1991 AHSME Problem 15

A circular table has 60 chairs around it. There are N people seated at this table in such a way that the next person seated must sit next to someone. What is the smallest possible value for N?

\textbf{(A) } 15\qquad \textbf{(B) } 20\qquad \textbf{(C) } 30\qquad \textbf{(D) } 40\qquad \textbf{(E) } 58

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