GMAT Integrated Reasoning

According to the given solution, we just have to calculate the minimum number of committee members needed, and then divide it by 3. Is this approach applicable for all cases or just for the case in question (which requires a minimum of 4 members for each committee)? I mean, let's say in the extreme case, if we adjust the number of members for each committee (each of the first 5 committees has 1 member, the 6th committee has 21 members) such that the total number remains the same (= 26 members), then the answer could not be just 26/3 = 8 2/3, right? I don't quite understand the logic of the solution, why it could be so and when it is applicable, I do think that I am not confident to use it if I have to face it in the real test

You're right: if 5 of the 6 committees had only 1 member each and the 6th had 21, we couldn't simply divide 26/3. In this case, the 6th committee by itself would need 21 members (though any of those 21 could be on the other 1-person committees).

The reason that this strategy works in this case is that each individual committee requires fewer people than the total divided by 3.

To your larger question, though - how can we find a rule that would apply in every context? Well... we shouldn't! I think it would take more time and effort to memorize a slew of different formulas for different scenarios, especially because you're unlikely to see the exact same question types again.

Take each problem on a case-by-case basis. On this problem, I personally would have worked backwards from the answer choices, starting with the smallest:

- Can I make 6 work? 6 people onto 6 committees, each person can sit on 3 committees... that only gets us up to 6 committees of exactly 3. Doesn't work.

- How about 8 people? people: A, B, C, D, E, F, G, H
1: ABCD
2: BCDE
3: CDEF
4: EFGH
5: FGHA
6: GHAB
It works for 6 committees of 4... but committees 5 and 6 need a minimum of 5 people. So 1 more person would do it.

The answer must be 9.