Question

If 21y5 is a multiple of 9, where y is a digit, what is the value of y?
[2 marks]
[NCERT - Ex 16.2, Q1]
[Divisibility by 9]

• A. 2
• B. 3
• C. 1
• D. 4

Answer 1

The correct option is C 1

Solution:
Given, $21y5$ is a multiple of $9$.

Therefore according to the divisibility rule of $9$, the sum of all the digits should be a multiple of $9$.

$\therefore 2+1+y+5=8+y$
[0.5 mark]

$8+y$ is a multiple of $9$ if its value is one of these numbers: $0,9,18,\mathrm{27...}$
[0.5 mark]

However, since $y$ is a single digit number, this sum can be $9$ only.
Therefore, $y=1$.
[1 mark]