Question

The sum of a two-digit number and the number obtained by reversing the digits is always divisible by

• A. 3
• B. 4
• C. 9
• D. 11

Answer 1

The correct option is D

11

Consider the number ab

ab = 10$\times$a + b

Reverse of ab is ba.

ba = 10$\times$b + a

Sum of the number and its reverse is,

ab + ba = 10$\times$a + b + 10$\times$b + a

$\Rightarrow$ 10$\times$(a + b) + (a + b) = 11$\times$ (a + b)

It is always divisible by 11.