2021 Pascal Problem 19

Suppose that R, S and T are digits and that N is the four-digit positive integer 8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones (units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the following conditions are all true:

- The two-digit integer 8R is divisible by 3. - The three-digit integer 8RS is divisible by 4. - The four-digit integer 8RST is divisible by 5. - The digits of N are not necessarily all different.

The number of possible values for the integer N is

\textbf{(A)}\ 8\quad \textbf{(B)}\ 16\quad \textbf{(C)}\ 12\quad \textbf{(D)}\ 10\quad \textbf{(E)}\ 14

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.