euclaise/mathqa_programs huggingface dataset:
Problem: the number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 54 , d ) 81 , e ) 162
Rationale: "explanations 1 ) this tells us that the number of boxes is evenly divisible by both 6 and 27 ; in other words , it ’ s a common multiple of 6 and 27 . the question says : what ’ s the smallest value it could have ? in other words , what ’ s the lcm of 6 and 27 ? ( this question is one example of a real - world set - up where the question is actually asking for the lcm . ) step ( a ) : 6 = 2 * 3 27 = 3 * 3 * 3 step ( b ) : 6 = 2 * 3 27 = 3 * 3 * 3 gcf = 3 step ( c ) : 6 = 3 * 2 27 = 3 * 9 step ( d ) lcm = 3 * 2 * 9 = 54 thus , 54 is the lcm of 6 and 27 . answer : c ."
Answer: c
Python program:
a = 2 * 2
b = a * 2
c = b * 3
d = c * 6
Problem: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 210 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 290 , b ) 320 , c ) 350 , d ) 380 , e ) 410
Rationale: let x be the minimum number of questionnaires to be mailed . 0.6 x = 210 x = 350 the answer is c .
Answer: c
Python program:
a = 60 / 100
b = 210 / a
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 4 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) ( a ) 7 / 16 , b ) ( b ) 7 / 15 , c ) ( c ) 10 / 21 , d ) ( d ) 7 / 31 , e ) ( e ) 1 / 2
Rationale: "a simpler way i guess would be to think that in total 5 cups were sold . out of which 4 are small and 1 is large . now let the small ones cost $ 6 . so the large ones would cost $ 7 . so , 4 * 6 = 24 and 1 * 7 = 7 . total revenue was 24 + 7 = 31 and large cup sales as found above is 7 therefore answer is 7 / 31 d"
Answer: d
Python program:
a = 4 / 5
b = a * 10
c = 10 - b
d = 7 / 6
e = 4 / 5
f = e * 10
g = d * f
h = c * g
i = 4 / 5
j = i * 10
k = 4 / 5
l = k * 10
m = j * l
n = 4 / 5
o = n * 10
p = 10 - o
q = 7 / 6
r = 4 / 5
s = r * 10
t = q * s
u = p * t
v = m + u 
w = h / v
Problem: 96 % of the population of a city is 23040 . find the total population of the city ?
Options: a ) 30000 , b ) 28000 , c ) 24000 , d ) 25000 , e ) 25500
Rationale: "population consider as x x * ( 96 / 100 ) = 23040 x = 240 * 100 = = > 24000 answer c"
Answer: c
Python program:
a = 100 / 96
b = a * 23040
Problem: the average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 58 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 83 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: since the average has increased by 2.5 kg , the weight of the man who stepped in must be equal to 58 + 10 x 2.5 58 + 25 = 83 kg ans : ' b '
Answer: b
Python program:
a = 1 / 2
b = 2 + a 
c = 10 * b
d = 58 + c
Problem: if 6 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 10 , b ) 11 , c ) 7 , d ) 12 , e ) 9
Rationale: 6 ( log 2 ^ 2 * 5 ^ 2 ) = x 6 log ( 5 * 2 ) ^ 2 = x 6 * 2 log ( 5 * 2 ) = x 12 log 10 = x log 10 base 10 = 1 so 12 * 1 = x x = 12 answer : d
Answer: d
Python program:
a = 5 ** 2
b = 4 * a
c = b ** 6
Problem: the price of a t . v . set worth rs . 40000 is to be paid in 20 installments of rs . 2500 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 29997 , b ) 28088 , c ) 27098 , d ) 37500 , e ) 2799
Rationale: "money paid in cash = rs . 2500 balance payment = ( 40000 - 2500 ) = rs . 37500 . answer : d"
Answer: d
Python program:
a = 40000 - 2500
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 2.4 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 250 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 400,000 / 4800 = 500 boxes total cost = 500 × $ 0.5 = $ 250 the answer is a ."
Answer: a
Python program:
a = 1000 * 1000
b = 2 * 4
c = 20 * 20
d = c * 12
e = b / d
f = e * 0
Problem: boy sells a book for rs . 450 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) rs . 320 , b ) rs . 450 , c ) rs . 550 , d ) rs . 640 , e ) rs . 680
Rationale: "find selling price to gain 10 % . now , we are asked to find selling price to gain 10 % profit . hint : selling price = ( 100 + gain % ) × c . p . 100 selling price = ( 100 + 10 ) × 500 100 selling price = ( 110 ) × 500 100 therefore , selling price = rs . 550 c"
Answer: c
Python program:
a = 10 / 100
b = 1 - a
c = 450 / b
d = 10 / 100
e = 1 - d
f = 450 / e
g = 10 / 100
h = f * g
i = c + h
Problem: in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 20 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 30 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 20 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 20 % of people have their job of choice , then 80 % of people do not have their job of choice . 25 % of 80 % = 20 % . we can also see that 10 % of the people have their job of choice and a diploma ( 20 % - 10 % = 10 % ) . 10 % + 20 % = 30 % . therefore 30 % of the people in country z have a diploma . ans a"
Answer: a
Python program:
a = 100 - 20
b = 25 * a
c = b / 100
d = 20 - 10
e = c + d
Problem: a batsman makes a score of 84 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 36 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 84 = 17 x therefore x = 36 answer : c"
Answer: c
Python program:
a = 17 * 3
b = 84 - a
c = b + 3
Problem: of the 120 passengers on flight 750 , 40 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 40 , b ) 48 , c ) 50 , d ) 52 , e ) 56
Rationale: "number of passengers on flight = 120 number of female passengers = . 4 * 120 = 48 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 48 - 8 = 40 answer a"
Answer: a
Python program:
a = 40 / 100
b = 120 * a
c = 10 / 100
d = 120 * c
e = 10 / 100
f = 120 * e
g = f / 3
h = d - g
i = b - h
Problem: the maximum numbers of students among them 451 pens and 410 toys can be distributed in such a way that each student gets the same number of pens and same number of toys is
Options: a ) 41 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
Rationale: "olution required number of students . = h . c . f of 451 and 410 . â € ¹ = â € º 41 . answer a"
Answer: a
Python program:
a = 451 - 410
Problem: find the average of all the numbers between 4 and 32 which are divisible by 5 .
Options: a ) 17.5 , b ) 20 , c ) 24 , d ) 30 , e ) 32
Rationale: "solution average = ( 5 + 10 + 15 + 20 + 25 + 30 ) / 6 ) = 105 / 6 = 17.5 . answer a"
Answer: a
Python program:
a = 4 + 4 
b = 32 - 4
c = a + b 
d = c / 2
Problem: a cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm . the radius of the cone will be :
Options: a ) 8 cm
b ) 9 cm
c ) 10 cm
d ) 11 cm
e ) none
Rationale: sol . let the radius of the cone be r cm . then , 1 / 3 ∏ * r ² * 6 = ∏ * 8 * 8 * 2 ⇔ r ² = [ 8 * 8 * 2 * 3 / 6 ] = 64 ⇔ r = 8 cm . answer a
Answer: a
Python program:
a = volume_cylinder * (
b = a / 3
c = b / 6
d = math.sqrt(c)
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 18 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 18 . then 4 n < 18 and n < 4.5 the largest possible integer is n = 4 . the answer is d ."
Answer: d
Python program:
a = 5 - 1
b = 18 / a
c = math.floor(b)
Problem: a runs twice as fast as b and gives b a start of 60 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 120 m . , b ) 80 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: ratio of speeds of a and b is 2 : 1 b is 60 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 60 m is 60 / 1 = 60 m so the total time taken by a and b to reach = 2 * 60 = 120 m answer : a
Answer: a
Python program:
a = 60 * 2
Problem: how long does a train 100 m long running at the speed of 80 km / hr takes to cross a bridge 142 m length ?
Options: a ) 10.7 sec , b ) 10.9 sec , c ) 10.1 sec , d ) 15.1 sec , e ) 12.7 sec
Rationale: "speed = 80 * 5 / 18 = 22.2 m / sec total distance covered = 100 + 142 = 242 m . required time = 242 / 22.2 ' = 10.9 sec . answer : b"
Answer: b
Python program:
a = 100 + 142 
b = 80 * const_0_2778
c = a / b
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 5 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 5 days , b can do 1 / 6 of the project . thus a and b must complete 5 / 6 of the project , which takes 10 days . the total number of days is 10 + 5 = 15 . the answer is b ."
Answer: b
Python program:
a = 1 / 30
b = a * 5
c = 1 - b
d = 1 / 20
e = 1 / 30
f = d + e 
g = c / f
h = g + 5
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 580 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,000 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 580 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 25000 answer : c"
Answer: c
Python program:
a = 8 / 100
b = 1 * 0
c = 580 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 1
i = math.floor(h)
Problem: a dessert recipe calls for 50 % melted chocolate and 50 % raspberry puree to make a particular sauce . a chef accidentally makes 15 cups of the sauce with 30 % melted chocolate and 70 % raspberry puree instead . how many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50 % of each ?
Options: a ) 1.5 , b ) 2.14 , c ) 3 , d ) 4.5 , e ) 5
Rationale: "yes , we assume that the mix is homogeneous . otherwise , we will not be able to solve the question . you have 15 cups of sauce with 30 % chocolate . you also have unlimited amount of pure chocolate sauce . now you need to mix these two in such a way that you get total 15 cups of sauce with 50 % chocolate . using scale method : w 1 / w 2 = ( 100 - 50 ) / ( 50 - 30 ) = 5 / 2 w 1 - amount of 30 % chocolate sauce w 2 - amount of pure chocolate sauce so for every 5 / 2 cups of 30 % chocolate sauce , we need 2 cup of pure chocolate sauce . this will give us 7 cups of 50 % chocolate sauce . but we need 15 cups of 50 % chocolate sauce . so we need to mix 5 * 15 / 7 = 12.5 cups of 40 % chocolate sauce with 1 * 15 / 7 = 2.14 cups of pure chocolate sauce . answer ( b )"
Answer: b
Python program:
a = 50 + 50 
b = a - 50
c = 50 - 30
d = b / c
e = d / 2
Problem: the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 35 cents less than the price of commodity y ?
Options: a ) 2006 , b ) 2007 , c ) 2008 , d ) 2009 , e ) 2010
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 35 cents less than commodity y . $ 1.75 / 25 cents = 7 years the answer is 2001 + 7 years = 2008 . the answer is c ."
Answer: c
Python program:
a = 35 / 100
b = 7 - 30
c = a + b 
d = 45 / 100
e = 7 - 30
f = d - e
g = c / f
h = 2001 + g
Problem: if log 1087.5 = 1.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 1.9421 + 1 ) = 10 ( 2.9421 ) = 29.421 x = antilog ( 29.421 ) therefore , number of digits in x = 30 . answer : a"
Answer: a
Python program:
a = 4 * 1
b = math.log(100)
c = math.log(10)
d = b / c
e = a + d
Problem: a river 4 m deep and 65 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 25000 , b ) 26000 , c ) 27000 , d ) 28000 , e ) 29000
Rationale: "rate of water flow - 6 kmph - - 6000 / 60 - - 100 m / min depth of river - - 4 m width of river - - 65 m vol of water per min - - 100 * 4 * 65 - - - 26000 answer b"
Answer: b
Python program:
a = 4 * 65
b = 6 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: in a garden , there are 10 rows and 17 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 34 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 17 plants . there are 15 gapes between the two corner trees ( 16 x 2 ) metres and 1 metre on each side is left . therefore length = ( 32 + 2 ) m = 34 m . answer : c"
Answer: c
Python program:
a = 17 - 1
b = a * 2
c = 10 / 2
d = b + c 
e = 10 / 2
f = d + e
Problem: a person spent rs . 6,040 from his salary on food and 8,000 on house rent . after that he was left with 70 % of his monthly salary . what is his monthly salary ?
Options: a ) 46,800 , b ) 66,800 , c ) 56,800 , d ) 26,800 , e ) 76,800
Rationale: "total money spent on food and house rent = 6,040 + 8,000 = 14,040 which is 100 - 70 = 30 % of his monthly salary ∴ his salary = 14040 x 100 / 30 = 46800 answer : a"
Answer: a
Python program:
a = 4 + 1 
b = a * 100
c = b + 70 
d = math.sqrt(100)
e = c / d
Problem: a basketball is dropped from a height of 40 feet . if it bounces back up to a height that is exactly half of its previous height , and it stops bouncing after hitting the ground for the fourth time , then how many total feet will the ball have traveled after 3 full bounces .
Options: a ) 50 , b ) 55 , c ) 110 , d ) 75 , e ) 80
Rationale: "initial distance = 40 feet first bounce = 20 feet up + 20 feet down = 40 feet second bouche = 10 feet up + 10 feet down = 20 feet third bounce = 5 feet up and 5 feet down = 10 feet total distance covered = 40 + 40 + 20 + 10 = 110 answer is c"
Answer: c
Python program:
a = 40 / 3
b = a / 3
c = b / 3
d = c / 3
e = 40 / 3
f = 40 + e 
g = 40 / 3
h = f + g 
i = 40 / 3
j = i / 3
k = h + j 
l = 40 / 3
m = l / 3
n = k + m 
o = 40 / 3
p = o / 3
q = p / 3
r = n + q 
s = 40 / 3
t = s / 3
u = t / 3
v = r + u 
w = d + v 
x = w * 3
y = 40 / 3
z = y / 3
A = z / 3
B = x - A
C = 40 / 3
D = C / 3
E = D / 3
F = B - E
G = 40 / 3
H = G / 3
I = H / 3
J = F - I
K = 40 / 3
L = K / 3
M = L / 3
N = J - M
Problem: 80 370 860 1550 ? 3530
Options: a ) 900 , b ) 2440 , c ) 750 , d ) 244 , e ) 960
Rationale: "10 ^ 2 - 20 = 80 20 ^ 2 - 30 = 370 30 ^ 2 - 40 = 860 40 ^ 2 - 50 = 1550 50 ^ 2 - 60 = 2440 60 ^ 2 - 70 = 3530 . answer : b"
Answer: b
Python program:
a = 370 / 860
b = 80 + a 
c = b * 1550
d = c / 100
Problem: a sum fetched a total simple interest of 4052.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 9005 , b ) 8925 , c ) 2345 , d ) 6474 , e ) 8723
Rationale: principal = ( 100 x 4052.25 ) / ( 9 x 5 ) = 405225 / 45 = 9005 . answer a
Answer: a
Python program:
a = 4052 * 25
b = a / 9
c = b / 5
Problem: a rotameter is a device that measures flow of liquid and gases . when measuring liquid phase flows , 2.5 inches represent 60 liters per minute of liquid . with gas measurements the rotameter moves 50 % of the movement he moves with the liquid phase . how many liters of gas passed through the rotameter if it measured 4 inches ?
Options: a ) 176 , b ) 192 , c ) 202 , d ) 218 , e ) 284
Rationale: in case of liquid - 2.5 inches represents 60 lit / min . in case of gas - 50 % of 2.5 inches represents 60 lit / min 1.25 inches represents 60 lit / min 4 inches will represent 60 * 4 / 1.25 = 192 b is the answer
Answer: b
Python program:
a = 60 * 4
b = a / 2
c = 50 / 100
d = b / c
Problem: if a trader sold two cars each at rs . 325475 and gains 10 % on the first and loses 10 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.44 % , b ) 1.74 % , c ) 1.84 % , d ) 1.47 % , e ) 1.00 %
Rationale: "sp of each car is rs . 325475 , he gains 10 % on first car and losses 10 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 10 ) ( 10 ) / 100 % = 1.00 % answer : e"
Answer: e
Python program:
a = 10 * 10
b = a / 100
Problem: how many positive integers less than 130 are there such that they are multiples of 13 or multiples of 12 but not both ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 28
Rationale: "for 13 : 13 . . . 130 = 13 * 10 for 12 : 12 . . . 130 = 12 * 10 but there is one integer 13 * 12 . so n = ( 10 ) + ( 10 ) = 20 c"
Answer: c
Python program:
a = 4 + 13 
b = a - 1
c = math.factorial(b)
d = math.factorial(13)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the marks obtained by polly and sandy are in the ratio 5 : 6 and those obtained by sandy and willy are in the ratio of 3 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 3 : 2 , b ) 5 : 4 , c ) 7 : 6 , d ) 9 : 8 , e ) 11 : 10
Rationale: "polly : sandy = 5 : 6 sandy : willy = 3 : 2 = 6 : 4 polly : sandy : willy = 5 : 6 : 4 polly : willy = 5 : 4 the answer is b ."
Answer: b
Python program:
a = 5 * 3
b = 6 * 2
c = a / b
Problem: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 7 ?
Options: a ) 5 , b ) 14 , c ) 10 , d ) 20 , e ) 30
Rationale: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 7 ? 9 ^ 7 = ( 3 ^ 2 ) ^ 7 = 3 ^ 14 b . 14
Answer: b
Python program:
a = 9 - 7
b = a * 7
Problem: if 70 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %
Rationale: "70 % answered the first question correctly and 20 % answered neither correctly . then 10 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 55 % - 10 % = 45 % . the answer is a ."
Answer: a
Python program:
a = 70 + 55 
b = a + 20 
c = b - 100
Problem: each machine of type a has 3 steel parts and 2 chrome parts . each machine of type b has 2 steel parts and 4 chrome parts . if a certain group of type a and type b machines has a total of 50 steel parts and 66 chrome parts , how many machines are in the group
Options: a ) 11 , b ) 21 , c ) 31 , d ) 61 , e ) 51
Rationale: "look at the below representation of the problem : steel chrome total a 3 2 50 > > no . of type a machines = 50 / 5 = 10 b 2 4 66 > > no . of type b machines = 66 / 6 = 11 so the answer is 21 i . e b . hope its clear ."
Answer: b
Python program:
a = 4 + 2 
b = 66 / a
c = 3 + 2 
d = 50 / c
e = b + d
Problem: a batsman in his 12 th innings makes a score of 75 and thereby increases his average by 1 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 64 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 1 ) + 75 ∴ x = 64 answer d"
Answer: d
Python program:
a = 12 * 1
b = 75 - a
c = b + 1
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 188 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 5 : 4 , e ) 3 : 1
Rationale: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 188 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 188 m ) / ( w + m ) = 180 170 w + 188 m = 180 w + 180 m 8 m = 10 w 4 m = 5 w m / w = 5 / 4 the ratio of men to women is 5 t ổ 4 . d"
Answer: d
Python program:
a = 180 - 170
b = 188 - 180
c = a / b
Problem: the average ( arithmetic mean ) of the integers from 100 to 200 , inclusive , is how much lesser than the average of the integers from 150 to 950 , inclusive ?
Options: a ) 350 , b ) 475 , c ) 300 , d ) 425 , e ) 400
Rationale: "for an ap the mean or average of series is average of first and last term . so , average of numbers between 150 to 950 , inclusive = ( 150 + 950 ) / 2 = 550 average of numbers between 100 to 200 , inclusive = ( 100 + 200 ) / 2 = 150 difference = 550 - 150 = 400 answer is e"
Answer: e
Python program:
a = 100 + 200 
b = a / 2
c = 150 + 950 
d = c / 2
e = b - d
Problem: the present ages of 3 persons are in the proportion of 4 : 7 : 9 . 8 years ago , the sum of their ages was 116 . find their present ages .
Options: a ) 20 , 35,45 , b ) 28 , 49,63 , c ) 16 , 28,36 , d ) 16 , 28,46 , e ) none of these
Rationale: let the present ages of three persons be 4 k , 7 k and 9 k respectively . ( 4 k - 8 ) + ( 7 k - 8 ) + ( 9 k - 8 ) = 116 20 k = 140 k = 7 therefore , then present ages are 28 , 49,63 . answer : b
Answer: b
Python program:
a = 3 * 8
b = a + 116 
c = 4 + 7 
d = c + 9 
e = b / d
f = 4 * e
g = f + 8
Problem: a car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 90 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 80 , c ) 74 , d ) 75 , e ) 78
Rationale: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 90 hours = 3,600 / 90 seconds = 40 seconds ; time to cover 1 kilometer at regular speed is 40 + 5 = 45 seconds = 45 / 3,600 hours = 1 / 80 hours ; so , we get that to cover 1 kilometer 1 / 80 hours is needed - - > regular speed 80 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : b ."
Answer: b
Python program:
a = 1 / 90
b = 3600 * a
c = b + 5 
d = c / 3600
e = 1 / d