2011 AMC 10A Problem 10

A majority of the $30$ students in Ms. Deameanor’s class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than $1$. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was $$17.71$. What was the cost of a pencil in cents?

$\textbf{(A)}\,7 \qquad\textbf{(B)}\,11 \qquad\textbf{(C)}\,17 \qquad\textbf{(D)}\,23 \qquad\textbf{(E)}\,77$