A number has two digits. If the digits are interchanged and the new number is added to the original, the result is divisible by what?

Problem restatement
Let the original number be 10a + b. After swapping digits we get 10b + a. Show that their sum is always divisible by a fixed number.

Concept/Approach
Algebraic expression of the sum reveals a common factor.

Step-by-Step calculation
(10a + b) + (10b + a) = 11(a + b)Thus the sum is a multiple of 11

Common pitfalls
Guessing 9 (digit-sum test) or 10 (last digit 0) without algebra; neither is generally true here.

Final Answer
11