How to test (admitted) grad students before hiring them in your lab
What tricks/procedures do you use?
I am especially looking forward to King Solomon's cutting the baby in half type of creative solutions. Perhaps PI can ask the student to do an impossible task and see how long it takes before the student says he/she thinks it is impossible.

You're contemplating starting out a long-term, intense professional relationship with this person. &quot;Tricks&quot; like this are dishonest. Dishonesty is not a good way to begin such a relationship.
The situation is similar to an ordinary job interview. In a job interview, it's not just the employer who is judging the candidate. The candidate is also judging whether the employer is someone they'd want to work for. Manipulative interview techniques are a flashing red light telling the candidate that this is not an employer who respects his employees.
Another thing that a job candidate is looking for is an employer who will support him in his long-term professional growth, rather than treating him as a labor commodity who needs to be productive from day one. This holds even more for a student getting started in a PhD program; the reason universities claim that grad students are not employees is that they're supposed to be focused on learning, not on acting as cheap labor.
In the usual case where the student does a rotation in your group, that's the opportunity for each of you to see if you're a good fit for the other. It's meant to be an experience that helps the student to learn and grow, not one that produces a lot of research. Part of what the university is paying you to do is to provide these opportunities for these students to learn and grow. If, by the end of the rotation, the student has shown a lack of aptitude, then you've provided the service you're being paid to provide.