This is an explanation of the fourth logic game from Section II of LSAT Preptest 74, the December 2014 LSAT.
At least two photographers will be assigned to each of two graduation ceremonies. The graduation ceremonies will be held at Silva and Thorne University (S, T). The six photographers are Frost, Gonzalez, Heideck, Knutson, Lai, and Mays (F, G, H, K, L, M). The rules allow you to determine the possible assignments of the photographers.
This game can be divided into two scenarios that greatly simplify the game. This is a common trend on modern logic games, so be sure you understand this setup.
I recommend drawing the diagrams on a sheet of paper yourself in order to follow along. Ideally, print a fresh copy of the game to use.
In this game, there are two groups: Silva and Thorne. Each group needs at least two photographers:
FH go together:
Technically this is a linear diagram, but it works just as well for grouping. Using the same symbols in both cases makes for simpler diagrams.
Next, L and M can’t go together:
Next, if G is in S, then L is in T:
I drew the diagram and its contrapositive in this explanation. On my own sheet, I didn’t draw the contrapositive because I can do it in my head. When you are still learning contrapositives, draw them, but aim to be able to instantly see them in your head.
The next rule is complicated. It says that if K isn’t assigned to T, then H and M must both go in T.
We could leave it at that, but both H and M were mentioned in other rules. F is with H, and L can’t go with M. So the full effect of the rule is this:
There’s still more. If something complicated happens when a rule occurs, follow the idea as far as it goes. It’s best to draw the scenario.
Lets do that. If K isn’t with T, then F, H and M are there:
We also know that L isn’t with T, because M is there (rule 2). This affects rule 3: G can’t go with S.
There’s till more. S needs at least two photographers. FHM are already at T. G can’t go to S. So only L and K are left, and they must go to S:
Only G is left uncertain. They could go to T, or they could not be assigned. (Not all photographers have to go somewhere).
So if K isn’t assigned to T, then we know almost everything. The scenario above is the only possible scenario.
Therefore, in all other scenarios, K is assigned to T:
Drawing K there may not seem like a major deduction, but this has two big effects.
- We no longer have to remember the fourth rule. This significantly reduces the difficulty of working with the remaining rules.
- The deduction about K solves question 18 completely, and largely solves 19, 20, and 21.
There are big payoffs for seeing if a game can be split into two scenarios.
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