1982 AHSME Problem 28

A set of consecutive positive integers beginning with 1 is written on a blackboard. One number is erased. The average (arithmetic mean) of the remaining numbers is 35\frac{7}{17}. What number was erased?

\text{(A)} 6\qquad \text{(B)}7 \qquad \text{(C)}8 \qquad \text{(D)} 9\qquad \text{(E)}\text{cannot be determined}

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