Question

The sum of a two-digit number and the number obtained by reversing the digits is always divisible by 1 and __.

• A. 11

Answer 1

The correct option is A 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
$=ab+ba$
$=(10\times a+b)+(10\times b+a)$
$=[10\times (a+b\left)\right]+(a+b)$
$=11\times (a+b)$

Therefore, it is always divisible by 11.