2013 Gauss 8 Problem 25

At the beginning of the winter, there were at least 66 students registered in a ski class. After the class started, eleven boys transferred into this class and thirteen girls transferred out. The ratio of boys to girls in the class was then 1:1. Which of the following is not a possible ratio of boys to girls before the transfers?

\textbf{(A)}\ 4:7\quad \textbf{(B)}\ 1:2\quad \textbf{(C)}\ 9:13\quad \textbf{(D)}\ 5:11\quad \textbf{(E)}\ 3:5

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 Gauss contests here.