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(The complete setup for this game can be found here: lsat/viewtopic.php?t=11359)
The correct answer choice is (E)
Both template #1 and template #3 meet the criteria in the question stem. An examination of the two templates reveals that the only constant between the two is that W is always on the third shelf. Thus, given that this is a Must be True question, you should immediately look for W on the third shelf.
Correspondingly, answer choice (E) is correct. Here are both possibilities with H and P on the same shelf: