5 digit number $a6a41$ divisible by 9 In the 5-digit number $a6a41$ each of the a's represent the same number. If the number is divisible by 9, what is the digit represented by $a$? I first approached this by saying $$2a + 11$$ since it's divisible by 9. I got stuck because I didn't know what to equate it to. So I randomly said $2a + 11 = 27$ and then I got $ a = 8$ and indeed the number was divisble by 9. My question is, how do I know what to equate it to?

Well if $(2a + 11)$ is a multiple of $9$, then

$$(2a + 11) = 0\ (mod \ 9)$$

so $$(2a + 2) = 0\ (mod\ 9)$$

and since $(2a + 2)$ is even, it follows that

$$(a + 1) = 0\ (mod\ 9)$$