euclaise/mathqa_programs huggingface dataset:
Problem: if p # q denotes the least common multiple of p and q , then w = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , w = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Python program:
a = 18 * 24
b = 12 * 16
c = a - b
d = c / 2
e = d + 24
Problem: a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 75 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 50 , e ) 55
Rationale: let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 150 + ( d / 2 ) / v d / 100 = d / 2 v and so v = 50 km / hr the answer is d .
Answer: d
Python program:
a = 75 * 60
b = 75 - 60
c = b * 60
d = a / c
e = 60 * d
f = 60 / 10
g = e / f
Problem: a rectangular table , kept against a wall has a three sides free and the wall along the fourth side . the side opposite the wall is twice the length of each of the other two free sides . if the area of the rectangular table is 128 square feet , what is the total length of the table free sides , in feet ?
Options: a ) 4
b ) 8
c ) 16
d ) 32
e ) 64
Rationale: two sides each = x the third = 2 x and the wall side is thus 2 x too x * 2 x = 2 x ^ 2 = 128 ie x ^ 2 = 64 ie x = 8 l = 16 w = 8 total lenght of table ' s free sides = 2 * 8 + 16 = 32 my answer is d
Answer: d
Python program:
a = 128 / 2
b = math.sqrt(a)
c = 128 / 2
d = math.sqrt(c)
e = d * 2
f = b + e 
g = 128 / 2
h = math.sqrt(g)
i = f + h
Problem: a boat having a length 8 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 120 kg , c ) 89 kg , d ) 80 kg , e ) 240 kg
Rationale: "volume of water displaced = ( 8 x 3 x 0.01 ) m 3 = 0.24 m 3 . mass of man = volume of water displaced x density of water = ( 0.24 x 1000 ) kg = 240 kg . answer : e"
Answer: e
Python program:
a = 8 * 3
b = 1 / 100
c = a * b
d = c * 1000
Problem: excluding stoppages , the speed of a bus is 86 kmph and including stoppages , it is 76 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7.5 min , b ) 16 min , c ) 20 min , d ) 7 min , e ) 40 min
Rationale: "d 7 min due to stoppages , it covers 10 km less . time taken to cover 10 km = ( 10 / 86 x 60 ) min = 7 min"
Answer: d
Python program:
a = 86 - 76
b = a / 86
c = const_60 * b
Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 15 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 22.78
b ) 23.54
c ) 24.5
d ) 25.55
e ) 23.51
Rationale: let the side of the square be a cm . perimeter of the rectangle = 2 ( 15 + 14 ) = 58 cm perimeter of the square = 58 cm i . e . 4 a = 58 a = 14.5 diameter of the semicircle = 14.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 14.5 ) = 1 / 2 ( 22 / 7 ) ( 14.5 ) = 22.78 cm to two decimal places answer : a
Answer: a
Python program:
a = 14 + 15 
b = 2 * a
c = b / 4
d = c / 2
e = circumface / (
f = math.floor(e, 2)
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 4 . their l . c . m is ?
Options: a ) 23 , b ) 77 , c ) 88 , d ) 48 , e ) 11
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 4 . so , the numbers are 12 and 16 . l . c . m of 12 and 16 = 48 . answer : d"
Answer: d
Python program:
a = 3 * 4
b = 4 * 4
c = math.lcm(a, b)
Problem: john makes $ 60 a week from his job . he earns a raise and now makes $ 120 a week . what is the % increase ?
Options: a ) 16 % , b ) 100 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 60 / 60 ) * 100 = ( 6 / 6 ) * 100 = 100 % . b"
Answer: b
Python program:
a = 120 - 60
b = a / 60
c = b * 100
Problem: a taxi leaves point a 5 hours after a bus left the same spot . the bus is traveling 20 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours .
Options: a ) 34 , b ) 32 , c ) 36 , d ) 38 , e ) 40
Rationale: "let the speed of bus be v - 20 , speed of taxi be v the bus travelled a total of 8 hrs and taxi a total of 3 hrs . hence 8 * ( v - 20 ) = 3 v 8 v - 160 = 3 v 5 v = 160 v = 32 mph b"
Answer: b
Python program:
a = 5 * 20
b = 5 * 20
c = a + b 
d = 5 + 5 
e = d - 5
f = c / e
Problem: a can finish a work in 12 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 4 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 12 * 1 / 3 ) = 4 days . correct option : a"
Answer: a
Python program:
a = 1 / 15
b = a * 10
c = b * 12
d = c / 2
Problem: two trains are moving in opposite directions with speed of 90 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 56 , b ) 40 , c ) 47 , d ) 26 , e ) 25
Rationale: "explanation : relative speed = 90 + 90 = 180 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 180 hr = 1 / 90 hr = 3600 / 90 seconds = 40 seconds answer : option b"
Answer: b
Python program:
a = 1 + 10 
b = 90 + 90 
c = a / b
d = c * 3600
Problem: a can do a piece of work in 40 days ; b can do the same in 20 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 24 days , b ) 65 days , c ) 86 days , d ) 40 days , e ) 17 days
Rationale: "10 / 40 + 10 / 20 + 10 / x = 1 x = 40 days answer : d"
Answer: d
Python program:
a = 10 + 10 
b = a / 40
c = 1 - b
d = 10 / c
Problem: for any number s , s * is defined as the greatest positive even integer less than or equal to s . what is the value of 5.2 – 5.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: since s * is defined as the greatest positive even integer less than or equal to s , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 – 5.2 * = 5.2 - 4 = 1.2 answer : b .
Answer: b
Python program:
a = 5 - 2
Problem: the present ages of a , b & c are in the ratio of 5 : 7 : 8 . 7 years ago , the sum oftheir ages was 59 . what is the present age of eldest one ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 35 , e ) 36
Rationale: let their present ages be 5 x , 7 x and 8 x . 7 years ago , sum of their ages was 59 . sum of their present ages = 59 + ( 3 x 7 ) = 80 sum of their present ages given is 5 x + 7 x + 8 x = 20 x 20 x = 80 = > x = 80 20 = 4 age of the eldest one = 8 x = 8 x 4 = 32 years . c
Answer: c
Python program:
a = 7 * 3
b = a + 59 
c = 5 + 7 
d = c + 8 
e = b / d
f = e * 8
Problem: ? % of 360 = 129.6
Options: a ) 277 , b ) 36 , c ) 64 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 129.6 or , ? = 129.6 × 100 / 360 = 36 answer b"
Answer: b
Python program:
a = 129 * 6
b = a / 360
Problem: if the average ( arithmetic mean ) of 16 consecutive odd integers is 414 , then the least of these integers is
Options: a ) a ) 399 , b ) b ) 418 , c ) c ) 519 , d ) d ) 521 , e ) e ) 525
Rationale: "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 16 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 7 th and 8 th numbers in the set ) . this means that numbers 7 and 8 in this set are 413 and 415 . because we know that number 7 is 413 , we know that the smallest number is 7 odd numbers below this , which means that it is 7 * 2 = 14 below this ( every odd number is every other number ) . therefore 413 - 14 = 399 , answer choice a ."
Answer: a
Python program:
a = 414 - 16
b = a + 1
Problem: a car gets 30 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 200 kilometers ?
Options: a ) 3.5 gallons , b ) 2.7 gallons , c ) 6.7 gallons , d ) 4.5 gallons , e ) 7.5 gallons
Rationale: "each 30 kilometers , 1 gallon is needed . we need to know how many 30 kilometers are there in 200 kilometers ? 200 ã · 30 = 6.7 ã — 1 gallon = 6.7 gallons correct answer is c ) 6.7 gallons"
Answer: c
Python program:
a = 200 / 30
Problem: maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability w , that a book selected at random is either a hard cover book or a chemistry book ?
Options: a ) 1 / 10 , b ) 3 / 20 , c ) 1 / 5 , d ) 1 / 4 , e ) 9 / 20
Rationale: "first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , w = 9 provide the desired outcome , making the answer e ."
Answer: e
Python program:
a = 2 + 4 
b = 2 + a 
c = b + 12 
d = 2 / c
e = 2 + 4 
f = 2 + e 
g = 2 + 4 
h = 2 + g 
i = h + 12 
j = f / i
k = d + j 
l = 2 + 4 
m = 2 + l 
n = m + 12 
o = 2 / n
p = 2 + 4 
q = 2 + p 
r = 2 + 4 
s = 2 + r 
t = s + 12 
u = q / t
v = o * u
w = k - v
Problem: the number 219 can be written as sum of the squares of 3 different positive integers . what is the difference of these 2 different larger integers ?
Options: a ) 6 , b ) 2 , c ) 3 , d ) 5 , e ) 4
Rationale: "sum of the squares of 3 different positive integers = 219 13 ^ 2 + 7 ^ 2 + 1 ^ 2 = 219 now , difference of these 2 different larger integers = 13 - 7 = 6 ans - a"
Answer: a
Python program:
a = 219 / 2
b = math.sqrt(a)
c = 2 * b
Problem: this year , mbb consulting fired 10 % 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 ) 99 % , b ) 100.0 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 10 % reduction in employees lead to 90 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 90 employees is 90 * 1100 = 99000 now the new salary is more than previous salary by x % . x = ( 99000 / 100000 ) * 100 = 99 % so the answer is a"
Answer: a
Python program:
a = 100 * 10
b = 100 + a 
c = 100 - 10
d = c + 4 
e = b * d
f = 100 * 10
g = e / f
Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 150 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 150 = 3 ^ 300 * 2 ^ 300 the answer is c ."
Answer: c
Python program:
a = 36 - 150
b = a * 150
Problem: real - estate salesman z is selling a house at a 30 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 15 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 40 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 39 / 6 , b ) 62 / 11 , c ) 11 / 61 , d ) 21 / 61 , e ) 20 / 61
Rationale: let the retail price be = x selling price of z = 0.7 x selling price of x = 0.85 * 0.7 x = 0.60 x selling price of y = ( ( 0.7 x + 0.6 x ) / 2 ) * 0.60 = 0.65 x * 0.60 = 0.39 x 0.39 x = k * 0.60 x k = 0.39 / 0.6 = 39 / 6 answer : a
Answer: a
Python program:
a = 100 - 30
b = 100 - 30
c = 100 - 15
d = c / 100
e = b * d
f = a + e 
g = f / 2
h = 100 - 40
i = g * h
j = i / 100
k = 100 - 30
l = 100 - 15
m = l / 100
n = k * m
o = j / n
p = o * 10
Problem: in a certain alphabet , 11 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 5 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 11 + 24 = 35 ; next , we find the total # of letters without line : 40 - 35 = 5 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 5 - 0 = 5 . a"
Answer: a
Python program:
a = 11 + 24 
b = 40 - a
Problem: an alloy of copper and zinc contains copper and zinc in the ratio 5 : 3 . another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 1 : 5 , b ) 7 : 3 , c ) 5 : 3 , d ) 3 : 1 , e ) 4 : 3
Rationale: "alloy - 1 : copper : zinc = 5 : 3 , let quantity = x i . e . copper in alloy - 1 = [ 5 / ( 5 + 3 ) ] * x = ( 5 / 8 ) x and zinc in alloy - 1 = [ 3 / ( 5 + 3 ) ] * x = ( 3 / 8 ) x alloy - 2 : copper : zinc = 1 : 7 , let quantity = y i . e . copper in alloy - 2 = [ 1 / ( 1 + 7 ) ] * y = ( 1 / 8 ) y and zinc in alloy - 1 = [ 7 / ( 1 + 7 ) ] * y = ( 7 / 8 ) y after combining the two alloys copper = ( 5 / 8 ) x + ( 1 / 8 ) y zinc = ( 3 / 8 ) x + ( 7 / 8 ) y now , ( 5 x + y ) / 8 = ( 3 x + 7 y ) / 8 i . e . 2 x = 6 y i . e . x = 3 y i . e . x / y = 3 / 1 answer : option d"
Answer: d
Python program:
a = 1 + 7 
b = 5 / a
c = 1 / 7
d = b - c
e = 1 / 7
f = 1 + 7 
g = 1 / f
h = e - g
i = d / h
Problem: the average weight of 30 boys sitting in a bus had some value . a new person added to them whose weight was 40 kg only . due to his arrival , the average weight of all the boys decreased by 2 kg . find the average weight of first 30 boys ?
Options: a ) 150 , b ) 122 , c ) 30 , d ) 120 , e ) 102
Rationale: 30 x + 40 = 31 ( x â € “ 2 ) x = 102 e
Answer: e
Python program:
a = 30 + 30 
b = 40 + a 
c = b + 2
Problem: the original price of a suit is $ 200 . the price increased 25 % , and after this increase , the store published a 25 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 25 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 178.50 , b ) $ 182.50 , c ) $ 185.50 , d ) $ 187.50 , e ) $ 200
Rationale: "0.75 * ( 1.25 * 200 ) = $ 187.50 the answer is d ."
Answer: d
Python program:
a = 200 * 25
b = a / 100
c = 200 + b 
d = 200 * 25
e = d / 100
f = 200 + e 
g = f * 25
h = g / 100
i = c - h
Problem: a , b and c rents a pasture for rs . 638 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 198 , c ) 676 , d ) 156 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 638 = 198 answer : b"
Answer: b
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 638 / e
g = 16 * 9
h = f * g
Problem: if x / 4 - x - 3 / 6 = 1 , then find the value of x .
Options: a ) 6 , b ) 4 , c ) 5 , d ) 1 , e ) 2
Rationale: ( x / 4 ) - ( ( x - 3 ) / 6 ) = 1 = > ( 3 x - 2 ( x - 3 ) ) / 12 = 1 = > 3 x - 2 x + 6 = 12 = > x = 6 . answer is a
Answer: a
Python program:
a = 3 / 6
b = a + 1 
c = b * 4
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 42 more . what was his original selling price ?
Options: a ) $ 480 , b ) $ 570 , c ) $ 660 , d ) $ 720 , e ) $ 850
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 42 0.07 = 42 p = 600 the original selling price was 600 * 1.1 = 660 . the correct answer is c ."
Answer: c
Python program:
a = 10 / 100
b = 1 - a
c = 30 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 + f 
h = e - g
i = 42 / h
j = 10 / 100
k = 1 + j 
l = i * k
Problem: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 14300 ?
Options: a ) 3200 , b ) 4000 , c ) 3250 , d ) 4160 , e ) 3985
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 14300 ã — 16 / 55 = rs . 4160 . share of z in the profit is rs . 4160 . option d"
Answer: d
Python program:
a = 3 * 4
b = a - 4
c = 48000 * b
d = 3 * 4
e = 36000 * d
f = 3 * 4
g = 42000 * f
h = e + g 
i = 3 * 4
j = i - 4
k = 48000 * j
l = h + k 
m = 14300 / l
n = c * m
Problem: hcf of two numbers is 15 and their lcm is 180 . if their sum is 105 , then the numbers are :
Options: a ) 30 and 75 , b ) 35 and 70 , c ) 40 and 65 , d ) 45 and 60 , e ) 55 and 70
Rationale: "explanation : let the numbers be 15 a and 15 b . then , 15 a + 15 b = 105 or a + b = 7 . . ( i ) lcm = 15 ab = 180 ab = 12 . . ( ii ) solving equations ( i ) and ( ii ) , we get a = 4 , b = 3 so , the numbers are 15 × 4 and 15 × 3 , i . e . , 60 and 45 answer : d"
Answer: d
Python program:
a = 180 / 15
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 10 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 25 , d ) 15 , e ) 6
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 = 10 run rate needed = 250 / 10 = 25 answer : option c"
Answer: c
Python program:
a = 10 * 3
b = 282 - a
c = b / 10
Problem: if the cost price of 50 articles is equal to the selling price of 25 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 100
Rationale: "percentage of profit = 25 / 25 * 100 = 100 % answer : e"
Answer: e
Python program:
a = 100 * 25
b = a / 50
c = 100 - b
d = 100 * 25
e = d / 50
f = c / e
g = 100 * f
Problem: jake can dig a well in 16 days . paul can dig the same well in 24 days . jake , paul and hari together dig the well in 8 days . hari alone can dig the well in
Options: a ) 96 days , b ) 48 days , c ) 32 days , d ) 24 days , e ) 28 days
Rationale: jake 1 day work = 1 / 16 paul 1 day work = 1 / 24 j + p + h 1 ady work = 1 / 8 1 / 16 + 1 / 24 + 1 / x = 1 / 8 1 / x = 1 / 48 x = 48 so , hari alone can dig the well in 48 days answer : b
Answer: b
Python program:
a = 1 / 8
b = 1 / 16
c = 1 / 24
d = b + c 
e = a - d
f = 1/(e)
Problem: 3 numbers are in the ratio 4 : 5 : 6 and their average is 20 . the largest number is :
Options: a ) 24 , b ) 32 , c ) 36 , d ) 42 , e ) 45
Rationale: explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 20 15 x = 60 x = 4 largest number = 6 x = 24 . answer a
Answer: a
Python program:
a = 4 + 5 
b = a + 6 
c = b / 3
d = 20 / c
e = d * 6
Problem: a father told his son ` ` i was as old as you are at present , at the time of your birth ' ' . if the father is 38 years old now , then what was the son ' s age 5 years ago in years ?
Options: a ) 14 , b ) 19 , c ) 38 , d ) 33 , e ) 35
Rationale: et son ' s present age is = x then 38 - x = x x = 19 son ' s age 5 years back is 19 - 5 = 14 years . answer : a
Answer: a
Python program:
a = 38 / 2
b = a - 5
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 120 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 240
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 120 total = 120 + 120 = 240 answer ( e )"
Answer: e
Python program:
a = 60 / 100
b = 120 * a
c = 55 / 100
d = 120 * c
e = b - d
f = 55 / 100
g = 50 / 100
h = f - g
i = e / h
Problem: the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 5600 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 4480 , b ) rs . 5275 , c ) rs . 6275 , d ) rs . 6725 , e ) none of these
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 5600 ( 100 / 125 ) = rs . 4480 . answer : a"
Answer: a
Python program:
a = 25 / 100
b = 1 + a 
c = 5600 / b
Problem: the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio o
Options: a ) 6 : 5 , b ) 4 : 7 , c ) 3 : 5 , d ) 5 : 7 , e ) 8 : 9
Rationale: "4 : 5 3 : 2 - - - - - - - 12 : 15 : 10 12 : 10 = = > 6.5 answer a"
Answer: a
Python program:
a = 4 * 3
b = 5 * 2
c = a / b
Problem: the sector of a circle has radius of 18 cm and central angle 135 o . find its perimeter ?
Options: a ) 78.4 cm , b ) 11.5 cm , c ) 91.8 cm , d ) 92.5 cm , e ) 99.5 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 18 ) + 2 ( 18 ) = 42.4 + 36 = 78.4 cm answer : a"
Answer: a
Python program:
a = 18 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 18
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 96 vehicles were involved in accidents . if 3 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 288 , b ) 320 , c ) 2,880 , d ) 3,200 , e ) 28,800
Rationale: to solve we will set up a proportion . we know that “ 100 million vehicles is to 96 accidents as 3 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 3,000 million rather than 3 billion . creating a proportion we have : 100 / 96 = 3,000 / x cross multiplying gives us : 100 x = 3,000 * 96 x = 30 * 96 = 2,880 correct answer is c .
Answer: c
Python program:
a = 3 * 10
b = 96 * a