# Arithmetic Aptitude :: Problems on Numbers

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In the reading room of a library, there are 23 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?

A8

B15

C16

D17

Explanation:

so, 8 spots have different readers.
remainings are 23-8= 15. (at least)

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The difference between two no is 9 and the product of the two is 14.What is the square of their sum?

A120

B130

C137

D145

Explanation:

let's two number are x and y (x>y)

Difference (x-y) = 9  ------- (1)

product x*y = 14 ----------- (2)

from eq. 1

(x-y)^2 = x^2 y^2 - 2xy = 81

=> x^2 y^2 = 81  2*14 = 81 28 = 109------------(3)

some of their Square  (x y)^2 = x^2 y^2 2xy

put the value from eq. 3

(x y)^2 = 109 2*14 = 109 28 = 137  (Ans)

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How many 9 digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4 if the repetition is allowed?

A57

B56

C59

D58

Explanation:

Here is no explanation for this answer

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A sporting goods store ordered an equal number of white and yellow balls. The tennis ball company delivered 45 extra white balls, making the ratio of white balls to yellow balls 1/5 : 1/6. How many white tennis balls did the store originally order for?

A450

B270

C225

DNone of these

Explanation:

initial the ratio is w/y =1 so w=y

then w+45/y=6/5----------(1)

put eq (1) w=y

then after solving we will be able to found out that w=265

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There are 100 wine glass. I offered my servant to 3 paise for every broken glass to be delivered safely and forefeit 9 paise for eyery glass broken. At end of day he received Rs.2.40. how many glass did he break?

A3

B4

C5

D6

Explanation:

Here is no explanation for this answer

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Raj writes a number. He sees that the number of two digits is 9 less than 3 times the number. If the number is increased by 45, the result is the same as the number formed by reversing the digit. Find the number.

A35

B27

C36

D49

Explanation:

Here is no explanation for this answer

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In the equation A + B + C + D + E = FG where FG is the two digit number whose value is 10F + G and letters A, B , C , D , E, F and G each represent different digits. If FG is as small as possible. What is the value of G?

A4

B2

C1

D3

Explanation:

FG is as large as possible and all the 7 numbers should be different.
By trial and Error method,
9 + 8 + 7 + 6 + 5 = 35....5 is getting repeated twice.
9 + 8 + 7 + 6 + 4 = 34...4 is getting repeated
9 + 8 + 7 + 5 + 4 = 33...3 repeats
9 + 8 + 6 + 5 + 4 = 32
None of the numbers repeat in the above case and 32 is the maximum number FG can have. The value of G is 2.

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Three non negative numbers, X, Y and Z are such that the mean is M and the median is 5. If M is 10 more than the smallest number and 15 less than the biggest number, find the value of X+Y+Z.

A15

B5

C20

D30

Explanation:

Given median=5,so y=5
x+y+z/3=10+z ---(1)
x+y+z/3=x-15 ---- (2)
By solving eq. (1) and (2) we get,
x=25,y=5,z=0
so x+y+z=30

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A number is divided by 5,2 and 3 successively in order to get remainders of 0,1, and 2 respectively. What will be the remainders when the same number is divided by 2,3 and 5 respectively?

A1,0,4

B1,2,3

C1,2,0

D1,0,2

Explanation:

when divided by 5, quotient is 11 and remainder is zero.
when 11 is divided by 2, quotient is 5 and remainder is 1.
when 5 is divided by three, quotient is 1 and remainder is 2.

when same operation is applied on 55 i.e. successively divided by 2,3,5..
we get remainders as 1,0,4 successively.

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Choose the correct option.

A company rented a machine for Rs.700/- a month. Five years later the treasurer calculated that if the company had purchased the machine and paid Rs.100/- monthly maintenance charge, the company would have saved Rs.2000/-. What was the purchase price of the machine?

ARs 24500

BRs 34500

CRs 30500

DRs 34000

Explanation:

Lets assume the price of the machine = x rupee
5 year maintenance charge = 100*60 = 6000
so total investment = x+6000
now total rental charges for five year = 700*60 = 42000
so according to given condition 42000-x-6000 = 2000 so x = 34000

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