SAT Counter-Examples

Algebra Level 3

If $p$ is a prime number, which of the following must be true?

$\begin{array}{r r l} &\text{I.} & p\ \text{is odd.}\\ &\text{II.} & p\ \text{is not divisible by}\ 6.\\ &\text{III.} & p\ \text{is not divisible by}\ 7.\\ \end{array}$

(A) $\ \$ I only
(B) $\ \$ II only
(C) $\ \$ I and II only
(D) $\ \$ I and III only
(E) $\ \$ II and III only