AMC 12 2003a Problem 18

Let $n$ be a $5$-digit number, and let $q$ and $r$ be the quotient and the remainder, respectively, when $n$ is divided by $100$. For how many values of $n$ is $q+r$ divisible by $11$?

$\mathrm{(A) \ } 8180 \mathrm{(B) \ } 8181 \mathrm{(C) \ } 8182 \mathrm{(D) \ } 9000 \mathrm{(E) \ } 9090$