euclaise/mathqa_programs huggingface dataset:
Problem: a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "assume hours worked : 10 hours hourly wage : 10 $ weekly wage : 100 $ after decrease of 20 % in hourly wage would become 8 $ hours worked would have to be 12.5 hours in order to maintain weekly wage of 100 $ % increase in number of hours worked = ( 12.5 - 10 ) / 10 = 0.25 * 100 = 25 % answer is c"
Answer: c
Python program:
a = 10 * 4
b = 100 - 20
c = b / 100
d = c * 10
e = a / d
f = e - 4
g = f / 4
h = g * 100
Problem: a and b can do a piece of work in 8 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
Options: a ) 40 days , b ) 20 days , c ) 8 days , d ) 60 days , e ) 40 days
Rationale: "c 8 days c = 1 / 4 – 1 / 8 = 1 / 8 = > 8 days"
Answer: c
Python program:
a = 4 / 8
b = 4 - a
c = 1/(b)
Problem: patrick purchased 60 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 60 pencils is how many times the selling price of 60 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.33 , e ) 1.75
Rationale: "say the cost price of 60 pencils was $ 60 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 60 - 60 p = 20 p - - > p = 3 / 4 . ( cost price ) / ( selling price ) = 1 / ( 3 / 4 ) = 4 / 3 = 1.33 . answer : d ."
Answer: d
Python program:
a = 60 + 20 
b = 60 / a
c = 1/(b)
Problem: the distance between two cities a and b is 600 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 am , b ) 07 am , c ) 01 pm , d ) 05 pm , e ) 03 pm
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 600 . therefore , 60 x + 75 ( x - 1 ) = 600 . = > x = 5 . so , they meet at ( 8 + 5 ) i . e , 1 p . m . answer : c )"
Answer: c
Python program:
a = 600 + 75 
b = 60 + 75 
c = a / b
d = c + 8
Problem: in a group of 800 people , 1 / 5 play at least one instrument , 128 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 25
Rationale: "p ( playing 2 or more instruments ) = 128 / 800 = 4 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 4 / 25 = 1 / 25 . answer e ."
Answer: e
Python program:
a = 800 * 1
b = a / 5
c = b - 128
d = c / 800
Problem: the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is :
Options: a ) 36 , b ) 52 , c ) 66 , d ) 96 , e ) none
Rationale: "sol . t . d . = √ p . w . * b . g . = √ 576 * 16 = 96 . answer d"
Answer: d
Python program:
a = 576 * 16
b = math.sqrt(a)
Problem: car a runs at the speed of 52 km / hr & reaches its destination in 10 hr . car b runs at the speed of 46 km / h & reaches its destination in 8 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 62 : 25 , b ) 66 : 52 , c ) 68 : 15 , d ) 65 : 41 , e ) 23 : 59
Rationale: "sol . distance travelled by car a = 52 × 10 = 520 km distance travelled by car b = 46 × 8 = 368 km ratio = 520 / 368 = 65 : 41 d"
Answer: d
Python program:
a = 52 * 10
b = 46 * 8
c = a / b
Problem: the distance from city a to city b is 60 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 60
Rationale: "the time it takes bob to drive to city b is 60 / 40 = 1.5 hours . alice needs to take less than 1 hour for the trip . alice needs to exceed a constant speed of 60 / 1 = 60 miles per hour . the answer is e ."
Answer: e
Python program:
a = 60 / 40
b = 30 / const_60
c = a - b
d = 60 / c
Problem: if 18 persons can build a wall 140 m long in 42 days , the number of days that 30 persons will take to complete a similar wall 100 m long , is ?
Options: a ) 28 , b ) 18 , c ) 24 , d ) 21 , e ) 16
Rationale: "explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x 140 x 30 x x = 100 x 18 x 42 or x = 18 answer : b"
Answer: b
Python program:
a = 18 * 100
b = a * 42
c = 140 * 30
d = b / c
Problem: a pharmaceutical company received $ 7 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 76 %
Rationale: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 7 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 7 / 20 ) x 60 = 21 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 9 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 21 ) / 21 ] x 100 - 1600 / 21 x 100 at this point we can stop and consider the answer choices . since we know that 1600 / 21 is just a bit less than ½ , we know that - 1600 / 21 x 100 is about a 76 % decrease . answer e ."
Answer: e
Python program:
a = 7 / 20
b = a * 100
c = 9 / 108
d = c * 100
e = b - d
f = 7 / 20
g = f * 100
h = e / g
i = h * 100
Problem: the sum of three consecutive even numbers is 93 . find the middle number of the three ?
Options: a ) 14 , b ) 35 , c ) 39 , d ) 31 , e ) 12
Rationale: "middle value = 93 / 3 = 31 ans d"
Answer: d
Python program:
a = 93 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 93 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 93 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 93 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height . find the diameter of each sphere .
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
Rationale: "explanation : in this type of question , just equate the two volumes to get the answer as , volume of cylinder = π r 2 h volume of sphere = 43 π r 3 = > 12 ∗ 4 / 3 π r 3 = π r 2 h = > 12 ∗ 4 / 3 π r 3 = π ∗ 8 ∗ 8 ∗ 2 = > r 3 = 8 ∗ 8 ∗ 2 ∗ 3 / 12 ∗ 4 = > r 3 = 8 = > r = 2 cm = > diameter = 2 ∗ 2 = 4 cm option a"
Answer: a
Python program:
a = 16 / 2
b = volume_cylinder / (
c = b * math.pi
d = c / 3
e = d / 4
f = e / 12
g = f / 4
h = g * 4
Problem: what is the decimal equivalent of ( 1 / 9 ) ^ 2 ?
Options: a ) 0.0123 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 9 ) ² = ( 1 / 9 ) ( 1 / 9 ) = 1 / 81 approach # 1 : use long division to divide 81 into 1 to get 1 / 81 = 0.0123 a"
Answer: a
Python program:
a = 1 / 9
b = a ** 2
Problem: 7589 - ? = 3434
Options: a ) 4242 , b ) 4155 , c ) 1123 , d ) 11023 , e ) none of them
Rationale: "let 7589 - x = 3434 then x = 7589 - 3434 = 4155 answer is b"
Answer: b
Python program:
a = 7589 / 3434
b = a * 100
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 30 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 8.3 , e ) 6.2
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 30 run rate needed = 250 / 30 = 8.3 answer : option d"
Answer: d
Python program:
a = 10 * 3
b = 282 - a
c = b / 30
Problem: with a slope of 4 , with a straight line in the xy - plane which has a point with x - coordinate of the point 14 and y - coordinate 19 , find the y - intercept .
Options: a ) - 19 , b ) 18 , c ) - 37 , d ) 50 , e ) 37
Rationale: eq of line = y = mx + c m = 4 x = 14 y = 19 c = y - mx substitute given : c = 19 - ( 4 ) ( 14 ) c = - 37 correct option is c
Answer: c
Python program:
a = 14 * 4
b = 19 - a
Problem: elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 16
Rationale: "number of cups flour needed for 3 ounces of butter = 4 number of cups flour needed for 1 ounce of butter = 4 / 3 number of cups flour needed for 12 ounces of butter = 4 / 3 * 12 = 16 answer e"
Answer: e
Python program:
a = 4 * 4
Problem: excluding stoppages , the speed of a bus is 52 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 6 min , c ) 9 min , d ) 8 min , e ) 11 min
Rationale: "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( 7 / 52 ) x 60 = 8 min answer : d"
Answer: d
Python program:
a = 52 - 45
b = a / 52
c = const_60 * b
Problem: what is the smallest positive integer x , such that √ 392 x is an integer ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 14
Rationale: "for a perfect square , the powers of prime factors should be even . 392 can be broken up as 2 ^ 3 * 7 ^ 2 . you just need 2 to be multiplied to this number so that the number finally becomes 2 ^ 4 * 7 ^ 2 which is a perfect square . therefore x = 2 . answer : a"
Answer: a
Python program:
a = 3 + 4
Problem: the cost of an article is decreased by 10 % . if the original cost is $ 60 , find the decrease cost .
Options: a ) 33 , b ) 12 , c ) 68 , d ) 36 , e ) 54
Rationale: "original cost = $ 60 decrease in it = 10 % of $ 60 = 10 / 100 ã — 60 = 600 / 100 = $ 6 therefore , decrease cost = $ 60 - $ 6 = $ 54 answer : e"
Answer: e
Python program:
a = 60 * 10
b = a / 100
Problem: if 4 people are selected from a group of 5 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 8 / 21
Rationale: "if we are to select 4 people from 5 couples without any restriction , how many ways can we make the selection ? 10 ! / 4 ! 6 ! = 210 if we are to select 4 people from 5 couples with restriction that no married couple can both make it to the group , only a representative ? 5 ! / 4 ! 1 ! = 5 but we know that to select a person from each couple , take 2 possibilities 5 * 2 * 2 * 2 * 2 = 80 probability = desired / all possibilities = 80 / 210 = 8 / 21 answer : e"
Answer: e
Python program:
a = 5 * 2
b = 5 * 2
c = a / b
d = 4 * 4
e = 5 * 2
f = e - 1
g = d / f
h = c * g
i = 4 * 4
j = i - 2
k = 4 * 4
l = j / k
m = h * l
n = 4 * 4
o = n - 2
p = o - 2
q = 4 * 4
r = q - 1
s = p / r
t = m * s
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 2.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5760 , c ) 2889 , d ) 3600 , e ) 2799
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 2.5 = 3600 . answer : d"
Answer: d
Python program:
a = 8 * const_60
b = 2 * 5
c = 8 * const_60
d = 6 * const_60
e = c / d
f = e - 1
g = b / f
Problem: the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 96 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 50 ) / 10 avg = 100 - 4 = 96 answer is c"
Answer: c
Python program:
a = 100 * 10
b = a - 50
c = b + 10 
d = c / 10
Problem: find the simple interest on $ 2500 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 750 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 2500 * 3 * 10 / 100 = $ 750 answer is c"
Answer: c
Python program:
a = 3 / 100
b = 2500 * a
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 4.1 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 40 = 10 * 3 / 2 = 15 time difference = 4.1 ans : b"
Answer: b
Python program:
a = 55 + 10 
b = a - 1
c = 10 / 40
d = 10 / 55
e = c - d
f = b * e
g = max(f)
Problem: p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 16 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 25 days
Rationale: "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 16 days = 16 ã — ( 1 / 40 ) = 2 / 5 remaining work = 1 â € “ 2 / 5 = 3 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 3 / 5 ) / ( 1 / 15 ) = 9 total days = 16 + 9 = 25 answer : option e"
Answer: e
Python program:
a = 16 / 40
b = 1 - a
c = 1/(40)
d = 1/(24)
e = c + d 
f = b / e
g = 16 + f
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 360 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 700 , c ) 900 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 360 ( 40 * 9 = 360 ) 100 % - - - - - > 900 ( 100 * 9 = 900 ) answer : option c"
Answer: c
Python program:
a = 100 * 360
b = 100 - 70
c = 70 - b
d = a / c
Problem: if the price of petrol increases by 25 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 25 ) i . e 125 . now , his consumption should be reduced to : - = 125 − 100125 ∗ 100 . hence , the consumption should be reduced to 20 % . answer : b"
Answer: b
Python program:
a = 100 + 25 
b = 100 / a
c = 1 - b
d = c * 100
Problem: an association of mathematics teachers has 1,260 members . only 640 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 30.47 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 640 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 640 = 384 percent of total membership that voted for winning candidate = ( 384 / 1260 ) * 100 = 30.47 % answer a"
Answer: a
Python program:
a = 60 / 100
b = a * 640
c = 4 ** 2
d = 100 * c
e = b / d
f = e * 100
Problem: there are 10 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 ) 45 , d ) 60 , e ) 90
Rationale: "10 players are there . two players play one game with one another . so 10 c 2 = 10 * 9 / 2 = 45 so option c is correct"
Answer: c
Python program:
a = 10 - 1
b = 10 * a
c = b / 2
Problem: by selling 24 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 16 , d ) 6 , e ) 4
Rationale: "80 % - - - 24 120 % - - - ? 80 / 120 * 24 = 16 answer : c"
Answer: c
Python program:
a = 100 + 20 
b = 100 - 20
c = 1 / b
d = a * c
e = 1 / d
f = e * 24
Problem: ramesh purchased a refrigerator for rs . 13500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 2899 , d ) 18975 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 13,500 discount offered = 20 % marked price = 13500 * 100 / 80 = rs . 16875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 17250 * 110 / 100 = rs . 18975 answer : d"
Answer: d
Python program:
a = 100 + 10 
b = 13500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 15 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 15 = 6 hours answer c"
Answer: c
Python program:
a = 9 / 15
b = 1 - a
c = b * 15
Problem: water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 4 meters . what is value of the radius ?
Options: a ) 0.5 , b ) 1.0 , c ) 1.5 , d ) 2.0 , e ) 2.5
Rationale: "10 * 0.31 = 3.1 m ^ 3 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 4 ) which is about 1 / 4 r = 1 / 2 the answer is a ."
Answer: a
Python program:
a = 10 * 0
b = a / 4
Problem: in a family 4 people eat only vegetarian , 3 people eat only non veg . , 2 people eat both veg and non veg . . how many people are in the family ?
Options: a ) 4 , b ) 3 , c ) 10 , d ) 2 , e ) 9
Rationale: "total number of people in family = veg + non veg + ( both veg and non veg ) total = 4 + 3 + 2 = 9 answer is e"
Answer: e
Python program:
a = 4 + 2
Problem: how many of the positive factors of 36 are not factors of 72
Options: a ) 0 , b ) 3 , c ) 4 , d ) 5 , e ) 1
Rationale: "factors of 36 - 1 , 2,3 , 4,6 , 9,12 , 18,36 , factors of 72 - 1,2 , 3,4 , 6,8 , 9,12 , 18,24 , 36,72 , comparing both , we have no factors of 36 which are not factors of 72 - 0 answer ( a )"
Answer: a
Python program:
a = 72 / 36
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 1 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 1 ) . what is its perimeter ?
Options: a ) 34 , b ) 36 , c ) 31 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 2 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 31 c"
Answer: c
Python program:
a = 1 + 1 
b = 10 + a 
c = 2 + 6 
d = b + c 
e = 7 + 1 
f = d + e
Problem: noelle walks from point a to point b at an average speed of 4 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 6 kilometers per hour ?
Options: a ) 6.75 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 6 = 2 * 4 * x / 4 + x x = 12 d is the answer"
Answer: d
Python program:
a = 6 * 4
b = 2 * 4
c = b - 6
d = a / c
Problem: the sum of all two digit numbers divisible by 4 is
Options: a ) 1242 , b ) 1542 , c ) 1742 , d ) 1610 , e ) 1842
Rationale: "required numbers are 12 , 16,20 . . . . . 96 this is an a . p . in which a = 12 , d = 4 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 12 + ( n - 1 ) * 6 = 96 , 12 + 4 n - 4 = 96 4 + 4 n = 96 4 n = 96 - 4 n = 92 / 4 then n = 23 . required sum = n / 2 ( a + l ) = 23 / 2 ( 12 + 96 ) = 1242 answer is a"
Answer: a
Python program:
a = 10 + 1 
b = 4 * a
c = 1 * 4
d = b - c
e = 4 * 2
f = 1 * 4
g = e - f
h = d / g
i = h / 2
j = 4 * 2
k = 10 + 1 
l = 4 * k
m = j + l 
n = i * m
Problem: the profits of qrs company rose 35 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 %
Rationale: assume 100 in march , then 135 in april as 35 % increase , then 108 in may as 20 % decrease from april , and then 162 in june which is 150 % of 108 . so overall increase is from 100 to 162 is 62 % answer d
Answer: d
Python program:
a = 50 / 100
b = 1 + a 
c = 35 / 100
d = 1 + c 
e = 20 / 100
f = 1 - e
g = d * f
h = b * g
i = h - 1
j = 100 * i
Problem: find the area of a parallelogram with base 36 cm and height 24 cm ?
Options: a ) 760 , b ) 284 , c ) 288 , d ) 864 , e ) 820
Rationale: "area of a parallelogram = base * height = 36 * 24 = 864 cm 2 answer : d"
Answer: d
Python program:
a = 36 * 24
Problem: what quantity of water should taken out to concentrate 18 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 18 ( 60 - 40 ) / 60 = 6 liters answer is e"
Answer: e
Python program:
a = 18 * 40
b = a / 60
c = 18 - b
Problem: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 26 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 32 , d ) 40 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 52 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 32 hence , the correct answer is c"
Answer: c
Python program:
a = 26 * 2
b = 10 * 2
c = a - b
Problem: a can do a work in 6 days . b can do the same work in 4 days . both a & b together will finish the work and they got $ 2000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,1200 , e ) 550,1450
Rationale: "ratio of their works a : b = 6 : 4 ratio of their wages a : b = 2 : 3 a ' s share = ( 2 / 5 ) 2000 = 800 b ' s share = ( 3 / 5 ) 2000 = 1200 correct option is d"
Answer: d
Python program:
a = 6 * 4
b = 6 + 4 
c = a / b
Problem: veena ranks 73 rd from the top in a class of 182 . what is her rank from the bottom if 35 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 110 , d ) 75 , e ) 93
Rationale: "total student = 182 failed = 35 paasd student = 182 - 35 = 160 from bottom her rank is = 147 - 73 + 1 = 75 answer : d"
Answer: d
Python program:
a = 182 - 35
b = 73 - 1
c = a - b
d = c - 4
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 20 ?
Options: a ) 30 , b ) 32 , c ) 34 , d ) 36 , e ) 38
Rationale: "$ 20 = 3 * $ 6 + $ 2 the number of doughnuts is 3 * 12 + 2 = 38 the answer is e ."
Answer: e
Python program:
a = 20 / 6
b = a * 12