euclaise/mathqa_programs huggingface dataset:
Problem: a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 35 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 950 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 1400 , e ) none of these
Rationale: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 35 = rs . 170 cp on 40 metres = 170 x 40 = rs . 6800 profit earned on 40 metres cloth = rs . 8200 – rs . 6800 = rs . 1400 . answer : option d"
Answer: d
Python program:
a = 35 * 40
Problem: a reduction of 25 % in the price of apples would enable a man to obtain 36 more for rs . 25 , what is reduced price per dozen ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 7 , e ) 10
Rationale: "a 25 * ( 25 / 100 ) = 6 - - - 36 ? - - - 12 = > rs . 2"
Answer: a
Python program:
a = 25 * 25
b = a / 100
c = b / 36
d = c * 12
Problem: the ratio between the present age of p and q is 6 : 7 . if q is 4 years old than p , what will be the ratio of the ages of p and q after 4 years ?
Options: a ) 8 : 7 , b ) 7 : 8 , c ) 8 : 6 , d ) 6 : 7 , e ) 6 : 8
Rationale: let p and q ' s age is 6 x and 7 x years respectively . 7 x - 6 x = 4 x = 4 required ratio = ( 6 x + 4 ) : ( 7 x + 4 ) = 28 : 32 = 7 : 8 option a is answer
Answer: a
Python program:
a = 6 * 4
b = 7 - 6
c = a / b
d = 4 + c 
e = 4 + d 
f = 6 * 4
g = 7 - 6
h = f / g
i = 4 + h 
j = e / i
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 60 ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 105 , e ) 115
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 60 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 60 = ( 2 ^ 2 * 5 ^ 2 ) ^ 60 = 2 ^ 120 * 5 ^ 120 answer : c"
Answer: c
Python program:
a = 100 / 60
b = 2 ** a
c = b - 1
d = 100 - c
Problem: if both 5 ^ 3 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ^ 2 ) , what is the smallest possible positive value of n ?
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
Rationale: "( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) has two appearances of 3 ( in 12 ^ 2 ) and two appearances of 5 ( in 10 ^ 2 ) . thus n must include at least 3 * 5 = 15 the answer is a ."
Answer: a
Python program:
a = 5 * 2
b = a * 3
c = 5 * 2
d = c * 3
e = b + d 
f = 5 * 2
g = f * 3
h = e + g 
i = h + 2 
j = i + 4 
k = j + 4
Problem: in one hour , a boat goes 8 km along the stream and 2 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 8 + 2 ) kmph . = 5 kmph . answer b"
Answer: b
Python program:
a = 8 + 2 
b = a / 2
Problem: the sale price sarees listed for rs . 200 after successive discount is 20 % and 10 % is ?
Options: a ) 187 , b ) 124 , c ) 172 , d ) 144 , e ) 175
Rationale: "200 * ( 80 / 100 ) * ( 90 / 100 ) = 144 answer : d"
Answer: d
Python program:
a = 200 * 20
b = a / 100
c = 200 - b
d = 200 * 20
e = d / 100
f = 200 - e
g = f * 10
h = g / 100
i = c - h
Problem: sandy is younger than molly by 20 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 20 x = 10 sandy is 70 years old . the answer is e ."
Answer: e
Python program:
a = 9 - 7
b = 7 / a
c = b * 20
Problem: 5 times a number equals one 100 . the number is
Options: a ) 50 , b ) 10 , c ) 15 , d ) 25 , e ) 20
Rationale: since five times the number equals one hundred , then the number equals one hundred divided by five . therefore the number is 100 / 5 = 20 . correct answer e
Answer: e
Python program:
a = 100 / 5
Problem: the manufacturing cost of a shoe is rs . 200 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 222 , b ) s 246 , c ) s 220 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 200 + ( 500 / 100 ) = 205 . gain = 20 % = > sp = 1.2 cp = 1.2 x 205 = 246 answer : b"
Answer: b
Python program:
a = 500 / 100
b = 200 + a 
c = 20 / 100
d = 500 / 100
e = 200 + d 
f = c * e
g = b + f
Problem: find the compound interest on $ 10,000 in 2 years at 4 % per annum , the interest being compounded half - yearly
Options: a ) 824 , b ) 824.36 , c ) 824.32 , d ) 824.24 , e ) 824.26
Rationale: "principal = $ 10000 ; rate = 2 % per half - year ; time = 2 years = 4 half - years . amount = $ [ 10000 * ( 1 + ( 2 / 100 ) ) 4 ] = $ ( 10000 * ( 51 / 50 ) * ( 51 / 50 ) * ( 51 / 50 ) * ( 51 / 50 ) ) = $ 10824.32 . : . c . i . = $ ( 10824.32 - 10000 ) = $ 824.32 . answer c ."
Answer: c
Python program:
a = 4 / 100
b = a / 2
c = b + 1 
d = c ** 4
e = d * 10
f = e - 10
Problem: in how many years will a sum of money doubles itself at 30 % per annum on simple interest ?
Options: a ) 7 % , b ) 3 % , c ) 5 % , d ) 8 % , e ) 2 %
Rationale: "p = ( p * 30 * r ) / 100 r = 3 % answer : b"
Answer: b
Python program:
a = 100 / 30
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 25 paise per sq m is
Options: a ) rs . 186 , b ) rs . 258 , c ) rs . 486 , d ) rs . 586 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 25 / 100 ) = rs . 186 answer : a"
Answer: a
Python program:
a = 25 / 100
b = 25 * 12
c = 25 * 6
d = 2 * c
e = 12 * 6
f = e * 2
g = d + f 
h = b + g 
i = a * h
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 2.00 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 144 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
Rationale: since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 2.00 ) or $ 144 . the best answer is therefore a . answer : a .
Answer: a
Python program:
a = 2 / 3
b = 36 * a
c = 1 / 3
d = b / c
e = 2 * d
Problem: in some quantity of ghee , 50 % is pure ghee and 50 % is vanaspati . if 20 kg of pure ghee is added , then the strength of vanaspati ghee becomes 30 % . the original quantity was ?
Options: a ) 25 , b ) 15 , c ) 30 , d ) 45 , e ) 20
Rationale: "let the original quantity be x then , vanaspati ghee in xkg = 50 x / 100 kg = x / 2 kg ( x / 2 ) / ( x + 20 ) = 30 / 100 x / ( 2 x + 40 ) = 3 / 10 x = 30 answer is c"
Answer: c
Python program:
a = 30 * 20
b = 50 - 30
c = a / b
Problem: the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 1024 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 42 . , d ) 48 . , e ) 46 .
Rationale: "let the width = x x * 4 x = 1024 x ^ 2 = 256 x = 16 length = 4 * 16 = 64 difference = 64 - 16 = 48 d is the answer"
Answer: d
Python program:
a = 1024 / 4
b = math.sqrt(a)
c = b * 4
d = 1024 / 4
e = math.sqrt(d)
f = c - e
Problem: at what price must an article costing rs . 38 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 52.5 , b ) 50 , c ) 62.3 , d ) 62.1 , e ) 62.4
Rationale: "cp = 38 sp = 38 * ( 125 / 100 ) = 38 mp * ( 95 / 100 ) = 47.5 mp = 50 answer : b"
Answer: b
Python program:
a = 38 * 25
b = a / 100
c = 38 + b 
d = c * 100
e = 100 - 5
f = d / e
Problem: if the given two numbers are respectively 6 % and 18 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 33 1 / 3 % , e ) none of these
Rationale: "here , l = 6 and m = 18 therefore , first number = l / m x 100 % of second number = 6 / 18 x 100 % of second number = 33 1 / 3 % of second number answer : d"
Answer: d
Python program:
a = 6 / 100
b = 18 / 100
c = a / b
d = c * 100
Problem: a 4 % stock yield 5 % . the market value of the stock is ?
Options: a ) rs . 125 , b ) rs . 80 , c ) rs . 99 , d ) rs . 109 , e ) rs . 101
Rationale: "for an income of rs . 5 , investment = rs . 100 for an income of rs . 4 , investment = rs . ( 100 / 5 ) x 4 = rs . 80 answer : b"
Answer: b
Python program:
a = 100 / 5
b = a * 4
Problem: a train is 288 meter long is running at a speed of 29 km / hour . in what time will it pass a bridge of 101 meter length ?
Options: a ) 48.29 , b ) 50 , c ) 26.8 , d ) 45.29 , e ) 30
Rationale: "speed = 29 km / hr = 29 * ( 5 / 18 ) m / sec = 145 / 18 m / sec total distance = 288 + 101 = 389 meter time = distance / speed = 389 * ( 18 / 145 ) = 48.29 seconds . answer : a"
Answer: a
Python program:
a = 288 + 101 
b = 29 * 1000
c = b / 3600
d = a / c
Problem: rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage c .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % c = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Python program:
a = 2 * 10
b = 2 * 10
c = b + 1 
d = a * c
e = 25 / 100
f = e + 1 
g = 10 / f
h = 15 + 2 
i = g * h
j = d + i 
k = 653 - j
l = 2 * 10
m = 2 * 10
n = m + 1 
o = l * n
p = 25 / 100
q = p + 1 
r = 10 / q
s = 15 + 2 
t = r * s
u = o + t 
v = k / u
w = v * 100
Problem: john had a stock of 1100 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 63.4 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1100 - n = 1100 - 402 = 698 percentage books not sold / total number of books = 698 / 1100 = 0.634 = 63.4 % correct answer b"
Answer: b
Python program:
a = 75 + 50 
b = 64 + 78 
c = a + b 
d = c + 135 
e = 1100 - d
f = e / 1100
g = f * 100
Problem: in the third grade of windblown school there are 108 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 , e ) 12
Rationale: "one third of them failed the math test = 1 / 3 of 108 = 36 . passed in math test = 82 . and 1 / 6 failed that literature test = 18 . it is a possible scenario that these 18 ( failed in literature ) were the ones who passed the math test . so in this case , no one failed in both . hence a ."
Answer: a
Python program:
a = 108 / 3
b = 108 / 6
c = min(a)
Problem: if a ( a - 4 ) = 21 and b ( b - 4 ) = 21 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 4 , d ) 46 , e ) 48
Rationale: "a ( a - 4 ) = 21 and b ( b - 4 ) = 21 = > a , b must be integers and if a is - 3 or 7 , b will be 7 and - 3 respectively = > a + b = 4 ans : c"
Answer: c
Python program:
a = 4 + 21 
b = 4 - 21
c = a + b 
d = c - 1
e = d - 1
f = e - 1
g = f - 1
Problem: a housing society has been allotted a square piece of land measuring 2550.25 sq . m . what is the side of the plot ?
Options: a ) 50.25 m
b ) 50.5 m
c ) 50.65 m
d ) 50.85
e ) none
Rationale: solution side = √ 2550.25 = √ 255025 / 100 = 505 / 10 = 50.5 m . answer b
Answer: b
Python program:
a = math.sqrt(2550)
Problem: in a certificate by mistake a candidate gave his height as 10 % more than actual height . in the interview panel , he clarified that his height was 5 feet 5 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 6.5 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.10 - 1 ) = 6.5 a"
Answer: a
Python program:
a = const_0_25 + const_0_25 
b = 10 + a 
c = b - 5
d = const_0_25 + const_0_25 
e = 10 + d 
f = e - 5
g = 100 + f 
h = c / g
i = h * 100
Problem: rs . 900 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 900 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1064 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 900 ) = rs . 56 rate = ( 100 x 56 / 900 x 3 ) = 56 / 27 % new rate = ( 56 / 27 + 4 ) % = 164 / 27 % new s . i . = rs . ( 900 x 164 / 27 x 3 / 100 ) rs . 164 . ∴ new amount = rs . ( 900 + 164 ) = rs . 1064 . answer c"
Answer: c
Python program:
a = 956 - 900
b = a * 100
c = 900 * 3
d = b / c
e = d + 4 
f = 900 * e
g = f * 3
h = g / 100
i = 900 + h
Problem: if the population of a certain country increases at the rate of one person every 20 seconds , by how many persons does the population increase in 30 minutes ?
Options: a ) 55 , b ) 20 , c ) 96 , d ) 90 , e ) 40
Rationale: answer = 3 * 30 = 90 answer = d
Answer: d
Python program:
a = const_60 / 20
b = a * 30
Problem: jake took a bus from home to market , that travels at 10 kmph . while walking back at 2 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 50 kmph . find the average speed .
Options: a ) 1.17 kmph , b ) 1.67 kmph , c ) 0.69 kmph , d ) 1.45 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 10 , by walking = x / 2 , by cycling = x / 50 hours : . average speed = total distance / total time = 2 x / x / 5 + x / 2 + x / 50 = 2 * 60 / 12 + 30 + 1.2 = 1.67 answer : b
Answer: b
Python program:
a = 50 * 2
b = 10 + 2 
c = b + 50 
d = a / c
Problem: a survey reveals that the average income of a company ’ s customers is $ 45000 per year . if 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $ 55000 , what is the average income of the other 40 customers ? is there a way to solve this using weighted average concept instead of doing tedious calculations ?
Options: a ) $ 27,500 , b ) $ 35,000 , c ) $ 37,500 , d ) $ 42,500 , e ) $ 50,000
Rationale: let x be the average of 40 customers 40 * x + 10 * 55000 = 50 * 45000 solving this we have x = 42500 answer is d .
Answer: d
Python program:
a = 45000 * 50
b = 10 * 55000
c = a - b
d = c / 40
Problem: hcf of two numbers is 11 and the product of these numbers is 363 , what is the the greater number ?
Options: a ) 28 , b ) 31 , c ) 33 , d ) 35 , e ) 38
Rationale: the numbers be 11 a and 11 b 11 a × 11 b = 363 ab = 3 co - primes with product 3 are ( 1 , 3 ) hence the numbers with hcf 11 and product 363 = ( 11 × 1 , 11 × 3 ) = ( 11 , 33 ) numbers are 11 and 33 the greater number = 33
Answer: c
Python program:
a = 363 / 11
Problem: if n divided by 7 has a remainder of 2 , what is the remainder when 4 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: "as per question = > n = 7 p + 2 for some integer p hence 4 n = > 28 q + 8 = > remainder = > 6 for some integer q alternatively = > n = 2 > 3 n = > 8 = > 8 divided by 7 will leave a remainder 1 hence a"
Answer: a
Python program:
a = 4 * 2
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 12 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 3360 , c ) 8400 , d ) 5040 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 12 machine produce 560 * 6 * ( 12 / 8 ) in 6 minutes 560 * 6 * 12 / 8 = 5040 answer is d ."
Answer: d
Python program:
a = 12 / 8
b = 560 * a
c = b * 6
Problem: if 8 workers can build 8 cars in 8 days , then how many days would it take 5 workers to build 5 cars ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 10 , e ) 12
Rationale: "8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 5 workers can build 5 / 8 car per day . the time required to build 5 cars is 5 / ( 5 / 8 ) = 8 days the answer is c ."
Answer: c
Python program:
a = 8 * 8
b = a / 8
c = 5 / 5
d = b * c
Problem: if both 7 ^ 2 and 3 ^ 4 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 120 , b ) 256 , c ) 343 , d ) 441 , e ) 512
Rationale: "the number a must include at least 3 ^ 2 * 7 ^ 2 = 441 the answer is d ."
Answer: d
Python program:
a = 7 * 2
b = a * 2
c = 7 * 2
d = c * 2
e = b + d 
f = 7 * 2
g = f * 2
h = e + g 
i = h + 2 
j = i + 4 
k = j + 4
Problem: how many times digit 6 is used while writing numbers from 100 to 1400 ?
Options: a ) 648 , b ) 350 , c ) 252 , d ) 225 , e ) 26
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 350 . hence b ."
Answer: b
Python program:
a = 1400 - 100
b = a / 10
c = 10 + 1 
d = 10 + 1 
e = c * d
f = b + e 
g = 6 * 2
h = f + g
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 25 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 300 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: "pastry is divided in 25 customers equally . so , total number of pastry must be a multiple of 25 only option a satisfies the condition , and hence is the answer"
Answer: a
Python program:
a = 49 * 6
b = 49 - 25
c = a / b
d = c * 25
Problem: the sum of the non - prime numbers between 40 and 50 , non - inclusive , is
Options: a ) 131 , b ) 176 , c ) 274 , d ) 405 , e ) 495
Rationale: "the sum of the non - prime numbers between 40 and 50 , non - inclusive , are { 42 , 44 , 45 , 46 , 48 , 49 } . 6 times 40 something is approx north of 240 hence the answer is ( c ) 274"
Answer: c
Python program:
a = 40 + 1 
b = 40 + 1 
c = b + 1 
d = a + c 
e = 40 + 1 
f = e + 1 
g = f + 2 
h = d + g 
i = 40 + 1 
j = i + 1 
k = j + 2 
l = k + 1 
m = h + l 
n = 40 + 1 
o = n + 1 
p = o + 2 
q = p + 1 
r = q + 1 
s = m + r 
t = 40 + 1 
u = t + 1 
v = u + 2 
w = v + 1 
x = w + 1 
y = x + 1 
z = s + y 
A = 40 + 1 
B = A + 1 
C = B + 2 
D = C + 1 
E = D + 1 
F = E + 1 
G = F + 1 
H = z + G
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 20 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) none of these
Rationale: "the weight of non - water in 20 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 20 ∗ 0.1 = x ∗ 0.8 - - > x = 2.5 answer : c ."
Answer: c
Python program:
a = 100 - 90
b = a * 20
c = b / 100
d = 100 - 20
e = c / d
f = e * 100
Problem: there are 9 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 36 , d ) 60 , e ) 90
Rationale: "9 players are there . two players play one game with one another . so 9 c 2 = 9 x 8 / 2 = 36 so option c is correct"
Answer: c
Python program:
a = 9 - 1
b = 9 * a
c = b / 2
Problem: in order to obtain an income of rs . 680 from 10 % stock at rs . 120 , one must make an investment of
Options: a ) 5363 , b ) 8160 , c ) 2368 , d ) 1987 , e ) 2732
Rationale: "to obtain rs . 10 , investment = rs . 120 . to obtain rs . 680 , investment = = rs . 8160 . answer : b"
Answer: b
Python program:
a = 120 / 10
b = a * 680
Problem: in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party
Options: a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . answer d"
Answer: d
Python program:
a = 105 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: the price of stock decreased by 8 % last year and rose by 10 % this year . what is the net percentage change in the price of the stock ?
Options: a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.6 % , e ) 2 %
Rationale: ( 100 % - 8 % ) * ( 100 % + 10 % ) = 0.92 * 1.10 = 1.012 = 101.2 % . the net percentage change in the price of the stock is ( + ) 1.2 % the answer is c
Answer: c
Python program:
a = 10 / 100
b = a + 1 
c = 8 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: two men and three women working 7 hours a day finish a work in 5 days . four men and four women working 3 hours a day complete the work in 7 days . the number of days in which only 7 men working 4 hours a day will finish the work is ?
Options: a ) 5 days , b ) 3 days , c ) 2 days , d ) 9 days , e ) 10 days
Rationale: answer : option a 2 m + 3 w - - - - - 35 h 4 m + 4 w - - - - - - - 21 h 7 m - - - - - - - ? d 70 m + 105 w = 84 m + 84 m 21 w = 14 m = > 2 m = 3 w 4 * 35 = 7 * x = > x = 20 hours 20 / 4 = 5 days
Answer: a
Python program:
a = 4 * 7
b = 3 * 7
c = 3 / b
d = 5 * 7
e = 4 / d
f = c - e
g = f / 4
h = a * g
i = 1 / h
Problem: a train is running at a speed of 40 km / hr and it crosses a post in 19.8 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 220 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 19.8 s distance covered , d = vt = ( 400 / 36 ) ã — 19.8 = 220 m distance covered is equal to the length of the train = 220 m correct answer is 220 metres d"
Answer: d
Python program:
a = 40 * const_0_2778
b = 19 * 8
Problem: the average age of 20 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 79 , b ) 86 , c ) 95 , d ) 72 , e ) 80
Rationale: "age of the 15 th student = 20 * 15 - ( 14 * 5 + 16 * 9 ) = 300 - 214 = 86 years answer is b"
Answer: b
Python program:
a = 20 * 15
b = 5 * 14
c = a - b
d = 9 * 16
e = c - d
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 8 , 1 ) , ( 1 , 1 ) , ( 1 , - 7 and ( - 8 , - 7 ) ?
Options: a ) 144 , b ) 36 , c ) 72 , d ) 56 , e ) 112
Rationale: "length of side 1 = 8 + 1 = 9 length of side 2 = 7 + 1 = 8 area of rectangle = 9 * 8 = 72 c is the answer"
Answer: c
Python program:
a = 8 + 1 
b = 1 + 7 
c = a * b
Problem: on a certain farm the ratio of horses to cows is 6 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 3 : 1 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "originally , there were 6 k horses and k cows . ( 6 k - 15 ) = 3 ( k + 15 ) 6 k - 3 k = 45 + 15 3 k = 60 k = 20 the difference between horses and cows is ( 6 k - 15 ) - ( k + 15 ) = 5 k - 30 = 70 the answer is d ."
Answer: d
Python program:
a = 15 * 3
b = 15 * 1
c = a + b 
d = 6 * 1
e = d - 3
f = c / e
g = 6 * f
h = g - 15
i = 15 * 3
j = 15 * 1
k = i + j 
l = 6 * 1
m = l - 3
n = k / m
o = n + 15 
p = h - o