Question

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

Answer 1

Step-by-step explanation:

Let x and y be the digits in a two-digit number A = xy.

Reversing the digits, we get B = yx.

⇒ Sum of the digits in A is (10x + y).

⇒ Sum of the digits in B is (10y + x).

⇒ Sum S = A + B = (10x + y) + (10y + x).

⇒ S = 10x + x + 10y + y = 11x + 11y = 11(x + y)

⇒ The number is divisible by 11.

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Answer 2

11

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