1975 AHSME Problem 9

Let a_1, a_2, \ldots and b_1, b_2, \ldots be arithmetic progressions such that a_1 = 25, b_1 = 75, and a_{100} + b_{100} = 100. Find the sum of the first hundred terms of the progression a_1 + b_1, a_2 + b_2, \ldots

\begin{array}{l} \textbf{(A)}\ 0 \qquad \textbf{(B)}\ 100 \qquad \textbf{(C)}\ 10,000 \qquad \textbf{(D)}\ 505,000 \qquad \\ \textbf{(E)}\ \text{not enough information given to solve the problem} \end{array}

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