - 10
g = f / 2
h = g + 1 
i = e + h
Problem: the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is : explanation :
Options: a ) 101 , b ) 107 , c ) 111 , d ) 117 , e ) 121
Rationale: let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer : option c
Answer: c
Python program:
a = 37 ** 2
b = 4107 / a
c = b * 37
Problem: if 42.36 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.36 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.36 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.36 = km / 50 . . . . . . 36 / 100 = 3 m / 50 . . . . . . m = 6 k + m = 3 + 6 = 9 answer : d"
Answer: d
Python program:
a = 1 / 100
b = const_0_25 - a
c = b * 50
d = 1 / 100
e = const_0_25 - d
f = 42 - 36
g = f / 14
h = c / g
i = 1 / 100
j = const_0_25 - i
k = 42 - 36
l = k / 14
m = h + l
Problem: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 14 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 16 , c ) 20 , d ) 30 , e ) 174
Rationale: the number of integers that belong to set x only is 14 - 6 = 8 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 8 + 12 = 20 . answer : c .
Answer: c
Python program:
a = 18 - 6
b = 14 - 6
c = a + b
Problem: how many seconds will a 700 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 287 , b ) 288 , c ) 600 , d ) 277 , e ) 121
Rationale: "let length of tunnel is x meter distance = 700 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 700 + x = ( 65 / 3 ) * 60 700 + x = 20 * 65 = 1300 x = 1300 - 700 = 600 meters answer : c"
Answer: c
Python program:
a = 63 - 3
b = a * const_0_2778
c = 700 / b
d = c - 1
e = d * 10
f = e * 2
Problem: a bakery has 6 employees . it pays annual salaries of $ 16,000 to each of 2 employees , $ 18,000 to 1 employee , and $ 19,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 17,200 , b ) $ 17,500 , c ) $ 17,800 , d ) $ 18,000 , e ) $ 18,400
Rationale: "average = 2 ( 16000 ) + ( 18000 ) + 3 ( 19000 ) / 6 = $ 17,833 the answer is c ."
Answer: c
Python program:
a = 10 + 10 
b = a + 1 
c = b + 1 
d = c * 3
e = 10 + 10 
f = e - 1
g = f * 2
h = d + g 
i = 10 + 10 
j = i + 1 
k = h + j 
l = k / 6
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 35 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1631
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 35 5 x = 1330 x = 266 large number = 266 + 1365 = 1631 e"
Answer: e
Python program:
a = 1365 - 35
b = 6 - 1
c = a / b
d = c * 6
e = d + 35
Problem: how many odd numbers between 10 and 1400 are the squares of integers ?
Options: a ) 14 , b ) 17 , c ) 20 , d ) 23 , e ) 26
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is b ."
Answer: b
Python program:
a = 10 + 4
Problem: a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 200 , b ) $ 900 , c ) $ 700 , d ) $ 600 , e ) $ 400
Rationale: "b ' s share = 2700 * 3 / 9 = $ 900 answer is b"
Answer: b
Python program:
a = 2 + 3 
b = a + 4 
c = 3 / b
d = c * 2700
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 18 . the larger of the two numbers is :
Options: a ) 276 , b ) 414 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 18 ) . larger number = ( 23 x 18 ) = 414 . answer : option b"
Answer: b
Python program:
a = 23 * 18
Problem: if 6 ^ k = 4 , then 6 ^ ( 2 k + 3 ) =
Options: a ) 2925 , b ) 3456 , c ) 4581 , d ) 3683 , e ) 1308
Rationale: 6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b
Answer: b
Python program:
a = 4 ** 2
b = 6 ** 3
c = a * b
Problem: a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together , what part of the same work they can finish in a day ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 1 , e ) 1 / 4
Rationale: given that b alone can complete the same work in days = half the time taken by a = 9 days a ’ s one day work = 1 / 18 b ’ s one day work = 1 / 9 ( a + b ) ’ s one day work = 1 / 18 + 1 / 9 = 1 / 6 answer : b .
Answer: b
Python program:
a = 18 / 2
b = 1 / a
c = 1 / 18
d = b + c
Problem: an empty fuel tank with a capacity of 212 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 98 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 212 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 212 - a gallons of fuel b is 0.16 ( 212 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 212 - a ) = 30 - - > a = 98 . answer : b ."
Answer: b
Python program:
a = 16 / 100
b = 212 * a
c = b - 30
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams r ?
Options: a ) 16 , b ) r = 32 , c ) r = 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Python program:
a = 8 * 4
Problem: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 2 women and 10 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 2 women + 10 children ) ' s 1 day work = ( 2 / 70 + 10 / 140 ) = 1 / 10 2 women and 10 children will complete the work in 10 days . e"
Answer: e
Python program:
a = 10 * 7
b = 2 / a
c = 10 * 14
d = 10 / c
e = b + d 
f = 1/(e)
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 8.5 , c ) 11 , d ) 9.5 , e ) 10
Rationale: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 11 110 660 it takes a total of nine hours to cover the 660 mile distance . answer : c . 11
Answer: c
Python program:
a = 10 + 20 
b = 30 + a 
c = 660 / b
Problem: how many integers are divisible by 2 between 10 ! and 10 ! + 20 inclusive ?
Options: a ) 6 , b ) 7 , c ) 21 , d ) 9 , e ) 10
Rationale: "c = 21 10 ! is divisible by 2 there are 20 numbers between 10 ! and 10 ! + 20 that are divisible by 1 . hence 21"
Answer: c
Python program:
a = 20 / 2
b = a + 1
Problem: ramesh purchased a refrigerator for rs . 14500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 20350 , d ) 17600 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 14,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 18125 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 18125 + 375 = rs . 18500 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 18500 * 110 / 100 = rs . 20350 answer : c"
Answer: c
Python program:
a = 100 + 10 
b = 14500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: if equation | x / 2 | + | y / 2 | = 4 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 50 , c ) 108 , d ) 200 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 8 | + | y / 8 | = 1 , so these are lines in four quadrants with x and y intercept as 8 , so it is a rhombus with diagonals of 16 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 16 * 16 = 108 . answer c .
Answer: c
Python program:
a = 2 * 2
b = a ** 2
c = 2 * 2
d = c ** 2
e = b + d
Problem: approximately how many revolutions will be made by a car tire with a 13 - inch diameter if the car travels 1 ⁄ 2 mile ?
Options: a ) 120 , b ) 180 , c ) 772 , d ) 720 , e ) 1,440
Rationale: "diameter of car tire = 13 inches radius of car tire = 6.5 inches = 6.5 * 2.54 cm = 16.51 cm circumference of the car tire = 2 * pi * 16.51 = 2 * 3.14 * 16.51 = 103.68 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 103.68 = 771.60 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c"
Answer: c
Python program:
a = 1 / 2
b = 3 * 2
c = b / 10
d = c + 1 
e = d / 10
f = e + 4 
g = f / 10
h = g + 1 
i = h / 10
j = i + 3 
k = j * 13
l = 3 * 2
m = l * 10
n = m + 3 
o = n * 10
p = o + 3 
q = p * 10
r = q + 3 
s = r + 2 
t = s * 10
u = k / t
v = a / u
Problem: if x / y = 2 / 5 , then ( x + y ) / ( x - y ) = ?
Options: a ) 5 , b ) 1 / 5 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 7 / 3
Rationale: any x and y satisfying x / y = 2 / 5 should give the same value for ( x + y ) / ( x - y ) . say x = 2 and y = 5 , then ( x + y ) / ( x - y ) = ( 2 + 5 ) / ( 2 - 5 ) = - 7 / 3 . answer : e .
Answer: e
Python program:
a = 2 + 5 
b = 2 - 5
c = a / b
Problem: if the radius of a circle is increased by 60 % then the area is increased by :
Options: a ) 44 % , b ) 120 % , c ) 156 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 160 / 100 r then area = pi * ( 160 r / 100 ) 2 area = 256 r / 100 that is area increases from 100 to 256 = increase in area = 156 % answer : c"
Answer: c
Python program:
a = 100 / 100
b = 100 / 100
c = 60 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
Problem: a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24
Rationale: "back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b"
Answer: b
Python program:
a = 12 / 2
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = math.factorial(2)
f = d * e
g = c / f
h = 12 / 2
i = h - 1
j = g - i
Problem: 10 binders can bind 1400 books in 21 days . how many binders will be required to bind 1800 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 16 , e ) 12
Rationale: "binders books days 10 1400 21 x 1600 20 x / 10 = ( 1800 / 1400 ) * ( 21 / 20 ) = > x = 12 answer : e"
Answer: e
Python program:
a = 1800 / 20
b = 10 * 21
c = 1400 / b
d = a / c
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 27 metre of cloth ?
Options: a ) 211 seconds , b ) 195 seconds , c ) 155 seconds , d ) 115 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 27 : x = > x = { \ color { blue } \ frac { 27 \ times 1 } { 0.128 } } = > x = 210.94 so time will be approx 211 seconds answer : a"
Answer: a
Python program:
a = 27 / 0
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 11 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 22.38 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 11 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 89 / 100 = ( 1 + p % ) profit % = 22.38 % b"
Answer: b
Python program:
a = 100 + 10 
b = 100 - 20
c = 11 + b 
d = a - c
e = d * 2
Problem: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 11 kmph ?
Options: a ) 21.23 , b ) 52.85 , c ) 23.26 , d ) 41.67 , e ) 25.15
Rationale: "distance covered in 1 min = ( 66 * 1000 ) / 60 = 183.33 cm circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 183.33 / 4.4 = 41.67 answer : d"
Answer: d
Python program:
a = 11 * 1000
b = a / const_60
c = 11 + 2 
d = 4 + 3 
e = c / d
f = e * 2
g = 140 / 100
h = g / 2
i = f * h
j = b / i
Problem: 1 * 2 + 2 * 2 ^ 2 + 3 * 2 ^ 3 + 4 * 2 ^ 4 … … … … … … … … + 2012 * 2 ^ 2012
Options: a ) 8100312 , b ) 8100313 , c ) 8100412 , d ) 8200312 , e ) 8300312
Rationale: take 2 outside as common we get 2 ( 1 + 2 * 1 ^ 2 + 3 * 1 ^ 3 + . . . . . . . . . 2012 * 1 ^ 2012 ) then 2 ( 1 + 2 + . . . . . 2012 ) we get 8100312 answer : a
Answer: a
Python program:
a = 2012 + 1 
b = 2 * a
c = b * 2012
Problem: stock / number of shares v - - - - - - - - - - - - 68 w - - - - - - - - - - 112 x - - - - - - - - - - - - 56 y - - - - - - - - - - - - 94 z - - - - - - - - - - - - 45 the table shows the number of shares of each of the 5 stocks owned by mr sami . if mr . sami was to sell 20 shares of stock x and buy 23 shares of stock y , what would be the increase in the range of the numbers of shares of the 5 stocks owned by mr . sami ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 14 , e ) 20
Rationale: based on the original number of shares , the range would be : 112 - 45 = 67 however , the prompt tells us that two of the values in the table are going to change . after the changes , the values will be : v 68 w 112 x 36 y 117 z 45 now the range is 117 - 36 = 81 the increase in the range requires us to compare thenewrange to theoldrange : 81 - 67 = 14 d
Answer: d
Python program:
a = 94 + 23 
b = 56 - 20
c = a - b
d = 112 - 45
e = c - d
Problem: if the cost price of 20 articles is equal to the selling price of 25 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 20 % loss , c ) 25 % profit , d ) 20 % profit , e ) 5 % profit
Rationale: "let the cost price of 1 article be rs . 1 . therefore , cost price of 20 articles = 20 * 1 = rs . 20 the selling price of 25 articles = cost price of 20 articles = rs . 20 . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = rs . 25 . therefore , profit made on sale of 25 articles = selling price of 25 articles - cost price of 25 articles = 20 - 25 = - rs . 5 . because the profit is in the negative , the merchant has made a loss of rs . 5 . therefore , % loss = loss / cost price ∗ 100 % loss = 5 / 25 ∗ 100 = 20 % loss . answer : b"
Answer: b
Python program:
a = 100 * 25
b = a / 20
c = 100 - b
d = 100 * 25
e = d / 20
f = c / e
g = 100 * f
Problem: the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 32.5 , c ) 36.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 32 × 50 + 48 – 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b"
Answer: b
Python program:
a = 32 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: 0.009 / x = 0.05 . find the value of x
Options: a ) 0.00018 , b ) 0.09 , c ) 0.018 , d ) 0.18 , e ) 90
Rationale: "x = 0.009 / 0.18 = 0.05 answer : d"
Answer: d
Python program:
a = 0 / 9
Problem: by selling an article at rs . 700 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 600 , b ) s . 480 , c ) s . 500 , d ) s . 450 , e ) s . 420
Rationale: "sp = 700 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 700 * [ 100 / 125 ] = 560 loss = 25 % = 25 % of 560 = rs . 140 sp = cp - loss = 560 - 140 = rs . 420 answer : e"
Answer: e
Python program:
a = 700 * 100
b = 25 + 100 
c = a / b
d = 700 * 100
e = 25 + 100 
f = d / e
g = f * 25
h = g / 100
i = c - h
Problem: in a office work is distribute between p persons . if 1 / 6 members are absent then work increased for each person is ?
Options: a ) 10 % , b ) 14.28 % , c ) 15 % , d ) 16 % , e ) 20 %
Rationale: let total % of work is 100 % total person = p 1 / 6 person are absent of total person . so absent person is 1 / 6 p ie p / 6 . left person is , p - p / 6 = 5 p / 6 . p person do the work 100 % 1 person do the work 100 * p % 5 p / 6 person do the work ( 100 * p * 6 ) / 5 p % = 120.00 % work increased for each person is = ( 120 - 100 ) % = 20 % answer : e
Answer: e
Python program:
a = 100 * 6
b = 6 - 1
c = a / b
d = c - 100
Problem: a cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom . if the cistern is full , in what time will the leak empty it ?
Options: a ) 50 hours , b ) 62 hours , c ) 90 hours , d ) 75 hours , e ) 100 hours
Rationale: "let the leak empty the full cistern in x hours 9 x / x - 9 = 9 + 1 x = 90 hours answer is c"
Answer: c
Python program:
a = 1 / 9
b = 1 / 10
c = a - b
d = 1/(c)
Problem: the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 10 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 35 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 10 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 10 ) / 2 = 35 . answer : a"
Answer: a
Python program:
a = 60 + 10 
b = a / 2