euclaise/mathqa_programs huggingface dataset:
Problem: if a is an integer greater than 7 but less than 25 and b is an integer greater than 34 but less than 44 , what is the range of a / b ?
Options: a ) 21 / 34 , b ) 1 / 12 , c ) 15 / 64 , d ) 17 / 35 , e ) 7 / 6
Rationale: "the way to approach this problem is 7 < a < 25 and 34 < b < 41 minimum possible value of a is 8 and maximum is 24 minimum possible value of b is 35 and maximum is 40 range = max a / min b - min a / max b ( highest - lowest ) 24 / 35 - 8 / 40 = 17 / 35 hence d"
Answer: d
Python program:
a = 25 - 1
b = 34 + 1 
c = a / b
d = 7 + 1 
e = 44 - 1
f = d / e
g = c - f
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 55 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 56.37 , b ) s . 53.22 , c ) s . 56.219 , d ) s . 51.18 , e ) s . 51.11
Rationale: "explanation : sum = ( 55 * 100 ) / ( 2 * 5 ) = rs . 550 amount = [ 550 * ( 1 + 5 / 100 ) 2 ] = rs . 606.375 c . i . = ( 606.375 - 550 ) = rs . 56.37 answer : a"
Answer: a
Python program:
a = 5 / 100
b = a * 2
c = 55 / b
d = c * 5
e = d / 100
f = 5 / 100
g = f * 2
h = 55 / g
i = e + h 
j = 5 / 100
k = j * 2
l = 55 / k
m = l * 5
n = m / 100
o = 5 / 100
p = o * 2
q = 55 / p
r = n + q 
s = r * 5
t = s / 100
u = i + t 
v = 5 / 100
w = v * 2
x = 55 / w
y = u - x
Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 4 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: 2 ^ ( 2 w ) = 8 ^ ( w − 4 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 4 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 12 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 12 w = 12 the answer is d .
Answer: d
Python program:
a = math.log(2)
b = 12 * a
c = math.log(2)
d = b / c
Problem: a is twice as good as b . and together they finish a piece of work in 18 days . in how many days will a alone finish the work
Options: a ) 25 , b ) 27 , c ) 15 , d ) 18 , e ) 21
Rationale: ( a ' s 1 day work ) : ( b ' s 1 day work ) = 2 : 1 a + b 1 day work = 1 / 18 a ' s 1 day work = ( 1 / 18 ) * ( 2 / 3 ) = 1 / 27 a alone can finish the work in 27 days answer is b
Answer: b
Python program:
a = 1/(18)
b = 2 + 1 
c = a / b
d = c * 2
e = 1/(d)
Problem: everyone shakes hands with everyone else in a room . total number of handshakes is 55 . number of persons = ?
Options: a ) 14 , b ) 12 , c ) 11 , d ) 15 , e ) 16
Rationale: "in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 55 or n ( n - 1 ) = 110 or n = 11 answer is ( c )"
Answer: c
Python program:
a = 55 * 2
b = a / 3
c = b / 4
Problem: what will be the fraction of 4 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 4 * 1 / 100 = 1 / 25 . friends i know it is quite simple , but trust me while solving percentage questions in hurry we use to do these types of mistake only . so i recommend you to have a bit practise of this option d"
Answer: d
Python program:
a = 4 / 2
b = circle_area / (
Problem: the least number which must be subtracted from 670 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 4 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 670 by 9 , we get remainder = 4 therefore , required number to be subtracted = 4 answer : c"
Answer: c
Python program:
a = 4 + 1 
b = a * 10
c = 4 + 2 
d = b + c 
e = d * 9
f = 670 - e
Problem: in an election a candidate who gets 84 % of the votes is elected by a majority of 476 votes . what is the total number of votes polled ?
Options: a ) 630 , b ) 700 , c ) 535 , d ) 450 , e ) 815
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 84 ) % of x = 16 % of x 84 % of x - 16 % of x = 476 68 x / 100 = 476 x = 476 * 100 / 68 = 700 answer is b"
Answer: b
Python program:
a = 100 - 84
b = 84 - a
c = b / 100
d = 476 / c
Problem: 3 numbers are in the ratio 5 : 6 : 8 . the sum of its longest and smallest numbers equals the sum of the third number and 49 . find the third number ?
Options: a ) a ) 54 , b ) b ) 75 , c ) c ) 48 , d ) d ) 42 , e ) e ) 63
Rationale: let the numbers be 5 x , 6 x , 8 x . largest number = 8 x . smallest number = 5 x . third number = 6 x . 8 x + 5 x = 6 x + 49 7 x = 49 = > x = 7 6 x = 42 = > third number is 42 . answer : d
Answer: d
Python program:
a = 5 + 8 
b = a - 6
c = 49 / b
d = c * 6
Problem: the price of an item changed from $ 120 to $ 100 . then later the price decreased again from $ 100 to $ 80 . which of the two decreases was larger in percentage term ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: first decrease in percent part / whole = ( 120 - 100 ) / 120 = 0.17 = 17 % second decrease in percent part / whole = ( 100 - 80 ) / 100 = 0.20 = 20 % the second decrease was larger in percent term . the part were the same in both cases but the whole was smaller in the second decrease . answer b
Answer: b
Python program:
a = 80 / 100
b = a * 100
c = 100 - b
Problem: what is the next number : 3 , 11 , 83 , __
Options: a ) 631 , b ) 731 , c ) 831 , d ) 849 , e ) 901
Rationale: "3 ^ 0 + 2 = 3 3 ^ 2 + 2 = 11 3 ^ 4 + 2 = 83 3 ^ 6 + 2 = 731 the answer is b ."
Answer: b
Python program:
a = 83 * 10
b = a - 100
c = b - 3
d = c - 3
Problem: a man sells a car to his friend at 14 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 22325.58 , b ) rs . 32325.58 , c ) rs . 52325.58 , d ) rs . 62325.58 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 14 % . now s . p = rs . 45000 and loss = 14 % c . p . rs . [ 100 / 86 ã — 45000 ] = rs . 52325.58 . correct option : c"
Answer: c
Python program:
a = 54000 * 100
b = 100 + 20 
c = a / b
d = c * 100
e = 100 - 14
f = d / e
Problem: a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 960 gm . for a kg . his gain is … % .
Options: a ) 4.16 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.26 %
Rationale: "his percentage gain is 100 * 40 / 960 as he is gaining 40 units for his purchase of 960 units . so 4.16 % . answer : a"
Answer: a
Python program:
a = 4 + 1 
b = a * 2
c = b * 100
d = 960 / c
e = 1/(d)
f = e - 1
g = f * 100
Problem: increasing the original price of an article by 10 percent and then increasing the new price by 10 percent is equivalent to increasing the original price by
Options: a ) 20 % , b ) 20.5 % , c ) 20.8 % , d ) 21 % , e ) 21.8 %
Rationale: "1.1 * 1.1 * x = 1.21 * x the answer is d ."
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = 10 / 100
d = 1 + c 
e = b * d
f = e - 1
g = 100 * f
Problem: a can run 1.5 km distance in 2 min 20 seconds , while b can run this distance in 2 min 30 sec . by how much distance can a beat b ?
Options: a ) 90 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) 190 m
Rationale: "a takes time 2.20 minutes = 140 sec b takes time 2.30 minutes = 150 sec diffrence = 150 - 140 = 10 sec now we are to find distance covered in 10 sec by b 150 sec = 1500 m 1 sec = 10 m 10 sec = 10 x 10 = 100 m answer : b"
Answer: b
Python program:
a = 1 * 5
b = 1 * 5
c = 2 * const_60
d = c + 30 
e = b / d
f = 1 * 5
g = f + 20 
h = e * g
i = a - h
Problem: a 6 % stock yields 8 % . the market value of the stock is ?
Options: a ) rs . 11 , b ) rs . 75 , c ) rs . 17 , d ) rs . 16 , e ) rs . 22
Rationale: "for an income of rs . 8 , investment = rs . 100 . for an income of rs 6 , investment = rs . \ inline \ left ( \ frac { 100 } { 8 } \ times 6 \ right ) = rs . 75 market value of rs . 100 stock = rs . 75 . answer : b"
Answer: b
Python program:
a = 100 / 8
b = a * 6
Problem: if y is the smallest positive integer such that 6300 multiplied by y is the square of an integer , then y must be
Options: a ) 5 , b ) 7 , c ) 15 , d ) 35 , e ) 45
Rationale: "6300 = 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 to be perfect square , we need to multiply by at least 7 . the answer is b ."
Answer: b
Python program:
a = 2 + 3 
b = a * 2
Problem: if the farmer sells 75 of his chickens , his stock of feed will last for 20 more days than planned , but if he buys 100 more chickens , he will run out of feed 15 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 275 , e ) 300
Rationale: let v denote the volume of feed one chicken consumes per day . then the total volume of feed in stock will be v ∗ d ∗ c where d is the number of days the feed will last if the number of chickens does not change and cc is the current number of chickens . from the question it follows that v ( d + 20 ) ( c − 75 ) = vdc v ( d − 15 ) ( c + 100 ) = vdc the first equation simplifies to 20 c − 75 d = 1500 . the second equation simplifies to ( − 15 ) c + 100 d = 1500 after dividing everything by 5 we get the linear system : 4 c − 15 d = 300 ( − 3 ) c + 20 d = 300 solving it we get c = 300 d = 60 answer : e
Answer: e
Python program:
a = 100 - 75
b = 20 - 15
c = a / b
d = 75 / c
e = 20 * d
f = 100 - 75
g = 20 - 15
h = f / g
i = 75 / h
j = 20 - i
k = e / j
l = 100 - 75
m = 20 - 15
n = l / m
o = k * n
Problem: if the average of t , b , c , 14 and 15 is 12 . what is the average value of t , b , c and 29
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: t + b + c + 14 + 15 = 12 * 5 = 60 = > t + b + c = 60 - 29 = 31 t + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d
Answer: d
Python program:
a = 2 + 3 
b = 12 * a
c = b / 4
Problem: a square of 2 unit is given and four circles are made on its corners having equal radius of each . and another circle of equal radius is made on the center of the square . find out the area of square which is not covered by circles ?
Options: a ) 0.76
b ) 0.86
c ) 0.96
d ) 1.16
e ) 1.26
Rationale: let the radius of circle is ' r ' area of the circle which is at corner = ( 22 / 7 * r ^ 2 ) / 4 hence the area of all four circles are = 22 / 7 * r ^ 2 areaof circle which is made on center of suare is = 22 / 7 * r ^ 2 total area of all circles are = 2 * 22 / 7 * r ^ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 1 ) if we construct the diagram we get the relation 4 r = 2 sqrt 2 r = 1 / sqrt 2 put the value of r in eqn 1 and we get 2 * 22 / 7 * 1 / 2 = 22 / 7 = 3.14 area of suare = 2 ^ 2 = 4 area of remaining part = 4 - 3.14 = 0.86 answer : b
Answer: b
Python program:
a = square_area - (
Problem: sachin is younger than rahul by 6 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 14 , c ) 15 , d ) 24.9 , e ) 24.1
Rationale: "if rahul age is x , then sachin age is x - 6 , so ( x - 6 ) / x = 7 / 9 = > 9 x - 42 = 7 x = > 2 x = 42 = > x = 21 so sachin age is 21 - 6 = 15 answer : c"
Answer: c
Python program:
a = 9 - 7
b = 6 / a
c = b * 7
Problem: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 13 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 51 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 24 , d ) d ) 25 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 52 . . not w = 52 - 31 = 21 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 21 or x = 9 . . so who won nobel but not wolf = x + 3 = 12 . . but people who won both w and n = 13 . . so total who won n = 12 + 13 = 25 . . d"
Answer: d
Python program:
a = 51 - 31
b = a - 3
c = b / 2
d = 3 + c 
e = d + 13
Problem: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area covered by the two roads ?
Options: a ) 400
b ) 1550
c ) 1575
d ) 1600
e ) 1625
Rationale: area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads = 1000 + 600 - 25 = 1575 answer : option c
Answer: c
Python program:
a = rectangle_area + (
Problem: if p # q denotes the least common multiple of p and q , then q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Python program:
a = 18 * 24
b = 12 * 16
c = a - b
d = c / 2
e = d + 24
Problem: the difference between a two - digit number and the number obtained by interchanging the digits is 9 . what is the difference between the two digits of the number ?
Options: a ) 8 , b ) 2 , c ) 7 , d ) can not be determined , e ) none of these
Rationale: "suppose the two - digit number be 10 x + y . then we have been given l 0 x + y – ( 10 y + x ) = 9 ⇒ 9 x – 9 y = 9 ⇒ x – y = 1 hence , the required difference = 1 note that if the difference between a two - digit number and the number obtained by interchanging the digits is d , then the difference between the two digits of the number = d ⁄ 9 answer e"
Answer: e
Python program:
a = 10 - 1
b = 9 / a
Problem: 81 , 64 , 27 , 16 . . .
Options: a ) 12 , b ) 4 , c ) 9 , d ) 3 , e ) 1
Rationale: "81 / 3 = 27 64 / 4 = 16 27 / 3 = 9 answer : c"
Answer: c
Python program:
a = negate - (
Problem: set x consists of all two - digit primes and set y consists of all positive odd multiples of 7 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 95
Rationale: set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 7 , 21 , 35 , . . . . . . . . . . . . . . . , 77 , 91 , } combining two sets , say set z set z = { 7 , 11 , 13 , 17,21 , . . . . . . . . . . . . . . . . . . . , 77 , 83 , 89 , 91 , 97 } range = max value - min value range ( z ) = 97 - 7 = 90 oa c is the answer .
Answer: c
Python program:
a = 100 - 3
b = a - 7
Problem: a shopkeeper sold an article offering a discount of 10 % and earned a profit of 25 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 39 % , b ) 52 % , c ) 15 % , d ) 21 % , e ) 28 %
Rationale: "let c . p . be $ 100 . then , s . p . = $ 125 let marked price be $ x . then , 90 / 100 * x = 125 x = 12500 / 90 = $ 139 now , s . p . = $ 139 , c . p . = rs . 100 profit % = 39 % . answer : a"
Answer: a
Python program:
a = 100 + 25 
b = a * 100
c = 100 - 10
d = b / c
e = d - 100
Problem: a certain high school has 500 students . of these students , 30 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 30 y = 20 z = 10 so , we have 30 students taking music , 20 taking art and 10 taking both music and art . 20 student taking just music 10 student taking just art 10 student taking both music and art total = 40 students we ' re asked for the total number of students who are taking neither course . that is 500 - 40 = 460 . d"
Answer: d
Python program:
a = 30 + 20 
b = a - 10
c = 500 - b
Problem: a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 130 , b ) 141 , c ) 152 , d ) 163 , e ) 174
Rationale: "3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 3 = 83 . the minimum number of horses and ponies is 163 . the answer is d ."
Answer: d
Python program:
a = 10 / 5
b = a * 8
c = math.lcm(10, b)
d = c + 3 
e = 10 / 5
f = e * 8
g = math.lcm(10, f)
h = d + g
Problem: two bullet trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 13 sec . , b ) 15 sec . , c ) 12 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: "c 12 sec . speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 15 m / sec = 8 m / sec . relative speed = ( 12 + 8 ) = 20 m / sec . required time = ( 120 + 120 ) / 20 sec = 12 sec ."
Answer: c
Python program:
a = 120 + 120 
b = speed + ( 
c = a / b
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 8 days more ?
Options: a ) 1122 , b ) 1140 , c ) 1199 , d ) 1188 , e ) 1166
Rationale: 760 - - - - 22 760 - - - - 20 x - - - - - 8 x * 8 = 760 * 20 x = 1900 760 - - - - - - - 1140 answer : b
Answer: b
Python program:
a = 22 - 2
b = 760 * a
c = b / 8
d = c - 760
Problem: if the price of a tv is first decreased by 20 % and then increased by 55 % , then the net change in the price will be :
Options: a ) 4 % increase , b ) 24 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these
Rationale: "explanation : solution : let the original price be rs . 100 . new final price = 155 % of ( 80 % of 100 ) = rs . 155 / 100 * 80 / 100 * 100 = rs . 124 . . ' . increase = 24 % answer : b"
Answer: b
Python program:
a = 100 - 20
b = 100 + 55 
c = a * b
d = c / 100
e = d - 100
Problem: what is the smallest integer c for which 27 ^ c > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ c > 3 ^ 24 converting into the same bases : 27 ^ c > 27 ^ 8 therefore for the equation to hold true , c > 8 or c = 9 option c"
Answer: c
Python program:
a = 24 / 3
b = math.floor(a)
c = b + 1
Problem: in order to obtain an income of rs . 600 from 12 % stock at rs . 106 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 2368 , d ) 7632 , e ) 7732
Rationale: "to obtain rs . 10 , investment = rs . 106 . to obtain rs . 600 , investment = = rs . 7632 answer : d"
Answer: d
Python program:
a = 106 / 12
b = a * 600
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7200 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7200 / 18 + 7200 / 14 = 400 + 514.2 = 914.2 hours answer : option a"
Answer: a
Python program:
a = 16 + 2 
b = 7200 / a
c = 16 - 2
d = 7200 / c
e = b + d
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 7000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 400 , c ) s . 600 , d ) s . 800 , e ) s . 875
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 7000 ) = rs . 875 answer = e"
Answer: e
Python program:
a = 1/(3)
b = 1/(8)
c = 1/(6)
d = b + c 
e = a - d
f = e * 7000
g = f * 3
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 400 inclusive ?
Options: a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 210
Rationale: "we ' re asked for the average of all of the multiples of 10 from 10 to 400 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 40 ( 10 ) = 400 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 400 = 410 20 + 390 = 410 30 + 380 = 410 etc . since there are 40 total terms , this pattern will create 20 ' pairs ' of 410 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 20 ) ( 410 ) / ( 40 ) = 410 / 2 = 205 final answer : d"
Answer: d
Python program:
a = 10 + 400 
b = 400 - 10
c = b / 10
d = c + 1 
e = a * d
f = e / 2
g = 400 - 10
h = g / 10
i = h + 1 
j = f / i
Problem: a train 130 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 4 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 10 , b ) 6.5 , c ) 7 , d ) 7.13 , e ) 10.2
Rationale: "speed of train relative to man = 60 + 4 = 64 km / hr . = 64 * 5 / 18 = 160 / 9 m / sec . time taken to pass the men = 130 * 9 / 160 = 7.13 sec . answer : option d"
Answer: d
Python program:
a = 60 + 4 
b = a * const_0_2778
c = 130 / b
Problem: after giving a discount of rs . 80 the shopkeeper still gets a profit of 10 % , if the cost price is rs . 200 . find the markup % ?
Options: a ) 31 % , b ) 33 % , c ) 28 % , d ) 30 % , e ) 32 %
Rationale: "cost price = 180 s . p = 200 * 110 / 100 = 220 disc = 80 so . . . mark price = 216 + 80 = 296 . . . . . . mark up % = 261 - 200 / 200 = 61 / 200 = 0.305 or 31 % answer : a"
Answer: a
Python program:
a = 100 / 10
b = 200 / a
c = 200 + b 
d = c + 80 
e = d - 200
f = e / 200
Problem: if the digits 27 in the decimal 0.00027 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00027 ) ?
Options: a ) 0.27 , b ) 0.027 , c ) 27 , d ) 0.0027 , e ) 2.7 e - 06
Rationale: "99 * 0.27 = 26.73 approx . 27 answer : c"
Answer: c
Python program:
a = 10 * 10
b = 10 * 10
c = b - 1
d = a * c
e = 10 * 10
f = e - 1
g = 27 / f
h = d * g
i = h / 1000
j = i * 10
Problem: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 200 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 80 2.5 h = 80 h = 80 . a is the answer ."
Answer: a
Python program:
a = 50 / 100
b = 2 + a 
c = 200 / b
Problem: in the coordinate plane , one of the vertices of a square is the point ( - 3 , - 4 ) . if the diagonals of that square intersect at point ( 5 , 3 ) , what is the area of that square ?
Options: a ) 100 , b ) 169 , c ) 225 , d ) 324 , e ) 256
Rationale: "one point ( - 3 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 3 - 5 = - 8 is the midpoint of the square - - > whole side 16 , 16 * 16 = 256 e"
Answer: e
Python program:
a = 3 * 5
b = 3 * 5
c = a * b