I do not use the binary chain that Manhattan uses. However, I wanted to post my setup in case it were to be of help to you.
Question 12 is really just a different variation of a hypothetical list question. Use the rules to eliminate answer choices. You may have a situation were a couple of choices are in compliance with the rules, in which case, you would take notice of other variables not mentioned in this choices because this is affecting whether it is viable scenario or not.
My set up for this game:
The checkmarks denote that the variable is mentioned in the rules. As you can see, the variable S3 is not mentioned. We do know however that, at most, one S can be selected. A student cannot take the same class twice according to the rules. So we know that one of S9 and S3 will be out. It could be the case that both are out.
I have 4 slots on the left side of the diagram to denote those classes that are selected and four on the right side to be selected.
We know that one of G and W is in and one of G and W is out.
Let us go to #12
Here are the answer choices and the X's by the ones that have a rule violation. which leaves us with one left, E.
A violates the 1 of G/W in rule
B violates the rule where one of J and M have to be out
C violates the rule where one of P and W have to be out
Dviolates the rule where one of P and W have to be out