Josanna's test scores to date are $90, 80, 70, 60,$ and $85$. Her goal is to raise here test average at least $3$ points with her next test. What is the minimum test score she would need to accomplish this goal?
$\textbf{(A)}\ 80 \qquad\textbf{(B)}\ 82 \qquad\textbf{(C)}\ 85 \qquad\textbf{(D)}\ 90 \qquad\textbf{(E)}\ 95$
The average of her current scores is $77$. To raise it $3$ points, she needs an average of $80$, and so after her $6$ tests, a sum of $480$. Her current sum is $385$, so she needs a $480 - 385 = \boxed{\mathrm{(E) \ } 95}$