Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of $6$. Which of the following integers cannot be the sum of the two numbers?
$\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9$
First, figure out all pairs of numbers whose product is 6. Then, using the process of elimination, we can find the following: 
$\textbf{(A)}$ is possible: $2\times 3$
$\textbf{(C)}$ is possible: $1\times 6$
$\textbf{(D)}$ is possible: $2\times 6$
$\textbf{(E)}$ is possible: $3\times 6$
The only integer that cannot be the sum is $\boxed{\textbf{(B)\ 6}}.$
-ILoveMath31415926535 & countmath1 & Nivaar