PE Consulting Case Studies

I have an interview coming up with a UMM buyout and growth firm. To those with experience with case studies, when presented with a consulting case study do you go through the same motions that consultants do with 1) restating the prompt 2) clarifying objectives 3) asking for time whenever they ask you what your strategy would be. My background is IBD and the idea of asking an interviewer for time to think seems uncomfortable and foreign.