In my experience, more often than not, interviewer is looking at your approach rather than getting the right answer. This stems from the fact that In consulting, the problems are often vague and there is no one correct answer. so what matters more is how you think about problem in a structured way and prepare a convincing reasoning

So coming back to your question, i would prioritize reasoning over speed. To convey to the interviewer that you can think fast, during the interview, jot down all the drivers in your hypothesis tree on paper so that even if you can't talk about it, interviewer can see that you thought of several possibilites.