AMC 10 2015a Problem 13

Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have? $\textbf{(A) }3 \textbf{(B) }4 \textbf{(C) }5 \textbf{(D) }6 \textbf{(E) }7$