euclaise/mathqa_programs huggingface dataset:
Problem: the circumferences of two circles are 132 meters and 352 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 2996 sq m , b ) 2897 sq m , c ) 4312 sq m , d ) 5768 sq m , e ) 8470 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 132 and 2 ∏ l = 352 s = 132 / 2 ∏ and l = 352 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 66 ^ 2 / ∏ ^ 2 - 132 ^ 2 / ∏ ^ 2 } = 66 ^ 2 / ∏ - 132 ^ 2 / ∏ = ( 66 - 132 ) ( 66 + 132 ) / ∏ = ( 110 ) ( 242 ) / ( 22 / 7 ) = 8470 sq m answer : e"
Answer: e
Python program:
a = 2 * math.pi
b = 352 / a
c = circle_area - (
Problem: the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and dinley have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if steve and dinley submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combinedno discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Python program:
a = 80 * 0
b = 2 * a
c = 100 - 25
d = c / 100
e = 160 * d
f = e * 0
g = b - f
h = g / 2
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 16000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 22 , b ) 21 , c ) 35 , d ) 37 , e ) 29
Rationale: "explanation : lot the total number of workers be v then , 8 ooov = ( 16000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 70000 < = > v = 35 answer : c ) 35"
Answer: c
Python program:
a = 16000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: when positive integer w is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation that can be formed w is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b
Answer: b
Python program:
a = 5 + 2 
b = 13 * a
c = reminder - (
Problem: a certain box has 11 cards and each card has one of the integers from 1 to 11 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 11 cards ?
Options: a ) 1 / 11 , b ) 2 / 11 , c ) 2 / 33 , d ) 4 / 55 , e ) 5 / 66
Rationale: the average of the numbers is 6 the total number of ways to choose 2 cards from 11 cards is 11 c 2 = 55 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 2,3 } the probability is 4 / 55 the answer is d .
Answer: d
Python program:
a = math.factorial(11)
b = math.factorial(2)
c = 11 - 2
d = math.factorial(c)
e = b * d
f = a / e
g = 4 / f
Problem: if a 2 + b 2 + c 2 = 281 and ab + bc + ca = 4 , then a + b + c is
Options: a ) 16 , b ) 18 , c ) 22 , d ) 17 , e ) 20
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 281 and ab + bc + ca = 4 , ( a + b + c ) ^ 2 = 281 + 2 ( 4 ) = 289 = 17 ^ 2 therefore : a + b + c = 17 answer : d"
Answer: d
Python program:
a = 4 * 2
b = 281 + a 
c = math.sqrt(b)
Problem: pradeep has to obtain 25 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are
Options: a ) 840 , b ) 600 , c ) 800 , d ) 1000 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 25 % of x = 185 + 25 = > 25 / 100 x = 210 x = ( 210100 / 25 ) x = 840 . answer : a"
Answer: a
Python program:
a = 185 + 25 
b = 25 / 100
c = a / b
Problem: how many digits will be there to the right of the decimal point in the product of 98 and . 08216 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 7 , e ) 8
Rationale: "product of 98 and . 08216 is 8.05168 . therefore number of digits to right of decimal point is 5 answer is a ."
Answer: a
Python program:
a = 100 - 98
b = a - 1
Problem: 9 men went to a theater . 8 of them spent rs . 3 each over their tickets and the ninth spent rs . 2 more than the average expenditure of all the 9 . determine the total money spent by them ?
Options: a ) 29 , b ) 29.25 , c ) 31 , d ) 31.23 , e ) 32
Rationale: average of 9 = x 9 x = 8 * 3 + x * 2 x = 3.25 total = 9 * 3.25 = 29.25 b
Answer: b
Python program:
a = 3 * 8
b = a + 2 
c = b / 8
d = c * 9
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 48 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 10 , e ) 12
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 48 = 6 k + 4 p = > k = 6 , p = 3 total red ' s in bag a will be 2 k = 12 e"
Answer: e
Python program:
a = 3 * 2
b = a + 4 
c = 48 / b
Problem: a runs 1 2 / 3 times as fast as b . if a gives b a start of 80 m , how far must the winning post be so that a and b might reach it at the same time ?
Options: a ) 200 m , b ) 300 m , c ) 270 m , d ) 160 m , e ) 150 m
Rationale: explanation : ratio of the speeds of a and b = 5 : 1 = 5 : 3 thus , in race of 5 m , a gains 2 m over b . 2 m are gained by a in a race of 5 m . 80 m will be gained by a in race of 5 / 2 x 80 m = 200 m winning post is 200 m away from the starting point . answer is a
Answer: a
Python program:
a = 1 * 3
b = a + 2 
c = b * 80
d = c / 2
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 18 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 468 , b ) 444 , c ) 676 , d ) 767 , e ) 663
Rationale: "1 h - - - - - 3 ? - - - - - - 60 12 h rs = 18 + 21 = 39 t = 12 d = 39 * 12 = 468 answer : a"
Answer: a
Python program:
a = 21 - 18
b = 60 / a
c = b * 18
d = 21 - 18
e = 60 / d
f = e * 21
g = c + f
Problem: if d = 1 / ( 2 ^ 3 * 5 ^ 6 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 6 ) = multiply and divide by 2 ^ 3 = 2 ^ 3 / ( 2 ^ 3 * 2 ^ 3 * 5 ^ 6 ) = 2 ^ 3 / 10 ^ 6 = > non zero digits are 8 = > ans a"
Answer: a
Python program:
a = 1 + 2
Problem: if the perimeter and diagonal of a rectangle are 14 and 5 cms respectively , find its area .
Options: a ) 12 cm 2
b ) 16 cm 2
c ) 20 cm 2
d ) 24 cm
e ) none of these
Rationale: in a rectangle , ( perimeter ) 2 / 4 = ( diagonal ) 2 + 2 × area ⇒ ( 14 ) 2 / 4 = 5 ( 2 ) + 2 × area 49 = 25 + 2 × area ∴ area = 49 − 25 / 2 = 24 / 2 = 12 cm 2 answer a
Answer: a
Python program:
a = 14 / 2
b = a ** 2
c = 5 ** 2
d = b - c
e = d / 2
Problem: a train 110 m long is running with a speed of 50 km / h . in how many seconds will the train pass a man who is running at 5 km / h in the direction opposite to that in which the train is going ?
Options: a ) 6.1 , b ) 7.2 , c ) 8.3 , d ) 9.4 , e ) 10.5
Rationale: "the speed of the train relative to the man = 50 + 5 = 55 km / h . 55000 m / h * 1 h / 3600 s = ( 550 / 36 ) m / s ( 110 m ) / ( 550 / 36 m / s ) = ( 110 * 36 ) / 550 = 36 / 5 = 7.2 seconds the answer is b ."
Answer: b
Python program:
a = 50 + 5 
b = a / const_3_6
c = 110 / b
Problem: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in h hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of h ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * h = 1 = > x = 1 / h when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / h = 4 / 3 = > 1 / h = ( 8 - 3 ) / 6 = 5 / 6 = > h = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Python program:
a = 4 - 2
b = 2 + 3 
c = 1 / b
d = a + c
Problem: if two - third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be .
Options: a ) 90 seconds , b ) 150 seconds , c ) 60 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: 2 / 3 filled in 100 seconds 1 / 3 filled in 50 secs then 2 / 3 + 1 / 3 = 100 + 50 seconds = 150 seconds answer : b
Answer: b
Python program:
a = 100 / 2
b = a * 3
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 14
Rationale: "for unit digit of a ^ 2 to be 9 . . . unit digit of a has to be 3 or 7 . . . now for unit digit of ( a + 1 ) ^ 2 to be 4 . . unit digit of a has to be 1 or 7 . . . . from the above two conditions , unit value of a has to be 7 , which will satisfy both the conditions . . . now id unit digit of a is 7 , unit digit of ( a + 2 ) ^ 2 hast to be 1 . answer : a"
Answer: a
Python program:
a = 9 * 2
b = a + 2 
c = b ** 2
Problem: if the cost price is 81 % of selling price then what is the profit percentage .
Options: a ) 22.45 , b ) 23.45 , c ) 32.45 , d ) 23.54 , e ) 23.55
Rationale: selling price = rs 100 : then cost price = rs 81 : profit = rs 19 . profit = { ( 19 / 81 ) * 100 } % = 23.45 % answer is b .
Answer: b
Python program:
a = 100 - 81
b = a / 81
c = b * 100
Problem: farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 5000 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 16 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 5000 ) x 100 = 9.6 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 9.6 % x ( 100 / 60 ) = 16 % the correct answer is ( b ) ."
Answer: b
Python program:
a = 480 / 5000
b = a * 100
c = b * 100
d = c / 60
Problem: in company j , the total monthly payroll for the 15 factory workers is $ 30000 and the total monthly payroll for the 30 office workers is $ 75000 . by how much does the average ( arithmetic mean ) monthly salary of an office worker exceed that of a factory worker in this company ?
Options: a ) $ 450 , b ) $ 500 , c ) $ 600 , d ) $ 650 , e ) $ 750
Rationale: the average monthly salary of a factory worker is : $ 30000 / 15 = $ 2000 . the average monthly salary of an office worker is : $ 75000 / 30 = $ 2500 . the difference in average salary is : $ 2500 - $ 2000 = $ 500 . the answer is b .
Answer: b
Python program:
a = 30000 / 30
b = a / 2
Problem: the average mark of the students of a class in a particular exam is 70 . if 5 students whose average mark in that exam is 50 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam ?
Options: a ) 20 , b ) 15 , c ) 10 , d ) 12 , e ) 25
Rationale: "let the number of students who wrote the exam be x . total marks of students = 70 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 70 x - ( 5 * 50 ) = 90 ( x - 5 ) 200 = 20 x = > x = 10 answer : c"
Answer: c
Python program:
a = 90 * 5
b = 5 * 50
c = a - b
d = 90 - 70
e = c / d
Problem: what is the smallest positive integer nn such that √ 6,480 ∗ n is a perfect cube ?
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4
Rationale: "sol : let ' s factorize 6480 and we get 6480 = 3 ^ 4 * 2 ^ 4 * 5 now we need to see for what minimum value of n √ n * 6480 = a ^ 3 where a is an integer so from 6480 we already have 2 ^ 4 * 3 ^ 4 * 5 * n √ n = ( 2 ^ 2 ) ^ 3 * ( 3 ^ 2 ) ^ 3 * ( 5 ) ^ 3 why cause a is an integer which will need to be have the same factors which are in lhs solving for n √ n = ( 2 ^ 6 * 3 ^ 6 * 5 ^ 3 ) / 2 ^ 4 * 3 ^ 4 * 5 and we get n √ n = 2 ^ 2 * 3 ^ 2 * 5 ^ 2 or n = 2 ^ 4 * 3 ^ 4 * 5 ^ 4 or 30 ^ 4 answer is e"
Answer: e
Python program:
a = 3 + 4
Problem: what will be the fraction of 12 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 3 / 25 , e ) none of these
Rationale: "explanation : 12 * 1 / 100 = 3 / 25 . option d"
Answer: d
Python program:
a = 12 / 2
b = circle_area / (
Problem: at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 20 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 8 / 23 , c ) 2 / 5 , d ) 8 / 14 , e ) 2 / 3
Rationale: "let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 20 % of 60 = 12 total new books = 28 fraction = 16 / 28 = 8 / 14 ans : d"
Answer: d
Python program:
a = 40 * 40
b = a / 100
c = 40 * 40
d = c / 100
e = 100 - 40
f = 20 * e
g = f / 100
h = d + g 
i = b / h
Problem: a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is ?
Options: a ) 26 , b ) 28 , c ) 80 , d ) 26 , e ) 21
Rationale: "let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = 40 * b
d = 20 / 100
e = 1 + d 
f = 50 * e
g = c + f 
h = 15 / 100
i = 1 + h 
j = 90 * i
k = g - j
l = 40 / k
Problem: a rectangle having length 120 cm and width 50 cm . if the length of the rectangle is increased by ten percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 33.33 % , c ) 40 % , d ) 7.69 % , e ) none of these
Rationale: "explanation : solution : ( 10 / ( 120 + 10 ) * 100 ) % = 7.69 % answer : d"
Answer: d
Python program:
a = 120 * 50
b = 3 * 10
c = b * 120
d = c / 100
e = 120 + d 
f = a / e
g = f / 50
h = 1 + g 
i = h * 10
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 39 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 73 degrees , c ) 31 degrees , d ) 34 degrees , e ) 74 degrees
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 39 tu + w + th = 192 - 39 = 153 f = 184 – 153 = 31 answer : c"
Answer: c
Python program:
a = 48 * 4
b = 46 * 4
c = a - b
d = 39 - c
Problem: it takes joey the postman 1 hours to run a 2 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 3 mile / hour , what is the speed with which joey returns ?
Options: a ) 1 , b ) 6 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 2 miles an hour let the other half be x miles an hour now , avg speed = 3 mile an hour 2 * 2 * x / 2 + x = 3 4 x = 3 x + 6 = > x = 6 b"
Answer: b
Python program:
a = 2 * 2
b = a / 3
c = b - 1
d = 2 / c
Problem: a man is 16 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 21 years , b ) 14 years , c ) 16 years , d ) 18 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 16 . = > 2 ( x + 2 ) = ( x + 16 + 2 ) = > 2 x + 4 = x + 18 = > x = 14 years option b"
Answer: b
Python program:
a = 2 * 2
b = a - 2
c = 16 - b
d = 2 - 1
e = c / d
Problem: a man ' s speed with the current is 15 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 20 , c ) 50 , d ) 30 , e ) 40
Rationale: "man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 15 - 2.5 = 12.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 12.5 - 2.5 = 10 km / hr answer is a ."
Answer: a
Python program:
a = 15 - 2
b = a - 2
Problem: a man ' s speed with the current is 21 km / hr and the speed of the current is 4.3 km / hr . the man ' s speed against the current is
Options: a ) 9.2 , b ) 10.3 , c ) 11.5 , d ) 12.4 , e ) 13
Rationale: "man ' s rate in still water = ( 21 - 4.3 ) km / hr = 16.7 km / hr . man ' s rate against the current = ( 16.7 - 4.3 ) km / hr = 12.4 km / hr . answer : d"
Answer: d
Python program:
a = 21 - 4
b = a - 4
Problem: martin buys a pencil and a notebook for 80 cents . at the same store , gloria buys a notebook and an eraser for 85 cents , and zachary buys a pencil and an eraser for 45 cents . how many cents would it cost to buy 3 pencils , 3 notebooks , and 3 erasers ? ( assume that there is no volume discount . )
Options: a ) 300 , b ) 315 , c ) 330 , d ) 345 , e ) 360
Rationale: pencil + notebook = 80 notebook + eraser = 85 pencil + eraser = 45 let ' s add all three equations . 2 pencils + 2 notebooks + 2 erasers = 210 cents the cost to buy 3 of each would be ( 3 / 2 ) ( 210 ) = 315 the answer is b .
Answer: b
Python program:
a = 80 - 45
b = 85 + a 
c = b / 2
d = 80 - c
e = 45 - d
f = e * 3
g = 80 - 45
h = 85 + g 
i = h / 2
j = 80 - i
k = j * 3
l = f + k 
m = 80 - 45
n = 85 + m 
o = n / 2
p = o * 3
q = l + p
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 25 % . what is the selling price of the cycle ?
Options: a ) s . 1050 , b ) s . 1160 , c ) s . 1190 , d ) s . 1202 , e ) s . 1204
Rationale: "since , c . p = 1400 loss % = ( c . p - s . p ) / c . p * 100 25 = ( 1400 - s . p ) / 1400 * 100 so , after solving answer = 1050 . answer : a"
Answer: a
Python program:
a = 100 - 25
b = a * 1400
c = b / 100
Problem: 1 + 3 = 2 2 + 3 = 10 3 + 3 = 30 4 + 3 = 68 5 + 3 = ? ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: 1 ^ 3 + 3 - 2 = 2 , 2 ^ 3 + 3 - 1 = 10 , 3 ^ 3 + 3 - 0 = 30 , 4 ^ 3 + 3 + 1 = 68 , 5 ^ 3 + 3 + 2 = 130 answer : c
Answer: c
Python program:
a = 5 * 5
b = a + 1 
c = b * 5
Problem: a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 90 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160 , b ) 240 , c ) 360 , d ) 495 , e ) 560
Rationale: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 90 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 90 = 405 . total area = 90 + 405 = 495 answer : d ."
Answer: d
Python program:
a = 90 * 3
b = a / 2
c = b * 3
d = 90 + c
Problem: what is the difference between the place value of 2 in the numeral 7669 ?
Options: a ) 160 , b ) 165 , c ) 180 , d ) 190 , e ) 540
Rationale: answer : option ' e ' 600 - 60 = 540
Answer: e
Python program:
a = 2 * 3
b = a * 100
c = 2 * 3
d = c * 10
e = b - d
Problem: machine a and machine b are each used to manufacture 770 sprockets . it takes machine a 10 hours longer to produce 770 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: "machine b : takes x hours to produce 770 sprockets machine a : takes ( x + 10 ) hours to produce 770 sprockets machine b : in 1 hour , b makes 770 / x sprockets machine a : in 1 hour , a makes 770 / ( x + 10 ) sprockets equating : 1.1 ( 770 / ( x + 10 ) ) = 770 / x 847 / ( x + 10 ) = 770 / x 847 x = 770 x + 7700 77 x = 7700 x = 100 a makes 770 / ( 110 ) = 7 sprockets per hour answer : b"
Answer: b
Python program:
a = 10 * 770
b = 100 + 10 
c = b / 100
d = a * c
e = 100 + 10 
f = e / 100
g = 770 * f
h = g - 770
i = d / h
j = 770 / i
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 370 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 100 , d ) rs . 350 , e ) none of these
Rationale: z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 740 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 37 3.7 z = 370 , z = 100 answer : . c
Answer: c
Python program:
a = 25 / 100
b = 1 + a 
c = 20 / 100
d = 1 + c 
e = b * d
f = 20 / 100
g = 1 + f 
h = e + g 
i = h + 1 
j = 370 / i
Problem: village x has a population of 70000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 14 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 70000 - 1200 p = 42000 + 800 p 2000 p = 28000 p = 14 answer is a ."
Answer: a
Python program:
a = 70000 - 42000
b = 800 + 1200 
c = a / b
Problem: a , b , c can do a piece of work in 11 days , 20 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by b and c on alternate days ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: a + b 1 day work = 1 / 11 + 1 / 20 = 31 / 220 a + c 1 day work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 days = 31 / 220 + 6 / 55 = 55 / 220 = 1 / 4 1 / 4 work is done by a in 2 days whole work will be done in 2 * 4 = 8 days answer is c
Answer: c
Python program:
a = 1 / 11
b = 1 / 20
c = a + b 
d = 1 / 11
e = 1 / 55
f = d + e 
g = c + f 
h = 2 / g
Problem: a group of men decided to do a work in 8 days , but 3 of them became absent . if the rest of the group did the work in 10 days , find the original number of men ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 25 , e ) 18
Rationale: "original number of men = 3 * 10 / ( 10 - 8 ) = 15 answer is a"
Answer: a
Python program:
a = 3 * 10
b = 10 - 8
c = a / b
Problem: x , y , and z are different prime numbers . the product x ^ 2 * y ^ 2 * z ^ 2 is divisible by how many different positive numbers ?
Options: a ) 9 , b ) 18 , c ) 27 , d ) 36 , e ) 45
Rationale: "the exponents of x ^ 2 * y ^ 2 * z ^ 2 are 2 , 2 , and 2 . the number of factors is ( 2 + 1 ) ( 2 + 1 ) ( 2 + 1 ) = 27 the answer is c ."
Answer: c
Python program:
a = 2 ** 4
b = a - 4