1992 AHSME Problem 23

Let S be a subset of \{1,2,3,...,50\} such that no pair of distinct elements in S has a sum divisible by 7. What is the maximum number of elements in S?

\text{(A) } 6\quad \text{(B) } 7\quad \text{(C) } 14\quad \text{(D) } 22\quad \text{(E) } 23

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