Diagramming Solutions for PrepTest 78

Utilizing methods taught in The LSAT Trainer.

Game 1

Step  1

Per the given scenario, we can write out the seven elements to be placed - Q, R, S, T, V, W, and X, and we can lay out the positions to be assigned in two groups - one group for the three that are selected, and one group for the four that are not. For the selected group, we can mark that one position is that of leader (L).

Step 2

Per the first rule, we can notate that if Q is in it must be the leader, and if R is in it must be the leader. We can also infer from this that both Q and R can’t be in together, and so one of those two must be out.

Step 3

Per the second rule, we can notate that if S is in, T must be in too, along with the contrapositive.

Step 4

Per the third rule, we can notate that if W is in, both R and V must be out, along with the contrapositives.

Step 5

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

Game 2

Step 1

Per the given scenario, we can write out the six elements to be placed - L, M, O, R, T, and Y - and we can lay out the six positions that need to be filled - four ordered for years 1921 - 1924, and two positions for those not assigned.

Step 2

Per the first rule, we can split our diagram into two frames, one in which L is assigned third, and one in which T is assigned third.

Step 3

Per the second rule, we can cross out M from underneath the fourth assignment in both frames.

Step 4

Per the third rule, we can split the first frame into two (which we will discuss as 1A and 1B), with T out in the first frame and T in in the second frame.

Step 5

For frame 1A, per the fourth rule, if R is in, O immediately precedes it.

Step 6

For frame 1B, per the third rule, since T is in, R must be in, and, per the fourth rule, if R is in, O must be placed right before it. The only way to satisfy these conditions in this frame is to place O in 1, R in 2, and T in 4. This puts M and Y into the out positions.

Step 7

For the second frame, per the third rule, since T is in, R must be in, and, per the fourth rule, that R must have an O right before it. In this frame, the O, R pairing can only go in 1 and 2. That leaves either L or Y to occupy the fourth position. This puts M and L or Y into the out positions.

Step 8

We can notate that Y 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 - H, L, M, S, T, and V - and we can lay out the six assignments to be filled, in order.

Step 2

Per the first rule, we can notate that S cannot go in the first position.

Step 3

Per the fourth rule, we can create two different ordering frames - one in which T comes after V and before H, and another in which T comes after H and before V.

Step 4

Per the third rule, we can notate, in both ordering frames,  that S comes before both V and M, and we can connect this to our notation for the fourth rule.

Step 5

In the first frame, we have the ordering of five elements, and, of the five, S must come earliest. However, we know, per the first rule, that S can’t be first. Thus, for the first ordering frame, we can infer that L must come before S.

Step 6

In the second frame, we don’t know where L goes in relation to the other elements, so we can notate that as well.

Step 7

Per the second rule, we can notate that if H is before L, M must be before L, as well as the contrapositive.

Game 4 (Option 1)

Step 1

Per the given scenario, we can write out the six elements - K, L, T, W, Y, and Z - and we can do so while also notating the subsets they fall into - recorded ( r ), or not recorded (n): Kr, Lr, Tn, Wn, Yn, and Zn. We can also lay out the six positions to be filled, in order.

Step 2

Per the first rule, we can notate that the fourth audition must be an n.

Step 3

Per the second rule, we can notate that the fifth audition must either be K or L (the two recorded sessions).

Step 4

Per the third rule, we can notate that W must come before both K and L (the two recorded sessions).

Step 5

Per the fourth rule, we can notate that T follows K, and we can connect this to our notation for the third rule.

Step 6

Per the fifth rule, we can notate that Z must come before Y.

Game 4 (Option 2)

Step 1

Per the given scenario, we can write out the six elements - K, L, T, W, Y, and Z - and we can do so while also notating the subsets they fall into - recorded ( r ), or not recorded (n): Kr, Lr, Tn, Wn, Yn, and Zn.

Step 2

Per the second rule, we can create two frames based off our options for the fifth position - Kr and Lr.

Step 3

In the first frame, we can infer, per the fourth rule, that T must go last.

Step 4

In the first frame, per the first rule, the fourth audition must be an n. Since, per the third rule, W can’t be in the fourth position, and, per the fifth rule, Z can’t be in the fourth position, we can infer that Y is the only n left that can fill the fourth position.

Step 5

That leaves us with Wn, Lr, and Zn to fill the first three positions, and, per the third rule, W must come before L.

Step 6

In the second frame, per the first rule, we can notate that the fourth recording is an n.

Step 7

In the second frame, per the third rule, we can notate that Wn is before Kr (there is no need to notate that Wn is before Lr because anything else is not possible in this frame).

Step 8

 In the second frame, per the fourth rule, we can notate that T must follow K. We can connect this to our notation for the third rule.

Step 9

In the second frame, per the fifth rule, we can notate that Y must follow Z.

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.