2011 AMC 10A Problem 10

Let $p$ be the number of pencils that each student bought, $s$ be the number of students that bought pencils, and $c$ be the cost of a pencil. We have that $$psc = 1771 = 7 \cdot 11 \cdot 23.$$ We also have the following restrictions: $$30 \geq s \gt 15, p \gt 1, c \gt p.$$ From the above prime factorization, we have that $s = 23$ is the only value that satisfies the conditions. Finally, we get that $p = 7$ and $c = 11$ are the only remaining values that satisfy the other conditions. Thus, B is the correct answer.