Question

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

• A. 11
• B. 9
• C. 10

Answer 1

The correct option is A 11

Let the 2-digit number be 'ab'
The number 'ab' written in expanded form is 10a + b
If we interchange the digits of 'ab', the new number is 'ba'.
The number 'ba' written in expanded form is 10b + a

Sum of the number and its reverse is,
10a + b + 10b + a = 11a + 11b
= 11 (a + b)

$\therefore$ It is always divisible by 11.