AMC 8 2007 Problem 15

Let $a, b$ and $c$ be numbers with $0 < a < b < c$. Which of the following is impossible? $\mathrm{(A)} \ a + c < b \mathrm{(B)} \ a \cdot b < c \mathrm{(C)} \ a + b < c \mathrm{(D)} \ a \cdot c < b \mathrm{(E)}\frac{b}{c} = a$