Diagramming Solutions for PrepTest 81

Game 1

Step  1

Per the given scenario, we can write out the five elements to be placed - F, G, H, J, and K - and the subset options - r, r, r, u, and u.

Step 2

Per the second and fourth rules, we can create two frames - one in which K is first, F is second, and G is third, and another in which G is third, K is fourth, and F is fifth.

Step 3

Per the first rule we can notate that the first element in both frames is an r.

Step 4

Per the third rule, we know and can notate that in the first frame, F must thus be a u, and in the second, K and F cannot have the same subset.

Step 5

Per the fifth rule, we can notate that J must have a u subset. Since either F or K must also have a u subset, and there are only 2 u’s available, that means the remaining elements - the F or K that didn’t get u, as well as G and H, must get r as a subset, and we can notate that accordingly.

Step 6

In the first frame, we have Ju and Hr remaining for the final two positions, and we can notate that.

Step 7

In the second frame, H must go into the first position and J into the second, and we can notate that.

Game 2

Step 1

Per the given scenario, we can write out the seven elements to be placed - L, M, N, O, P, S, and T - and we can lay out the seven positions to be filled, in order.

Step 2

Per the fifth rule, we can create two frames, one in which P is first and another in which P seventh.

Step 3

Per the fourth rule, we can place M two spaces away from P in both frames.

Step 4

Per the second rule, we can notate, in the first frame, that T can’t be second, and, in the second frame, that T must be sixth.

Step 5

Per the third rule, we can notate that L and O must have exactly one element in between them.

Step 6

Per the first rule, we can notate that N must follow L.

Step 7

We can notate that S is not directly restricted by any of the given rules.

Game 3

Step 1

Per the given scenario, we can write out the six elements to be placed- R, S, T, V, W, and Z, and we can lay out the six positions to be filled, in order.

Step 2

Per the first rule, we can notate that S must be third or fourth.

Step 3

Per the second rule, we can notate that W must immediately precede Z.

Step 4

Per the third rule, we can notate that V and R cannot be next to one another.

Step 5

We can notate that T is not directly restricted by any of the given rules.

Game 4 (Option 1)

Step 1

Per the given scenario, we can write out the four elements to be placed - F, G, H, I, and the three groups for assignments - M, S, and T - with each group getting exactly two assignments.

Step 2

Per the first rule, we can notate that there must be exactly 2 I’s.

Step 3

Per the second rule, we can notate that F and H cannot be grouped together.

Step 4

Per the third rule, we can notate that if G is assigned to M, H must be assigned to T, as well as the contrapositive.

Step 5

Per the fourth rule, we can notate that G cannot be assigned to S.

Step 6

We can infer that since G cannot be assigned to S, and  (per the second rule) F and H can’t be assigned together, that I (the only available element left to assign) must be assigned to S, and that either F or H will fill the other position for S.

Game 4 (Option 2)

Step 1

Per the given scenario, we can write out the four elements to be placed - F, G, H, I, and the three groups for assignments - M, S, and T - with each group getting exactly two assignments.

Step 2

Per the first rule, we can notate that we have exactly 2 I’s.

Step 3

Per the fourth rule, we can create three frames based on the possible assignment of G’s - either G can be assigned to M and not T (frame 1), T and not M (frame 2), or both M and T (frame 3). We can also notate that for all these frames we will not have G’s assigned to S.

Step 4

In frame 1, per the third rule, H must be assigned to T.

Step 5

In frame 1, per the second rule, F cannot be assigned to T. That leaves I as our only option for filling the second position in T.

Step 6

In frame 1, since G can’t be assigned to S, and  (per the second rule) F and H cannot be assigned together, I (the only available element left to assign) must be assigned to S, with either F or H filling the other assignment for S.

Step 7

In frame 1, since both I’s have been utilized, either F or H must fill the final assignment in M.

Step 8

Similarly, in frame 2, since both M and S cannot have G assigned to them, and since (per the second rule) F and H cannot be assigned together, both M and S must be assigned an I (the only available element left to assign), as well as either an F or an H.

Step 9

In frame 2, once both I’s have been placed, we can infer that the final position for T must be filled by F or H.

Step 10

In frame 3, per the third rule, H must be assigned to T.

Step 11

In frame 3, per the first rule, we must fit in two I’s, and so they must be assigned to M and S.

Step 12

In frame 3, we must also assign an F, and so that must go into the final assignment for S.

These pages offer diagramming suggestions for every game that has appeared in every Logic Games section from PrepTests 52 through 81. Please keep in mind that there are many different ways to effectively diagram Logic Games, and it’s often a very subjective decision as to which inferences to notate, when to split diagrams, and so on.

One significant advantage of the Trainer diagramming methods is that they provide a universal diagramming system that you can use for any game that appears in the section. This is in contrast to most other LSAT learning systems, which separate games out into distinct categories, each with its own, and often conflicting, notational system.

General Suggestions on How to Diagram Logic Games

1. Always read through the scenario and rules completely, and pause to mentally consider and visualize  the game, before setting pencil to paper.

2. Think of all games in terms of elements to place and positions to place them into. Nearly every game places these positions into an order, into groups, or both.

3. Whenever you find it useful, feel free to deal with the rules in an order that makes it most convenient for you to draw an effective diagram.

4. Always be on the lookout for inferences - things that you can figure out by bringing information, such as rules, together. The purpose of your diagram is to, in fact, help you uncover inferences correctly, and these inferences (more so than the rules as they are given) are what determine right and wrong for the vast majority of problems.

5. Look for opportunities to split up your game board into multiple frames - which are a set of diagrams that collectively represent all of the possibilities of a game. Most commonly, we can create frames around a very limited set of options for how to fill a certain position or positions (“either F or K must be third,” for example) or where to place an element or elements (“K must go first or last,” for example).

6. Whenever you have trouble notating a rule clearly, don’t be afraid to write it out or provide as much detail as you feel necessary. Better to be safe than overly clever.

7. When you are done with your diagram, evaluate your notations carefully and check them back against the scenario and rules as written. Make sure that you understand what your notations mean, and that they represent the given information correctly.

Table of Commonly Used Notations

Here is a downloadable and printable infographic that includes the symbols and notations that we will most commonly utilize to set up games. Please click to open full screen.

The LSAT Trainer is available on Amazon and Apple iBooks, and in your local bookstore.