2025 Fermat Problem 10

There are 186 students on a class trip. Each student is placed into exactly one of 50 groups. Each group has exactly 3 students or exactly 4 students. There are m groups that have 3 students and n groups that have 4 students. The value of m - n is

\textbf{(A)}\ -22\quad \textbf{(B)}\ -10\quad \textbf{(C)}\ -14\quad \textbf{(D)}\ -26\quad \textbf{(E)}\ -18

If there are no answer choices shown, enter a numerical answer.

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