euclaise/mathqa_programs huggingface dataset:
Problem: a bus started its journey from mumbai and reached pune in 65 min with its average speed of 60 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ?
Options: a ) 2 hrs , b ) 3 hrs , c ) 1 hrs , d ) 1 1 / 2 hrs , e ) 2 1 / 2 hrs
Rationale: sol . distance between ramgarh and devgarh = ( 60 * 65 ) / 60 = 60 average speed of the bus is increased by 5 km / hr then the speed of the bus = 60 km / hr required time = 60 / 60 = 1 hr c
Answer: c
Python program:
a = 65 / 60
b = 60 * a
c = 60 + 5 
d = b / c
Problem: the mean of 50 observations is 200 . but later he found that there is decrements of 47 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 185 , c ) 153 , d ) 198 , e ) 199
Rationale: "153 answer is c"
Answer: c
Python program:
a = 200 - 47
Problem: a bag contains 4 red , 6 blue and 3 green balls . if 3 balls are picked at random , what is the probability that both are blue ?
Options: a ) 11 / 144 , b ) 12 / 455 , c ) 10 / 143 , d ) 11 / 125 , e ) 14 / 368
Rationale: "p ( both are red ) , = 6 c 3 / 13 c 3 = 10 / 143 c"
Answer: c
Python program:
a = math.comb(4, 2)
b = 4 + 6 
c = b + 4 
d = math.comb(c, 2)
e = a / d
Problem: what is 120 % of 13 / 24 of 360 ?
Options: a ) 52 , b ) 117 , c ) 234 , d ) 312 , e ) 576
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 15 = 234 the answer is c ."
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 120 * n
p = o / 100
Problem: if a farmer sells 10 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 15 more chickens , he will run out of feed 3 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 12 , b ) 24 , c ) 48 , d ) 35 , e ) 60
Rationale: "say farmer has n chicken and he is good for d days . : - we have 3 equations given in question : - ( n - 10 ) * d + 4 = ( n + 15 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 15 d - 3 n = 45 4 n - 10 d = 40 = > n = 35 ans d it is !"
Answer: d
Python program:
a = 2 + 4 
b = 3 * 4
c = a * b
Problem: how many 1 / 2 s are there in 37 1 / 2 ?
Options: a ) 75 , b ) 150 , c ) 300 , d ) 600 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 2 ) = ( 75 / 2 x 2 / 1 ) = 75 answer : a"
Answer: a
Python program:
a = 1 / 2
b = 37 + a 
c = 1 / 2
d = b / c
Problem: a , b , c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 175 , then how much amount should c pay as his share of rent ?
Options: a ) 23 , b ) 45 , c ) 15 , d ) 28 , e ) 18
Rationale: a : b : c = 10 * 7 : 12 * 5 : 15 * 3 = 2 * 7 : 12 * 1 : 3 * 3 = 14 : 12 : 9 amount that c should pay = 175 * ( 9 / 35 ) = 5 * 9 = 45 answer is b
Answer: b
Python program:
a = 3 * 15
Problem: in a box of 12 pens , a total of 6 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 5 / 22 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 6 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 6 / 12 ) i . e . probability of second pen not being defective = ( 5 / 11 ) [ 11 pen remaining with 5 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 6 / 12 ) * ( 5 / 11 ) = 5 / 22 answer : option b"
Answer: b
Python program:
a = 12 - 6
b = a / 12
c = 12 - 6
d = c - 1
e = 12 - 1
f = d / e
g = b * f
Problem: a part of certain sum of money is invested at 6 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 6 , b ) 4 : 9 , c ) 4 : 3 , d ) 5 : 2 , e ) 4 : 2
Rationale: "15 : 6 = 5 : 2 answer : d"
Answer: d
Python program:
a = 15 / 100
b = a * 6
Problem: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 5 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 5 ) / 2 = 4 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c .
Answer: c
Python program:
a = 4 / 10
Problem: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 630 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 8 % , b ) 10 % , c ) 12 % , d ) 14 % , e ) 16 %
Rationale: "difference in c . i . and s . i for 2 years = $ 630 - $ 600 = $ 30 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 30 rate = ( 100 * 30 ) / ( 300 ) = 10 % the answer is b ."
Answer: b
Python program:
a = 630 - 600
b = 100 * a
c = 600 / 2
d = b / c
Problem: there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle .
Options: a ) 165 ∏ cm , b ) 65 ∏ cm , c ) 12 ∏ cm , d ) 14 ∏ cm , e ) 16 ∏ cm
Rationale: "let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c"
Answer: c
Python program:
a = square_edge_by_area / (
b = a / 2
c = 3 + 4 
d = c / 3
e = b + d
Problem: y and z walk around a circular track . they start at 5 a . m from the same point in the opposite directions . y and z walk at a speed of 3 rounds per hour and 4 rounds per hour respectively . how many times shall they cross each other before 7 a . m
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: explanation : relative speed = ( 3 + 4 ) = 9 rounds per hour so , they cross each other 9 times in an hour hence , they cross 18 times before 7 a . m answer : option e
Answer: e
Python program:
a = const_60 / 4
b = a / 10
c = const_60 / 3
d = c / 10
e = b + d 
f = const_60 / e
Problem: a box contains 10 black , 5 red and 4 green marbles . 3 marbles are drawn from the box at random . what is the probability that all the three marbles are of the same color ?
Options: a ) 143 / 969 , b ) 134 / 969 , c ) 120 / 969 , d ) 19 / 969 , e ) 120 / 134
Rationale: "explanation : total marbles in a box = 10 black + 5 red + 4 green marbles = 19 marbles 3 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 3 = 969 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 10 c 3 + 5 c 3 + 4 c 3 = 120 + 10 + 4 = 134 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 134 / 969 answer : b"
Answer: b
Python program:
a = 5 + 4 
b = 5 + 3 
c = 10 + b 
d = a + c 
e = 10 + 5 
f = e * 4
g = d / f
Problem: a towel , when bleached , lost 20 % of its length and 10 % of its breadth . what is the percentage decrease in area ?
Options: a ) 26 , b ) 28 , c ) 24 , d ) 20 , e ) 22
Rationale: "formula for percentage change in area is : = ( − x − y + ( xy ) / 100 ) % = ( − 20 − 10 + ( 20 × 10 ) / 100 ) % = − 28 % i . e . , area is decreased by 28 % answer is b ."
Answer: b
Python program:
a = 100 * 100
b = 100 - 20
c = 100 - 10
d = b * c
e = a - d
f = e / 100
Problem: two numbers are respectively 35 % and 50 % more than a third number . the percentage that is first of the second is ?
Options: a ) 90 % , b ) 47 % , c ) 38 % , d ) 52 % , e ) 83 %
Rationale: "i ii iii 135 150 100 150 - - - - - - - - - - 135 100 - - - - - - - - - - - ? = > 90 % answer : a"
Answer: a
Python program:
a = 35 + 100 
b = 50 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 272 less than the sum lent . what was the sum lent ?
Options: a ) 400 , b ) 278 , c ) 289 , d ) 500 , e ) 821
Rationale: "p - 272 = ( p * 4 * 8 ) / 100 p = 400 answer : a"
Answer: a
Python program:
a = 4 * 8
b = a / 100
c = 1 - b
d = 272 / c
Problem: a marketing firm determined that , of 200 households surveyed , 80 used neither brand r nor brand b soap , 60 used only brand r soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap r and soap b ( d ) 40
Answer: d
Python program:
a = 80 + 60 
b = 200 - a
c = 3 + 1 
d = b / c
e = 80 + 60 
f = 200 - e
g = 3 + 1 
h = f / g
i = d + h 
j = i + 10
Problem: if x and y are numbers such that ( x + 4 ) ( y - 4 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 9 , c ) 12 , d ) 16 , e ) 18
Rationale: "from ( x + 4 ) ( y - 4 ) = 0 it follows that either x = - 4 or y = 4 . thus either x ^ 2 = 16 or y ^ 2 = 16 . now , if x ^ 2 = 16 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 16 + 0 = 16 . similarly if y ^ 2 = 16 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 16 = 16 . answer : d ."
Answer: d
Python program:
a = 4 ** 2
Problem: in the set of positive integers from 1 to 90 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 320 , d ) 405 , e ) 450
Rationale: "reduce 1 - 90 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 - - 85 are valid multiples . add them - - > 405 d"
Answer: d
Python program:
a = 3 * 5
b = 90 * a
c = b / 5
Problem: 1000 men have provisions for 18 days . if 400 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.8 , c ) 12.6 , d ) 12.2 , e ) 12.1
Rationale: 1000 * 18 = 1400 * x x = 12.8 answer : b
Answer: b
Python program:
a = 18 * 1000
b = 1000 + 400 
c = a / b
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2014 ) = ?
Options: a ) 2015 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2014 ) = 2015 ans : a"
Answer: a
Python program:
a = 1 + 2014
Problem: a , b and c can do a piece of work in 30 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 30 + 1 / 30 + 1 / 40 = 1 / 11 work done by a and b together in the last 4 days = 4 * ( 1 / 30 + 1 / 30 ) = 4 / 15 remaining work = 11 / 15 the number of days required for this initial work = 8 days . the total number of days required = 4 + 8 = 12 days . answer : a"
Answer: a
Python program:
a = 1 / 30
b = 1 / 30
c = a + b 
d = c * 4
e = 1 - d
f = 2 + 3 
g = 2 * 4
h = f * g
i = 1 / h
j = 1 / 30
k = 1 / 30
l = j + k 
m = i + l 
n = e / m
o = n + 4
Problem: a man buys an article for $ 100 . and sells it for $ 110 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 110 gain = $ 10 gain % = 10 / 100 * 100 = 10 % answer is a"
Answer: a
Python program:
a = 100 / 100
b = 110 / a
c = b - 100
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) rs . 650 , b ) rs . 690 , c ) rs . 698 , d ) rs . 700 , e ) rs . 740
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 815 - 117 ) = rs . 698 . answer : option c"
Answer: c
Python program:
a = 854 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: if the average ( arithmetic mean ) of x + 1 , x + 5 , and x + 9 is 0 , then x =
Options: a ) – 5 , b ) – 4 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 1 + x + 5 + x + 9 ) / 3 = 0 = > 3 x + 15 = 0 = > x = - 5 answer a"
Answer: a
Python program:
a = 5 * 2
b = 1 * 2
c = a - b
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 14 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 5333 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.14 t + 0.08 ( p - t ) = 1440 - - - - > t = 5333 . b is the correct answer ."
Answer: b
Python program:
a = 2 * 3
b = 3 * a
c = b * 1000
d = 8 / 100
e = c * d
f = 1440 - e
g = 14 / 100
h = 8 / 100
i = g - h
j = f / i
Problem: what should be added to 4750 so that it may become a perfect square ?
Options: a ) 11 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "69 x 69 = 4761 4761 - 4750 = 11 if added to 11 get perfect square answer = a"
Answer: a
Python program:
a = 10 + 10 
b = 10 + 10 
c = a + b 
d = 10 + 10 
e = c + d 
f = 4 + 3 
g = e + f 
h = 10 + 10 
i = 10 + 10 
j = h + i 
k = 10 + 10 
l = j + k 
m = 4 + 3 
n = l + m 
o = g * n
p = o - 4750
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 72 a week . what is the % increase ?
Options: a ) 20 % , b ) 16.66 % , c ) 16.56 % , d ) 17.66 % , e ) 18.1 %
Rationale: "increase = ( 12 / 60 ) * 100 = ( 1 / 5 ) * 100 = 20 % . a"
Answer: a
Python program:
a = 72 - 60
b = a / 60
c = b * 100
Problem: 50 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 51 , e ) 81
Rationale: "explanation : 50 + 5 * 12 / ( 180 / 3 ) = 50 + 5 * 12 / ( 60 ) = 50 + ( 5 * 12 ) / 60 = 50 + 1 = 51 . answer : d"
Answer: d
Python program:
a = 5 * 12
b = 180 / 3
c = a / b
d = 50 + c
Problem: find number which is 50 % less than 60 .
Options: a ) 18 , b ) 30 , c ) 32 , d ) 26 , e ) 98
Rationale: explanation : 50 % less is 50 % of the given number therefore , 50 % of 60 is 30 . answer : b
Answer: b
Python program:
a = 60 * 50
b = a / 100
Problem: mark bought a set of 6 flower pots of different sizes at a total cost of $ 7.80 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.93 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30
Rationale: this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 7.80 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.75 the other 5 pots are . . . . 1.75 1.50 1.25 1.00 0.75 total = $ 7.80 so this must be the answer . b
Answer: b
Python program:
a = 6 - 1
b = a * 6
c = b / 2
d = c * 0
e = 7 - 8
f = e / 6
g = 6 - 1
h = g * 0
i = f + h
Problem: a certain basketball team that has played 2 / 3 of its games has a record of 18 wins and 2 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "18 wins , 2 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 2 games so it can lose another 5 at most . answer ( c )"
Answer: c
Python program:
a = 3 / 2
b = 18 + 2 
c = a * b
d = 3 / 4
e = 3 / 2
f = 18 + 2 
g = e * f
h = d * g
i = math.floor(h)
j = i + 1 
k = c - j
Problem: a sum fetched a total simple interest of $ 4241.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8930
Rationale: "e 8930 principal = $ 100 x 4241.25 / 9 x 5 = $ 424125 / 45 = $ 8930 ."
Answer: e
Python program:
a = 4241 * 25
b = a / 9
c = b / 5
Problem: the unit digit in the product ( 635 * 767 * 984 * 489 ) is :
Options: a ) 0 , b ) 8 , c ) 3 , d ) 2 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 5 * 7 * 4 * 9 ) = 0 answer : a"
Answer: a
Python program:
a = 635 * 767
b = a * 984
c = b * 489
d = 635 * 767
e = d * 984
f = e * 489
g = 4 + 4 
h = f - g
i = c - h
Problem: in a survey of political preferences , 78 % of those asked were in favour of at least one of the proposals : i , ii and iii . 50 % of those asked favoured proposal i , 30 % favoured proposal ii , and 20 % favoured proposal iii . if 5 % of those asked favoured all 3 of the proposals , what x percentage of those asked favoured more than one of the 3 proposals .
Options: a ) 10 , b ) 12 , c ) 17 , d ) 22 , e ) 30
Rationale: bunuel , my answer for exactly 2 people was 17 and this was my approach : 100 % = ( a + b + c ) - ( anb + anc + bnc ) - 5 % + 22 % which leads me to x = 100 % = ( 50 + 30 + 20 ) - ( at least 2 people ) - 5 % + 22 % . c
Answer: c
Python program:
a = 50 + 30 
b = a - 5
c = b + 20 
d = c - 5
e = d - 78
f = e + 5
Problem: a certain bag contains 60 balls — 22 white , 18 green , 2 yellow , 15 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.7 , b ) 0.15 , c ) 0.54 , d ) 0.85 , e ) 0.91
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 2 ) / 60 = 42 / 60 = 0.7 . answer : a ."
Answer: a
Python program:
a = 22 + 18 
b = a + 2 
c = b / 60
Problem: if the personal income tax rate is lowered from 38 % to 30 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 36500 ?
Options: a ) $ 1825 , b ) $ 5000 , c ) $ 3150 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 38 - 33 ) % of 36500 = 1825 . answer : a"
Answer: a
Python program:
a = 36500 / 100
b = 38 - 30
c = a * b
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 48 and elvin ' s total telephone bill for february was 90 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 6 , e ) $ 28
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 48 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 90 i . e . x + y = 48 and 2 x + y = 90 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 90 - 48 i . e . x = 42 i . e . fixed monthly charge , y = 6 answer : option d"
Answer: d
Python program:
a = 48 * 2
b = a - 90
Problem: in the recent , climate conference in new york , out of 500 men , 300 women , 500 children present inside the building premises , 10 % of the men , 60 % of the women and 70 % of the children were indians . find the percentage of people who were not indian ?
Options: a ) 59.54 % , b ) 66.25 % , c ) 55.39 % , d ) 63.21 % , e ) 64.22 %
Rationale: "solution : number of indians men present there = 500 * 10 / 100 = 50 indian women = 300 * 60 / 100 = 180 indian children = 500 * 70 / 100 = 350 . total member present in climate conference = 500 + 300 + 500 = 1300 total indian = 50 + 180 + 350 = 580 hence , % of indian present there = 580 * 100 / 1300 = 44.61 % % of people who were not indian = 100 - 44.61 = 55.39 % . answer c"
Answer: c
Python program:
a = 10 / 100
b = 1 - a
c = 500 * b
d = 60 / 100
e = 1 - d
f = 300 * e
g = c + f 
h = 70 / 100
i = 1 - h
j = 500 * i
k = g + j 
l = 500 + 300 
m = l + 500 
n = k / m
o = n * 100
Problem: two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ?
Options: a ) 122,195 , b ) 121,199 , c ) 120,192 , d ) 102,192 , e ) 126,109
Rationale: "( 5 x - 30 ) : ( 8 x - 30 ) = 5 : 9 x = 24 = > 120,192 answer : c"
Answer: c
Python program:
a = 5 * 30
Problem: find k if 56 / k = 4 .
Options: a ) 16 , b ) 17 , c ) 18 , d ) 14 , e ) 13
Rationale: "since 56 / k = 4 and 56 / 14 = 4 , then k = 14 correct answer d"
Answer: d
Python program:
a = 56 / 4
Problem: a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 30 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a"
Answer: a
Python program:
a = 1/(45)
b = 1/(45)
c = b / 2
d = a + c 
e = 1/(d)
Problem: a 400 meter long train crosses a man standing on the platform in 10 sec . what is the speed of the train ?
Options: a ) 144 , b ) 108 , c ) 278 , d ) 126 , e ) 112
Rationale: "s = 400 / 10 * 18 / 5 = 144 kmph answer : a"
Answer: a
Python program:
a = 400 / 10
b = a * const_3_6
Problem: a man took a loan from a bank at the rate of 9 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 2000 , b ) rs . 10,000 , c ) rs . 15,000 , d ) rs . 20,000 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d"
Answer: d
Python program:
a = 5400 * 100
b = 3 * 9
c = a / b
d = const_60 / 4
e = d * 100
f = c / e
Problem: what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 / 44444444 ^ 2 )
Options: a ) 88888883 , b ) 88888884 , c ) 88888885 , d ) 88888886 , e ) 88888873
Rationale: "let x = 44444444 , then 44444445 = x + 1 88888885 = 2 x - 3 44444442 = x - 2 44444438 = x - 6 44444444 ^ 2 = x ^ 2 then substitute it in equation ( x + 1 ) ( 2 x - 3 ) ( x - 2 ) + ( x - 6 ) / x ^ 2 ans is 2 x - 5 i . e 88888883 answer : a"
Answer: a
Python program:
a = 44444445 ** negate