euclaise/mathqa_programs huggingface dataset:
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 10 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,10 = 10 / 100 x = 80 * 10 / 100 x = 8 8 / 10 = 0.8 = 800 % , answer a"
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 10 * b
d = c / 10
e = d * 100
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 60 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 12 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 60 = 6 k + 4 k = > k = 6 total red ' s in bag a will be 2 k = 12 d"
Answer: d
Python program:
a = 3 * 2
b = a + 4 
c = 60 / b
Problem: solution a is 20 % barium and solution b is 80 % barium . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % barium solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 20 ) = 1 / 1 so the volume of the two solutions will be equal . answer has to be 4 : 4 = c
Answer: c
Python program:
a = 80 / 20
b = 80 / 20
c = a / b
Problem: a cyclist bikes x distance at 12 miles per hour and returns over the same path at 8 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.3 , c ) 9.6 , d ) 8.9 , e ) 9.0
Rationale: "distance = d 1 = x miles speed = s 1 = 12 miles per hour time = t 1 = distance / speed = x / 12 2 . going from b to a distance = d 2 = x miles speed = s 2 = 8 miles per hour time = t 2 = distance / speed = x / 8 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 12 + x / 8 = x ( 1 / 12 + 1 / 8 ) = = 5 x / 24 speed = 2 x / ( 5 x / 24 ) = 48 / 5 = 9.6 answer : c"
Answer: c
Python program:
a = 12 + 8 
b = a / 2
Problem: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 85 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 59 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.85 = 51 democrats are expected to vote for candidate a ; 40 * 0.20 = 8 republicans are expected to vote for candidate a . thus total of 51 + 8 = 59 registered voters are expected to vote for candidate a , which is 59 % of the total number of registered voters . answer : b ."
Answer: b
Python program:
a = 85 / 100
b = 60 * a
c = 100 - 60
d = 20 / 100
e = c * d
f = b + e
Problem: while driving from a - ville to b - town , harriet drove at a constant speed of 100 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 150 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 180
Rationale: "5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 180 min * leg a - b - - - > d = 100.180 / 60 = 18000 / 60 * leg b - a - - - - > d = 150 * 120 / 60 = 18000 / 60 so the correct ans . ise"
Answer: e
Python program:
a = 100 * 5
b = 100 + 150 
c = a / b
d = 5 - c
e = d * const_60
Problem: find the value for x from below equation : x / 3 = - 7 ?
Options: a ) - 6 , b ) - 21 , c ) - 2 , d ) - 3 , e ) 4
Rationale: "1 . multiply both sides by 3 : x * 3 / 3 = - 7 / 3 simplify both sides : x = - 21 b"
Answer: b
Python program:
a = 7 - 4
b = a * 3
Problem: at a speed of 50 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 15 gallon tank of gasoline and travels for 5 hours at 50 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 11 / 36 , c ) 5 / 9 , d ) 2 / 3 , e ) 25 / 36
Rationale: gas used = ( 5 hours ) * ( 50 miles / hour ) * ( 1 gallon / 30 miles ) = 8 + 1 / 3 gallons portion used = ( 8 + 1 / 3 ) / 15 = 5 / 9 ans c
Answer: c
Python program:
a = 50 * 5
b = a / 30
c = b / 15
Problem: robert ate 13 chocolates , nickel ate 4 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 13 - 4 = 9 . answer is c
Answer: c
Python program:
a = 13 - 4
Problem: by selling an article at rs . 150 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 486 , b ) s . 455 , c ) s . 487 , d ) s . 120 , e ) s . 489
Rationale: "sp = 150 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 150 * [ 100 / ( 100 + 25 ) ] = 150 * [ 100 / 125 ] = rs . 120 answer : d"
Answer: d
Python program:
a = 150 * 100
b = 100 + 25 
c = a / b
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 600 kms and city a and city c is 360 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 20 / 9
Rationale: "distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 600 / 3 = 200 km / hour distance traveled by freddy = 360 km time taken by freddy = 4 hours average speed of freddy = 360 / 4 = 90 km / hour ratio of average speed of eddy to freddy = 200 / 90 = 20 / 9 answer e"
Answer: e
Python program:
a = 600 / 3
b = 360 / 4
c = a / b
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 120,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "the 15 managers have an average salary of $ 120,000 . the sum of their salaries is : sum = ( average ) * ( number of salaries ) = $ 120,000 * 15 = $ 1 , 800,000 the 75 associates have an average salary of $ 30,000 . the sum of their salaries is : sum = ( average ) * ( number of salaries ) = $ 30,000 * 75 = $ 2 , 250,000 when we add those two sums , we get the total payroll of all 90 employees . $ 1 , 800,000 + $ 2 , 250,000 = $ 4 , 050,000 so , we have 90 employees , and together they earn $ 4 , 050,000 , so the average is average = $ 4 , 050,000 ÷ 90 = $ 45,000 answer : b ."
Answer: b
Python program:
a = 3 * 3
b = a * 10
c = 100 * 10
d = b * c
e = 3 * 10
f = 100 * 10
g = e * f
h = d + g 
i = 75 + 15 
j = h / i
Problem: excluding stoppages , the speed of a bus is 5454 kmph and including stoppages , it is 4545 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 12 , b ) 11 , c ) 10 , d ) 9 , e ) 8
Rationale: "explanation : speed of the bus excluding stoppages = 54 = 54 kmph speed of the bus including stoppages = 45 = 45 kmph loss in speed when including stoppages = 54 â ˆ ’ 45 = 9 kmph = 54 â ˆ ’ 45 = 9 kmph â ‡ ’ â ‡ ’ in 11 hour , bus covers 99 km less due to stoppages . hence , time in which the bus stops per hour = time taken to cover 99 km = distancespeed = 954 hour = 16 hour = distancespeed = 954 hour = 16 hour = 606 min = 10 min answer is c"
Answer: c
Python program:
a = 5454 - 4545
b = a / 5454
c = const_60 * b
Problem: sheela deposits rs . 2500 in bank savings account . if this is 25 % of her monthly income . what is her monthly income in ?
Options: a ) 10000 , b ) 20000 , c ) 25000 , d ) 22235 , e ) none of these
Rationale: explanation : 25 % of income = rs . 2500 100 % of income = 2500 x 100 / 25 = rs . 10000 answer : a
Answer: a
Python program:
a = 2500 * 100
b = a / 25
Problem: in one hour , a boat goes 15 km along the stream and 5 km against the stream . the sped 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 ( 15 + 5 ) km / hr = 10 kmph . answer e"
Answer: e
Python program:
a = 15 + 5 
b = a / 2
Problem: what percent of 9.6 kg is 28 gms ?
Options: a ) 25 , b ) 66 , c ) 288 , d ) 29 , e ) 17
Rationale: "explanation : required percentage = ( 28 / 9600 * 100 ) % = 29 / 100 % = 0.29 % answer : d ) . 29 %"
Answer: d
Python program:
a = 9 / 6
b = a * 100
Problem: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 400 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 400 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 a"
Answer: a
Python program:
a = 3 + 3
Problem: the difference between simple and compound interests on a certain sum for 2 years at 4 % per annum is rs . 50 . the sum is
Options: a ) rs . 20,400 , b ) rs . 25,000 , c ) rs . 31,250 , d ) rs . 38,000 , e ) rs . 48,000
Rationale: "difference between 2 yr ci and si is given by pr ^ 2 . . pr ^ 2 = 50 p * r / 100 * r / 100 = 50 p * 4 / 100 * 4 / 100 = 50 p = ( 50 * 100 * 100 ) / 4 * 4 p = 31,250 answer : c"
Answer: c
Python program:
a = 4 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = 4 / 100
f = e + 1 
g = d - f
h = g * 2
Problem: if a certain number is divided by 3 , the quotient , dividend , and divisor , added together , will amount to 63 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 45 , d ) 38 , e ) 59
Rationale: "let x = the number sought . then x / 3 + x + 3 = 63 . and x = 45 . c"
Answer: c
Python program:
a = 63 - 3
b = a * 3
c = 3 + 1 
d = b / c
Problem: an electric pump can fill a tank in 7 hours . because of a leak in the tank , it took 14 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 10 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 14 hours
Rationale: "work done by the leak in 1 hour = 1 / 7 - 1 / 14 = 1 / 14 the leak will empty the tank in 14 hours answer is e"
Answer: e
Python program:
a = 14 / 1
Problem: a vendor sells 30 percent of the apples he had and throws away 20 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: let x be the original number of apples . on day one , the vendor throws away ( 0.2 ) ( 0.7 ) x = 0.14 x . the remaining apples are ( 0.8 ) ( 0.7 ) x = 0.56 x . on day two , the vendor throws away ( 0.5 ) ( 0.56 ) x = 0.28 x . the vendor throws away a total of 0.14 x + 0.28 x = 0.42 x . the vendor throws away 42 percent of the apples . the answer is b .
Answer: b
Python program:
a = 100 - 30
b = 20 / 100
c = 100 - 30
d = b * c
e = a - d
f = e / 2
g = 20 / 100
h = 100 - 30
i = g * h
j = f + i
Problem: if log 2 = 0.3010 and log 3 = 0.4771 , the values of log 5 512 is
Options: a ) 3.879 , b ) 3.875 , c ) 3.872 , d ) 3.828 , e ) 3.192
Rationale: "ans : log 5512 = { \ color { black } \ frac { \ log 512 } { \ log 5 } } = { \ color { black } \ frac { \ log 2 ^ { 9 } } { \ log ( \ frac { 10 } { 2 } ) } } = { \ color { black } \ frac { 9 \ log 2 } { \ log 10 - \ log 2 } } = { \ color { black } \ frac { ( 9 \ times 0.3010 ) } { 1 - 0.3010 } } = { \ color { black } \ frac { 2.709 } { 0.699 } } = { \ color { black } \ frac { 2709 } { 699 } } = 3.876 answer : b ) 3.875"
Answer: b
Python program:
a = 0 / 3010
b = 0 * 3010
Problem: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,071 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 11 , c ) 10 ^ 9 , d ) 10 ^ 10 , e ) 10 ^ 8
Rationale: "79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,071 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,071 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is e ."
Answer: e
Python program:
a = 79 * 48
b = const_0_25 * 1000
c = b * 100
d = 3 + 4 
e = d * 10
f = c + e 
g = f + 3 
h = a * g
Problem: there is a train and car . the ratio btw the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 480 km in 8 h . the speed of the bus is 3 / 4 th of the speed of the train . how much distance will the car cover in 6 h ?
Options: a ) 300 km , b ) 320 km , c ) 370 km , d ) 430 km , e ) 450 km
Rationale: sol . speed of bus = 480 / 8 = 60 km / h speed of train = ( 60 * 4 ) / 3 = 80 km / h speed of train : speed of car = 16 : 15 speed of car = 80 / 16 * 15 = 75 km / h distance covered by car in 6 hr = 75 × 6 = 450 km e
Answer: e
Python program:
a = 480 / 8
b = a * 4
c = b / 3
d = c * 15
e = d / 16
f = e * 6
Problem: how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 41 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 1 . so , one more solution , where a = b is not possible . so , answer will be d ."
Answer: d
Python program:
a = 34 / 41
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what is the compound interest on the same at the same rate and for the same time ?
Options: a ) rs . 52 , b ) rs . 51.25 , c ) rs . 54.25 , d ) rs . 60 , e ) rs . 70
Rationale: "simple interest for 2 years = rs . 50 ie . for 1 years rs . 25 . . in the first year the s . i and c . i are same ie . rs . 25 . so in the 2 nd year in c . i calculated for 1 years interest also . so in second years for rs . 25 interest is 25 * 5 / 100 = 1.25 . so total c . p = 51.25 . answer : b"
Answer: b
Python program:
a = 5 / 100
b = a * 2
c = 50 / b
d = c * 5
e = d / 100
f = 5 / 100
g = f * 2
h = 50 / g
i = e + h 
j = 5 / 100
k = j * 2
l = 50 / k
m = l * 5
n = m / 100
o = 5 / 100
p = o * 2
q = 50 / p
r = n + q 
s = r * 5
t = s / 100
u = i + t 
v = 5 / 100
w = v * 2
x = 50 / w
y = u - x
Problem: of 61 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 53 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 61 thrower = 37 rest = 61 - 37 = 24 left handed = 24 / 3 = 8 right handed = 16 if all thrower are right handed then total right handed is 37 + 16 = 53 so a . 53 is the right answer"
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 61 - 37
d = b * c
e = 37 + d
Problem: what is the remainder when 7 ^ 498 is divided by 5 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "7 ^ 0 = 1 7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = . . . 1 7 ^ 5 = . . . . 7 7 ^ 6 = . . . . . . 9 and so on in a recurring pattern of 1,7 , 9,3 , 1,7 , 9,3 . . . . 498 / 4 = 124 ( with a remainder 2 ) so the last number is a 9 . so when 7 ^ 498 is divided by 5 the remainder is 4 , ans = a"
Answer: a
Python program:
a = 5 / 2
b = 7 * 7
c = a - b
Problem: a person bought 118 glass bowls at a rate of rs . 12 per bowl . he sold 102 of them at rs . 15 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 300 / 11 , c ) 243 / 7 , d ) 475 / 59 , e ) 279 / 8
Rationale: cp = 118 * 12 = 1416 and sp = 102 * 15 = 1530 gain % = 100 * ( 1530 - 1416 ) / 1100 = 11400 / 1416 = 475 / 59 answer : d
Answer: d
Python program:
a = 102 * 15
b = 118 * 12
c = a - b
d = 118 * 12
e = c / d
f = e * 100
Problem: an engineering student has to secure 36 % marks to pass . he gets 130 marks and fails by 14 marks . the maximum no . of marks obtained by him is ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: "130 14 - - - - - - - 361 - - - - - - 144 100 % - - - - - - ? = > 400 answer : b"
Answer: b
Python program:
a = 130 + 14 
b = a * 100
c = b / 36
Problem: he ratio between the sale price and the cost price of an article is 7 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 5
Rationale: "let c . p . = rs . 5 x and s . p . = rs . 7 x . then , gain = rs . 2 x required ratio = 2 x : 5 x = 2 : 5 . answer : e"
Answer: e
Python program:
a = 3 / 0
b = 1 - a
c = 1/(b)
Problem: what is the cp of rs 100 stock at 2 discount , with 1 / 5 % brokerage ?
Options: a ) 99.6 , b ) 96.2 , c ) 97.5 , d ) 98.2 , e ) none of these
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 2 + 1 / 5 98.2 thus the cp is rs 98.2 . answer d"
Answer: d
Python program:
a = 100 - 2
b = 1 / 5
c = a + b
Problem: two trains of length 100 meters and 200 meters are 840 meters apart . they are moving towards each other on parallel tracks , at speeds of 54 km / h and 72 km / h . after how many seconds will the trains meet ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the speeds are 54000 / 3600 = 15 m / s and 72000 / 3600 = 20 m / s the relative speed is 35 m / s . time = 840 / 35 = 24 seconds the answer is c ."
Answer: c
Python program:
a = 54 + 72 
b = a * const_0_2778
c = 840 / b
Problem: if a man walks to his office at ¾ of his usual rate , he reaches office 1 / 3 of an hour late than usual . what is his usual time to reach office ?
Options: a ) 2 hour , b ) 5 hour , c ) 1 hour , d ) 3 hour , e ) 2 hour
Rationale: c 1 hour speed ratio = 1 : 3 / 4 = 4 : 3 time ratio = 3 : 4 1 - - - - - - - - 1 / 3 3 - - - - - - - - - ? 1 hour
Answer: c
Python program:
a = 3 / 4
b = 1 / 3
c = a * b
d = 3 / 4
e = 1 - d
f = c / e
Problem: a batsman in his 15 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 15 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 42
Rationale: "average score before 15 th innings = 85 - 3 × 15 = 40 average score after 15 th innings = > 40 + 3 = 43 answer : d"
Answer: d
Python program:
a = 3 * 15
b = 85 - a
c = b + 3
Problem: a candidate appearing for an examination has to secure 40 % marks to pass paper i . but he secured only 40 marks and failed by 20 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "he secured 40 marks nd fail by 20 marks so total marks for pass the examinatn = 60 let toal marks x x * 40 / 100 = 60 x = 150 answer : e"
Answer: e
Python program:
a = 40 + 20 
b = 40 / 100
c = a / b
Problem: two - third of a positive number and 49 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 7 / 12 , c ) 25 / 144 , d ) 144 / 25 , e ) 146 / 25
Rationale: "let the number be x . then , 2 / 3 x = 49 / 216 * 1 / x x 2 = 49 / 216 * 3 / 2 = 49 / 144 x = 7 / 12 answer : b"
Answer: b
Python program:
a = 49 * 3
b = 216 * 2
c = a / b
d = math.sqrt(c)
Problem: a 160 meter long train crosses a man standing on the platform in 16 sec . what is the speed of the train ?
Options: a ) 36 kmph , b ) 54 kmph , c ) 92 kmph , d ) 86 kmph , e ) 76 kmph
Rationale: "s = 160 / 16 * 18 / 5 = 36 kmph answer : a"
Answer: a
Python program:
a = 160 / 16
b = a * const_3_6
Problem: a race course is 400 m long . aa and bb run a race and aa wins by 5 m . bb and cc run over the same course and bb win by 4 m . cc and dd run over it and dd wins by 16 m . if aa and dd run over it , then who would win and by how much ?
Options: a ) 7.1 m , b ) 7.2 m , c ) 8 m , d ) 9 m , e ) 11 m
Rationale: if aa covers 400 m , bb covers 395 m if bb covers 400 m , cc covers 396 m if dd covers 400 m , cc covers 384 m now if bb covers 395 m , then cc will cover 396400 × 395 = 391.05396400 × 395 = 391.05 m if cc covers 391.05 m , then dd will cover 400384 × 391.05 = 407.24400384 × 391.05 = 407.24 if aa and dd run over 400 m , then dd win by 7.2 m option b
Answer: b
Python program:
a = 16 - 5
b = a / 4
c = b + 5 
d = c - const_0_25
Problem: a boat takes 19 hours for travelling downstream from point a to point b and coming back to a point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 160 km , b ) 180 km , c ) 200 km , d ) 220 km , e ) 240 km
Rationale: down stream speed : ( 14 + 4 ) km / hr = 18 km / hr up stream speed : ( 14 - 4 ) km / hr = 10 km / hr ( x / 18 ) + ( x / 2 / 20 ) = 19 x = 180 km answer : b
Answer: b
Python program:
a = 14 + 4 
b = 1 / a
c = 14 - 4
d = c * 2
e = 1 / d
f = b + e 
g = 19 / f
Problem: 12.5 * 4.2 * 8.8 = ?
Options: a ) 352 , b ) 435 , c ) 462 , d ) 646 , e ) 742
Rationale: "c 462 ? = 12.5 * 4.2 * 8.8 = 462"
Answer: c
Python program:
a = 12 * 5
Problem: sonika bought a v . c . r . at the list price of 18,900 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,412 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,900 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,900 = 8 ⁄ 100 × 18500 = 1512 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,900 + 1512 = 20,412 . answer a"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = b + 8 
d = c * 100
e = 1 + 4 
f = e * 2
g = d * f
h = 1 + 4 
i = h * 100
j = g + i 
k = 100 + 8 
l = j * k
m = l / 100
n = 1 + 4 
o = n * 100
p = o * 2
q = m / p
r = math.floor(q)