2020 Cayley Problem 19

A multiple choice test has 10 questions on it. Each question answered correctly is worth 5 points, each unanswered question is worth 1 point, and each question answered incorrectly is worth 0 points. How many of the integers between 30 and 50, inclusive, are *not* possible total scores?

\textbf{(A)}\ 2\quad \textbf{(B)}\ 3\quad \textbf{(C)}\ 4\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 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 Cayley contests here.