A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n$?
$\textbf{(A) } 3\qquad \textbf{(B) } 4\qquad \textbf{(C) } 5\qquad \textbf{(D) } 6\qquad \textbf{(E) } 7$
Since there are $n^2$ little [faces](https://artofproblemsolving.com/wiki/index.php/Face) on each face of the big wooden [ cube](https://artofproblemsolving.com/wiki/index.php/Cube_(geometry)), there are $6n^2$ little faces painted red. 
Since each unit cube has $6$ faces, there are $6n^3$ little faces total. 
Since one-fourth of the little faces are painted red, 
$\frac{6n^2}{6n^3}=\frac{1}{4}$
$\frac{1}{n}=\frac{1}{4}$
$n=\boxed{\textbf{(B) }4}$