# Number system questions

Numbers are a powerful tool to measure an individual's mental aptitude. Aptitude questions on numbers are designed to test your knowledge of basic arithmetic operations, such as addition, subtraction, multiplication, division, finding squares and square roots, and so on. To ace such questions, you must be good at mental arithmetic and have a good command of the basic rules of number operations. To get familiar with aptitude questions related to numbers, Here are some of the most common questions and answers.

1. If a nine-digit number 985x3678y is divisible by 72, then the value of $4x-3y$ is

• Here, $78y$ should be a multiple of 8.
• $y=4$
• $9+8+5+x+3+6+7+8+y=$multiple of 9
• $x= 4$
• $4x-3y=4$
• Hence, option B is the correct answer.
1. If the number 4A306768B2 is divisible by both 8 and 11, then the smallest possible values of A and B will be:

Number 4A306768B2 is divisible by both 8 and 11.

Divisibility by 8:

A number is divisible by 8 if number formed using last three digits of the given number is divisible by 8.

Last three digits of 4A306768B2 = 8B2

By hit and trial we can say that 832 is divisible by 8.

Then possible smallest value of B = 3

Hence, Resultant number = 4A30676832

Divisibility by 11:

Sum of digits at odd place – Sum of digits at even place = 11k , where k can be any whole number

Consider: 4A30676832

⇒ (22) – (17 +A) = 0

⇒ 5 – A = 0

⇒ A = 5

Hence, A = 5 and B = 3

1. The sum of the two digits of a two-digit number is 13 and the number obtained by interchanging the two digits is 27 less than the original number. What is the original number?

Possible numbers $= 94, 85, 76, 67, 58, 49$

$94- 49 = 45$

$85- 58= 27$

$76- 67 = 9$

1. If a nine-digit number 389x 3678 y is divisible by 72 , then the value of $\sqrt{6 x+7 y}$ will be:

389x 6378 y
Divisibility by 72= Divisible by 8 and 9
78 y if y=4 the last
3 -digit is divisible by 8
and if sum of digit is divisible by 9 if x=6
\begin{aligned} &\therefore \sqrt{6 x+7 y}\\ &\sqrt{6\times 6+7 \times 4}\\ &\sqrt{36+28}\\ &\sqrt{64}\\ &= 8 \end{aligned}

1. If a nine-digit number 785x3678y is divisible by 72, then the value of (x + y) is:

For a number to be divisible by 72 i.e.,(8 × 9) it must be divisible by 8 and 9 both.

For the number to be divisible by 8, last 3 digits must be divisible by 8

78y = (700 + 80 + y) = 780 + y

When we divide 780 by 8 the remainder = 4

For y + 4 divisible by 8, y should be equal to 4.

For the number to be divisible by 9, sum of the digits should be divisible by 9

7+ 8 + 5 + x + 3 + 6 + 7 + 8 + 4 = 48 + x

Nearest number divisible by 9 after 48 = 54

So x = 54 -48 = 6

Therefore, x + y = 6 + 4 = 10