Setup and Rule Diagrams

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Setup and Rule Diagram Explanation

This is a Pure Sequencing game.

Because Pure Sequencing is generally easy to handle for most test takers, this was an excellent way to begin the Logic Games section of the December 2011 LSAT.

The game scenario establishes that five students must be ordered in a sequence to perform in a piano recital. Because there are no ties, this is a Balanced game. The following linear scenario underpins the sequence:

PT65_D11 LG Explanations_game_#1_setup_diagram 1.png

Although Pure Sequencing games involve relationships that are relative and not precisely fixed, a linear diagram can help us represent inferences that could result from the application of the rules.

The first rule establishes the following sequence:

G F

The second rule establishes the following sequence:

PT65_D11 LG Explanations_game_#1_setup_diagram 2.png

The third, and last, rule indicates that H and F must perform consecutively, establishing a HF rotating block:

PT65_D11 LG Explanations_game_#1_setup_diagram 3.png

Alternatively, you can represent this rule with a circle, as shown below:

PT65_D11 LG Explanations_game_#1_setup_diagram 4.png

You should immediately notice that the last rule can be combined with each of the preceding two rules, as follows:

PT65_D11 LG Explanations_game_#1_setup_diagram 5.png

And also:

PT65_D11 LG Explanations_game_#1_setup_diagram 6.png

At this point, you should realize that H and F are functionally identical: the two variables are adjacent to each other, and consequently any sequencing rule that applies to one of them will also apply to the other. The sequencing chain produced by the combination of the three rules can be diagrammed as follows:

PT65_D11 LG Explanations_game_#1_setup_diagram 7.png

In determining relationships between variables, do not let physical proximity on the diagram influence your evaluation. For instance, J appears to the right of G in either sequencing chain, but there is no direct relationship between G and J. It is possible, for instance, that J is second and G—third. The key in Pure Sequencing games is to avoid making unwarranted assumptions such as this.

Finally, it pays off to represent any inferences produced by these relationships within a linear diagram. The sequencing chain clearly shows that either G or K must be first, establishing a G/K dual option. Additionally, notice that the HF rotating block must follow both G and K, and as a result can only be placed in positions 3-4 or 4-5. Either way, the fourth variable must be either H or F:

PT65_D11 LG Explanations_game_#1_setup_diagram 8.png

Thus, we arrive at the following final setup for this game:

PT65_D11 LG Explanations_game_#1_setup_diagram 9.png

Before we proceed to the questions, we should note an alternative approach to this game. With only five variables to consider, the game has a limited number of solutions. While by no means necessary, a Templates-based approach would not be difficult to implement, and will certainly obviate the need to make additional diagrams when attacking the questions. The best way to undertake it would be to focus on the HF rotating block, and orient the remaining three variables relative to it:

PT65_D11 LG Explanations_game_#1_setup_diagram 10.png

According to our sequencing chain, G and K must both precede the HF rotating block, forcing J into fifth position in Template 1:

PT65_D11 LG Explanations_game_#1_setup_diagram 11.png

In Template 2, the only rule affecting the relationship between the remaining three variables—G, K and J—is the second rule, whereby K must precede J. The rule produces three possible sequences between G, K and J, which would be too laborious to diagram. Instead, Template 2 can be completed more “loosely” as follows:

PT65_D11 LG Explanations_game_#1_setup_diagram 12.png

While a Templates approach typically requires an initial investment of time, here this investment is minimal given the scarcity of variables and the strength of the rules that govern them. Even if you did not approach the game with templates, however, combining the rules into a singular sequencing chain should arm you with enough information to attack the questions.