2009 Gauss 8 Problem 25

A list of six positive integers p, q, r,\ \text{s}, t, u satisfies p < q < r < s < t < u. There are exactly 15 pairs of numbers that can be formed by choosing two different numbers from this list. The sums of these 15 pairs of numbers are:

25, 30, 38, 41, 49, 52, 54, 63, 68, 76, 79, 90, 95, 103, 117.

Which sum equals r + s?

\textbf{(A)}\ 52\quad \textbf{(B)}\ 54\quad \textbf{(C)}\ 63\quad \textbf{(D)}\ 68\quad \textbf{(E)}\ 76

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.