euclaise/mathqa_programs huggingface dataset:
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 26,000 is made ?
Options: a ) rs . 1 , 10,000 , b ) rs . 1 , 20,000 , c ) rs . 1 , 22,000 , d ) rs . 1 , 21,000 , e ) none of these
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 24,000 is made = 96,000 + 26,000 = rs . 1 , 22,000 answer : c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 20 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: caleb spends $ 64.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 29 , b ) 10 , c ) 20 , d ) 40 , e ) 45
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 64.50 . by solving the equations y = 29 . ans a ."
Answer: a
Python program:
a = 64 - 50
b = 1 - 50
c = a / b
Problem: if two integers x , y ( x > y ) are selected from - 10 to 4 ( inclusive ) , how many possible cases are there ?
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 105
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 15 c 2 = 15 * 14 / 2 = 105 . therefore , the answer is e ."
Answer: e
Python program:
a = 4 + 10 
b = 4 + 2 
c = a + b 
d = 4 + 1 
e = c + d 
f = e + 4 
g = f + 10 
h = g + 2 
i = h + 1
Problem: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 30800 . how many times did he participate in the competition ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "30800 = 2 * 2 * 2 * 2 * 5 * 5 * 7 * 11 john participated 8 times . the answer is d ."
Answer: d
Python program:
a = 11 * 7
b = a * 5
c = b * 2
d = 30800 / c
e = math.sqrt(d)
f = math.floor(e)
Problem: a rectangular plot measuring 40 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 46 m , b ) 36 m , c ) 26 m , d ) 56 m , e ) 25 m
Rationale: "perimeter of the plot = 2 ( 40 + 50 ) = 180 m no of poles = 180 / 5 = 36 m answer : b"
Answer: b
Python program:
a = 40 + 50 
b = a * 2
c = b / 5
Problem: the no 2.52 , when written as a fraction and reduced to lowest terms , the sum of the numeratr n denominator is :
Options: a ) 7 , b ) 141 , c ) 29 , d ) 349 , e ) 359
Rationale: the actual question has bar on decimal part . hence the number is 2.5252525252 . . . . . . so let x = 2.525252 . . then 100 x = 252.525252 100 x - x = 250 x = 250 / 99 so ans = num + den = 349 answer : d
Answer: d
Python program:
a = 2 * 52
b = a - 2
c = 100 - 1
d = b + c
Problem: if sharon ' s weekly salary increased by 15 percent , she would earn $ 575 per week . if instead , her weekly salary were to decreased by 12 percent , how much would she earn per week ?
Options: a ) rs . 540 , b ) rs . 580 , c ) rs . 560 , d ) rs . 620 , e ) rs . 650
Rationale: "soln : - ( 575 / 115 ) 112 = 560 in this case long division does not take much time . ( 23 / 5 ) = 4.6 4.6 * 112 = rs . 560 answer : c"
Answer: c
Python program:
a = 15 / 100
b = 1 + a 
c = 575 / b
d = 12 / 100
e = 15 / 100
f = 1 + e 
g = 575 / f
h = d * g
i = c + h
Problem: of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 20 percent was planted with potato and 70 percent of the cleared land was planted with tomato . if the remaining 630 acres of cleared land was planted with corn , how many acres did the farmer own ?
Options: a ) 7000 , b ) 6800 , c ) 8000 , d ) 5400 , e ) 7100
Rationale: 20 % od 90 % = 18 % , 70 % 0 f 90 % = 63 % so the remaining 90 - 18 - 63 = 9 % = 630 acres or 10 % of 90 % = 9 % - - > 630 / 9 * 100 = 7000 acres answer ( a )
Answer: a
Python program:
a = 100 - 20
b = a - 70
c = b / 100
d = 90 / 100
e = c * d
f = 630 / e
Problem: a , band c can do a piece of work in 11 days , 20 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day ' s = 31 / 220 + 6 / 55 = 55 / 220 = 1 / 4 1 / 4 th work done in 2 days work done = 4 * 2 = 8 days answer : b"
Answer: b
Python program:
a = 55 / 11
b = 55 / 20
c = a + b 
d = 55 / 11
e = 55 / 55
f = d + e 
g = c + f 
h = g / 2
i = 55 / h
Problem: a man buys an article for $ 10 . and sells it for $ 30 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 150 % , e ) 300 %
Rationale: "c . p . = $ 10 s . p . = $ 30 gain = $ 20 gain % = 20 / 10 * 100 = 300 % answer is e"
Answer: e
Python program:
a = 10 / 100
b = 30 / a
c = b - 100
Problem: a man buys 56 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 20.52 % , d ) 23.62 % , e ) 27.82 %
Rationale: "explanation : let marked price be re . 1 each c . p . of 56 pens = rs . 46 s . p . of 56 pens = 99 % of rs . 56 = rs . 55.44 profit % = ( profit / c . p . ) x 100 profit % = ( 9.44 ) x 100 = 20.52 % answer : c"
Answer: c
Python program:
a = 100 - 1
b = 56 * a
c = 46 * 100
d = b - c
e = 46 * 100
f = d / e
g = 100 * f
Problem: a train running at the speed of 58 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 145 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 58 * ( 5 / 18 ) m / sec = 145 / 9 m / sec length of train ( distance ) = speed * time ( 145 / 9 ) * 9 = 145 meter answer : a"
Answer: a
Python program:
a = 58 * 1000
b = a / 3600
c = b * 9
Problem: what is the least common multiple of 812 , 3214
Options: a ) 672 , b ) 682 , c ) 328 , d ) 964 , e ) 285
Rationale: the given numbers are 8,12 , 32,14 thus the l . c . m is 2 * 2 * 2 * 1 * 3 * 4 * 7 = 672 the answer is a
Answer: a
Python program:
a = 2 * 100
b = 812 - a
c = 2 + 3 
d = 12 * c
e = b + d
Problem: a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 1.1 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 1.0 , b ) 1.2 , c ) 1.4 , d ) 1.6 , e ) 1.8
Rationale: "72 km / hr = 1.2 km / min the total distance is 1.2 km . 1.2 / 1.2 = 1 minute the answer is a ."
Answer: a
Python program:
a = 100 / 1000
b = 1 + 1 
c = b / 72
d = c * const_60
Problem: the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 20 , what is the perimeter of the garden in feet ?
Options: a ) 32
b ) 36
c ) 40
d ) 44
e ) 48
Rationale: let x be the length of one side of the square garden . x ^ 2 = 8 x + 20 x ^ 2 - 8 x - 20 = 0 ( x - 10 ) ( x + 2 ) = 0 x = 10 , - 2 p = 4 ( 10 ) = 40 the answer is c .
Answer: c
Python program:
a = 2 * 20
Problem: a student is ranked 13 th from right and 8 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: from right 13 , from left 8 total = 13 + 8 - 1 = 20 answer : c
Answer: c
Python program:
a = 13 + 8 
b = a - 1
Problem: a train crosses a platform of 200 m in 20 sec , same train crosses another platform of length 350 m in 25 sec . then find the length of the train ?
Options: a ) 150 m , b ) 180 m , c ) 400 m , d ) 250 m , e ) 155 m
Rationale: "length of the train be ‘ x ’ x + 200 / 20 = x + 350 / 25 5 x + 1000 = 4 x + 1400 x = 400 m answer : c"
Answer: c
Python program:
a = 20 / 3
b = 20 / a
c = 350 * b
d = 20 / 3
e = 25 / d
f = 200 * e
g = c - f
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 30 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 8 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.30 * 8 = 0.2 ( x + 8 ) - - > x = 8 . answer : b ."
Answer: b
Python program:
a = 30 - 20
b = a * 8
c = b / 10
Problem: 8 + 8
Options: a ) 5 , b ) 17 , c ) 16 , d ) 23 , e ) 19
Rationale: c
Answer: c
Python program:
a = 8 / 8
b = a * 100
Problem: on dividing a number by 357 , we get 40 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 6 , b ) 5 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 40 = ( 17 * 21 * y ) + ( 17 * 2 ) + 6 = 17 * ( 21 y + 2 ) + 6 . required number = 6 . answer is a"
Answer: a
Python program:
a = 40 ** 2
b = a / 357
c = 40 ** 2
d = c / 357
e = math.floor(d)
f = b - e
g = f * 357
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 14 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 105
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 5 x + 2 / 3 x + 14 x - 13 / 15 x = 14 2 / 15 x = 14 = > so x = ( 15 / 2 ) * 14 = 105 km answer e"
Answer: e
Python program:
a = 1 / 5
b = 2 / 3
c = a + b 
d = 1 - c
e = 1/(d)
f = 14 * e
Problem: a certain protective additive increases from 30 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 100 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by ( 60 − 30 ) / 30 ∗ 100 = 100 answer : c"
Answer: c
Python program:
a = 60 - 30
b = a / 30
c = b * 100
Problem: the present worth of rs . 1404 due in two equal half - yearly instalments at 8 % per annum . simple interest is :
Options: a ) 1320 , b ) 1300 , c ) 1325 , d ) 120 , e ) none of these
Rationale: "explanation : required sum = pw of rs . 702 due 6 months hence + pw of rs . 702 due 1 year hence = rs . [ 100 × 702 / 100 + ( 8 × 12 ) + 100 × 702 / 100 + ( 8 × 1 ) ] = rs . 1325 answer : c"
Answer: c
Python program:
a = 1404 / 2
b = 100 + 8 
c = b / 100
d = a / c
e = 1404 / 2
f = 8 / 2
g = 100 + f 
h = g / 100
i = e / h
j = d + i
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 19 , what was the price before the first discount ?
Options: a ) $ 45.10 , b ) $ 34.31 , c ) $ 28.44 , d ) $ 67.54 , e ) $ 33.77
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 19 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 19 solve for x x = $ 33.77 correct answer e"
Answer: e
Python program:
a = 100 * 100
b = a * 19
c = 100 - 25
d = c * 100
e = 100 - 25
f = e * 25
g = d - f
h = b / g
Problem: sum of two numbers is 40 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) 26 , 14 , b ) 23 , 17 , c ) 17 , 23 , d ) 14 , 26 , e ) 15 , 25
Rationale: "explanation : x + y = 15 3 y ã ¢ â ‚ ¬ â € œ 2 x = 5 x = 23 y = 17 answer : b"
Answer: b
Python program:
a = 5 / 2
b = 40 - a
c = b / 2
d = 40 - c
Problem: a cab driver 5 days income was $ 600 , $ 250 , $ 450 , $ 400 , $ 800 . then his average income is ?
Options: a ) $ 460 , b ) $ 480 , c ) $ 500 , d ) $ 520 , e ) $ 540
Rationale: "avg = sum of observations / number of observations avg income = ( 600 + 250 + 450 + 400 + 800 ) / 5 = 500 answer is c"
Answer: c
Python program:
a = 600 + 250 
b = a + 450 
c = b + 400 
d = c + 800 
e = d / 5
Problem: what is the units digit of ( 3 ^ 10 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 10 = 3 ^ 4 * 2 + 2  3 ^ 2 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 10 ) ( 4 ^ 13 )  ( 3 ^ 2 ) ( ~ 4 ) = ( ~ 9 ) ( ~ 4 ) = ~ 6 . therefore , the answer is c ."
Answer: c
Python program:
a = 4 + 3 
b = a + 2
Problem: two trains of equal are running on parallel lines in the same direction at 52 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 50 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 52 - 36 = 16 km / hr . = 16 * 5 / 18 = 40 / 9 m / sec . 2 x / 36 = 40 / 9 = > x = 80 . answer : c"
Answer: c
Python program:
a = 52 - 36
b = a * 1000
c = b / 3600
d = 36 * c
e = d / 2
Problem: a volume of 11780 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 4222 , e ) 2945
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 11780 l can be kept in ( 11780 / 4 ) hemispheres ans . 2945 answer : e"
Answer: e
Python program:
a = 11780 / 4
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.2 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.2 then x = 0.2 / 1000 = 0.0002 . the answer is e"
Answer: e
Python program:
a = 0 / 2
Problem: square x is inscribed in circle y . if the perimeter of x is 64 , what is the circumference of y ?
Options: a ) 16 √ 2 π
b ) 8 √ 2 π
c ) 22 √ 2 π
d ) 12 √ 2 π
e ) 9
Rationale: square forms two right angled triangles . any time we have a right angle triangle inside a circle , the hypotenuse is the diameter . hypotenuse here = diagonal of the square = 16 sqrt ( 2 ) = diameter = > radius = 8 sqrt ( 2 ) circumference of the circle = 2 pi r = 16 pi sqrt ( 2 ) answer is a .
Answer: a
Python program:
a = 64 / 4
b = 64 / 4
c = diagonal * (
Problem: two trains of length 210 m and 120 m are 160 m apart . they start moving towards each other on parallel tracks , at speeds 74 kmph and 92 kmph . after how much time will the trains meet ?
Options: a ) 35 / 10 , b ) 31 / 10 , c ) 31 / 10 , d ) 36 / 10 , e ) 37 / 10
Rationale: they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 74 + 92 ) * 5 / 18 = 46.1 mps . the time required = d / s = 160 / 46.1 = 35 / 10 sec . answer : a
Answer: a
Python program:
a = 74 + 92 
b = a * const_0_2778
c = 160 / b
Problem: a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.98 , b ) 7.98 , c ) 7.96 , d ) 5.87 , e ) 5.82
Rationale: "m = 8 s = 1.2 ds = 9.6 us = 6.8 x / 9.6 + x / 6.8 = 1 x = 3.98 d = 3.98 * 2 = 7.96 answer : c"
Answer: c
Python program:
a = 8 + 1 
b = 8 - 1
c = a * b
d = 8 + 1 
e = 8 - 1
f = d + e 
g = c / f
h = g * 2
Problem: after getting 2 successive discounts , a shirt with a list price of rs 150 is available at rs 105 . if the second discount is 12.55 , find the first discount
Options: a ) 22 % , b ) 23 % , c ) 21 % , d ) 20 % , e ) 17 %
Rationale: let the first discount be x % then , 87.5 % of ( 100 - x ) % of 150 = 105 87.5 / 100 * ( 100 - x ) / 100 * 450 = 150 = > 105 = > 100 - x = ( 105 * 100 * 100 ) / ( 150 * 87.5 ) = 80 x = ( 100 - 80 ) = 20 first discount = 20 % option d
Answer: d
Python program:
a = 105 * 100
b = 100 - 12
c = a / b
d = 150 - c
e = d * 100
f = e / 150
Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability of one is a spade and one is a heart ?
Options: a ) 102 / 102 , b ) 5 / 102 , c ) 1 / 102 , d ) 8 / 102 , e ) 13 / 102
Rationale: solution let s be the sample space . then , n ( s ) = 52 c 2 = ( 52 × 51 ) / ( 2 × 1 ) = 1326 . let e = event of getting 1 spade and 1 heart . n ( e ) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = ( 13 c 1 * 13 c 1 ) = 169 . p ( e ) = n ( e ) / n ( s ) = 169 / 1326 = 13 / 102 . answer e
Answer: e
Python program:
a = 52 / 4
b = 52 / 4
c = a * b
d = math.comb(52, 2)
e = c / d
Problem: 10 is added to a certain number , the sum is multiplied by 2 , the product is divided by 2 and 2 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 25 , d ) 36 , e ) 45
Rationale: "let number is x . when 10 added to it , = ( x + 10 ) 2 multiplied to sum , = 2 * ( x + 10 ) now , = [ { 2 * ( x + 10 ) } / 2 ] and , = [ { 2 * ( x + 10 ) } / 2 ] - 2 according to question , [ { 2 * ( x + 10 ) } / 2 ] - 2 = half of 88 [ ( 2 x + 20 ) / 2 ) = 44 + 2 x + 10 = 46 x + 10 = 46 x = 46 - 10 x = 36 so , required number is : 36 . answer : d"
Answer: d
Python program:
a = 88 / 2
b = a + 2 
c = b * 2
d = c / 2
e = d - 10
Problem: four dice are thrown simultaneously . find the probability that all of them show the same face .
Options: a ) 1 / 216 , b ) 1 / 215 , c ) 5 / 300 , d ) 1 / 415 , e ) 1 / 500
Rationale: "total no of elementary events = 6 ^ 4 n ( s ) = 6 ^ 4 x = { ( 1,1 , 1,1 ) ( 2,2 , 2,2 ) . . . . . ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) / n ( s ) = 6 / 6 ^ 4 = 1 / 216 answer a"
Answer: a
Python program:
a = 3 + 3 
b = 3 / a
c = 3 + 3 
d = 3 / c
e = b * d
Problem: when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 2 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 375 , c ) 450 , d ) 500 , e ) 575
Rationale: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 2 of 300 = 150 total amount in her account = 450 answer c"
Answer: c
Python program:
a = 3 / 5
b = 1 - a
c = 200 / b
d = c - 200
e = 1 / 2
f = 1 + e 
g = d * f
Problem: the simple form of the ratio 8 / 5 : 2 / 3 is ?
Options: a ) 12 : 5 , b ) 12 : 7 , c ) 7 : 12 , d ) 5 : 7 , e ) 4 : 7
Rationale: "8 / 5 : 2 / 3 = 12 : 5 answer : a"
Answer: a
Python program:
a = 2 / 3
Problem: in measuring the sides of a rectangle , one side is taken 16 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 10.2 % , d ) 5 % , e ) 2.6 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 116 * 95 = 11,020 , which is 10.2 % greater than the actual area . answer : c ."
Answer: c
Python program:
a = 16 - 5
b = 16 * 5
c = b / 100
d = a - c
Problem: a can do a work in 6 days . b can do the same work in 8 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,800 , b ) 500,500 , c ) 300,700 , d ) 800,200 , e ) 550,450
Rationale: "ratio of their works a : b = 6 : 8 ratio of their wages a : b = 3 : 4 a ' s share = ( 3 / 5 ) 1000 = 600 b ' s share = ( 4 / 5 ) 1000 = 800 correct option is a"
Answer: a
Python program:
a = 6 * 8
b = 6 + 8 
c = a / b
Problem: what is the sum of all the multiples of 12 between 30 and 200 ?
Options: a ) 1648 , b ) 1632 , c ) 1626 , d ) 1612 , e ) 1800
Rationale: "you first have to know all the multiples of 12 between 30 and 200 . they are 12 , 24,36 , 48,60 , 72,84 , 96,108 , 120,132 , 144,156 , 168,180192 . if you add all these numbers together , you get 1632 . final answer : b"
Answer: b
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 12 
t = 2 + 4 
u = s + t
Problem: what is the least number should be added to 1100 , so the sum of the number is completely divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 4 , e ) 8
Rationale: "( 1100 / 23 ) gives remainder 19 19 + 4 = 23 , so we need to add 4 answer : d"
Answer: d
Python program:
a = 1100 / 23
b = math.floor(a)
c = b + 1 
d = c * 23
e = d - 1100
Problem: ritesh and co . generated revenue of rs . 1,250 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,250 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1250 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1250 . = > 10,000 . hence , the total revenue by end of 2007 is rs . 10,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 10000 ) × 100 . = > 25 % . answer : c"
Answer: c
Python program:
a = 1 + 4 
b = 2 * a
c = b * 100
d = 2 * c
e = 1 + 4 
f = e * 100
g = d + f 
h = 1 + 4 
i = 2 * h
j = i * 100
k = 2 + 4 
l = k * 100
m = j + l 
n = 12 / 5
o = m / n
p = g / o
q = p * 100
Problem: if p ( a ) = 4 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 8 / 25 , b ) 1 / 25 , c ) 2 / 25 , d ) 3 / 14 , e ) 25 / 8
Rationale: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 4 / 5 . 2 / 5 p ( a n b ) = 8 / 25 . a"
Answer: a
Python program:
a = 4 / 5
b = 2 / 5
c = a * b
Problem: a making a cube with dimension 5 * 5 * 5 using 1 * 1 * 1 cubes . what is the number of cubes needed to make hollow cube looking of the same shape .
Options: a ) 98
b ) 99
c ) 100
d ) 101
e ) 102
Rationale: 125 1 * 1 * 1 small cubes = 5 * 5 * 5 cubes because hallow in inner we do n ' t have 3 * 3 * 3 cubes so 125 - 27 = 98 cubes required answer : a
Answer: a
Python program:
a = 5 * 5
b = a * 5
c = 5 - 2
d = 5 - 2
e = c * d
f = e * 3
g = b - f
Problem: how many 4 digit numbers have no repeat digits , do not contain zero , and have a sum of digits f equal to 28 ?
Options: a ) 14 , b ) 24 , c ) 28 , d ) 48 , e ) 96
Rationale: first , look for all 4 digits without repeat that add up to 28 . to avoid repetition , start with the highest numbers first . start from the largest number possible 9874 . then the next largest number possible is 9865 . after this , you ' ll realize no other solution . clearly the solution needs to start with a 9 ( cuz otherwise 8765 is the largest possible , but only equals 26 ) . with a 9 , you also need an 8 ( cuz otherwise 9765 is the largest possible , but only equals 27 ) . with 98 __ only 74 and 65 work . so you have two solutions . each can be rearranged in 4 ! = 24 ways . so f = 24 + 24 = 48 . d
Answer: d
Python program:
a = math.factorial(4)
b = 2 * a