This may be somewhat intuitive but I have been hearing various approaches, so I am looking to gain more perspectives. When I verify the problem statement in the beginning of every case, I either repeat back word-to-word in order to absolutely make sure that I understood the problem or simply paraphrase. Of those times I paraphrased to show my ability to synthesize a set of information, I ended up losing a very important key information via phraphrasing, which the interviewer never pointed that out to me (which is not their job anyways, so it's expected, but it was fatal in recognizing the key step). So, what do you suggest for verifying a problem statement in the beginning of the case? Once I re-state (or vs. paraphrase), I always make sure to state the goal of the case I understood and confirm with the interviewer.