2018 Pascal Problem 24

In Mrs. Warner's class, there are 30 students. Strangely, 15 of the students have a height of 1.60 m and 15 of the students have a height of 1.22 m. Mrs. Warner lines up n students so that the average height of any four consecutive students is greater than 1.50 m and the average height of any seven consecutive students is less than 1.50 m. What is the largest possible value of n?

\textbf{(A)}\ 8\quad \textbf{(B)}\ 12\quad \textbf{(C)}\ 11\quad \textbf{(D)}\ 9\quad \textbf{(E)}\ 10

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 Pascal contests here.