The sum of a two-digit number

Question:

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

Solution:

11

Let ab be any two-digit number, then the number obtained by reversing its digits is ba.

Now, ab + ba = (10a + b) + (10b + a) = 11a + 11b = 11(a + b)

Hence, ab + ba is always divisible by 11 and (a + b).

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