2021 Cayley Problem 20

How many four-digit positive integers are divisible by both 12 and 20, but are not divisible by 16?

\textbf{(A)}\ 111\quad \textbf{(B)}\ 113\quad \textbf{(C)}\ 125\quad \textbf{(D)}\ 150\quad \textbf{(E)}\ 149

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 Cayley contests here.