LSAT 90, Logic Game 3, Question 14, LSATHacks

We’re looking for an impossible partial assignment of cities to semesters. This is a difficult question, and to solve it, the best approach is actually to quickly copy the answers onto your scratch paper. Then fill in letters based on the rules until you find something impossible. I’ll show you how I actually drew it. I just wrote letters on my sheet and partially filled things in.

A few tips for filling things in:

• Start with any existing rules triggered by the variables placed
• If you can, place VT in fall or HM in Spring or place either pair of variables together. You know these combos are possible, so it makes sense to default to them when trying to prove an answer could be true.
• Place H, V, T, M first. O can go anywhere, so placing the tricky variables first allows you to be sure you’ve handled the hard bits.

A: This answer has H in F, and V in S, so start by fulfilling rules 1 and 2:

F: H, M

S: H, V, T

Only one space is left (in fall), and O can go there.

B: This answer has M in F, and HT in Spring. First, put V with T in Spring and H with M in Fall. The rules don’t force us to put those there, but since each combo fulfills rules 2 and 1 respectively, we know the combos work. When testing a could be true scenario, it’s always good to fill in things you know work.

F: M, H

S: H, T, V

Once again, we’re left with just O. This is the exact same diagram as A!

C: This starts with O in Fall, and MT in Spring. So I just added VT to fall and H to spring to go along with M. As with B, nothing forces us to put these letters together. But we know they can go together, and so for the purposes of knowing if an answer works it’s what I default to. They also help fulfill rule 3 by ensuring each group has M or V:

F: O, V, T

S: M, T, H

This obeys rules 1, 2 and 3

D is CORRECT. It places H and T in Fall and M in Spring. Let’s see what deductions we can get. H in Fall requires M. And, V has to go somewhere, so we have to put VT in Spring (rule 2 requires T with V):

F: H, T, M

S: M, V, T

So far so good. The problem? There’s no space for O! And every city needs to be placed.

E: This places H and V in Fall and V in Spring. It is very similar to D, except that V instead of M is in Spring, which allows this answer to work. So, let’s obey rules 1 and 2 and put M with H and T with V:

F: H, V, M

S: V, T

Only O is left to place, and we can place it in Spring. Notice a pattern. A, B, and E all had O as the remaining variable once we applied the rules.

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