If Irving serves on every subcommittee on which Magnus serves, which one of the following could be true?

on August 12 at 02:12AM

Difference of B & D

I was going to go with B but I thought it was a Must Be True answer instead of Could Be True answer so I chose D. Please explain the difference and Why B is right over D

1 Reply

Shunhe on August 12 at 03:25PM

Hi @anchelle,

Thanks for the question! (B) isn’t actually a “must be true” situation since I can go once or twice, which makes it a “could be true.” (D), on the other hand, is a “must be false” situation. It’s actually impossible for F to be with M in this situation. Let me explain.

We’re told here that I is on every subcommittee on which M serves. In other words

M —> I

So let’s go back for a bit and think about the numerical distributions of this game. There are 6 members that we’re trying to put into 9 slots. And we know that one of the committee members goes three times, and that each committee member has to be picked at least once. So that gives us 3 + 5*1 = 8 slots accounted for just based on the bare rules. But we have one more slot we need to fill. And that has to go to one of the people who just go once, so we know that in this game, someone serves on all 3 subcommittees, one other person serves on 2, and everyone else serves on 1 subcommittee.

Now who can be the person who serves on all 3 subcommittees? Well, it can’t be F, G, H, or I, since if it was any of them, someone wouldn’t be able to be on any subcommittee (based on rules 2 and 3). So the only two possibilities for the person who serves thrice are M and P. This tells us that M and I are always together. So M can’t be the one on every subcommittee here, since that would mean that I’s also on every subcommittee, which is a no-go. So that means P has to be the one that goes in each subcommittee.

OK, so M can’t go 3 times. Can M go twice? No, because then I would go twice as well, and we can only have one person who goes twice. So M only goes once. And when M goes, I goes, and P is in every subcommittee. So M is with P and I only. So M can’t be with F, which rules out (D).

(B), on the other hand, could be true. Remember, M —> I does not mean I —> M. In other words, while M means we have to have I, we can have I without M. So I can go twice or once, and that makes (B) a could be true and the correct answer.

Hope this helps! Feel free to ask any other questions that you might have.