2025 Gauss 8 Problem 15

The ages of three students are consecutive integers. Their mean (average) age is 13. A fourth student joins the group and the mean of their four ages is 14. How old is the fourth student?

\textbf{(A)}\ 15\quad \textbf{(B)}\ 18\quad \textbf{(C)}\ 16\quad \textbf{(D)}\ 14\quad \textbf{(E)}\ 17

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 Gauss contests here.