euclaise/mathqa_programs huggingface dataset:
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 30 per square m ?
Options: a ) s . 28500 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 30 * 950 = rs . 28,500 a"
Answer: a
Python program:
a = 20 * 15
b = a * 2
c = b * 30
d = 20 * 5
e = d * 2
f = e * 30
g = c + f 
h = 15 * 5
i = h * 2
j = i * 30
k = g + j
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 16 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 16 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 16 ( x - y ) - - > x + y = 16 . answer : d ."
Answer: d
Python program:
a = math.floor(16)
Problem: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 960 grams . find the profit percent .
Options: a ) 4.166 , b ) 3.1 , c ) 2.1 , d ) 1.256 , e ) 3.759
Rationale: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 960 100 + g / 100 + 0 = 1000 / 960 100 + g = 100 / 96 * 100 g = 4.166 answer : a"
Answer: a
Python program:
a = 4 + 1 
b = 4 + 1 
c = a + b 
d = c * 100
e = d - 960
f = e / 960
g = f * 100
Problem: the sum of the numbers is 220 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 60 , e ) 27
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 220 11 x / 3 = 220 x = 60 answer : d"
Answer: d
Python program:
a = 220 * 3
b = 10 + 1 
c = a / b
Problem: the profit earned by selling an article for 832 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: "let the profit or loss be x and 832 – x = 448 + x or , x = 384 ⁄ 2 = 192 \ cost price of the article = 832 – x = 448 + x = 640 \ sp of the article = 640 × 150 ⁄ 100 = 960 answer a"
Answer: a
Python program:
a = 832 + 448 
b = a / 2
c = 50 / 100
d = 1 + c 
e = b * d
Problem: for what value of â € œ k â €  will the equation ( 2 kx 2 + 6 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 4 / 9 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 6 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 4 / 9 answer : b"
Answer: b
Python program:
a = 2 + 2 
b = 2 ** a
c = 6 ** 2
d = b / c
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1305 , find the loss % ?
Options: a ) 13 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 195 100 - - - - ? = > 13 % answer : a"
Answer: a
Python program:
a = 1500 - 1305
b = a / 1500
c = b * 100
Problem: $ 366 is divided amongst a , b and c so that a may get 1 / 2 as much as b and c together , b may get 2 / 3 as much as a and c together , then the share of a is
Options: a ) $ 122 , b ) $ 150 , c ) $ 176 , d ) $ 200 , e ) $ 250
Rationale: "a : ( b + c ) = 1 : 2 a ' s share = 366 * 1 / 3 = $ 122 answer is a"
Answer: a
Python program:
a = 1 / 2
b = a + 1 
c = 366 / b
d = 1 / 2
e = c * d
Problem: a constructor estimates that 5 people can repair mr rohan ' s house in 6 days . if he uses 6 people instead of 5 , how long will they take to complete the job ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 3 , e ) 5
Rationale: explanation : use formula for a work members ã — days = constant 5 ã — 6 = 6 ã — a a = 5 so answer is 3 days answer : e
Answer: e
Python program:
a = 5 * 6
b = a / 6
Problem: if 12 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 43 , d ) 66 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 12 * 11 / 2 = 66 answer : d"
Answer: d
Python program:
a = math.factorial(12)
b = 12 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: if the cost price is 25 % of selling price . then what is the profit percent .
Options: a ) 150 % , b ) 200 % , c ) 300 % , d ) 350 % , e ) none of these
Rationale: "explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % . answer : c"
Answer: c
Python program:
a = 100 - 25
b = a / 25
c = b * 100
Problem: in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 16 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 16 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 16 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 16 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 16 ) ( 1 ) 11 x = 7 x + 16 4 x = 16 x = 4 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 4 ) = 60 final answer : e"
Answer: e
Python program:
a = 7 * 16
b = 11 - 7
c = a / b
d = c / 7
e = d * 15
Problem: in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 4 , - 3 ) , ( 4 , 7 ) , ( 12 , 2 ) , ( 12 , - 7 ) ?
Options: a ) 64
b ) 68
c ) 72
d ) 76
e ) 80
Rationale: by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 10 + 9 ) × 8 = 76 . the answer is d .
Answer: d
Python program:
a = 3 + 7 
b = 2 + 7 
c = a + b 
d = 12 - 4
e = c * d
f = e / 2
Problem: circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 5 more revolutions than gear p ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "gear q makes 30 more revolutions each 60 seconds . the time to make 5 = 30 / 6 more revolutions is 60 / 6 = 10 seconds . the answer is c ."
Answer: c
Python program:
a = 40 / const_60
b = 10 / const_60
c = a - b
d = 5 / c
Problem: 8 liters of a 25 percent solution of alcohol in water are mixed with 2 liters of a 12 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 21.2 % , b ) 21.6 % , c ) 22.0 % , d ) 22.4 % , e ) 22.8 %
Rationale: the total amount of alcohol is 0.25 ( 8 ) + 0.12 ( 2 ) = 2.24 liters . the percentage is 2.24 / 10 = 22.4 / 100 which is 22.4 % the answer is d .
Answer: d
Python program:
a = 25 / 100
b = 8 * a
c = 12 / 100
d = 25 / 100
e = 8 * d
f = c * e
g = b + f 
h = 8 + 2 
i = g / h
j = i * 100
Problem: a certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 270 , c ) 140 , d ) 165 , e ) 315
Rationale: "1 of 6 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 6 candidates for the math dep . , which gives as 6 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 6 * 45 = 270 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans b"
Answer: b
Python program:
a = 10 * 3
b = a * 6
Problem: in a school 20 % of the boys are same in number as 1 / 4 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 4 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "20 % of b = 1 / 4 g 20 b / 100 = g / 4 b = 5 g / 4 b / g = 5 / 4 b : g = 5 : 4 answer is a"
Answer: a
Python program:
a = 20 / 100
b = 1 / 4
c = a / b
Problem: find the least number must be subtracted from 5264 so that remaining number is divisible by 17 .
Options: a ) 11 , b ) 14 , c ) 18 , d ) 20 , e ) 29
Rationale: when dividing 5264 by 17 , we get the remainder 11 , so 11 should be subtracted . the answer is a .
Answer: a
Python program:
a = 5264 / 17
b = math.floor(a)
c = b * 17
d = 5264 - c
Problem: a salesman ' s income consists of a commission and a base salary of $ 400 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 245 , c ) $ 365 , d ) $ 315 , e ) $ 730
Rationale: "total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1430 - $ 800 = $ 630 for 2 weeks avg weekly commission = $ 315 answer d"
Answer: d
Python program:
a = 500 * 7
b = 406 + 413 
c = 436 + 420 
d = b + c 
e = d + 395 
f = a - e
g = f / 2
h = g - 400
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 4 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 260 miles , d ) 425 miles , e ) 525 miles
Rationale: during each hour , the car travels 65 miles . for 4 hours it will travel 65 + 65 + 65 + 65 = 4 × 65 = 260 miles correct answer is c ) 260 miles
Answer: c
Python program:
a = 65 * 4
Problem: a can give b 150 meters start and c 300 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 111.67 , c ) 111.64 , d ) 111.11 , e ) 176.47
Rationale: "a runs 1000 m while b runs 850 m and c runs 700 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 700 ) / 850 = 823.53 m . b can give c = 1000 - 823.53 = 176.47 m . answer : e"
Answer: e
Python program:
a = 100 * 10
b = 100 * 10
c = 100 * 10
d = c - 300
e = b * d
f = 100 * 10
g = f - 150
h = e / g
i = a - h
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 100 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 100 - 55 = 45 n = 9 the answer is d ."
Answer: d
Python program:
a = 100 - 50
b = 55 - 50
c = a / b
d = c - 1
Problem: 5 is added to a certain number , the sum is multiplied by 5 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 60 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 2 , d ) 30 , e ) 45
Rationale: "let number is x . when 5 added to it , = ( x + 5 ) 5 multiplied to sum , = 5 * ( x + 5 ) now , = [ { 5 * ( x + 5 ) } / 5 ] and , = [ { 5 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 5 * ( x + 5 ) } / 5 ] - 5 = half of 60 [ ( 5 x + 25 ) / 5 ) = 30 + 5 5 x + 25 = 35 * 5 x + 5 = 7 * 1 x + 5 = 7 x = 7 - 5 x = 2 so , required number is : 2 . answer : c"
Answer: c
Python program:
a = 60 / 2
b = a + 5 
c = b * 5
d = c / 5
e = d - 5
Problem: how many points ( x , y ) lie on the line segment between ( 32 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?
Options: a ) one , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 32 ) = - 1 / 5 y = mx + b = > 12 2 / 3 = - 22 / 3 + b = > b = 19 y = - x / 5 + 19 only integer values work , and the only multiples of 5 between 7 and 32 for x values are 10 , 15 , 20 , 25 and 30 , thus 5 points . c"
Answer: c
Python program:
a = 7 / 7
Problem: a train 250 m long running at 72 kmph crosses a platform in 15 sec . what is the length of the platform ?
Options: a ) 50 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 15 = 300 â € “ 250 = 50 m answer : a"
Answer: a
Python program:
a = 72 * const_0_2778
b = 15 * a
c = b - 250
Problem: a bag holds 2 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be green ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 2 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 2 red and 3 green marbles after one red has been picked , we need to pick 1 green from a total of 2 green and 2 red marbles . p ( both green ) = ( 3 / 5 ) * ( 2 / 4 ) = 3 / 10 option c"
Answer: c
Python program:
a = math.comb(2, 2)
b = 2 + 3 
c = math.comb(b, 2)
d = a / c
Problem: a baseball card decreased in value 20 % in its first year and 30 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 44 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.8 = 80 after second year price = 80 * 0.7 = 56 final decrease = [ ( 100 - 56 ) / 100 ] * 100 = 44 % correct answer - e"
Answer: e
Python program:
a = 30 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: a batsman makes a score of 300 runs in the 17 th inning and thus increases his averages by 10 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 140 , c ) 42 , d ) 40.5 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 300 then average run after 17 th inning = ( 16 x + 300 ) / 17 ( 16 x + 300 ) / 17 = x + 10 = > 16 x + 300 = 17 x + 170 x = 130 average after 17 th inning = 130 + 10 = 140 answer : b"
Answer: b
Python program:
a = 17 * 10
b = 300 - a
c = b + 10
Problem: solve : 0.6 * 0.6 + 0.6 * 0.6
Options: a ) 0.46 , b ) 0.56 , c ) 0.64 , d ) 0.65 , e ) none of them
Rationale: "= 0.6 * 0.6 + ( 0.6 * 6 ) = 0.36 + 0.1 = 0.46 answer is a ."
Answer: a
Python program:
a = 0 / 6
b = 0 * 6
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 12 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 78 , c ) 86 , d ) 126 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 12 = 30 5 * quotient = 30 quotient = 6 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 6 ) + 6 = 126 . d )"
Answer: d
Python program:
a = 6 * 3
b = a + 12 
c = 6 * 3
d = c + 12 
e = d / 5
f = b * e
g = f + 6
Problem: a can do a piece of work 30 days . b can do work in 55 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16 days , c ) 19.4 days , d ) 17.2 days , e ) 18 days
Rationale: "lcm = 330 , ratio = 30 : 45 = 6 : 11 no of days = 330 / ( 6 + 11 ) = 330 / 17 = 19.4 days answer : c"
Answer: c
Python program:
a = 1 / 30
b = 1 / 55
c = a + b 
d = 1 / c
Problem: the diameter of a garden roller is 1.2 m and it is 2 m long . how much area will it cover in 5 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 40 m 2
b ) 44 m 2
c ) 48 m 2
d ) 37.7 m 2
e ) none of these
Rationale: required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 â  „ 7 ã — 0.6 ã — 2 = 37.7 m 2 answer d
Answer: d
Python program:
a = 22 / 7
b = 2 * a
c = 1 / 2
d = b * c
e = d * 2
f = 5 * e
Problem: rs . 2080 is divided so that 3 times the first share , thrice the 2 nd share and four times the third share amount to the same . what is the value of the second share ?
Options: a ) s 802 , b ) s 208 , c ) s 960 , d ) s 690 , e ) s 906
Rationale: "a + b + c = 2080 3 a = 2 b = 4 c = x a : b : c = 1 / 3 : 1 / 2 : 1 / 4 = 4 : 6 : 3 6 / 13 * 2080 = rs 960 answer : c"
Answer: c
Python program:
a = 3 + 2 
b = a + 3 
c = 2080 / b
d = 3 * c
Problem: two trains running in opposite directions cross a man standing on the platform in 67 seconds and 17 seconds respectively and they cross each other in 73 seconds . the ratio of their speeds is :
Options: a ) 3 / 2 , b ) 3 / 9 , c ) 3 / 6 , d ) 3 / 1 , e ) 3 / 5
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 23 = = > 27 x + 17 y = 23 x + 23 y = = > 4 x = 6 y = = > x / y = 3 / 2 . answer : a"
Answer: a
Python program:
a = 67 - 73
b = 73 - 17
c = a / b
Problem: you make a cube that is made of 10 x 10 x 10 smaller cubes which sums up to a total of 1000 smaller cubes . now , if someone takes one layer of cubes , how many will remain ?
Options: a ) 357 , b ) 834 , c ) 500 , d ) 512 , e ) 216
Rationale: d 512 the cube that remains will be 8 x 8 x 8 . this will make a total of 512 . this is because , when a layer is taken , it will be taken from all sides of the cube which will reduce the dimension be two and not one .
Answer: d
Python program:
a = 10 - 2
b = a ** 3
Problem: if a - b = 4 and a 2 + b 2 = 30 , find the value of ab .
Options: a ) a ) 7 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 30 - 16 = 14 ab = 7 answer : a"
Answer: a
Python program:
a = 4 ** 2
b = 30 - a
c = b / 2
Problem: in a regular week , there are 5 working days and for each day , the working hours are 8 . a man gets rs . 2.40 per hour for regular work and rs . 3.20 per hours for overtime . if he earns rs . 432 in 4 weeks , then how many hours does he work for ? a . 160 b . 175 c . 180 d . 195 explanation :
Options: a ) 160 , b ) 175 , c ) 180 , d ) 185 , e ) 195
Rationale: suppose the man works overtime for x hours . now , working hours in 4 weeks = ( 5 x 8 x 4 ) = 160 . 160 x 2.40 + x x 3.20 = 432 3.20 x = 432 - 384 = 48 x = 15 . hence , total hours of work = ( 160 + 15 ) = 175 . answer : option b
Answer: b
Python program:
a = 8 * 5
b = a * 4
c = 8 * 2
d = c * 5
e = d * 4
f = 432 - e
g = f / 3
h = b + g
Problem: of the 200 stamps in a collection , 90 are foreign and 60 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 50 , b ) 70 , c ) 100 , d ) 130 , e ) 150
Rationale: "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 40 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 40 ) = 70 the answer is b ."
Answer: b
Python program:
a = 90 + 60 
b = a - 20
c = 200 - b
Problem: a cylindrical cube of radius 12 cm contains water upto a depth of 20 cm . a spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm . the radius of the ball is :
Options: a ) 7 cm
b ) 8.5 cm
c ) 9 cm
d ) 9.5 cm
e ) none
Rationale: sol . let the radius of the ball be r cm . volume of ball = volume of water displaced by it . ∴ 4 / 3 ∏ r ³ = ∏ * 12 * 12 * 6.75 ⇒ r ³ = 9 * 9 * 9 ⇒ r = 9 cm . answer c
Answer: c
Python program:
a = volume_cylinder * (
b = a / 3
c = 4 * math.pi
d = b ** c
Problem: a batsman in his 12 th innings makes a score of 92 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 70 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 92 ∴ x = 70 answer c"
Answer: c
Python program:
a = 12 * 2
b = 92 - a
c = b + 2
Problem: a snail , climbing a 36 feet high wall , climbs up 8 feet on the first day but slides down 4 feet on the second . it climbs 8 feet on the third day and slides down again 4 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 20 , e ) 21
Rationale: "total transaction in two days = 8 - 4 = 4 feet in 15 days it will climb 36 feet thus reaching the top therefore , total no of days required = 15 c"
Answer: c
Python program:
a = 36 - 8
Problem: what is the least number by which 16800 must be divided to get a number perfect square
Options: a ) 21 , b ) 42 , c ) 24 , d ) 40 , e ) 45
Rationale: 16,800 / 42 = 400 400 = ( 20 ) ^ 2 ans - 42 answer : b
Answer: b
Python program:
a = 10 * 2
b = 10 * 2
c = a * b
d = 16800 / c
Problem: addison high school ’ s senior class has 300 boys and 240 girls . if 30 % of the boys did not attend the college then 70 % of the total class attended college , what percentage of the girls class did not attend college ?
Options: a ) 70 , b ) 45 , c ) 50 , d ) 46 , e ) 30
Rationale: "% of boy attending the college = 100 - 30 = 70 % number of boys attending the college : 0.70 * 300 = 210 total people = 300 + 240 = 540 total number of students attending the college : 0.70 * 540 = 378 number of girls attending the college = 378 - 210 = 168 number of girls not attending the college = 240 - 168 = 72 % of girls not attending = 72 / 240 = 30 % . e is the correct answer"
Answer: e
Python program:
a = 30 / 100
b = a * 300
c = 70 / 100
d = 1 - c
e = d * 240
f = b + e 
g = 300 + 240 
h = f / g
i = h * 100
Problem: if the average ( arithmetic mean ) of a and b is 140 , and the average of b and c is 100 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 135 , e ) 80
Rationale: "a + b = 280 b + c = 200 a - c = 80 . imo option e ."
Answer: e
Python program:
a = const_60 * 0
b = 140 * 2
c = a - b
Problem: on dividing 95 by a number , the quotient is 6 and the remainder is 5 . find the divisor .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "d = ( d - r ) / q = ( 95 - 5 ) / 6 = 90 / 6 = 15 b"
Answer: b
Python program:
a = 95 / 6
b = math.floor(a)
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 54 / r years . if joe ' s parents invested $ 5,000 in a long - term bond that pays 6 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when joe is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 54 / r years , then for r = 6 it ' ll double in 54 / 6 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 2 = $ 10,000 . answer : d ."
Answer: d
Python program:
a = 2 + 3 
b = a * 1000
c = b * 6
d = c / 2