Question

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

• A. 3
• B. 4
• C. 9
• D. 11

Answer 1

The correct option is D 11

Let the 2- digit number be ab.
General form of ab is 10a + b.

If we reverse the digits of ab, the new number is ba.
General form of ba is 10b + a.

Sum of the two-digit number and the number obtained by reversing its digits
= (10a + b) + (10b + a)
= 11a + 11b
= 11 (a + b)

Therefore, this sum is always divisible by 11.