2007 AMC 8 Problem 15

Let a, b and c be numbers with 0 < a < b < c. Which of the following is impossible?

\textbf{(A)} \ a + c < b \qquad \textbf{(B)} \ a \cdot b < c \qquad \textbf{(C)} \ a + b < c \qquad \textbf{(D)} \ a \cdot c < b \qquad \textbf{(E)}\frac{b}{c} = a

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