Are all 4-digit palindromes divisble by 11?

Answer 1

-7

Answer 2

Yes

To check for divisibility by 11 take the number one digit at a time from the right hand end alternatively subtracting and adding them. If this result is 0 or divisible by 11, then so is the original number.

A 4 digit palindrome is of the form ABBA (where a is any digit, b is any digit), so applying the test:

a - b + b - a = 0

(the 'a's cancel, so do the 'b's) so the original number (abba) is divisible by 11.