This is an explanation of the second logic game from Section III of LSAT Preptest 37, the June 2002 LSAT.
Seven trucks – S, T, U, W, X, Y, and Z arrive at a warehouse in a single day. Each truck is colored green or red (G, R) and no truck arrives more than once that day. You must use the rules to determine their possible orders of arrival.
This is a linear game with a twist. Not only do we have to figure out the order of the trucks, we also have to figure out which colors they are. Fortunately, the rules about color let us figure out almost everything about this game.
The first rule tells us we can’t have two reds in a row. That means we always need a green between two reds (green is the only other color.) Here’s how I drew that:
The variables go on top of the slots, and the colors go on the bottom.
The next rule is straightforward sequencing. Y comes in front of T and W. We’ll put it directly on our diagram later, but for now here’s how to draw it.
The next two rules are interesting. If exactly two trucks before Y are red (rule 3), then Y must come at fourth at the earliest. There are two red trucks and a green truck in front of Y. Y could go fifth if there is more than one green truck in front of Y.
But…we also know S is sixth (rule 4). Y can’t go last (because T and W come after Y), so S must come after Y.
T, W and S all come after Y. That means Y has to go fourth at the latest.
If Y has to go fourth at the latest and fourth at the earliest…then Y just has to go fourth!
S, T and W fill up spots 5, 6 and 7. Here’s to draw all that:
The three trucks in front of Y are r, g and r because that’s the only way to fit in two red trucks. So Y must be green, since we can’t have two reds together.
S is in sixth. T and W come after Y in 5 and 7, in either order. We don’t know anything about the colors of trucks 5, 6 and 7: they could even all be green.
Lastly, Z comes before U (rule 5). X wasn’t mentioned in any rule, so it could go anywhere in spots 1-3. I’ve drawn these directly onto the diagram:
Z –U and X are drawn overhead and separated by a comma to indicate that they all must go before Y. The comma indicates that we don’t know if X comes before Z and U, after them, or even in between.
As far as I know, I invented this style of drawing. It’s an easy way to keep track of all remaining variables. This frees up mental space and lets you focus on the question.
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