euclaise/mathqa_programs huggingface dataset:
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 4 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 5
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 4 ) / ( 10 - 5 ) = 1 / 5 so they should be mixed in the ratio 1 : 5 answer - e"
Answer: e
Python program:
a = 5 - 4
b = 10 - 5
c = a / b
Problem: what is the hcf of 2 / 3 , 4 / 9 and 6 / 18
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 1 / 9 , d ) 8 / 45 , e ) 9 / 45
Rationale: explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 9 , 18 ) = 2 / 18 = 1 / 9 answer : option c
Answer: c
Python program:
a = 2 / 18
Problem: the mean proportional between 234 and 104 is
Options: a ) 12 , b ) 39 , c ) 54 , d ) 156 , e ) none
Rationale: "sol . required mean proportional = √ 234 x 104 = √ 13 x 9 x 2 x 13 x 8 = ( 13 x 3 x 4 ) = 156 . answer d"
Answer: d
Python program:
a = 234 * 104
b = math.sqrt(a)
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 6.30 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 6.30 when c . p = ( 100 * 6.30 ) / 21 = 30 answer : a"
Answer: a
Python program:
a = 6 * 30
b = 25 + 100 
c = 30 + 100 
d = 100 - 20
e = c * d
f = e / 100
g = b - f
h = a / g
Problem: a bus starts from city x . the number of women in the bus is half of the number of men . in city y , 16 men leave the bus and 8 women enter . now , number of men and women is equal . in the beginning , how many passengers entered the bus ?
Options: a ) 15 , b ) 30 , c ) 36 , d ) 72 , e ) 46
Rationale: explanation : originally , let number of women = x . then , number of men = 2 x . so , in city y , we have : ( 2 x - 16 ) = ( x + 8 ) or x = 24 . therefore total number of passengers in the beginning = ( x + 2 x ) = 3 x = 72 . answer : d
Answer: d
Python program:
a = 16 + 8 
b = 3 * a
Problem: at tea factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ?
Options: a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8
Rationale: at tea factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a .
Answer: a
Python program:
a = 4 * 2
b = 3 * 3
c = 4 * 2
d = b + c 
e = a / d
Problem: there are two concentric circles with radii 6 and 4 . if the radius of the outer circle is increased by 50 % and the radius of the inner circle decreased by 25 % , by what percent does the area between the circles increase ?
Options: a ) 160 , b ) 210 , c ) 260 , d ) 310 , e ) 360
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 36 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 20 pi . when the big circle ' s radius increases , the new area is 81 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 72 pi . the ratio of a 2 / a 1 is 72 / 20 = 3.6 which is an increase of 260 % . the answer is c ."
Answer: c
Python program:
a = 100 + 50 
b = a / 100
c = 6 * b
d = c ** 2
e = 100 - 25
f = e / 100
g = 4 * f
h = g ** 2
i = d - h
j = 6 ** 2
k = 4 ** 2
l = j - k
m = i - l
n = 6 ** 2
o = 4 ** 2
p = n - o
q = m / p
r = q * 100
Problem: john works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 6 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 8 , b ) 1 / 7 , c ) 1 / 2 , d ) 1 / 4 , e ) 1 / 6
Rationale: first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 6 x total tips for all months = 6 * x + 6 x = 12 x tips for august / total tips for all months = 6 x / 12 x = 1 / 2 answer : c
Answer: c
Python program:
a = 6 * 2
b = 6 / a
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 192,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,500 , d ) $ 2,050 , e ) $ 2,250
Rationale: "number of boxes = total volume / volume of one box = 192,000 / ( 8 * 10 * 12 ) = 200 one box costs 7.50 , so 200 box will cost = 200 * 7.5 = 1500 c is the answer"
Answer: c
Python program:
a = 3 * 100
b = 8 * 10
c = a + b 
d = c + 4 
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 7
j = i / 1000
Problem: x does a work in 15 days . y does the same work in 45 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 11.25 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 15 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 15 + 1 / 45 ) = 1 / 11.25 both together will finish the work in 11.25 days . correct option is d"
Answer: d
Python program:
a = 1 / 15
b = 1 / 45
c = a + b 
d = 1/(c)
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 75 percent of the republicans and 15 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 3 : 2 = = 60 : 40 represents the number ratio of republicans : democrats . if 75 % of republicans ( which is ( 60 * 0.75 ) = 45 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 51 ( 45 + 6 ) voters voted for candidate x and 49 voted for candidate y . thus we can infer that candidate x is expected to win the election by 2 ( 51 - 49 ) votes . therefore candidate x is expected to win the election by ( 2 / 100 ) votes which is equivalent to 2 % . i think the answer is a ."
Answer: a
Python program:
a = 15 / 100
b = a * 2
c = 75 / 100
d = c * 3
e = b + d 
f = 75 / 100
g = f * 3
h = 3 - g
i = 15 / 100
j = i * 2
k = 2 - j
l = h + k 
m = e - l
n = 3 + 2 
o = m / n
p = o * 100
Problem: the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 4000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 500 , b ) 1,600 / 3 , c ) 1,000 , d ) 1,500 , e ) 2,500
Rationale: "st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 4000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 4000 2 = 2000 d = s * t d = 2000 * ( 1 / 2 ) d = 1000 answer : c"
Answer: c
Python program:
a = 4000 / 2
b = 1 / 2
c = a * b
Problem: a corporation that had $ 10 billion in profits for the year paid out $ 500 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 %
Rationale: "required answer = [ employee benefit / profit ] * 100 = [ ( 500 million ) / ( 10 billion ) ] * 100 = [ ( 500 * 10 ^ 6 ) / ( 10 * 10 ^ 9 ) ] * 100 = ( 50 / 1000 ) * 100 = 5 % so answer is ( c )"
Answer: c
Python program:
a = 3 + 3 
b = 10 ** a
c = 500 * b
d = 10 ** 9
e = 10 * d
f = c / e
g = f * 100
Problem: if 0.75 : x : : 3 : 8 , then x is equal to :
Options: a ) a ) 2.12 , b ) b ) 2.2 , c ) c ) 1.25 , d ) d ) 1.3 , e ) e ) 2.0
Rationale: ( x * 3 ) = ( 0.75 * 8 ) x = 6 / 3 x = 2 answer = e
Answer: e
Python program:
a = 0 * 75
b = a / 3
Problem: a train 280 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 89 kmph , c ) 72 kmph , d ) 50 kmph , e ) 18 kmph
Rationale: "length = speed * time speed = l / t s = 280 / 20 s = 14 m / sec speed = 14 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 50 kmph answer : d"
Answer: d
Python program:
a = 280 / 1000
b = 20 / 3600
c = a / b
Problem: the tax on a commodity is diminished by 25 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 12 % decrease , b ) 18 % decrease , c ) 19 % decrease , d ) 13.75 % decrease , e ) 12.5 % decrease
Rationale: "100 * 100 = 10000 75 * 115 = 9200 - - - - - - - - - - - 10000 - - - - - - - - - - - 1375 100 - - - - - - - - - - - ? = > 13.75 % decrease answer : c"
Answer: c
Python program:
a = 15 / 100
b = 1 + a 
c = 25 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 83200 ?
Options: a ) 81000 , b ) 81028 , c ) 105300 , d ) 29889 , e ) 22312
Rationale: 83200 * 9 / 8 * 9 / 8 = 105300 . answer : c
Answer: c
Python program:
a = 1 / 8
b = a * 83200
c = 83200 + b 
d = 1 / 8
e = 1 / 8
f = e * 83200
g = 83200 + f 
h = d * g
i = c + h
Problem: the length of a side of a hexagon is 2 inches . what is the perimeter ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "hexagon . it means 6 equal sides . p = 2 + 2 + 2 + 2 + 2 + 2 = 4 + 4 + 4 = 8 + 4 = 12 inches answer b"
Answer: b
Python program:
a = 3 * 2
b = 2 * a
Problem: a student is ranked 12 th from right and 6 th from left . how many students are there in totality ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 12 , from left 6 total = 12 + 6 - 1 = 17 answer : b"
Answer: b
Python program:
a = 12 + 6 
b = a - 1
Problem: x starts a business with rs . 35000 . y joins in the business after 3 months with rs . 25000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 28 : 15 , b ) 29 : 16 , c ) 25 : 23 , d ) 14 : 15 , e ) none of these
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 35000 * 12 : 25000 * 9 = 35 * 12 : 25 * 9 = 7 * 4 : 5 * 3 = 28 : 15 . answer : option a"
Answer: a
Python program:
a = 35000 * 12
b = 4 + 3 
c = 25000 * b
d = a / c
Problem: how many 3 digit even numbers do not use any digit more than once
Options: a ) 280 , b ) 216 , c ) 2240 , d ) 246 , e ) 2520
Rationale: the way i solved it is a b c ( hundreds , tens , units ) c can be 0 2 4 6 8 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilities b can be anything execpt ( a d c ) so 7 possibilities total ways are 7 * 8 * 5 = 280 ans : a
Answer: a
Python program:
a = 1000 - 10
b = 3 * 3
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
Problem: a circular path of 19 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 25 p per m 2 ?
Options: a ) rs . 49.25 , b ) rs . 40.50 , c ) rs . 44.20 , d ) rs . 62.85 , e ) rs . 43.10
Rationale: "explanation : π ( 21 ^ 2 - 19 ^ 2 ) = 22 / 7 * ( 441 - 361 ) = 251.43 251.43 * 1 / 4 = rs . 62.85 answer : option d"
Answer: d
Python program:
a = 19 + 2 
b = circle_area - (
c = 25 * b
Problem: a money lender lent rs . 1000 at 3 % per year and rs . 1200 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 3.88 , d ) 4.25 , e ) 4.5
Rationale: ( 1000 xtx 3 / 100 ) + ( 1200 xtx 5 / 100 ) = 350 â † ’ t = 3.88 answer c
Answer: c
Python program:
a = 3 * 1000
b = a / 100
c = 1200 * 5
d = c / 100
e = b + d 
f = 350 / e
Problem: mother , her daughter and her grand child weighs 130 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: mother + daughter + child = 130 kg daughter + child = 60 kg mother = 130 - 60 = 70 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 70 = 14 kg so now daughter = 130 - ( mother + child ) = 130 - ( 70 + 14 ) = 46 kg answer : a
Answer: a
Python program:
a = 130 - 60
b = a / 5
c = 60 - b
Problem: an aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 2200 kmph , b ) 1800 kmph , c ) 1900 kmph , d ) 2100 kmph , e ) none
Rationale: "explanation : distance = ( 1500 x 2 ) = 3000 km . speed = distance / time speed = 3000 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 3000 x 3 / 5 km / hr = 1800 km / hr . answer : option b"
Answer: b
Python program:
a = 1500 * 2
b = 2 / 3
c = 1 + b 
d = a / c
e = d / 2
Problem: the length of a room is 10 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 42750 , e ) 55725
Rationale: "area = 10 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 10 × 4.75 × 900 = 10 × 4275 = rs . 42750 answer is d ."
Answer: d
Python program:
a = 10 * 4
b = 900 * a
Problem: two stations a and b are 200 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: "suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 200 45 x = 225 x = 5 . so , they meet at 12 a . m . answer : option d"
Answer: d
Python program:
a = 200 - 20
b = 25 + 20 
c = a / b
d = 8 + c
Problem: a certain box has 13 cards and each card has one of the integers from 1 to 13 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 13 cards ?
Options: a ) 1 / 7 , b ) 1 / 13 , c ) 1 / 15 , d ) 1 / 22 , e ) 1 / 26
Rationale: "the average of the numbers is 7 the total number of ways to choose 2 cards from 13 cards is 13 c 2 = 78 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 1,5 } , { 2,3 } , { 2,4 } the probability is 6 / 78 = 1 / 13 the answer is b ."
Answer: b
Python program:
a = math.factorial(13)
b = math.factorial(2)
c = 13 - 2
d = math.factorial(c)
e = b * d
f = a / e
g = 4 / f
Problem: the value of ( 0.625 * 0.0729 * 28.9 ) / ( 0.0017 * 0.025 * 8.1 ) is
Options: a ) 0.3825 , b ) 3.825 , c ) 38.25 , d ) 382.5 , e ) 0.0382
Rationale: ( 0.625 * 0.0729 * 28.9 ) / ( 0.0017 ) * 0.025 * 8.1 = { ( 625 / 1000 ) * ( 729 / 10000 ) * ( 289 / 10 ) } / { ( 17 / 10000 ) * ( 25 / 1000 ) * ( 81 / 10 ) = 382.5 answer : d
Answer: d
Python program:
a = 0 * 625
b = a * 28
c = 8 * 1
d = c * 0
e = b / d
f = e / 10
Problem: the length of a rectangle is increased by 25 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 10000
b ) 10008
c ) 10005
d ) 10004
e ) 10001
Rationale: 100 * 100 = 10000 125 * 80 = 10000 no change answer : a
Answer: a
Python program:
a = 25 + 100 
b = 100 - 20
c = a * b
Problem: the effective annual rate of interest corresponding to a nominal rate of 10 % per annum payable half - yearly is ?
Options: a ) 10.06 % , b ) 10.25 % , c ) 10.35 % , d ) 16.09 % , e ) 16.19 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 5 / 100 ) 2 ] = rs . 110.25 effective rate = ( 110.25 - 100 ) = 10.25 % answer : b"
Answer: b
Python program:
a = 10 / 2
b = 10 / 2
c = a + b 
d = 10 / 2
e = 10 / 2
f = d * e
g = f / 100
h = c + g
Problem: in a certain parking lot , 5 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 5 % * x = 20 % * y y / x = 1 / 4 = 25 % the answer is b ."
Answer: b
Python program:
a = 80 / 100
b = 1 - a
c = 5 / 100
d = b / c
Problem: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "14 n / 60 must be an integer . = > 7 n / 30 must be an integer . hence n must be a multiple of 2 * 3 * 5 . = > n has 3 different prime integers and can not have more than 3 different prime integers because 2 * 3 * 5 * 7 = 210 > 200 answer : b"
Answer: b
Python program:
a = 1 + 4 
b = 60 / 2
c = b / 2
d = c / 3
e = a / d
f = e + 2
Problem: if x is to be chosen at random from the integers between 1 to 6 , inclusive , and y is to be chosen at random from the integers between 7 and 11 , inclusive , what is the probability that x + y will be even ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 6 * 2 / 5 = 1 / 5 p ( x and y are both odd ) = 3 / 6 * 3 / 5 = 3 / 10 p ( x + y is even ) = 1 / 5 + 3 / 10 = 1 / 2 the answer is a ."
Answer: a
Python program:
a = 2 * 2
b = 3 * 2
c = a + b 
d = 6 - 1
e = 6 * d
f = c / e
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 290 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 24.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 290 = 400 m s = 60 * 5 / 18 = 50 / 3 t = 400 * 3 / 50 = 24.00 sec answer : d"
Answer: d
Python program:
a = 110 + 290 
b = 60 * const_0_2778
c = a / b
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 8 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 45 , b ) 40 , c ) 35 , d ) 30 , e ) 25
Rationale: 1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 7 th year : 6 - 7 ( age ) , we take age = 6 8 th year : 7 - 8 ( age ) , we take age = 7 thus for the 3 rd year = 50 , 4 th year = 50 - 3 = 47 5 th year = 47 - 4 = 43 6 th year = 43 - 5 = 38 . 7 th year = 38 - 6 = 32 8 th year = 32 - 7 = 25 the correct answer is e .
Answer: e
Python program:
a = 8 - 1
b = a - 1
c = 8 - 1
d = 50 + c 
e = b + d 
f = e / 3
g = f + 3
Problem: a man covers a distance of 180 km at 72 kmph and next 190 km at 88 kmph . what is his average speed for his whole journey of 370 km ?
Options: a ) 77 kmph , b ) 77.15 kmph , c ) 77.25 kmph , d ) 79 kmph , e ) 80 kmph
Rationale: formula = 2 * f . s * s . p / f . s + s . p = 2 * 72 * 88 / 88 + 72 = 79.2 kmph option ' c '
Answer: c
Python program:
a = 180 / 72
b = 190 / 88
c = a + b 
d = 370 / c
Problem: find the sum of first 16 natural numbers
Options: a ) 136 , b ) 468 , c ) 465 , d ) 463 , e ) 485
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 16 ( 16 + 1 ) / 2 = 16 ( 17 ) / 2 = 136 answer : option a"
Answer: a
Python program:
a = 16 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 16 / e
g = f / 2
h = 16 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 16 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: in a zoo , the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same 5 years ago . if the increase in the number of cheetahs in the zoo since then is 2 , then what is the increase in the number of pandas ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 15
Rationale: one short cut to solve the problem is c : p = 1 : 3 c increased to 3 = > 1 : 3 = 3 : x = > x = 9 = > p increased by 6 d is the answer
Answer: d
Python program:
a = math.lcm(1, 3)
b = a * 2
Problem: ramesh purchased a refrigerator for rs . 16500 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 ) 22899 , d ) 23100 , e ) 32778
Rationale: "price at which the tv set is bought = rs . 16,500 discount offered = 20 % marked price = 16500 * 100 / 80 = rs . 20625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 20625 + 375 = rs . 21000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 21000 * 110 / 100 = rs . 23100 answer : d"
Answer: d
Python program:
a = 100 + 10 
b = 16500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: john bought a total of 16 mangoes and oranges . each mango costs 80 cents and each orange costs 60 cents . if the average price of the 16 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: let number of mangoes be x , number of oranges be 16 - x 0.80 x + ( 16 - x ) 0.60 / 16 = 0.65 solving for x , we get x = 4 - - > mangoes 4 , oranges 12 now , number of oranges to be returned be y 0.80 * 4 + ( 12 - y ) * 0.60 / 16 - y = 0.72 solving for y , y = 10 ans : e
Answer: e
Python program:
a = 65 / 100
b = a * 16
Problem: 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 30 meters deep by working for 6 hours ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "45 workers * 8 hours / 30 meters = x * 6 / 30 x = 60 total workers 60 - 45 = 15 new workers the answer is b ."
Answer: b
Python program:
a = 8 / 6
b = 45 * a
c = 30 / 30
d = b * c
e = d - 45