In a real interview you usually have around 30 minutes to solve your case. You have to be really careful to listen to your interviewer during the interview: every case has hundreds ways to be "complicated" by the candidate.
It's good to mention all the critical points that come up to your mind, showing your critical reasoning skills, but always ask the interviewer before getting lost in useless and complex analysis. Most of the times, since you have only half hour, the interviewer will say "Okay, let's assume that.." giving you the solution for that critical point.
Hope it helps,