2003
Problem - 2828
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 $11$?
Answer
B
We note that $11\mid (q+r)\implies 11\mid(100q +r)$. This means $11\mid n$. There are $\boxed{8181}$ five-digit integers which are multiple of $5$.