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Here's a Logic Games question from the June 2004 LSAT.
Before we diagram, let's just think about the rules. The first one says Z goes to the museum. So, Z can't belong to the private collector, and we can eliminate A, D and E right there.
Now, let's start diagramming to test one of the remaining choices. Let's do B...if it works, we'll know it's B, and if not, we'll know C is right. So, we'll put R and T in with S, belonging to the collector. T will go first and Q will go first with the museum to obey the second rule. V will go second with the museum to obey the third rule. Z will go last will the museum to obey to the first rule. So, we have:
Museum: Q, V, Z
Private collector: T, S, R
That works, so we know B is correct.
Remember:
1) Think about the rules and try to eliminate some choices without diagramming, but if this is fruitless after about 30 seconds, just go ahead and diagram. When it works, as it did here, it's very helpful though...we got rid of 3 choices very quickly.
2) Diagram when you can't deduce anything else from the rules easily.
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