euclaise/mathqa_programs huggingface dataset:
Problem: guy drives 60 miles to attend a meeting . halfway through , he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half . his average speed for the entire trip is 30 miles per hour . guy drives on average how many miles per hour during the first half of the way ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 24 , e ) 40
Rationale: let x be the average speed for 1 st half of the distance . then the average speed for 2 nd half of the distance will be x + 16 avg speed = total distance / total time 30 = 60 / { ( 30 / x ) + ( 30 / ( x + 16 ) ) } solving we get x ^ 2 - 14 x - 240 = 0 x = - 10 or 24 x cant be negative hence x = 24 answer : d
Answer: d
Python program:
a = 16 * 30
b = a / 2
c = 3 * 2
d = 60 / c
e = b / d
Problem: 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 18 men , 4 women and 10 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 4 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 18 men ’ s 1 day ’ s work = 1 × 18 / 96 = 3 / 16 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 18 men + 4 women + 10 children ) ’ s 1 day ’ s work = 3 / 16 + 1 / 48 + 1 / 24 = 1 / 4 the required no . of days = 4 days answer : option d"
Answer: d
Python program:
a = 24 * 10
b = 1/(a)
c = 10 * b
d = 12 * 8
e = 1/(d)
f = e * 10
g = 48 * 4
h = 1/(g)
i = h * 4
j = f + i 
k = c + j 
l = 1/(k)
Problem: 15 years hence , rohan will be just 4 times as old as he was 15 years ago . how old is rohan at present ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: let the present age of rohan be x years then , given : x + 15 = 4 ( x - 15 ) x = 25 answer : b
Answer: b
Python program:
a = 4 * 15
b = a + 15 
c = 4 - 1
d = b / c
Problem: dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 54 of gas ?
Options: a ) 236 , b ) 354 , c ) 432 , d ) 512 , e ) 670
Rationale: 54 / 4 = 13.5 gallons 13.5 * 32 = 432 miles the answer is c .
Answer: c
Python program:
a = 54 * 32
b = a / 4
Problem: if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 3 ø 1 ) ø 1 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "3 ø 1 = 2 ^ 3 / 2 ^ 1 = 4 4 ø 1 = 2 ^ 4 / 2 = 8 the answer is c ."
Answer: c
Python program:
a = 2 ** 3
b = 2 ** 2
c = a / b
d = 2 ** c
e = 2 ** 1
f = d / e
Problem: what will be the remainder when ( 67 ^ 67 ) + 67 is divided by 68 ?
Options: a ) 52 , b ) 62 , c ) 66 , d ) 68 , e ) 72
Rationale: "x ^ n + 1 will be divisible by x + 1 only when n is odd 67 ^ 67 + 1 will be divisible by 67 + 1 ( 67 ^ 67 + 1 ) + 66 , when divided by 68 will give 66 as remainder answer is c"
Answer: c
Python program:
a = 2 ** 0
Problem: walking at the rate of 5 kmph a man cover certain distance in 5 hr . running at a speed of 15 kmph the man will cover the same distance in .
Options: a ) 12 min , b ) 36 min , c ) 40 min , d ) 48 min , e ) 60 min
Rationale: distance = speed * time 5 * 5 = 25 km new speed = 15 kmph therefore time = 25 / 15 = 5 / 3 = 36 min answer : b
Answer: b
Python program:
a = 5 * 5
b = 15 / a
c = b * const_60
Problem: subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 18 pages .
Options: a ) 8 , b ) 10 , c ) 2 , d ) 14 , e ) 16
Rationale: subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 5 / 2.5 ) = 2 hrs answer : c
Answer: c
Python program:
a = 300 / 40
b = 50 / 10
c = a - b
d = math.floor(c)
Problem: a pair of articles was bought for $ 720 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 300 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600
Rationale: "s . p . of each of the article = 720 / 2 = $ 360 let m . p = $ x 90 % of x = 360 x = 360 * 100 / 90 = $ 400 answer is d"
Answer: d
Python program:
a = 100 - 10
b = 720 / 2
c = a * b
d = c / 100
Problem: average expenditure of a person for the first 3 days of a week is rs . 330 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 330 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 330 + rs . 40 = rs . 370 correct option : b"
Answer: b
Python program:
a = 420 - 330
b = 4 * a
c = 3 + 4 
d = b / c
e = 330 + d
Problem: set x consists of 10 integers and has median of 30 and a range of 30 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 40 , 50 this is possible . hence it is the greatest such number . answer ( e )"
Answer: e
Python program:
a = 30 + 30
Problem: in a class there are 55 pupil , out of them 10 are in debate only and 18 in singing only . then how many in both ?
Options: a ) 132 , b ) 26 , c ) 17 , d ) 11 , e ) 12
Rationale: explanation : total pupil = 55 debate + singing = 10 + 18 = 28 the intersection for two = 55 â € “ 10 â € “ 28 = 17 play both games . answer : c
Answer: c
Python program:
a = 55 - 18
b = a - 10
c = b - 10
Problem: in a hostel , the number of students decreased by 8 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 9.4 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.92 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.92 * 1.2 ) = > f ( new ) = 0.906 f therefore the new cost of food must be 90.6 % of the old cost , or the cost of food must decrease by 9.4 % answer : e"
Answer: e
Python program:
a = 100 * 100
b = 100 - 8
c = 100 + 20 
d = b * c
e = a / d
f = 1 - e
g = f * 100
Problem: the total circumference of two circles is 88 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 5.7 , b ) 6.0 , c ) 6.7 , d ) 9.7 , e ) 14.0
Rationale: "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 88 where 2 r = r thus : 2 π r + 4 π r = 88 6 π r = 88 r = approx 4.7 π r + 2 r π = 88 3 π r = 88 r = approx 9.3 r + r = approx 14.0 answer : e"
Answer: e
Python program:
a = 88 / 3
b = a / 3
c = 88 / 3
d = c * 2
e = d / 3
f = b + e 
g = f / 2
Problem: how many multiples of 2 are there between 101 and 999 ?
Options: a ) 250 , b ) 440 , c ) 510 , d ) 575 , e ) 449
Rationale: "2 multiples are 102 , 104,106 , - - - - - - - - - , 994 , 996,998 it should be mentioned whether 1 and 89 are inclusive . the answer is ( 998 - 102 ) / 2 + 1 = 449 answer is e"
Answer: e
Python program:
a = 999 - 101
b = a / 2
c = b + 1
Problem: find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5 .
Options: a ) 128 , b ) 197 , c ) 127 , d ) 182 , e ) 091
Rationale: "explanation : let ' n ' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5 . required number = ( lcm of 13 and 16 ) - ( common difference of divisors and remainders ) = ( 208 ) - ( 11 ) = 197 . answer : b"
Answer: b
Python program:
a = 13 * 16
b = 10 + 1 
c = a - b
Problem: how much is 80 % of 40 is greater than 4 / 5 of 20 ?
Options: a ) 12 , b ) 27 , c ) 18 , d ) 16 , e ) 81
Rationale: "( 80 / 100 ) * 40 â € “ ( 4 / 5 ) * 20 32 - 16 = 16 answer : d"
Answer: d
Python program:
a = 80 / 100
b = 40 * a
c = 4 / 5
d = c * 20
e = b - d
Problem: if the price of sugar rises from rs . 10 per kg to rs . 13 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 23 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 13 = x = 77 kg . ∴ reduction in consumption = 23 % . answer c"
Answer: c
Python program:
a = 1 * 10
b = a / 13
c = 1 - b
d = c * 100
Problem: a train crosses a bridge of length 800 m in 45 seconds and a lamp post on the bridge in 15 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 m , c ) 400 m , d ) 800 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 800 + l ( while crossing the bridge ) time = 45 seconds i . e . speed = distance / time = ( 800 + l ) / 45 case - 2 : distance = l ( while passing the lamp post ) time = 15 seconds i . e . speed = distance / time = ( l ) / 15 but since speed has to be same in both cases so ( 800 + l ) / 45 = ( l ) / 15 i . e . 800 + l = 3 l i . e . 2 l = 800 i . e . l = 400 answer : option c"
Answer: c
Python program:
a = 45 - 15
b = 800 / a
c = b * 15
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 20 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 64.8 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 10 % discount = 810 price in day 3 after 20 % discount = 648 so , price in day 3 as percentage of the sale price on day 1 will be = 648 / 900 * 100 = > 72 % answer will definitely be ( e )"
Answer: e
Python program:
a = 20 / 100
b = 1 / 10
c = 1 - b
d = a / c
e = d * 100
f = e + 2
Problem: the sum of three consecutive numbers is 87 . the greatest among these three number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 31
Rationale: "let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 87 3 x = 84 x = 28 greatest number , ( x + 2 ) = 30 . answer : d"
Answer: d
Python program:
a = 87 + 1 
b = a / 2
Problem: a train travels 290 km in 4.5 hours and 400 km in 5.5 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 69 kmph , c ) 70 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 290 + 400 = 690 km thus , total speed = 10 hrs or , average speed = 690 / 10 or , 69 kmph . answer : b"
Answer: b
Python program:
a = 290 + 400 
b = 4 + 5 
c = a / b
Problem: what is the average of 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1 , 125,2140 , 2345 ?
Options: a ) 419 , b ) 551 , c ) 601 , d ) 620 , e ) 858.54
Rationale: "add 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1,125 , 2140 , 2345 grouping numbers together may quicken the addition sum = 9444 4959 / 11 = 858.54 . e"
Answer: e
Python program:
a = 12 + 13 
b = a + 14 
c = b + 510 
d = c + 520 
e = d + 530 
f = e + 12 
g = 3 + 4 
h = f / g
Problem: when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 3 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 3 / 10 , b ) 2 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5
Rationale: "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 3 ) ( 4 + 4 x ) or , x = 2 answer b"
Answer: b
Python program:
a = 6 - 4
b = a * 3
c = b - 4
d = 4 / c
Problem: how many integerskgreater than 100 and less than 800 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be six pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 6 * 10 = 60 hence b ."
Answer: b
Python program:
a = 100 / 10
b = 2 * 4
c = a * b
d = 100 / 10
e = c + d
Problem: local kennel has cats and dogs in the ratio of 5 : 10 . if there are 40 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 80 , b ) 70 , c ) 60 , d ) 50 , e ) 45
Rationale: "lets work with the data given to us . we know that there ratio of cats to dogs is 5 : 10 or cats 5 dogs 10 we can write number of cats as 5 x and number of dogs as 10 x and we know that 10 x - 5 x = 40 ( therefore 5 x = 40 = > x = 8 ) then # of dogs = 10 x 8 = 80 answer is a"
Answer: a
Python program:
a = 40 * 3
Problem: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 45 true ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "answer b ( a + b ) ( a - b ) = 45 3 cases for ( a + b ) , ( a - b ) 45 , 1 15 , 3 9 , 5 answer b"
Answer: b
Python program:
a = math.log(45)
b = 4 + 1 
c = math.log(b)
d = a / c
Problem: if the number 892 , 142,24 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 0 , e ) 5
Rationale: "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 892 , 142,24 x sum of digits at odd places = 8 + 2 + 4 + 2 + x = 16 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 4 = 16 ( ii ) ( i ) - ( ii ) = 16 + x - 16 = x - 0 hence x should be = 0 to make this a multiple of 11 ( 0 ) option d"
Answer: d
Python program:
a = 3 * 10
b = a + 1 
c = b * 2
d = c * 4
e = d * 11
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio w of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore w , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
Answer: b
Python program:
a = 3 + 2 
b = 3 / a
c = 20 - 10
d = b * c
e = d + 10 
f = e / 20
g = 20 - 10
h = f * g
i = h + 10 
j = 3 + 2 
k = 2 / j
l = 20 - 10
m = k * l
n = m / 20
o = 20 - 10
p = n * o
q = i / p
Problem: of the families in city x in 1992 , 60 percent owned a personal computer . the number of families in city x owning a computer in 1993 was 50 percent greater than it was in 1992 , and the total number of families in city x was 3 percent greater in 1993 than it was in 1992 . what percent of the families in city x owned a personal computer in 1993 ?
Options: a ) 68.99 % , b ) 66.55 % , c ) 91.23 % , d ) 77.77 % , e ) 87.37 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 60 number of families owning computer in 1998 = 60 * 150 / 100 = 90 number of families in 1998 = 103 the percentage = 90 / 103 * 100 = 87.37 % . answer : e"
Answer: e
Python program:
a = 50 + 100 
b = a * 60
c = b / 100
d = 100 + 3 
e = c / d
f = 100 * e
Problem: find the value of ( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.00 ) / ( √ 0.49 ) is
Options: a ) 2.65 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63
Rationale: ( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.00 ) / ( √ 0.49 ) 11 / 9 + 10 / 7 = > 2.65 answer is a
Answer: a
Python program:
a = math.sqrt(1)
b = math.sqrt(0)
c = a / b
d = math.sqrt(1)
e = math.sqrt(0)
f = d / e
g = c + f
Problem: louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louis have to pay each month ?
Options: a ) 333 , b ) 383 , c ) 402 , d ) 433 , e ) 483
Rationale: after 1 st month : ( 1000 ) ( 1.1 ) - x = 1100 - x after 2 nd month : ( 1100 - x ) ( 1.1 ) - x = 1210 - 2.21 x after 3 rd month : ( 1210 - 2.21 x ) ( 1.1 ) - x = 1331 - 3.31 x now , the amount after the last payment in 3 rd month must bring the total to 0 . hence : 1331 - 3.31 x = 0 x = 1331 / 3.31 = 402.11 the answer is c
Answer: c
Python program:
a = 1000 * 3
b = 10 / 100
c = a * b
d = 1000 * 3
e = 10 / 100
f = d * e
g = 10 / 100
h = f * g
i = c + h 
j = i + 1 
k = 1000 + j 
l = 1000 * 3
m = 10 / 100
n = l * m
o = 1000 * 3
p = 10 / 100
q = o * p
r = 10 / 100
s = q * r
t = n + s 
u = t + 1 
v = u / 100
w = k / v
Problem: if the perimeter of a rectangular garden is 600 m , its length when its breadth is 200 m is ?
Options: a ) 299 m , b ) 777 m , c ) 200 m , d ) 100 m , e ) 128 m
Rationale: "2 ( l + 200 ) = 600 = > l = 100 m answer : d"
Answer: d
Python program:
a = 600 / 2
b = a - 200
Problem: rs 3000 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 400 , b ) s 280 , c ) s 300 , d ) s 350 , e ) s 310
Rationale: explanation : average rate = ( 144 / 3000 ) * 100 = 4.8 ratio = 2 : 18 so , first part = ( 2 / 20 ) * 3000 = rs 300 . answer : c
Answer: c
Python program:
a = 5 / 100
b = 3000 * a
c = b - 144
d = 5 / 100
e = 3 / 100
f = d - e
g = c / f
Problem: a machine , working at a constant rate , manufactures 18 dies in 25 minutes . how many dies does it make in 1 hr 15 min ?
Options: a ) 55 , b ) 53 , c ) 54 , d ) 52 , e ) 50
Rationale: "change 1 hr 15 min to 75 min . for this , we need to set up a simple proportion of dies per time 18 / 25 = s / 75 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . we can cancel the common factor of 25 in the two denominators . 18 / 1 = s / 3 s = 3 * 18 s = 54 the machine would be 54 dies in 1 hr 15 min . answer : c"
Answer: c
Python program:
a = 1 * const_60
b = a + 15 
c = b / 25
d = c * 18
Problem: a room 5.44 m long and 3.74 m broad is to be paved with square tiles . the least number of square tiles required to cover the floor is :
Options: a ) 176
b ) 192
c ) 184
d ) 162
e ) 172
Rationale: area of the room = 544 * 374 sq . cm size of largest square tile = hcf of 544 cm & 374 cm area of 1 tile = 34 * 34 sq . cm therefore , number of tiles = ( 544 * 374 / 34 * 34 ) = 176 answer : a
Answer: a
Python program:
a = 5 * 44
b = 3 * 74
c = a * b
d = 10 + 10 
e = d + 10 
f = e + 4 
g = 10 + 10 
h = g + 10 
i = h + 4 
j = f * i
k = c / j
Problem: find the maximum value of n such that 50 ! is perfectly divisible by 2520 ^ n
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: 2520 = 2 ^ 3 * 3 ^ 2 * 5 * 7 here , 7 is the highest prime , so find the no . of 7 ' s in 50 ! only no . of 7 ' s in 50 ! = [ 50 / 7 ] + [ 50 / 7 ^ 2 ] = 7 + 1 = 8 answer : b
Answer: b
Python program:
a = 50 / 10
b = a + 3
Problem: in two triangle , the ratio of the areas is 4 : 3 and that of their heights is 3 : 4 the ratio of their bases is
Options: a ) 16 : 9
b ) 9 : 16
c ) 9 : 12
d ) 16 : 12
e ) 4 : 12
Rationale: explanation : given a 1 / a 2 = 4 / 3 , h 1 / h 2 = 3 / 4 also , we know that a 1 / a 2 = ( 1 / 2 × b 1 × h 1 ) / ( 1 / 2 × b 2 × h 2 ) on substituting in above equation , we get b 1 / b 2 = 16 / 9 therefore b 1 : b 2 = 16 : 9 answer : option a
Answer: a
Python program:
a = 4 * 4
b = 3 * 3
c = a / b
Problem: a number exceeds by 30 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 48
Rationale: "x – 3 / 8 x = 30 x = 48 answer : e"
Answer: e
Python program:
a = 30 * 8
b = 8 - 3
c = a / b
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 520 . if one of the numbers is 480 , then the other is :
Options: a ) 13 , b ) 18 , c ) 21 , d ) 24 , e ) 38
Rationale: "other number = ( 12 x 520 ) / 480 = 13 . answer : a"
Answer: a
Python program:
a = 12 * 480
Problem: the radius of a cylinder is 12 m , height 21 m . the lateral surface area of the cylinder is :
Options: a ) 1584
b ) 1854
c ) 1458
d ) 1485
e ) none of them
Rationale: lateral surface area = 2 π rh = 2 × 22 / 7 × 12 × 21 = 44 × 36 = 1584 m ( power 2 ) answer is a .
Answer: a
Python program:
a = circumface * (
Problem: in an election between two candidates , the first candidate got 80 % of the votes and the second candidate got 240 votes . what was the total number of votes ?
Options: a ) 600 , b ) 900 , c ) 1200 , d ) 1500 , e ) 1800
Rationale: "let v be the total number of votes . 0.2 v = 240 v = 1200 the answer is c ."
Answer: c
Python program:
a = 240 * 100
b = 100 - 80
c = a / b
Problem: how many of the positive factors of 19 are not factors of 29 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 19 - 1 , 19 factors of 29 - 1 , 29 comparing both , we have three factors of 19 which are not factors of 29 - 19 , the answer is b"
Answer: b
Python program:
a = 29 / 19
Problem: a retailer buys a radio for rs 225 . his overhead expenses are rs 30 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 25 % , d ) 17.6 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 30 ) = 255 sell price = 300 gain = ( 45 / 255 ) * 100 = 17.6 % . answer : d"
Answer: d
Python program:
a = 225 + 30 
b = 300 / a
c = b * 100
d = c - 100