Given$\displaystyle N = 10^{22} + 1$. If ‘N’ is divided by 11, then

Col A: The remainder

Col B: 2

This is a gre math Q. Would the fastest way to solve be to recognize that for every even power of 10, there is a remainder of 1 when product is divided by 11? Then the +1 on the end would make remainder 2. Any other ways to tackle this problem?