This is an explanation of the third logic game from Section II of LSAT Preptest 38, the October 2002 LSAT.
Chroma Inc. hired seven job applicants to fill seven new positions. The applicants are Feng, Garcia, Herrera, Ilias, Weiss, Xavier, and Yates (F, G, H, I, W, X, Y). One of them will work in the management department (M), three in the production department (P), and three in the sales department (S). You must determine the possible placements of the new hires to jobs.
Game Setup
This is a grouping game. Seven candidates are divided between three departments.
It might not be obvious how to draw the basic setup diagram. If you’re ever stuck on how to represent a game, you can glance down at the first question. The layout of the answers usually shows the most efficient way to draw everything.
We should put the departments vertically. I’ve placed F in P because the last rule says F goes there.
(It’s important to read the rules first, in part because you can spot some obvious rules that go directly on the diagram)
The first two rules tell us that H and Y must go together and that F and G can’t go together.
It’s important to realize that H and Y form a pretty restrictive bloc. They can only go in P or S, and they’ll take two of the three spaces.
The rule that F and G can’t go together tells us that G goes in M or S, since F is in P. You can add “not G” beside P in all future diagrams.
The next rule says that if X is in S, then W is in S. We can draw this using sub-scripts.
You might think this game looks pretty open ended. But it would be a big mistake to stop here. None of the rules can be directly combined, but we can still draw deductions.
Look for the most restrictive variable. There are only two options for placing H and Y. We can put them in P, or we can put them in S.
When there are only two options, you should always try both. Often it leads to deductions.
If we put H and Y in P, then everything is settled. X has to go in M.
Why? Well, if X went in S, then W would have to go in P (rule 3). But P is full. So X goes in M, not S.
G and I take up the other two spaces in S because every other spot is full.
We’ll call that scenario 1.
There are a couple of possibilities if H and Y go in S instead of P.
If X also goes in S then W goes in P (rule 3).
G then has to go in M, because G can’t go with F in P. That leaves I to go in P.
We’ll call that scenario 2.
The third alternative is simply where X doesn’t go in S. It could go in P or M. G can go in M or S, but not P since F and G can’t go together.
We got these scenarios first by seeing where we could put HY. Then we added in the third rule, Xs ➞ Wp
Scenarios aren’t essential, but I find they help us think through the rules.
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