2013 Gauss 8 Problem 21

An *arithmetic sequence* is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, 2, 4, 6, 8 and 1, 4, 7, 10 are arithmetic sequences.

In the grid shown, the numbers in each row must form an arithmetic sequence and the numbers in each column must form an arithmetic sequence. The value of x is

\begin{array}{|c|c|c|c|}\hline 5 & & & \\ \hline & & & 1211 \\ \hline & & 1013 & \\ \hline 23 & x & & \\ \hline\end{array}

\textbf{(A)}\ 17\quad \textbf{(B)}\ 619\quad \textbf{(C)}\ 515\quad \textbf{(D)}\ 446\quad \textbf{(E)}\ 793

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.