2013 Fermat Problem 15

The cookies in a cookie jar contain a total of 100 raisins. All but one of the cookies are the same size and contain the same number of raisins. One cookie is larger and contains one more raisin than each of the others. The number of cookies in the jar is between 5 and 10, inclusive. How many raisins are in the larger cookie?

\textbf{(A)}\ 10\quad \textbf{(B)}\ 11\quad \textbf{(C)}\ 20\quad \textbf{(D)}\ 17\quad \textbf{(E)}\ 12

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 Fermat contests here.