Hi jbryan96!
The correct answer choice is (C)--Q and S can never be together. Your diagrams seem to provide support for this. In both of your diagrams, Q and S are not together.
For another way to approach this one, consider that the rules give some definite parameters for Q and S. This allows one to test possible variations of how the game may unfold. If we work with S, there are only two possible spots it can occur--either Wednesday afternoon or Friday afternoon.
The first of these can be diagrammed as:
p.m. S, __
a.m. __ __
In this diagram, S is on Wednesday afternoon. Under that possibility, we know that S and Q cannot be together, because the rules stipulate that Q occurs on Friday. This leaves the second possibility:
p.m. __, S
a.m. __ __
Since we know that Q occurs on Friday, there are two possible ways this might unfold--either with Q occurring on Friday morning or Friday afternoon.
However, note that the final rule of the game kicks in with this situation. Because there's a Friday afternoon session, this means that the number of employees who attend the Wednesday afternoon session must be greater than the number that attend the Friday afternoon session.
With that in mind, suppose that Q and S both attended the Friday afternoon session. This would mean that the remaining three variables--M, P, and T--all must attend the Wednesday afternoon session. That wouldn't work, though, since the third rule tells us T must be scheduled for an earlier session than P. If S attends the Friday afternoon session, we can therefore eliminate the possibility that Q attends the same session; rather, Q would have to be in the morning. This is how we know that Q and S can never be in the same session.
