# Diagramming Solutions for PrepTest 67

### Game 1

Step  1

Per the given scenario, and the first rule, we can write out the five elements to be placed - M, N, O, P, R - and the subsets (majors) - (g, g, h, h, j). We can also lay out the two position assignments for friendship and the three for liberty.

Step 2

Per the second rule, we can notate that the two friendship slots must be occupied by a g and an h. We can infer from this that the other g, the other h, and the j must be assigned to Liberty.

Step 3

Per the third rule, we can notate that M speaks on friendship.

Step 4

Per the fourth rule, we can notate that R speaks on liberty.

Step 5

Per the fifth rule, we can notate that Rg is not an option.

Step 6

Per the fifth rule, we can notate that Pg is not an option.

Step 7

Per the sixth rule, we can notate that N is a g.

Step 8

We can notate that O has not been discussed in any of the rules.

### Game 2

Step 1

Per the given scenario, we can write out the seven elements to be placed - P, S, T, V, W, Y, and Z - and the seven positions to be assigned.

Step 2

Per the first rule, we can notate that P goes before W.

Step 3

Per the second rule, we can notate that T goes before S.

Step 4

Per the third rule, we can notate that V goes before Z.

Step 5

Per the fourth rule, combined with the fact that, per the second rule, T must go before S, we can infer and notate that S must go in positions 2 or 3, and T in positions 1 or 2.

Step 6

Per the fifth rule, we can notate that Y is not last.

Step 7

Per the sixth rule, we can notate the biconditional relationship between P being first and Y being before V, as well as the contrapositive.

### Game 3

Step 1

Per the given scenario, we can write out the six elements to be placed - F, H, M, P, R, and S - and lay out the three aisles to which they can be assigned.

Step 2

Per the first rule, we can notate that R must be with F or M.

Step 3

Per the second rule, we can notate that F must come before both M and P.

Step 4

Per the third rule, we can notate that S must come before P. We can connect this to our notation for the second rule.

Step 5

Per the fourth rule, we can split our ordering chain into two frames - one where S and H are on the same aisle, and another where H is on an earlier aisle than S.

Step 6

We can redraw the positions for each of the frames - for the second frame, we can notate that H would have to go in the first aisle, S in the second, and P in the third, with F coming at some point before M.

### Game 4

Step 1

Per the given scenario, write out three of each type of subzone - H, I, R - as the potential elements to be placed, and lay out subzones 1, 2, and 3 as the assignments.

Step 2

Per the first rule, cross out R from underneath 1.

Step 3

Per the second rule, notate that we can’t have 3 H’s in one zone.

Step 4

Per the third rule, notate that if a zone has H, it can have at most one R.

Step 5

Per the fourth rule, notate that if a zone has H, it has no I.

Step 6

Also per the fourth rule, notate that if a zone has 3 R’s, it can’t have I.

Step 7

Please note we did not notate contrapositives for this diagram, but you certainly could have if you preferred.

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.

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