Very tricky question. The key is noticing that $s$, $t$, and $u$ don't have to be integers. Also, this is a must question, meaning that if even one selection for $s$, $t$, and $u$ provides a non-integer, the answer choice is incorrect. The goal would be to find that incorrect combination of $s$, $t$, and $u$.

A. $stu$

$s = t = u = \frac{1}{2}$

$stu = \frac{1}{2}*\frac{1}{2}*\frac{1}{2}$
$stu = \frac{1}{8}$

In this case, $stu$ is not an integer.
Therefore A is not the answer.


B. $\frac{3s^2t^2}{u^2}$

We know that $\frac{st}{u}$ is an integer, so $\frac{s^{2}t^{2}}{u^{2}}$ must be an integer as well. Multiplying this by 3 will also keep it as an integer.

B looks like the answer, but let's check the rest.


C. $\frac{su}{t}$

Let $s = 2$, $u = \frac{1}{2}$, and $t = 3$

$\frac{st}{u} = \frac{2*3}{0.5} = 2*3*2 = 12$

So we know that our selection of values for $s$, $t$, $u$ produce an integer. But what happens when we rearrange the variables?

$\frac{su}{t} = \frac{2*0.5}{3} = \frac{1}{3}$

In this case, $\frac{su}{t}$ is not an integer.
Therefore, C is not the answer.


Using the same logic from C, we can eliminate D and E.


Therefore, our answer is B