Test to evaluate a UX designer in product company

We are in the process of hiring a UX designer for our company, for which the primary skill set is:

  1. Ability to understand the product and its features
  2. Provide input on requirements
  3. Ask questions
  4. Come up with design solutions

We have a few candidates shortlisted for the testing round, but I find it difficult to come up with a test to evaluate candidates on the above mentioned skill set.

I was thinking of sharing some real UX design problems that we face in our organization but that would need a lot context which could be distracting for someone who doesn't know anything about our system.