2018 Pascal Problem 25

P.J. starts with m = 500 and chooses a positive integer n with 1 \le n \le 499. He applies the following algorithm to m and n:

- P.J. sets r equal to the remainder when m is divided by n. - If r = 0, P.J. sets s = 0. If r > 0, P.J. sets s equal to the remainder when n is divided by r. - If s = 0, P.J. sets t = 0. If s > 0, P.J. sets t equal to the remainder when r is divided by s.

For example, when n = 8, P.J. obtains r = 4, s = 0, and t = 0. For how many of the positive integers n with 1 \le n \le 499 does P.J.'s algorithm give 1 \le r \le 15 and 2 \le s \le 9 and t = 0?

\textbf{(A)}\ 14\quad \textbf{(B)}\ 12\quad \textbf{(C)}\ 16\quad \textbf{(D)}\ 15\quad \textbf{(E)}\ 13

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.