2018 Pascal Problem 16

Reading from left to right, a sequence consists of 6 X's, followed by 24 Y's, followed by 96 X's. After the first n letters, reading from left to right, one letter has occurred twice as many times as the other letter. The sum of the four possible values of n is

\textbf{(A)}\ 72\quad \textbf{(B)}\ 54\quad \textbf{(C)}\ 135\quad \textbf{(D)}\ 81\quad \textbf{(E)}\ 111

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.