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