I'm glad you posted this question,
vincent.meyer!
When you're dealing with a
conditional question, you always want to carry the hypothetical as far as is reasonable. It sounds like you started the process (and realized the RX block was restricted to 5-6-7), but you could have carried it a step further. Doing so eliminates the need to use 'plug-n-chug', which can be extraordinarily time-consuming.
In a situation like this, don't be afraid to split your hypothetical into two. Drawing a quick second version shouldn't take more than a few seconds, and can save valuable time by allowing you to avoid the error-prone trial-and-error approach.
I've split this hypothetical on the grounds that either Q is in 4th or T is. You could just as easily split based on the RX block being 5-6 or 6-7, and it would be equally useful.
If T is 4th, we know RX is in the 5-6-7 zone, but it may not be immediately apparent what else follows.
However, if Q is 4th, W is also forced into the 5-6-7 zone. That forces S to be 1st, and T takes the only remaining spot - 3rd!
The correct answer is (C), T could be 3rd!This is enough information to answer the question without doing any plug-n-chug whatsoever!
And just so you know, you can actually carry the "if T is 4th" version to completion. If T is 4th, W is prevented from being next to it (3rd or 5th), and it could never have been 1st. So here too, W is pushed into the 5-6-7 zone along with the RX block. In fact, to keep it away from T, W must be 7th, leaving the RX block in 5-6. S must therefore be 1st, and Q takes the only spot left - 3rd. Check out the diagram:
Carrying this out shows you that if P is 2nd, the only products that could be 3rd are Q and T. But remember, playing this scenario out entirely turned out not to be strictly necessary to answer the question.
Always play your conditional out fully, and don't be afraid to split the diagram into two when there's a clear divide with obvious consequences. Never resort to sheer plug-n-chug unless you have no other immediately accessible choice.
I hope this helps you strategize your games!