Club X has more than 10 but fewer than 40 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Answer:
The correct answer is (E) 5. There’s a lot to take in on this question, so it can take some time to understand what’s really going on, but at its core this is a question about multiples and remainders. Given that the members can sit at tables of 4 or 5 and then have 3 people left over to sit at a table of 3, the number of members must be a multiple of 4 plus 3 and also a multiple of 5 plus 3. But we need a single number that satisfies both of those conditions. The first positive number that is a multiple of both 4 and 5 is 20, so 23 could be the number of members. The next multiple of 4 and 5 is 40, but that’s already too high. Thus, we know there are 23 members. So, if the members are seated at tables of 6, there will be 3 tables of 6 (18 people) and 5 members left over to sit at the final table.
This is in fact a real GMAT question, but it has a lot in common with typical brain teasers and just goes to show how “brain teaser-like” real GMAT and GRE questions can often be.