The Josephus Problem is not a GMAT problem and it doesn’t directly cover any GMAT-related concepts. It’s not a data sufficiency question, it’s not multiple-choice, and it certainly can’t be done in 2-3 minutes. 99% of people with an MBA will have never heard of it. And yet, it might be the single greatest question you can learn to improve your GMAT quant score.
The fact that you won’t find The Josephus Problem in any GMAT Textbook is precisely what makes it so valuable. Its worth lies entirely in the fact that it forces you to confront a situation for which there is no textbook solution. It requires you to ask, “How do I solve a problem that’s never been proposed before?”
What the Josephus Problem is teaching is not math and neither is what the GMAT is testing. The Josephus Problem is a logic problem and the GMAT is a logic test. Math problems have solutions that can be memorized top down. Logic problems must be solved from the bottom up and rarely have a single optimal approach. Yes, the GMAT requires you to know things like adding fractions, but if that’s what ad-coms were really interested in, Wharton would be out recruiting at your little cousins middle school instead of the Fortune 500. In other words, any math knowledge needed on the GMAT is a NECESSARY but not SUFFICIENT condition to doing well.
Above the fundamentals, the skills the GMAT is really testing are your abilities to organize, simplify, and translate information. These are the exact skills needed to crack The Josephus Problem which is why I encourage all my students to take the time to learn it now and thank me later.
Stay safe and study hard!