1976 AHSME Problem 12

A supermarket has 128 crates of apples. Each crate contains at least 120 apples and at most 144 apples. What is the largest integer n such that there must be at least n crates containing the same number of apples?

\textbf{(A) }4\qquad \textbf{(B) }5\qquad \textbf{(C) }6\qquad \textbf{(D) }24\qquad \textbf{(E) }25

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.