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Complete Question Explanation

The correct answer choice is (E). Let's start with the basic set-up, as, I want to clarify where we are starting.

We have 9 total spots, and 5 variables. Each variable can be used a max of 2 times (per our rule that no one can be used on all three days), which tells us that we have 2-2-2-2-1 distribution of variables to slots. That means there is only 1 variable that can be used only once. All the other variables show up on two days.

We know that if you have M--->L. That tells us that L cannot be our solo variable. Why? Because if L is our solo variable, then M would be used twice. If M is used twice, then L has to be used twice (because if M--->L). Those two facts our inconsistent, meaning that L cannot be our solo variable.

We also know that N is on Friday, and P is not on Saturday. From that final rule, we can figure out who COULD be on Saturday.
Option 1: MLN Option 2: MLQ and Option 3: LNQ. Notice that all of those options include....L. So no matter what, we have to have L on Saturday.

Great, so our basic set up includes N on Friday, L on Saturday, with the knowledge that we need one more L.

Now (finally) let's turn to our local question: M is on Thursday.

Let's build out our diagram.

Thursday: M, L ___
(because if M--->L)

Friday N ____ ____

Saturday L ____ ____

Can we go further? Well, we see we've used our two Ls! That means that our day without an L (Friday) can neither have an L nor an M (because M--->L). That means that our Friday team can only be NPQ.

Personally, this is where I'd check the answer choices. It's possible I could figure out a bit more, but I don't immediately see anything, and I already know a bunch.

Answer choice (A): L works on Friday. I know this CANNOT be true. L is on Thurs and Sat.

Answer choice (B): M works on Saturday. This one COULD be true. But I don't know for sure. And I recognize that the test makers are trying to test the mistaken reversal of our M--->L rule.

Answer choice (C): N is on Saturday. Again, I don't see anything against this answer choice, but I don't see it proven either. I'll keep it as a contender, but an unlikely one.

Answer choice (D): P works on Thursday. Exactly the same as answer choice (C). I'm not saying it CANNOT be true, but I'm not saying it MUST BE TRUE.

Answer choice (E): This is the correct answer choice. Q works on Friday. This is our correct answer. Woohoo! We see this in our prephrase. if neither M nor L can be on Friday, NPQ all have to be. So it must be true that Q works on Friday.

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