Which one of the following must be true?

BenMingov on December 3, 2019

Hi, ca_teran, thanks for the question!

You can set this game up as an in/out game with both groups (Green and Red).

You should note that the distribution of variables within the groups is 2-3 or 3-2 respectively. We are not sure which team will have 3 nor which will have 2. But we do know that this is the only distribution possible. No 4-1, 5-0 etc.

As far as noting the facilitators, there is no fantastic way to do this. It really just boils down to personal preference.

When you note who the facilitator is, you can make it prime (O') or double prime (O''), you can put an asterisk next to the facilitator (O*), or you can note it within the groups that 1 space for each is reserved for a facilitator. If you note it this way, block off one slot in both groups that you will reserve for facilitators only. This way you will always be able to keep track.

For the specific question at hand, we need to see which one of the answer choices must be true. For must be true questions, one of the answer choices must be true, while the incorrect four could be false. Meaning they do not have to be true!

Let's examine A, B, and C: each of these could be false. J can go on the Green team, L does not have to be a facilitator, O can go on Red team.

Now D: If you try proving that D could be false, then you will realize it cannot be. It must be true. If we were to make both J and M facilitators (trying to prove D false), we would see that this violates the rule that O is a facilitator.

Answer choice E: Try to make either J or K a facilitator and you will see that it is possible that one of them is. This doesn't violate O being a facilitator.

I hope this was helpful. Please let me know if you have any other questions.