You Derive Me Crazy: 2×2 Inferences (LSAT Logic Games Series)
No matter how good you get at Logic Games, finding those difficult inferences will always be a challenge! In our “You Derive Me Crazy” blog series, we’ll take a look at some of the higher-level inferences that repeat on the LSAT, ensuring that you have all the tools necessary to tackle anything the LSAT throws at you on test day
Frames. Amirite?
We’ve discussed framing Ordering games and Grouping games before, bringing up the rules that generally lead to these game-changing inferences (see what we did there?).
However, rules of thumb can only get you so far. The LSAT – especially in recent years – has started to buck trends, and has included things that seem to intentionally go against the traditions that have emerged on the exam throughout the years.
Let’s look at an example!
If you’ve read either of our other posts on framing, you know the two criteria for it. If not, head back and check them out (here and here)!
Back? Okay, the two criteria are:
1) There is a 2-3 way division in the game
2) Each of these divisions has consequences (i.e. you’ll be able to fill stuff in in each frame)
The second criterion is pretty important – if you’re just building out frames to build out frames, and there are no inferences to be made, you’re wasting your time.
However, the first one can, at first, seem arbitrary – why 2-3? Why not 4, 5, or – let’s get crazy here – even 6?
The reason for that is time investment. Building each frame takes time. It should save you time in the questions, but it takes more time up front. We need to make sure that the investment of time up front saves us at least that much time on the questions.
With 2-3 frames, it’s a safe bet. Even if you’re wrong, you didn’t spend all that much time up front. Once you start pressing past that into more frames, though, you’re taking a bigger risk. If those frames don’t pay off, you wasted a lot of time.
However, as with all rules of thumb, there are times when you can break it.
When will I build four frames?
Generally, this comes from what I call 2×2 (2 by 2) frames. In both of our previous articles (here and here), we saw a similar type of rule leading to frames. In Ordering games, we had options; in Grouping games, we can use bi-conditionals and “at least one/but not both” rules. Both of these create a binary state in the game – in other words, they create 2 frames.
But what if you have two of these rules? How do you pick which one to frame around?
Well, your first option is to just pick one and go with it. Nothing wrong with that. Think about which one of the two rules will have more consequences (i.e. which one has elements that show up in the most other rules).
But what if you want your frames to be a little bit more comprehensive? What if you don’t want to have to deal with two frames AND the other option on top of it?
Enter 2×2 frames.
If you have two sets of options, you can mix and match them to get exactly 4 frames. As an analogy, think about the meal selection at a wedding. As a starter, you can get the soup or the salad (but not both!). For the entrée, you have your option of beef or fish (again, not both – unless your friends are made of money). You have two options, resulting in four possible meals – soup and steak (the obvious choice); salad and steak; soup and fish; salad and fish.
Same with a Logic Game with two sets of options – if you mix and match the options, you’ll have 4 frames that will almost certainly be pretty filled in.
Here are a few examples:
Ordering
1) Either M is before P or Q is after P, but not both
2) Either S or T is before Q, but not both
Build four Trees to represent all the options!
Grouping
1) Either Andrew or Jack is in Cavanaugh Park, but not both
2) Either Richard or Harris is in MacArthur Park, but not both
Build four frames with the different combinations of people in parks! Would either of these frames be a good idea? I don’t know. I’d need the rest of the game and the rules to make this call. But if you see the elements in both of the rules showing up in many other rules, building some 2×2 frames might end up netting you a set of inferences that completely answer all the questions with almost no work left to be done. Even if you invest 4-5 minutes on that set of frames, it can be worth it when you breeze through the questions.
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Matt Shinners is a Manhattan Prep instructor based in New York City. After receiving a science degree from Boston College, Matt scored a perfect 180 on his LSAT and holds a J.D. from Harvard Law School. There’s nothing that makes him happier than seeing his students receive the scores they want to get into the schools of their choice. Check out Matt’s upcoming LSAT courses here!