Fill in the blanks to make the statements true.
The sum of a two-digit number and the number obtained by reversing the digits is always divisible by ………………… .

Question

Fill in the blanks to make the statements true. The sum of a two-digit number and the number obtained by reversing the digits is always divisible by ………………… .

Philoid · Accepted Answer

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.

Fill in the blanks to make the statements true.The sum of a two-digit number and the number obtained by reversing the digits is always divisible by ………………… .

Fill in the blanks to make the statements true.
The sum of a two-digit number and the number obtained by reversing the digits is always divisible by ………………… .