This is an explanation of the third logic game from Section III of LSAT Preptest 35, the October 2001 LSAT.
Five members of the Kim family attend an opera. They are Quentin, Robert, Shiro, Tony, and Umeko (Q, R, S, T, U). Each of them sits in either row G or H, and their seats are numbered 1 through 3.
Time for a night at the opera. But where to sit? There are five people and six seats. And everybody has to sit beside someone. So the seats in the middle can’t be empty. It’s not much fun to go to the opera and sit all by yourself.
Here’s the setup plus the first rule:
Two horizontal rows of three seats. T and U have to be in row H, so I’ve drawn them beside it.
The next rule tells us that T comes after S and U. T and U are in row H. We don’t know which row S is in; it could be in row G. We also don’t know whether U or S comes first.
The third rule tells us that R needs either Q or S in the same row.
And the last rule tells us R is in seat two. We can combine this with the other rules to figure out that R must be in the second seat of row G.
R needs at least one other variable with it: Q or S. So there must be space for two variables in R’s row.
But row H only has space for one variable: T and U are already there.
So R is in seat 2 of row G.
I’ve added a line between U and T to indicate that T goes first.
At this point, you might think we’re done. Not so fast! We still get to do my very favorite thing: split the setup into two scenarios.
Always be on the lookout for this. It can be tricky to develop an intuition for it. The place to start is to look at the most restricted variables. In this case, U and S must go before T. There aren’t many ways to do that.
If U and S both go in row H, then we get this scenario:
It doesn’t matter where Q goes.
If we put S in row G, then it can’t go in the third spot. It wouldn’t be before T. It can only go in the first spot. (U can’t go in row G, because of the first rule)
Here’s what we get:
I placed Q in the middle to show that it could be either in row G or H.
The rule about R having to be with Q or S is superfluous. Every correct scenario automatically takes care of that.
There’s only one more thing to remember about this scenario: the second seat in row H always has to be full. The first rule says that everyone sits beside someone else.
If it helps you remember, draw U/T/Q in there to show that somebody has to fill that seat.
And that’s it. There’s no other way to place S, so there’s really only two scenarios in this game!
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