Diagramming Solutions for PrepTest 53

Utilizing methods taught in The LSAT Trainer.

Game 1 (Option 1)

Step  1

Per the given scenario, we can write out the five elements to be placed - T, W, X, Y, and Z, and we can lay out positions in three groups - F, P, and S - with an indication that each group gets at least one and up to three assignments.

Step 2

Per the first rule, we can notate that X signs with F.

Step 3

Per the second rule, we can notate that Y does not sign with F.

Step 4

Per the third rule, we can notate that Z and Y must be grouped together.

Step 5

Per the fourth rule, we can notate that if T is assigned to S, W will be assigned to S as well. If we wanted, we could also notate the contrapositive.

Game 1 (Option 2)

Step 1

Per the given scenario, we can write out the five elements to be placed - T, W, X, Y, and Z, and we can lay out positions in three groups - F, P, and S - with an indication that each group gets at least one and up to three assignments.

Step 2

Per the first rule, we can notate that X signs with F.

Step 3

Per the second and third rules, we can split our diagram into two frames, one in which Z and Y are assigned to P (frame 1), and another in which Z and Y are assigned to S (frame 2).

Step 4

In frame 1, T and W are our only remaining options for the minimum one element assigned to S. Since, per the fourth rule T signing with S means W must sign with S, we can infer that W must, whether with T or by itself, sign with S in this frame.

Step 5

For frame 1, we can notate that T is the only element not yet assigned.

Step 6

For frame 2, T cannot be assigned to S, because if it were, per the fourth rule, W would have to be as well, and if that were the case we would have no one left to assign to P.

Step 7

For frame 2, W and T are our only remaining options for the minimum one element assigned to P.

Game 2

Step 1

Per the given scenario and rules, we can write out the six elements to be placed - G, J, L, M, P, and V - and the six positions to be filled, in order.

Step 2

Per the first rule, we can notate that we must have the order P - M - L.

Step 3

Per the second rule, we can split our diagram into two frames, one in which G is before both L and J (frame 1), and another in which G is after both L and J (frame 2).

Step 4

Per the third rule, we can split each of our diagrams up further. We can split up frame 1 in order to have V before both P and G (frame 1a) or after both P and G (frame 1b), and we can split up frame 2 in order to have V before both P, which guarantees it is also before G (frame 2a), or V after G, which guarantees it is also after P (frame 2b).

Game 3

Step 1

Per the given scenario, we can write out the seven elements to be placed - S, T, V, W, X, Y, and Z, note the two types of subsets, confess (c) and not confess (cross out c), and lay out the seven positions to be assigned, in order.

Step 2

Per the first rule, we can place T into the third position.

Step 3

Per the second rule, we can notate that the element in the fourth position did not confess.

Step 4

Per the third rule, we can notate that W must come before S.

Step 5

Per the fourth rule, we can notate that Z must come before both X and V.

Step 6

Per the fifth rule, we can notate that no one confessed after W was questioned.

Step 7

Per the sixth rule, we can notate that two of the final three who were questioned confessed.

Step 8

Having notated the sixth rule, the only way to satisfy the third condition that S follows W and the fifth condition that no one confessed after W is to have someone confess in 5, W confess in 6, and S not confess in 7.

Step 9

We can notate that Y 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 six elements to be placed - M, N, O, P, S, and T, as well as the subsets (schools) they could belong to - f, g, and h. We can also lay out the positions to be filled, in order, and we can separate out the positions for the schools from those for the two students from each school.

Step 2

Per the first rule, we can notate that S is from g.

Step 3

Per the second rule, we can notate that T is on the second place team.

Step 4

Per the third rule, we can notate that M and P cannot be on the same team.

Step 5

Per the fourth rule, we can notate that P must come before N.

Step 6

Per the fifth rule, we can notate that g must come before h. We can infer and notate that, per the first rule, this also means S cannot be on the third place team.

Step 7

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

Game 4 (Option 2)

Step 1

Per the given scenario, we can write out the six elements to be placed - M, N, O, P, S, and T, as well as the subsets (schools) they could belong to - f, g, and h. We can also lay out the positions to be filled, in order, and we can separate out the positions for the schools from those for the two students from each school.

Step 2

Per the first rule, we can notate that S is from g.

Step 3

Per the second rule, we can notate that T is on the second place team.

Step 4

Per the fifth rule, we can notate that g must be before h.

Step 5

Per the fourth rule, we can split our diagram up into three frames, representing the different ways in which P can come before N - P in 1 and N in 2 (frame 1), P in 1 and N in 3 (frame 2), and P in 2 and N in 3 (frame 3).

Step 6

In the first frame, per the third rule, we must place M into the third group.

Step 7

In the first frame, since, per the first and fifth rules S can’t be in the third group, S must be in the first group. Per the first rule, we can infer and notate from this that the first group will be subset g.

Step 8

In the first frame, the final element remaining, O, must fill the final position.

Step 9

In the second frame, per the third rule, there are two options for where to place M, and we can split the second frame further to represent these two options. M can be placed in group 2 (frame 2a) or group 3 (frame 2b).

Step10

 In frame 2a, since S can’t go in group 3, S must go in group 1 and thus O in group 3. Since S is in group 1, we can infer that group 1 is subset g.

Step 11

In frame 2b, S and O will fill the remaining two positions in either order.

Step 12

In the third frame, per the third rule, there are two options for where to place M, and we can split the third frame further to represent these two options. M can be placed in group 1 (frame 3a) or group 3 (frame 3b).

Step 13

In frame 3a, since, because of the first and fifth rules, S can’t go in group 3, S must go in group 1 and thus O in group 3. Since S is in group 1, we can infer that group 1 is subset g.

Step 14

In frame 3b, S and O must fill the remaining two positions, in group 1, and we can infer that group 1 is subset g.

More Information About The Trainer
Logic Games Diagrams

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.

Diagramming LSAT Logic Games Infographic

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