euclaise/mathqa_programs huggingface dataset:
Problem: 8 people decided to split the restaurant bill evenly . if the bill was $ 314.12 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20
Rationale: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 412 not divisible by a hence , we need to add 4 to this number for it to be divisible by 8 correct option : a"
Answer: a
Python program:
a = 3 / 100
b = 314 + 12
Problem: the average ( arithmetic mean ) monthly income of 4 workers is $ 1000 . after one worker ’ s income increases by 50 percent the new average income is $ 1200 . what was the original income of the worker whose monthly income increased ?
Options: a ) $ 1,800 , b ) $ 1,500 , c ) $ 1,300 , d ) $ 1,600 , e ) $ 1,100
Rationale: increase in total income was 200 * 4 = $ 800 , we know that this increase was 50 % ( 1 / 2 ) of the workers original income , thus his / her original income was 800 * 2 = $ 1,600 . answer : d
Answer: d
Python program:
a = 1200 * 4
b = 4 - 1
c = b * 1000
d = a - c
e = 1200 * 4
f = 4 - 1
g = f * 1000
h = e - g
i = 50 / 100
j = i + 1 
k = h / j
l = d - k
m = l - 100
Problem: if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction .
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 , e ) none of them
Rationale: "let the original fraction be x / y . then ( 115 % of x ) / ( 92 % of y ) = 15 / 16 = > ( 115 x / 92 y ) = 15 / 16 = ( ( 15 / 16 ) * ( 92 / 115 ) ) = 3 / 4 answer is a ."
Answer: a
Python program:
a = 100 - 8
b = a * 15
c = 100 + 15 
d = c * 16
e = b / d
Problem: in town x , 72 percent of the population are employed , and 36 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 50 %
Rationale: "total employed people 72 % , out of which 36 are employed males , hence 36 % are employed females . ( employed females ) / ( total employed people ) = 36 / 72 = 1 / 2 = 50 % answer : e ."
Answer: e
Python program:
a = 72 - 36
b = a / 72
c = b * 100
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 100 resolutions .
Options: a ) 140 m , b ) 141 m , c ) 142 m , d ) 143 m , e ) 144 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 100 resolutions . = 100 * 2 * 22 / 7 * 22.4 = 14100 cm = 141 m answer : b"
Answer: b
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 * 100
i = h / 100
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 92 hours , b ) 24 hours , c ) 84 hours , d ) 48 hours , e ) none
Rationale: "sol . speed upstream = 3 kmph ; speed downstream = 9 kmph . ∴ total time taken = [ 210 / 3 + 210 / 9 ] hours = 84 hours . answer c"
Answer: c
Python program:
a = 9 + 6 
b = 210 / a
c = 9 - 6
d = 210 / c
e = b + d
Problem: a cistern 9 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 68.5 m 2 , e ) 57 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 9 x 1.25 ) + 9 x 4 ] m 2 = 68.5 m 2 . answer : option d"
Answer: d
Python program:
a = 25 / 100
b = a + 1 
c = b * 4
d = 25 / 100
e = d + 1 
f = e * 9
g = c + f 
h = 2 * g
i = 4 * 9
j = h + i
Problem: at a contest with 2,500 participants , 1 / 2 of the people are aged 10 to 12 . next year , the number of people aged 10 to 12 will increase by 1 / 5 . after this change , what percentage of the total 2,500 people will the 10 - to 12 - year - olds represent ?
Options: a ) 55 % , b ) 60 % , c ) 50 % , d ) 45 % , e ) 66 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 5 , we are multiplying it by 1 + 1 / 5 = 6 / 5 , so the answer here must be ( 1 / 2 ) * ( 6 / 5 ) = 3 / 5 = 60 % . answer : b"
Answer: b
Python program:
a = 2 / 500
b = 1 / 5
c = 1 + b 
d = a * c
e = d / 2
f = e * 100
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 140 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 140 km time taken = distance / speed = 140 / 28 = 5 hours answer : option c"
Answer: c
Python program:
a = 24 + 4 
b = 140 / a
Problem: there are 10 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 90 , b ) 85 , c ) 75 , d ) 95 , e ) 82
Rationale: first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 10 and for second = 9 so total methods = 10 * 9 = 90 answer : a
Answer: a
Python program:
a = math.comb(10, 2)
b = math.comb(10, 2)
c = a + b
Problem: a large box contains 17 small boxes and each small box contains 26 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 442 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 690
Rationale: the only thing you have to do is a simple multiply we have : 17 * 26 = 442 correct answer is : a ) 442
Answer: a
Python program:
a = 17 * 26
Problem: find out the ratio of milk to that of water , if a mixture is formed after mixing milk and water of 3 different vessels containning the mixture of milk to that of water in the proportion 3 : 2 , 7 : 3 , 9 : 2 respectively .
Options: a ) 233 : 97 , b ) 235 : 98 , c ) 236 : 97 , d ) 265 : 98 , e ) 234 : 97
Rationale: 3 + 2 = 57 + 3 = 109 + 2 = 11 now , 3 / 5 + 7 / 10 + 9 / 11 : 2 / 5 + 3 / 10 + 2 / 11 = > 233 / 110 : 97 / 110 = > 233 : 97 answer : a
Answer: a
Python program:
a = 9 + 2 
b = 9 / a
c = 3 + 2 
d = 3 / c
e = 7 + 3 
f = 7 / e
g = d + f 
h = b + g 
i = 9 + 2 
j = 2 / i
k = 3 + 2 
l = 2 / k
m = 7 + 3 
n = 3 / m
o = l + n 
p = j + o 
q = h / p
Problem: a student scored an average of 85 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 16 , c ) 76 , d ) 65 , e ) 26
Rationale: given m + p + c = 85 * 3 = 255 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 255 = 65 answer : d
Answer: d
Python program:
a = 90 * 2
b = 70 * 2
c = a + b 
d = 85 * 3
e = c - d
Problem: if you write down all the numbers from 1 to 100 , then how many times do you write 2 ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 20 , d ) d ) 21 , e ) e ) 22
Rationale: "explanation : clearly , from 1 to 100 , there are ten numbers with 2 as the unit ' s digit - 2 , 12 , 22 , 32 , 42 , 52 , 62 , 72 , 82 , 92 ; and ten numbers with 2 as the ten ' s digit - 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 . so , required number = 10 + 10 = 20 . answer : c"
Answer: c
Python program:
a = 100 - 1
b = a / 2
Problem: abce is an isosceles trapezoid and acde is a rectangle . ab = 10 and ec = 20 . what is the length of ae .
Options: a ) 5 , b ) 10 , c ) 12 , d ) 15 , e ) 20
Rationale: as abce is an isosceles trapezoid and ec is twice times ab , we can consider the given trapezoid as half of a regular hexagon ( as length of diagonal in regular hexagon is always double the side ) . thus , sides ab = ae = bc . = > ae = 10 . answer : b
Answer: b
Python program:
a = 20 ** 2
b = 20 - 10
c = b / 2
d = 20 - c
e = d ** 2
f = a - e
g = 20 - 10
h = g / 2
i = h ** 2
j = f + i 
k = j / 2
l = math.sqrt(k)
Problem: evaluate 24.39 + 562.093 + 35.96
Options: a ) 631.344 , b ) 622.443 , c ) 623.434 , d ) 632.423 , e ) 632.443
Rationale: "24.39 + 562.093 + 35.96 = 622.443 option b"
Answer: b
Python program:
a = 562 / 93
b = 24 / 39
Problem: rs 3400 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 4000 , b ) s 1800 , c ) s 800 , d ) s 500 , e ) s 1300
Rationale: "explanation : average rate = ( 144 / 3400 ) * 100 = 4.24 ratio = 7.65 : 12.35 so , first part = ( 7.65 / 20 ) * 3400 = rs 1300 . answer : e"
Answer: e
Python program:
a = 5 / 100
b = 3400 * a
c = b - 144
d = 5 / 100
e = 3 / 100
f = d - e
g = c / f
Problem: at a certain college , 40 percent of the total number of students are freshmen . if 50 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 %
Rationale: "let ' s say there is a total of 100 students at this college . 40 percent of the total number of students are freshmen . # of freshmen = 40 % of 100 = 40 50 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 50 % of 40 = 20 . . . and , of these , 50 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 50 % of 20 = 10 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 10 / 100 = 10 % answer : a"
Answer: a
Python program:
a = 40 * 50
b = a / 100
c = b * 50
d = c / 100
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 40 % of the total school population of x students , what is x ?
Options: a ) 125 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = ( x / 100 ) * ( # boys ) # boys = . 4 x substitute and solve : 90 = ( x / 100 ) * ( . 4 x ) 9000 = . 4 ( x ^ 2 ) 25000 = x ^ 2 x = 150 answer : b"
Answer: b
Python program:
a = 90 * 100
b = 40 / 100
c = a / b
d = math.sqrt(c)
Problem: in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 100 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "c 25 x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 100 = ( 100 * 30 ) / 40 = 25 * 3 = 75 . in x game of 100 points , y gives ( 100 - 75 ) = 25 points to c ."
Answer: c
Python program:
a = 60 - 20
b = a * 3
c = 60 - 30
d = c * 3
e = b - d
Problem: 3500 – ( 1000 ÷ 20.50 ) is equal to :
Options: a ) 3451.21 , b ) 3029.0 , c ) 2993.03 , d ) 2984.36 , e ) none of these
Rationale: explanation : given exp . = 3500 - ( ( 1000 ÷ 2050 ) * 100 ) = 3451.21 answer a
Answer: a
Python program:
a = 1000 / 20
b = 3500 - a
Problem: a man swims downstream 60 km and upstream 40 km taking 4 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 2.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 60 - - - 4 ds = 15 ? - - - - 1 40 - - - - 4 us = 10 ? - - - - 1 s = ? s = ( 15 - 10 ) / 2 = 2.5 answer : option b"
Answer: b
Python program:
a = 40 / 4
b = 60 / 4
c = a + b 
d = c / 2
Problem: two trains of equal length 120 metres move in the same direction . the faster train completely overtakes the slower one in 15 seconds . if the slower train were to move at half its speed , the over taking would take in 10 seconds . at what speeds are the 2 trains moving ( faster and slower respectively in m / s )
Options: a ) 24 , 22 , b ) 32 , 16 , c ) 30 , 18 , d ) 28 , 14 , e ) none of these
Rationale: the total distance covered for over taking = length of the two trains = 120 + 120 = 240 speed of faster train be x m / s and slower train be y m / s in the first case relative speed = x - y relative speed = distance / time taken = x - y = 240 / 15 = 16 m / s … … … ( 1 ) in the second case , the slower train moves at half its speed relative speed = x - 0.5 y = 240 / 10 = 24 m / s … … … … … … … . . ( 2 ) solving equation 1 & 2 we get x = 32 and y = 16 . : . the speed of the faster and slower trains are 32 m / s and 16 m / s respectively answer : b
Answer: b
Python program:
a = 120 + 120 
b = a / 10
c = b * 2
d = 120 + 120 
e = d / 15
f = c - e
Problem: present ages of abi and suji are in the ratio of 5 : 4 respectively . 3 years hence , the ratio of their ages will become 11 : 9 respectively . what is suji ' s present age in years ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: present ages = 5 x : 4 x three hence = 5 x + 3 : 4 x + 3 5 x + 3 : 4 x + 3 = 11 : 9 weget x = 6 suji age is = 4 x = 4 * 6 = 24 answer : e
Answer: e
Python program:
a = 5 + 4 
b = a - 3
c = b * 4
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 8 , b ) 8 / 11 , c ) 8 / 13 , d ) 8 / 15 , e ) none
Rationale: a ' s 1 day ' s work = 1 ; 15 b ' s 1 day ' s work = 1 ; 20 ( a + b ) ' s 1 day ' s work = ( 1 + 1 ) = 7 . 15 20 60 ( a + b ) ' s 4 day ' s work = ( 7 x 4 ) = 7 . 60 15 therefore , remaining work = ( 1 - 7 ) = 8 . 15 15 option d
Answer: d
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = c * 4
e = 1 - d
Problem: the ratio of flour to water to sugar in a recipe is 8 : 4 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "the ratio of flour to water is 16 : 4 = 4 : 1 . the ratio of flour to sugar is 4 : 3 . the new ratio of flour to water to sugar is 4 : 1 : 3 if we need 2 cups of water , then we need 6 cups of sugar . the answer is a ."
Answer: a
Python program:
a = 2 / 4
b = 4 * 3
c = a * b
Problem: a train 165 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 8 , e ) 5
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 165 * 3 / 55 ] sec = 9 sec answer : c"
Answer: c
Python program:
a = 165 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 12100 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 5 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 12100 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 121 so we have 1 , 3 , 9 , 27 . . . . . 12100 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r 121 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 121 x - 2 = 1 - 3 ^ n - 242 = 1 - 3 ^ n - 243 = - 3 ^ n 243 = 3 ^ n ( negatives cancel out ) 243 can also be re written as 3 ^ 5 therefore ; 3 ^ 5 = 3 ^ n thus n = 5 ( d )"
Answer: d
Python program:
a = 12100 * 2
b = a / 100
c = b + 1 
d = math.log(c)
e = math.log(3)
f = d / e
Problem: the diagonals of two squares are in the ratio of 2 : 5 . find the ratio of their areas .
Options: a ) 4 : 25
b ) 4 : 15
c ) 3 : 25
d ) 3 : 15
e ) none of these
Rationale: explanation : let the diagonals of the squares be 2 x and 5 x . then ratio of their areas will be area of square = 1 / 2 ∗ diagonal 2 1 / 2 ∗ 2 x 2 : 1 / 2 ∗ 5 x 2 4 x 2 : 25 x 2 = 4 : 25 option a
Answer: a
Python program:
a = 5 ** 2
b = 4 / a
Problem: s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits q are in s ( 99 ) ?
Options: a ) q = 350 , b ) q = 353 , c ) q = 354 , d ) q = 356 , e ) 357
Rationale: focus on the points where the number of digits q in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b
Answer: b
Python program:
a = const_60 + 4 
b = a + 4 
c = const_60 + 4 
d = c + 4 
e = d * 4
f = b + e 
g = 3 * 1
h = 3 * 2
i = h * 2
j = g + i 
k = f + j
Problem: bhanu spends 30 % of his income on petrol on scooter 30 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 140 , c ) 128 , d ) 210 , e ) 123
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 30 % ( 700 ) = rs . 210 answer : d"
Answer: d
Python program:
a = 30 / 100
b = 300 / a
c = b - 300
d = 30 / 100
e = c * d
Problem: the slant height of a right circular cone is 10 m and its height is 8 m . find the area of its curved surface .
Options: a ) 30 pi m ^ 2
b ) 40 pi m ^ 2
c ) 60 pi m ^ 2
d ) 80 pi m ^ 2
e ) 100 pi m ^ 2
Rationale: l = 10 m h = 8 m r = root ( i ^ 2 - h ^ 2 ) = root ( 10 ^ 2 - 8 ^ 2 ) = 6 m curved surface area = pi ri = 60 pi m ^ 2 answer c
Answer: c
Python program:
a = 10 ** 2
b = 8 ** 2
c = a - b
d = math.sqrt(c)
e = 10 * d
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 150 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 150 male associates implies 60 female associates which means the remaining 30 females must be managers d . 30"
Answer: d
Python program:
a = 40 * 1
Problem: the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 181.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b"
Answer: b
Python program:
a = 35 * 183
b = a - 166
c = b + 106 
d = c / 35
e = math.floor(d)
Problem: 65 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 66 , e ) 21
Rationale: "65 + 5 * 12 / ( 180 / 3 ) = 65 + 5 * 12 / ( 60 ) = 65 + ( 5 * 12 ) / 60 = 65 + 1 = 66 . answer : d"
Answer: d
Python program:
a = 5 * 12
b = 180 / 3
c = a / b
d = 65 + c
Problem: what is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other ?
Options: a ) 3 : 6 , b ) 1.5 : 1 , c ) 3 : 1.5 , d ) 2 : 1 , e ) 3 : 2
Rationale: "d = 1.5 d d = d a √ 2 = 1.5 d a √ 2 = d a = 1.5 d / √ 2 a = d / √ 2 = > 1.5 : 1 answer : b"
Answer: b
Python program:
a = 1 / 5
b = 1 / 5
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 6 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 12
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 6 ( pir ^ 2 ) pir ^ 2 = 12 pir r = 12 answer : e"
Answer: e
Python program:
a = 6 ** 2
b = math.sqrt(a)
c = 2 * b
Problem: what is the 28 th digit to the right of the decimal point in the decimal form of 4 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "4 / 11 = 0.363636 . . . the even numbered positions in the decimal expansion are all 6 . the answer is d ."
Answer: d
Python program:
a = 4 / 11
Problem: the radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 125 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 140 cm . then , circumference of wheel = 2 ï € r = 280 ï € = 880 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 880 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 880 = 125 answer a"
Answer: a
Python program:
a = 1000 * 66
b = 100 * a
c = const_60 * 1
d = b / c
e = 2 * 140
f = 3 * 4
g = 2 + f 
h = 4 * 2
i = 2 + h 
j = i ** 2
k = g / j
l = 3 + k 
m = e * l
n = d / m
Problem: a can finish a work in 15 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 15 * 1 / 3 ) = 5 days . correct option : a"
Answer: a
Python program:
a = 1 / 15
b = a * 10
c = b * 15
d = c / 2