euclaise/mathqa_programs huggingface dataset:
Problem: a jar contains only red , yellow , and orange marbles . if there are 1 red , 5 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 1 / 45 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 45 ) * ( 1 ) , which indeed is 1 / 45 . b"
Answer: b
Python program:
a = math.comb(5, 2)
b = math.comb(1, 1)
c = a * b
d = 5 + 4 
e = d + 1 
f = math.comb(e, 1)
g = c / f
Problem: a scale 6 ft . 8 inches long is divided into 4 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 4 parts = 80 / 4 = 20 inches answer : a"
Answer: a
Python program:
a = 6 * 12
b = a + 8 
c = b / 4
Problem: if w is the set of all the integers between 59 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 27 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: multiples of 2 from 59 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 58 = [ 99 / 2 ] - [ 58 / 2 ] = 49 - 29 = 20 multiples of 3 from 59 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 58 = [ 99 / 3 ] - [ 58 / 3 ] = 33 - 169 = 14 multiples of 2 and 3 bothi . e . 6 from 59 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 58 = [ 99 / 6 ] - [ 58 / 6 ] = 16 - 9 = 7 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 20 + 14 - 7 = 27 answer option a
Answer: a
Python program:
a = 99 - 59
b = a / 3
c = math.floor(b)
d = 99 - 59
e = d / 2
f = c + e 
g = 99 - 59
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 4 x + 2 = 0 ?
Options: a ) 8 , b ) 10 , c ) 2 , d ) 16 , e ) 24
Rationale: "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 4 / 1 = - 4 ab = 2 / 1 = 2 hence a / b + b / a = [ ( - 4 ) 2 - 2 ( 2 ) ] / 2 = 4 / 2 = 2 . c )"
Answer: c
Python program:
a = negate ** (
b = a / 2
c = b - 2
Problem: what least no . must be subtracted from 50248 so that remaining no . is divisible by 20 ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 8 , e ) 6
Rationale: "explanation : on dividing 50248 by 20 we get the remainder 8 , so 8 should be subtracted option d"
Answer: d
Python program:
a = 50248 / 20
b = math.floor(a)
c = b * 20
d = 50248 - c
Problem: find the area of a parallelogram with base 32 cm and height 15 cm .
Options: a ) 200 , b ) 384 , c ) 345 , d ) 480 , e ) 242
Rationale: "area of a parallelogram = base * height = 32 * 15 = 480 cm 2 answer : option d"
Answer: d
Python program:
a = 32 * 15
Problem: a clock shows the time as 10 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 4 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 55 min
Rationale: "there are 6 hours in between 10 a . m . to 4 p . m . 6 * 5 = 30 minutes . answer : a"
Answer: a
Python program:
a = 3 + 4 
b = a * 5
Problem: a space shuttle orbits the earth at about 6 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 21,600 , d ) 28,800 , e ) 48,000
Rationale: seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 6 * 3600 = 21,600 answer : c
Answer: c
Python program:
a = 6 * 3600
Problem: a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose there own dress ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 3 / 7
Rationale: explanation : let 1 st girl come and she choose wrong dress so probability of that girl to choose wrong dress out of 3 is = 2 / 3 . now 2 nd girl come nd she choose wrong dress so probability of that girl to choose wrong dress out of 2 is 1 / 2 . now for 3 rd girl probability is 1 to choose wrong dress . so probability tht all the 3 wil not choose der own dress is = 2 / 3 * 1 / 2 * 1 = 1 / 3 . hence ( a ) is the correct answer . answer : a
Answer: a
Python program:
a = math.comb(2, 1)
b = math.factorial(3)
c = a / b
Problem: a man has some hens and cows . if the number of heads be 48 and the number of feet equals 144 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 144 heads : x * 1 + y * 1 = 48 implies , 2 x + 4 y = 144 and x + y = 48 solving these two equations , we get x = 24 and y = 24 therefore , hens are 26 . answer : c"
Answer: c
Python program:
a = 48 * 4
b = a - 144
c = b / 2
Problem: a batsman in his 10 th innings makes a score of 60 , and thereby increases his average by 3 . what is his average after the 10 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 33
Rationale: "average score before 10 th innings = 60 - 3 × 10 = 30 average score after 10 th innings = > 30 + 3 = 33 answer : e"
Answer: e
Python program:
a = 3 * 10
b = 60 - a
c = b + 3
Problem: the radius of a cylinder is 10 m , height 14 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4400
Rationale: "cylinder volume = π r ( power 2 ) h = 22 / 7 × 10 × 10 × 14 = 4400 m ( power 3 ) answer is e ."
Answer: e
Python program:
a = circumface * (
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 30 % on the cost price ?
Options: a ) 62.5 , b ) 62.3 , c ) 65 , d ) 62.2 , e ) 62.9
Rationale: "cp = 47.50 sp = 47.50 * ( 130 / 100 ) = 61.75 mp * ( 95 / 100 ) = 61.75 mp = 65 answer : c"
Answer: c
Python program:
a = 47 * 50
b = a / 100
c = 47 + 50 
d = c * 100
e = 100 - 5
f = d / e
Problem: income and expenditure of a person are in the ratio 5 : 3 . if the income of the person is rs . 10000 , then find his savings ?
Options: a ) rs . 4000 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 3 x respectively . income , 5 x = 10000 = > x = 2000 savings = income - expenditure = 5 x - 3 x = 2 x so , savings = rs . 2 * 2000 = rs . 4000 answer : a"
Answer: a
Python program:
a = 3 / 5
b = a * 10000
c = 10000 - b
Problem: in a triangle , one side is 6 cm and another side is 8 cm . which of the following can be the perimeter of the triangle ?
Options: a ) 22 .
b ) 25 .
c ) 30 .
d ) 32 .
e ) 34 .
Rationale: given : one side is 6 cm and another side is 8 cm . so the 3 rd side will be > 3 and < 15 . thus the perimeter will be : 18 < perimeter < 30 . only option satisfying this condition is 22 . hence a .
Answer: a
Python program:
a = 6 ** 2
b = 8 ** 2
c = a + b 
d = math.sqrt(c)
e = triangle_perimeter - (
Problem: in 50 l can , milk and water in the ratio of 3 : 1 . if the ratio has made 1 : 3 then the quantity of water that has to be added further is ?
Options: a ) 100 , b ) 120 , c ) 90 , d ) 80 , e ) 70
Rationale: 100 litre water is to be added . let ' x ' liter water is to be added more . then 1 / 3 = 37.5 / ( 12.5 + x ) x = 100 answer : a
Answer: a
Python program:
a = 3 + 1 
b = 50 / a
c = b * 3
d = c * 3
e = 3 + 1 
f = 50 / e
g = f * 1
h = d - g
Problem: find the sum of all 4 digit numbers formed using digits 1,2 , 5,6 .
Options: a ) 93324 , b ) 92324 , c ) 93424 , d ) 93424 , e ) 93824
Rationale: "( n - 1 ) ! * ( 111 . . . n ) * ( sum of the digits ) = ( 4 - 1 ) ! * 1111 * ( 1 + 2 + 5 + 6 ) = 93324 answer : a"
Answer: a
Python program:
a = 100 + 4 
b = 100 * 10
c = b - 1
d = a + c 
e = 100 * 10
f = e - 1
g = 100 + 4 
h = f - g
i = h / 1
j = i + 1 
k = j / 2
l = d * k
Problem: 8.036 divided by 0.04 gives :
Options: a ) 200.9 , b ) 2.06 , c ) 20.06 , d ) 100.9 , e ) 200.6
Rationale: "= 8.036 / 0.04 = 803.6 / 4 = 200.9 answer is a ."
Answer: a
Python program:
a = 8 / 36
Problem: the simple interest on rs . 20 for 6 months at the rate of 5 paise per rupeeper month is
Options: a ) 1.2 , b ) 1.4 , c ) 6 , d ) 7 , e ) none
Rationale: "sol . s . i . = rs . [ 20 * 5 / 100 * 6 ] = rs . 6 answer c"
Answer: c
Python program:
a = 20 * 6
b = a * 5
c = b / 100
Problem: tom has travelling to 7 cities . gasoline prices varied from city to city . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.84 , c ) $ 1.98 , d ) $ 2.34 , e ) $ 2.56
Rationale: ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.84 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.84 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b
Answer: b
Python program:
a = 7 + 1 
b = a * 10
c = b + 4 
d = c + 100 
e = d / 100
Problem: if n is an integer and 102 n ^ 2 is less than or equal to 8100 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "102 * n ^ 2 < = 8100 n ^ 2 < = 8100 / 102 which will be less than 81 since 8100 / 100 = 81 which is the square of 9 next closest value of n where n ^ 2 < = 81 is 8 ans b"
Answer: b
Python program:
a = 8100 / 102
b = math.sqrt(a)
c = math.floor(b)
Problem: 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 12 mat - weavers in 12 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 36
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 12 : : 4 : x days 4 : 12 4 * 4 * x = 12 * 12 * 4 x = ( 12 * 12 * 4 ) / ( 4 x 4 ) x = 36 . answer is e ."
Answer: e
Python program:
a = 12 / 4
b = 4 * a
c = 12 / 4
d = b * c
Problem: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 6 people to do 6 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 9
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 6 people can do 6 / 3 of the work in one day . 6 people can do 6 times the work in 3 days . the answer is c ."
Answer: c
Python program:
a = 6 / 6
b = 3 * a
Problem: if 4 xz + yw = 7 and xw + yz = 14 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 35 . , d ) 16 . , e ) 18 .
Rationale: "( 2 x + y ) * ( 2 z + w ) = 7 + 2 ( 14 ) = 35 answer : c"
Answer: c
Python program:
a = 14 * 2
b = 4 + a
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 120 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 2 hours to travel 240 km , so c leaves 6 hours after a . the answer is c ."
Answer: c
Python program:
a = 40 - 30
Problem: a river 3 m deep and 55 m wide is flowing at the rate of 1 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 2338.9 , b ) 2748.9 , c ) 2148.9 , d ) 2745.9 , e ) 2718.9
Rationale: "rate of water flow - 1 kmph - - 1000 / 60 - - 16.66 m / min depth of river - - 3 m width of river - - 55 m vol of water per min - - 16.66 * 3 * 55 - - - 2748.9 answer b"
Answer: b
Python program:
a = 3 * 55
b = 1 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 100 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
Options: a ) 12 , b ) 18 , c ) 24 , d ) 28 , e ) 80
Rationale: slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 100 ^ 2 16 x ^ 2 + 9 x ^ 2 = 10000 25 x ^ 2 = 400 x ^ 2 = 400 x = 20 therefore ab = 20 * 4 = 80 answer : e
Answer: e
Python program:
a = 4 ** 2
b = 3 ** 2
c = a + b 
d = math.sqrt(c)
e = 100 / d
f = 4 * e
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg , what is his percent ?
Options: a ) 25 % , b ) 17 % , c ) 29 % , d ) 55 % , e ) 45 %
Rationale: "850 - - - 150 100 - - - ? = > 17.64 % answer : b"
Answer: b
Python program:
a = 100 / 850
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: a bag contains 7 red , 9 blue and 5 green balls . if 3 balls are picked at random , what is the probability that both are red ?
Options: a ) 2 / 21 , b ) 3 / 41 , c ) 5 / 26 , d ) 1 / 38 , e ) 5 / 32
Rationale: "p ( both are red ) , = 7 c 3 / 21 c 3 = ( 7 * 6 * 5 ) / 21 * 20 * 19 = 1 / 38 d"
Answer: d
Python program:
a = math.comb(7, 3)
b = 7 + 9 
c = b + 5 
d = math.comb(c, 3)
e = a / d
Problem: 40 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 13.2 , b ) 17.5 , c ) 12.8 , d ) 34.25 , e ) 31.25
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 40 = 17.5 answer : b"
Answer: b
Python program:
a = 4 + 3 
b = 4 + 3 
c = b + 2 
d = a / c
e = d * 40
f = e / 2
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and three wrenches is one - third that of 8 hammers and 4 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "x b é the weight of a hammer and y be the weight of a wrench . ( 2 x + 3 y ) = 1 / 3 * ( 8 x + 4 y ) 3 ( 2 x + 3 y ) = ( 8 x + 4 y ) 6 x + 9 y = 8 x + 4 y 5 y = 2 x y = 2 x / 5 ans - b"
Answer: b
Python program:
a = 3 * 2
b = 8 - a
c = 3 * 2
d = c - 4
e = b / d
Problem: a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back . how far is that place .
Options: a ) . 4 km , b ) 1.4 km , c ) 2.4 km , d ) 3.4 km , e ) none of these
Rationale: "explanation : let the distance is x km rate downstream = 5 + 1 = 6 kmph rate upstream = 5 - 1 = 4 kmph then x / 6 + x / 4 = 1 [ because distance / speed = time ] = > 2 x + 3 x = 12 = > x = 12 / 5 = 2.4 km option c"
Answer: c
Python program:
a = 5 - 1
b = a * 3
c = b / 5
Problem: in a certain school , the ratio of boys to girls is 5 to 13 . if there are 80 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 36 , c ) 45 , d ) 50 , e ) 117
Rationale: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 80 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 80 . so 1 part corresponds to 80 / 8 = 10 and so 5 parts correspond to 5 * 10 = 50 . d"
Answer: d
Python program:
a = 5 / 13
b = 1 - a
c = 80 / b
d = c - 80
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 300 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.6
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 300 / 45 = $ 6.6 answer : e ."
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = b * 300
d = 300 - c
e = 1 / 2
f = 5 - e
g = d / f
Problem: it costs a publishing company 50000 dollars to make books . the 50000 is a fixed cost or a cost that can not change . to help the publishing company sell the books , a marketing company charges 4 dollars for each book sold . if the company charges 9 dollars per book , how many books should they sell to break even ?
Options: a ) 100 , b ) 1000 , c ) 10000 , d ) 100000 , e ) none
Rationale: let c be the cost of producing and selling x books let r be the revenue made for selling x books r = selling price of 1 book × number of books sold r = 9 x c = fixed cost + variable cost variable cost = fee charged for 1 book × number of books sold variable cost = 4 x c = 50000 + 4 x r = c 9 x = 50000 + 4 x 9 x - 4 x = 50000 + 4 x - 4 x 5 x = 50000 x = 10000 since 5 × 10000 = 50000 the break even point is to sell 10000 books . answer c
Answer: c
Python program:
a = 9 - 4
b = 50000 / a
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation s of the mean , what percent of the distribution is less than m + s ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + s 34 % ________________________________________________ m 34 % ________________________________________________ m - s 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - s and 16 % lie above m + s now below m + s = 16 + 34 + 34 = 84 % hence d"
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b
Problem: sam invested rs . 6000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 5300.0 , b ) 24580.0 , c ) 16537.5 , d ) 7120.0 , e ) 6615.0
Rationale: p = rs . 6000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 6000 * ( 1 + 5 / 100 ) 2 ] = ( 6000 * 21 / 20 * 21 / 20 ) = rs . 6615.00 answer : e
Answer: e
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 6000
Problem: 30 men can do a work in 40 days . when should 20 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 22 days , b ) 10 days , c ) 77 days , d ) 88 days , e ) 55 days
Rationale: "total work to be done = 30 * 40 = 1200 let 20 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 20 * 40 ) = 1200 40 p = 400 = > p = 10 days answer : b"
Answer: b
Python program:
a = 30 * 40
b = 40 * 20
c = a - b
d = c / 40
Problem: find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 10 cm and 8 cm ?
Options: a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 450 cm 2 , e ) 187 cm 2
Rationale: "1 / 2 * 50 ( 10 + 8 ) = 450 cm 2 answer : d"
Answer: d
Python program:
a = 1 / 2
b = 8 + 10 
c = a * b
d = c * 50
Problem: sachin borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends money to rahul at 25 / 4 % p . a . for 2 years . find the gain of one year by sachin .
Options: a ) 110.5 , b ) 111.5 , c ) 112.5 , d ) 113.5 , e ) none of these
Rationale: explanation : two things need to give attention in this question , first we need to calculate gain for 1 year only . gain in 2 year = [ ( 5000 × 254 × 2100 ) − ( 5000 × 4 × 2100 ) ] = ( 625 − 400 ) = 225 so gain for 1 year = 2252 = 112.50 answer : c
Answer: c
Python program:
a = 25 / 4
b = p_after_gain - (
Problem: this year , mbb consulting fired 8 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 101.2 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 8 % reduction in employees lead to 92 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 92 employees is 92 * 1100 = 101200 now the new salary is more than previous salary by x % . x = ( 101200 / 100000 ) * 100 = 101.2 % so the answer is b"
Answer: b
Python program:
a = 100 * 10
b = 100 + a 
c = 100 - 8
d = c + 4 
e = b * d
f = 100 * 10
g = e / f
Problem: on average , the bottle - nosed dolphin comes up for air once every 3 minutes ; the beluga whale , a close relative , comes up for air on average once every 6 minutes . the number of times a bottle - nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 150 %
Rationale: dolphin once in 3 min ; beluga once in 6 min ; so , dolphin comes up 2 times frequently than beluga , which is 150 % ( 6 - 3 ) / 2 * 100 . answer : e .
Answer: e
Python program:
a = 6 - 3
b = a / 2
c = b * 100
Problem: the circumference of a circle is equal to 72 pi . find the radius of this circle .
Options: a ) 35
b ) 36
c ) 37
d ) 38
e ) 39
Rationale: the circumference of a circle is given by c = 2 pi r , where r is the radius of the circle . substitute c by 72 pi to obtain the equation 72 pi = 2 pi r simplify and solve for r to obtain r = 36 answer b
Answer: b
Python program:
a = 72 / 2
Problem: the average of 25 results is 50 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 741 , b ) 752 , c ) 878 , d ) 785 , e ) 458
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 50 or , x = 878 . answer : option c"
Answer: c
Python program:
a = 25 * 50
b = 12 * 17
c = a - b
d = 12 * 14
e = c - d
Problem: two trains each 475 m long are running in opposite directions on parallel tracks . their speeds are 55 km / hr and 40 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 77 sec , b ) 66 sec , c ) 48 sec , d ) 36 sec , e ) 45 sec
Rationale: relative speed = 55 + 40 = 95 km / hr . 95 * 5 / 18 = 475 / 18 m / sec . distance covered = 475 + 475 = 950 m . required time = 950 * 18 / 475 = 36 sec . answer : d
Answer: d
Python program:
a = 475 / 1000
b = a * 2
c = 55 + 40 
d = b / c
e = d * 3600
Problem: mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 65
Rationale: "if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 10 feet hence no of poles = 600 / 10 = 60 answer : d"
Answer: d
Python program:
a = 150 * 4
b = a / 10
c = b / 2
Problem: in a city where all streets run east - to - west , all avenues run north - to - south , and all intersections are right angles as shown below , jenn needs to walk from the corner of 1 st street and 1 st avenue to the corner of 6 th street and 3 rd avenue . if her friend amanda is sitting on a bench on 4 th street halfway between 1 st and 2 nd avenues , and jenn chooses her path randomly from any route that will allow her to walk exactly 7 blocks to her destination , what is the probability that jenn will walk down 4 th st . past amanda ?
Options: a ) 1 / 42 , b ) 1 / 21 , c ) 1 / 7 , d ) 1 / 3 , e ) 1 / 2
Rationale: all routes between ( 1,1 ) to ( 3,6 ) = 7 ! / ( 2 ! * 5 ! ) = 21 routes which pass 4 th st . between 1 st and 2 nd avenue = routs between ( 1,1 ) to ( 1,4 ) * routs between ( 2,4 ) to ( 3,6 ) = 1 * ( 3 ! / ( 2 ! * 1 ! ) ) = 3 the probability that jenn will walk down 4 th st . past amanda = 3 / 21 = 1 / 7 c is correct .
Answer: c
Python program:
a = 7 * 3
b = 3 / a