1971 AHSME Problem 16

After finding the average of 35 scores, a student carelessly included the average with the 35 scores and found the average of these 36 numbers. The ratio of the second average to the true average was

\textbf{(A) }1:1\qquad \textbf{(B) }35:36\qquad \textbf{(C) }36:35\qquad \textbf{(D) }2:1\qquad \textbf{(E) }\text{None of these}

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