June 2016 LSAT scores have been released, and test takers are now getting the opportunity to analyze their results. With the test in hand we’re going through it too, putting together summaries of the most commonly-misunderstood components. Here we’ll cover Logic Games, while elsewhere we’ve got a detailed look at the scoring scale and exactly what it means for overall test difficulty (and possibly even future exams).
Of course, if you’re anything like me then the Logic Games section was the first thing you reviewed, so let’s take a look at each game and see exactly what happened. I’m going to do this in two parts–Games 1 and 2, followed by Games 3 and 4–to make it easier for readers to jump right to their most pressing concerns.
Here are overviews for the first two games from the June 2016 LSAT:
Game #1: Seven Special Project Workers, a Grouping Game
The section begins with a fairly straightforward Grouping game, where seven candidates–Q through X–are available to fill just three spots, with one of those three spots assigned the title of Leader. Because the numbers are given to us this is a Defined game, and with seven variables to fill only three spaces it is Unbalanced: Overloaded. Fortunately that seeming imbalance can be quickly resolved by showing four spaces in your “out” group, something like this:
__ __ __ | __ __ __ __
Now we have seven spaces for our seven people, and all we have to track is the in/out nature of our rules and inferences. Note too how I’ve designated a spot with an L for Leader. Just be careful not to confuse that with a Not Law and you’re good (although that would be tough to do here since there are no L variables).
The three rules are also relatively benign, where the first rule establishes that if Q or R is in then it’s in the L position (this means that Q and R can never both be in–there’s only one L after all–so one of your out spots can be filled with a Q/R); rule 2 is a simply S –> T; and rule 3 is a slightly more complex W –> R + V.
The contrapositives of those last two rules are crucial here! For rule 2 consider what happens when T is out: S is out as well, and now three of your out spaces have been filled by Q/R, T, and S. That leaves only one more open space out before the game gets very, very restricted! And when we think of what we’re told by rule 3, that W and V cannot be selected together, then you know an out spot must be filled by the W/V split, as well.
And this leads to one of the most powerful inferences in the game: when T is out, then all four of your unselected spaces have been filled: Q/R, T, S, and W/V. That means your “in” group is: Q/R as Leader, W/V (avoiding R and W together), and our wildcard variable X. By filling the out group we de facto fill our in group, with X guaranteed and the rest extremely limited.
This singular notion immediately answers question 4, very nearly solves 5, and goes a long way towards answering 3. It’s Grouping 101 that you always pay close attention to both the selected and unselected sets, and this shows why.
Another interesting point to make about this game, and really the section as a whole as we’ll see, is that opportunities abound to consider, or even completely reuse, prior work. This is a huge bonus to students who don’t erase earlier diagrams and who remember exactly what they’ve already done as they move through the questions. Take question 3: what could allow V to be the Leader? The correct answer to 1 has V as the leader, so should immediately be considered (and sure enough, spotting that Q and R need to be out so neither is the Leader, and that T needs to then be in accords nicely with answer choice C in the first question).
So test takers well-versed in Grouping and hoping for a friendly start to the section were in luck with Game 1. The only downside is that it has just five questions, so little opportunity to pad your scorecard, so to speak.
Game #2: Four Student History Assignment, a Grouping/Linear Combination Game
After a start to the section that can only be described as fortuitous, savvy test takers were likely expecting something more challenging in their future. Game 2, I’m pleased to report, mostly failed to provide it.
The second game once again presents a Defined Grouping scenario (also, once again Unbalanced: Overloaded, as we’ll see), where a history project has four students out of a group of six candidates assigned to one of four years: 1921-1924. This is clearly an Unbalanced situation (more people than spots), but the six students–L through Y–can, much like we saw in the first game, be balanced by including an out group:
__ __ __ __ | __ __
1 2 3 4
With this simple setup we’ve also introduced the Linear aspect of the game, since the 1-4 years (I’m abbreviating 1921-1924 with their units digits) of the assigned group are sequential, and at least one of the rules includes the concept of ordered placement (rule 4, as we’ll see).
What is striking to me about this setup, and hopefully got your attention as well, is how small the out group is: only two members! The significance of that really can’t be overstated. It means that as soon as we can determine just two people who are unassigned, the entirety of the project’s membership is known. And sure enough, several of the questions revolve around that very idea.
The rules are primarily Grouping in nature, and present the following:
Space 3 must be either L or T. Note that this doesn’t mean L or T can’t go somewhere else (both L and T can both be used, so long as one is on 3). This only prohibits the other four students from going in that space.
M can only go in 1 or 2. Again, pay close attention to a third option for M: out. It’s only when M is assigned to the project that she’s in the first two years. I showed this simply as a Not Law for M under 4 (M not 3 is implied by the first rule), and a conditional: M –> 1 or 2.
If T is assigned then so is R. This is also conditional: T –> R. But the key, and it’s one of the most powerful ideas in this game, is the contrapositive, R –> T. Think about what happens when R is out: T must also be out, which fills our two out spots and forces the other four people–L, M, O, and Y–to be in. That would put L on 3, M in 1 or 2, and O/Y in 4. By removing R an entire cascade of consequences occurs, and if you’re focused on the heavily restricted unassigned pair you’ll catch it.
Lastly, and combining both conditionality and linearity, the fourth rule tells us that if we have R then we get an OR block (in that order). Three things stand out with this rule: first, R becomes very limited in its placement options. For instance, R cannot go in 1 because then there would be no room for O ahead of it. Similarly, R cannot go in 4 because that would force O into 3, which must be either L or T. That means that if R is assigned, it MUST be in 2! That’s the only position for R where O could immediately precede it. (Careful here: that doesn’t mean that O is similarly limited; O is only tied to this rule when R is in, so until that happens O is free to do as he pleases)
Second, since R can only go in 2, forcing O into 1, then M is left with nowhere to go. Remember, M had to be 1 or 2, so if we fill those spots with the OR block then M is out. Take away? M and R can never be in together; one of the two must always be out! But can they both be out? No! Don’t forget that if R is gone then T is gone too, and that fills our out group. So R or M in = the other out. R or M out = the other in.
The third notable aspect of rule 4 is its connection to rule 3, where T –> R. The shared R between these rules is important: T tells us R, which tells us the OR block is in 1 and 2. So if L is out and T is 3, then we’d have OR in 1-2. If T is 4, then L is 3 and OR is 1-2. But what if T is 1, or 2? Then we have a problem: O and R need those spaces if T is in. Inference? T cannot be in 1 or 2.
You’re probably getting the sense at this point that there are a lot of Not Laws present in this game. You’re right. Take a look:
___ ___ L/T ___ | M/R ___
1 2 3 4
R T M
T L R
That’s a lot of useful information, and it makes the questions entirely manageable. Consider:
8. If R is in then it’s O and R in 1 and 2. If Y is also in then Y is 4. The only “could” then is space 3, which is either L or T (L in 3 is your answer).
9. We have three who can’t be in 1 from our Not Laws, leaving 3 who could.
10. If Y is out then R must be in: R out brings T out with it, and that, along with Y, is 3 people out (too many). With R in you have OR in 1-2, M out (see above) with Y, L or T in 3, and then L, T, or X in 4. Remember that L and T can possibly go together. Here L in 4 is the “could” answer.
11. Who can’t be in 2? T and L (L is the answer)
So this was a trickier game that the first, but once again well-prepared test takers, particularly those who caught R’s significance in this game and how impactful it is on the out group, were still sitting pretty in this games section as they hit the midpoint.
In the next post we’ll examine the final two games from June 2016 and see just what challenges the second half of this section presents. Stay tuned…