euclaise/mathqa_programs huggingface dataset:
Problem: a gardener wants to plant trees in his garden in rows in such away that the number of trees in each row to be the same . if there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row ?
Options: a ) 21 , b ) 28 , c ) 34 , d ) 32 , e ) 76
Rationale: required number of trees = 24 / 36 * 42 = 28 . answer : b
Answer: b
Python program:
a = 24 * 42
b = 24 + 12 
c = a / b
Problem: a contractor undertook to do a piece of work in 10 days . he employed certain number of laboures but 5 of them were absent from the very first day and the rest could finish the work in only 13 days . find the number of men originally employed ?
Options: a ) 21.6 , b ) 23.6 , c ) 22.6 , d ) 21.8 , e ) 21.3
Rationale: "let the number of men originally employed be x . 10 x = 13 ( x â € “ 5 ) or x = 21.6 answer a"
Answer: a
Python program:
a = 13 * 5
b = 13 - 10
c = a / b
Problem: a string of 25 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.06 , what is the probability that the string of light bulbs will fail during the time period t ?
Options: a ) 0.06 , b ) ( 0.06 ) ^ 25 , c ) 1 - ( 0.06 ) ^ 25 , d ) 1 - ( 0.94 ) ^ 25 , e ) ( 0.94 ) ^ 25
Rationale: "the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 25 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.06 = 0.94 the probability that none of the 25 light bulbs fails is 0.94 ^ 25 . hence , the probability that at least one light bulb fails is 1 - 0.94 ^ 25 . answer : d . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 25 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.06 = 6 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."
Answer: d
Python program:
a = 1 - 0
b = a ** 25
c = 1 - b
Problem: in a race where 16 cars are running , the chance that car x will win is 1 / 4 , that y will win is 1 / 12 and that z will win is 1 / 7 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 10 / 21 , c ) 27 / 410 , d ) 11 / 21 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 4 + 1 / 12 + 1 / 7 = 10 / 21 answer : b"
Answer: b
Python program:
a = 1 / 4
b = 1 / 12
c = a + b 
d = 1 / 7
e = c + d
Problem: a certain machine produces 650 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 7 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 109,200 , e ) 168,000
Rationale: "since 7 days consist of 24 * 7 hours the total hours of a week is 168 hours . since every hour the machine produces 650 units of product p the total product during 168 hours is 650 * 168 = 109,200 correct option : d"
Answer: d
Python program:
a = 4 * 10
Problem: a 20 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 110 , c ) 200 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 20 , money invested = rs . ( 100 / 10 x 20 ) = rs . 200 . â ˆ ´ market value of rs . 100 stock = rs . 200 answer c"
Answer: c
Python program:
a = 100 / 10
b = a * 20
Problem: a cricket player whose bowling average was 24.50 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.50 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 141 , d ) 96 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 24.50 w + 52 total wickets after last match = w + 5 ( 24.50 w + 52 ) / ( w + 5 ) = 24.5 - 0.50 = 24 w = 136 so total wickets aftr last match = w + 5 = 141 answer : c"
Answer: c
Python program:
a = 24 - 50
b = a * 5
c = b - 52
d = c / 0
Problem: a polling company found that , of 300 households surveyed , 120 spent at least $ 100 per month on both gasoline and electricity , 60 spent at least $ 100 per month on gasoline but not on electricity , and for every household that did not spend at least $ 100 per month on gasoline or electricity , 4 spent at least $ 100 per month on electricity but not on gasoline . how many of the 300 households did not spend at least $ 100 per month on either gasoline or electricity ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 90 , e ) 96
Rationale: 120 spend $ 100 on gas & electricity 60 spend $ 100 on gas but not on electricity for every one that spent < $ 100 on both there are 4 that spent $ 100 on electricity not gas let the ones that spent on neither be x the ones that spent on just electricity will be 4 x total households = those who spend > $ 100 on both + those who spend > $ 100 on just one + those who spend < $ 100 on both = 120 + 60 + 4 x + x 300 = 180 + 5 x implies x = 24 answer is ( a )
Answer: a
Python program:
a = 120 + 60 
b = 300 - a
c = 4 + 1 
d = b / c
Problem: the cash realised on selling a 14 % stock is rs . 107.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 107 , c ) 102 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 107.25 - 0.25 ) = rs . 107 . answer : b"
Answer: b
Python program:
a = 1 / 4
b = 107 - 25
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 38.7 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 46 , c ) 30 , d ) data inadequate , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 38.7 ) / ( 100 â ˆ ’ 5 ) = 146 hence , required % profit = 146 â € “ 100 = 46 % answer b"
Answer: b
Python program:
a = 100 + 38 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: the price of rice is reduced by 2 % . how many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier ?
Options: a ) 48 kg , b ) 49 kg , c ) 50 kg , d ) 51 kg , e ) none
Rationale: sol . let the original price be rs . 100 per kg . money required to buy 49 kg of rice = rs . ( 100 x 49 ) = rs . 4900 . new price = rs . 98 per kg . ∴ quantity of rice bought = [ 4900 / 98 ] kg = 50 kg . answer c
Answer: c
Python program:
a = 100 * 49
b = 100 - 2
c = a / b
Problem: set a contains all the even numbers between 10 and 50 inclusive . set b contains all the even numbers between 110 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2100 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 10 , 12,14 , 16 . . . 50 set b contains 110 , 112 , 114 . . . 150 number of terms in each set = 21 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 21 = 2100 answer a"
Answer: a
Python program:
a = 110 - 10
b = 50 - 10
c = b / 2
d = c + 1 
e = a * d
Problem: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 15 nor by 20 ?
Options: a ) 887 , b ) 678 , c ) 765 , d ) 345 , e ) 256
Rationale: "in 1000 consecutive numbers , number of multiples of 15 = 1000 / 15 = 66 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 20 = 1000 / 20 = 50 number of multiples of 15 * 20 i . e . 300 = 1000 / 300 = 3 number of integers from 1 to 1000 that are divisible by neither 15 nor by 20 = 1000 - ( 66 + 50 - 3 ) { using the concept of sets here ) = 887 answer is a"
Answer: a
Python program:
a = 1000 / 15
b = 1000 / 20
c = a + b 
d = 15 * 20
e = 1000 / d
f = c - e
g = 1000 - f
Problem: if x is an integer such that 5 < x < 21 , 7 < x < 18 , 13 > x > 2 , 12 > x > 9 , and x + 1 < 13 , then x is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: 5 < x < 21 , 7 < x < 18 , 2 < x < 13 9 < x < 12 x < 13 from above : 10 < x < 12 - - > x = 11 . answer : e .
Answer: e
Python program:
a = 13 - 1
b = a - 1
Problem: the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 20 more than the number who did not , and if receipts for registration and lunch totaled $ 50,240 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 800 , c ) 1,300 , d ) 1,500 , e ) 400
Rationale: hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 20 more than the number who did not . that means , total number of people who registered and paid for lunch = 20 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 20 + x ) = 1440 + 72 x now , total amount received was 50240 . thus , from the above data , 50 x + 1440 + 72 x = 50240 122 x = 50240 - 1440 122 x = 48800 x = 400 . hence the correct ans is e
Answer: e
Python program:
a = 1 * 1
Problem: 23 , 29 , 31 , 37 , 41 , 43 , 47 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 48 , d ) 59 , e ) 45
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 53 answer : a"
Answer: a
Python program:
a = negate - (
Problem: the denominator of a fraction is 15 greater than the numerator . if the numerator and the denominator are increased by 3 , the resulting fraction is equal to 3 â  „ 4 . what is the value of the original fraction ?
Options: a ) 23 / 38 , b ) 29 / 44 , c ) 33 / 48 , d ) 38 / 53 , e ) 42 / 57
Rationale: "let the numerator be x . then the denominator is x + 15 . x + 3 / x + 18 = 3 / 4 . 4 x + 12 = 3 x + 54 . x = 42 . the original fraction is 42 / 57 . the answer is e ."
Answer: e
Python program:
a = 3 + 15 
b = 3 * a
c = b - 4
d = 4 - 3
e = c / d
f = 3 + 15 
g = 3 * f
h = g - 4
i = 4 - 3
j = h / i
k = j + 15 
l = e / k
Problem: a and b started a business investing rs . 50,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 5 : 2 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4
Rationale: "a : b = 50000 : 20000 = 5 : 2 answer : a"
Answer: a
Python program:
a = 3 * 3
b = 3 * 3
c = b + 1 
d = a * c
e = d + 2 
f = 3 * 3
g = f + 1 
h = 2 * g
i = e / h
Problem: a grocer has a sale of rs . 6345 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) rs . 3000 , b ) rs . 4991 , c ) rs . 5991 , d ) rs . 6001 , e ) none
Rationale: "sol . total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . ∴ required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 34009 ) = rs . 4991 . answer b"
Answer: b
Python program:
a = 5 + 1 
b = a * 6500
c = 6345 + 6927 
d = c + 6855 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: at deluxe paint store , fuchsia paint is made by mixing 4 parts of red paint with 2 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 24
Rationale: "in 24 liters , red = 4 / 6 * 24 = 16 and blue = 8 so , 16 / ( 8 + x ) = 3 / 6 or , x = 24 ( answer e )"
Answer: e
Python program:
a = 4 + 2 
b = 4 / a
c = 24 * b
d = 4 + 2 
e = 3 / d
f = c / e
g = 4 + 2 
h = 6 / g
i = f * h
j = 4 + 2 
k = 4 / j
l = 24 * k
m = 24 - l
n = i - m
Problem: h . c . f of 136 , 144 and a third number is 8 and their l . c . m is 2 ^ 4 * 3 ^ 2 * 17 * 7 . the third number is :
Options: a ) 154 , b ) 248 , c ) 360 , d ) 424 , e ) 168
Rationale: 136 = 2 ^ 3 * 17 ; 144 = 2 ^ 4 * 3 ^ 2 h . c . f = 2 ^ 3 = 8 since h . c . f is the product of lowest powers of common factors , so the third number must have ( 2 ^ 3 ) as its factor . since l . c . m is the product of highest powers of common prime factors , so the third number must have 3 and 7 as its factors . third number = 2 ^ 3 * 3 * 7 = 168 answer : e
Answer: e
Python program:
a = 2 ** 4
b = 3 ** 2
c = a * b
d = c * 17
e = d * 7
f = 8 * e
g = 136 * 144
h = f / g
i = h * 8
j = i * 3
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 25 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 100 , e ) 112.5
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 25 % = 90 * 1.25 = 112.5 thus ratio = 112.5 / 100 = 1.125 ( in % terms = 12.5 % ) . thus e is the correct answer ."
Answer: e
Python program:
a = 100 + 20 
b = a / 100
c = 100 * b
d = 100 - 25
e = d / 100
f = c * e
g = 100 + 25 
h = g / 100
i = f * h
Problem: express a speed of 70 kmph in meters per second ?
Options: a ) 10 mps , b ) 19.44 mps , c ) 97.44 mps , d ) 17.44 mps , e ) 18.44 mps
Rationale: "70 * 5 / 18 = 19.44 mps answer : b"
Answer: b
Python program:
a = const_0_2778 * 70
Problem: if n = ( 33 ) ^ 43 + ( 43 ) ^ 32 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: first of all , the units digit of ( 33 ) ^ 43 is the same as that of 3 ^ 43 and the units digit of ( 43 ) ^ 32 is the same as that of 3 ^ 32 . so , we need to find the units digit of 3 ^ 43 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 43 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 43 + ( 43 ) ^ 32 is 7 + 5 = 2 . answer : b .
Answer: b
Python program:
a = reminder ** (
b = a + reminder 
c = reminder - (
Problem: on a certain transatlantic crossing , 20 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 20 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.2 t had round trip tickets and took their cars . 0.8 x had round trip tickets and took their cars . 0.8 x = 0.2 t x = 0.25 t the answer is b ."
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 20 / b
Problem: a train running at the speed of 126 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 315 meter , e ) 265 meter
Rationale: "speed = 126 * ( 5 / 18 ) m / sec = 35 m / sec length of train ( distance ) = speed * time ( 35 ) * 9 = 315 meter answer : d"
Answer: d
Python program:
a = 126 * 1000
b = a / 3600
c = b * 9
Problem: what is the smallest number which when diminished by 20 , is divisible 15 , 30 , 45 and 60 ?
Options: a ) 200 , b ) 220 , c ) 240 , d ) 322 , e ) 342
Rationale: "required number = ( lcm of 15 , 30 , 45 and 60 ) + 20 = 180 + 20 = 200 option a"
Answer: a
Python program:
a = math.lcm(15, 30)
b = math.lcm(45, 60)
c = math.lcm(a, b)
d = c + 20
Problem: mrs . evans gave a test to her freshmen economics class , which has 25 students enrolled and 22 of them answered question 1 correctly . if 20 answered question 2 correctly and 3 did not take the test then how many answered both questions correctly ?
Options: a ) 30 , b ) 20 , c ) 23 , d ) 17 , e ) 19
Rationale: "total number of enrolled students = 25 number of students who did not take test = 3 hence , number of students who took test = 25 - 3 = 22 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 20 . number of students who answered both q 1 & q 2 correctly = 20 . answer : b"
Answer: b
Python program:
a = 22 + 20 
b = a + 3 
c = b - 25
Problem: in two alloys , copper and tin are related in the ratios of 4 : 1 and 1 : 3 . 10 kg of ist alloy , 16 kg of 2 nd alloy and some pure copper melted together . an alloy obtained in which the ratio of copper and tin was 3 : 2 . find the weight of the new alloy .
Options: a ) 34 kg , b ) 35 kg , c ) 36 kg , d ) 30 kg , e ) 32 kg
Rationale: suppose x kg of pure copper is melted with 10 kg of ist alloy and 16 kg of 2 nd alloy , then pure cooper in new alloy = 10 * 4 / 5 + 16 * 1 / 4 + x = 12 + x kg pure tin in new alloy = 10 * 1 / 5 + 16 * 3 / 4 = 14 kg as per given condition ( 12 + x ) / 14 = 3 / 2 24 + 2 x = 42 x = 9 kg total weight of new alloy = 10 + 16 + 9 = 35 kg answer : b
Answer: b
Python program:
a = 10 + 16 
b = 3 / 4
c = 16 * b
d = 4 + 1 
e = 10 / d
f = c + e 
g = f * 3
h = g / 2
i = 3 / 4
j = 16 * i
k = h - j
l = a + k
Problem: a farmer planned to plough a field by doing 120 hectares a day . after two days of work he increased his daily productivity by 25 % and he finished the job two days ahead of schedule . a ) what is the area of the field ? b ) in how many days did the farmer get the job done ? c ) in how many days did the farmer plan to get the job done ?
Options: a ) 2337 , b ) 2667 , c ) 1440 , d ) 2887 , e ) 2661
Rationale: first of all we will find the new daily productivity of the farmer in hectares per day : 25 % of 120 hectares is 25100 ⋅ 120 = 3025100 ⋅ 120 = 30 hectares , therefore 120 + 30 = 150120 + 30 = 150 hectares is the new daily productivity . lets x be the planned number of days allotted for the job . then the farm is 120 ⋅ x 120 ⋅ x hectares . on the other hand , we get the same area if we add 120 ⋅ 2120 ⋅ 2 hectares to 150 ( x − 4 ) 150 ( x − 4 ) hectares . then we get the equation 120 x = 120 ⋅ 2 + 150 ( x − 4 ) 120 x = 120 ⋅ 2 + 150 ( x − 4 ) x = 12 x = 12 so , the job was initially supposed to take 12 days , but actually the field was ploughed in 12 - 2 = 10 days . the field ' s area is 120 ⋅ 12 = 1440120 ⋅ 12 = 1440 hectares . answer : c
Answer: c
Python program:
a = 120 * 2
b = 120 * 25
c = b / 100
d = 120 + c 
e = 4 * 2
f = d * e
g = a + f
Problem: 12 men complete a work in 9 days . after they have worked for 6 days , 6 more men join them . how many days will they take to complete the remaining work ?
Options: a ) 2 days , b ) 7 days , c ) 8 days , d ) 9 days , e ) 45 days
Rationale: 1 man ' s 1 day work = 1 / 108 12 men ' s 6 day ' s work = 1 / 9 * 6 = 2 / 3 remaining work = 1 - 2 / 3 = 1 / 3 18 men ' s 1 day work = 1 / 108 * 18 = 1 / 6 1 / 6 work is done by them in 1 day . 1 / 3 work is done by them in 6 * 1 / 3 = 2 days . answer : a
Answer: a
Python program:
a = 12 * 9
b = 12 * 6
c = a - b
d = 12 + 6 
e = c / d
Problem: joe has a total of $ 200 in his two pockets . he takes one fourth of the money in his left pocket and puts it in his right pocket . he then takes $ 20 from his left pocket and puts it in his right pocket . if he now has an equal amount of money in each pocket , then how much money did he originally have in his left pocket ?
Options: a ) $ 120 , b ) $ 130 , c ) $ 140 , d ) $ 150 , e ) $ 160
Rationale: joe had $ 100 in his left and $ 100 in his right pocket at the end . so , he had $ 120 in his left pocket ( and $ 80 in his right pocket ) before moving $ 20 from his left to his right pocket . thus , he had $ 160 in his left pocket originally ( solve x − x / 4 = 120 ) . correct answer e
Answer: e
Python program:
a = 200 + 20 
b = a + 20 
c = 1 / 4
d = 1 - c
e = 1 / 4
f = 1 - e
g = d + f 
h = b / g
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 200 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 25 hours , d ) 12 hours , e ) 8 hours
Rationale: here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 200 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 200 units is ' 10 times ' 20 , we need ' 10 times ' more time . ( 2.5 hours ) ( 10 times ) = 25 hours final answer : [ reveal ] spoiler : c
Answer: c
Python program:
a = 20 / 10
b = a / 5
c = b * 20
d = 200 / c
Problem: the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 60 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 70 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 60 percent is reduced which means the new price is merely 40 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 2 / 5 ) p = 6 / 20 p is the new price after both deduction which is 30 percent of the original value p . this implies this entire series of deduction is worth having discounted 70 % of p . so answer is b = 70 %"
Answer: b
Python program:
a = 100 - 60
b = a / 100
c = 100 - 25
d = b * c
e = 100 - d
Problem: given a number , there is an algorithm described here to find it ' s sum and number of factors . for example , let us take the number 1225 ?
Options: a ) 1767 , b ) 1800 , c ) 1812 , d ) 1890 , e ) none
Rationale: solving for 1225 = 52 × 72 sum of divisors = ( ap + 1 – 1 ) / ( a – 1 ) × ( bq + 1 – 1 ) / ( b – 1 ) here a = 5 , b = 7 prime factors p = 2 and q = 2 sum of divisors = ( 53 – 1 ) / ( 5 – 1 ) × ( 73 – 1 ) / ( 7 – 1 ) = ( 124 / 4 ) × ( 342 / 6 ) = ( 31 × 57 ) = 1767 option a
Answer: a
Python program:
a = 3 + 4 
b = 1 + a 
c = 2 + 3 
d = 1225 / c
e = 2 + 3 
f = d / e
g = b + f 
h = 2 + 3 
i = 1 + h 
j = 2 + 3 
k = j ** 2
l = i + k 
m = g * l
Problem: total 60 cows 20 cow gives each 2 liter milk 20 cow gives each 3 / 4 liter milk 20 cow gives each 1 / 4 liter milk this is split into 3 son per each 20 cows & 20 liter milk how ?
Options: a ) 20 , b ) 10 , c ) 15 , d ) 16 , e ) 18
Rationale: 20 cow 2 liter each = 40 liter 20 cow 3 / 4 liter each = 3 / 4 = 0.75 * 20 = 15 20 cow 1 / 4 liter each = 1 / 4 = 0.25 * 20 = 5 add 40 + 15 + 5 = 60 milk split into 3 son each 20 liter then 60 / 3 = 20 answer : a
Answer: a
Python program:
a = 3 / 4
b = 3 / 4
c = b * 20
d = a + c 
e = const_0_25 * 20
f = d + e
Problem: x starts a business with rs . 45000 . y joins in the business after 5 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 1 : 3 , d ) 3 : 1 , e ) 18 : 7
Rationale: explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 7 = 45 ã — 12 : 30 ã — 7 = 3 ã — 12 : 2 ã — 7 = 18 : 7 answer : option e
Answer: e
Python program:
a = 45000 * 12
b = 4 + 3 
c = 30000 * b
d = a / c