Question 11
Compute the sum of all two-digit positive integers $x$ such that for all three-digit (base 10) positive integers $\underline{a}\ \underline{b}\ \underline{c}$, if $\underline{a}\ \underline{b}\ \underline{c}$ is a multiple of $x$, then the three-digit (base 10) number $\underline{b}\ \underline{c}\ \underline{a}$ is also a multiple of $x$.