2002 Gauss 8 Problem 24

Veronica has 6 marks on her report card.

The mean of the 6 marks is 74.

The mode of the 6 marks is 76.

The median of the 6 marks is 76.

The lowest mark is 50.

The highest mark is 94.

Only one mark appears twice and no mark appears more than twice.

Assuming all of her marks are integers, the number of possibilities for her second lowest mark is

\textbf{(A)}\ 17\quad \textbf{(B)}\ 16\quad \textbf{(C)}\ 25\quad \textbf{(D)}\ 18\quad \textbf{(E)}\ 24

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.