Diagramming Solutions for PrepTest 62

Utilizing methods taught in The LSAT Trainer.

Game 1 (Option 1)

Step  1

Per the given scenario, we can write out the six elements to be placed - G, L, P, S, T, and W, and lay out the six positions to be assigned.

Step 2

Notate the first rule by indicating that W goes before L.

Step 3

Notate the second rule by indicating that P goes before both G and S.

Step 4

Notate the third rule by crossing out G, S, and T from underneath the second and third positions.

Step 5

Notate the fourth rule by crossing out T from underneath the final position.

Game 1 (Option 2)

Step 1

Per the given scenario, we can write out the six elements to be placed - G, L, P, S, T, and W, and lay out the six positions to be assigned.

Step 2

Notate the first rule by indicating that W goes before L.

Step 3

Notate the second rule by indicating that P goes before both G and S.

Step 4

We can frame around the limited options (W, P, and L) we have for filling the second and third positions. We have three pairings that could fill those two positions (W, P), (W, L), and (P, L) and we can create three frames around those three options.

Step 5

If W and L fill the second and third positions, since W must go before L, W must go in 2 and L in 3. And, since G and S must go after P, we know they must go into slots 4, 5, or 6. We also know that G and S are, in this frame, our only options for the final slot.

Step 6

If P and W fill the two positions, we don’t know their order, so we can place them into a cloud above the two positions. Per the first and second rules, L, G, and S must all follow P and W, so they must fill up the remaining three positions in some order. That leaves the first position as the only slot for T to fit into.

Step 7

If P and L fill positions two and three, again, we don’t know their respective order. We do know that since W must go before L, W must, in this frame, go in 1, and that leaves the remaining three elements, G, S, and T as our options for the final three positions. Of the three, G and S are the only two that can fill the final position.

Game 2

Step 1

Per the given scenario, we can write out the five colors - G, O, P, R, and Y, and positions for the three different stained glass windows. Each group starts with two boxes, indicating that each window must have at least two colors, and we know that each window can have more than two colors as well.

Step 2

Per the first rule, we can write G and P into one of the windows, and cross out the G, P pairing from the rest of the windows.

Step 3

We can notate the second rule by the R in our elements list.

Step 4

Notate the conditional relationships between Y, G, and O in the third rule by showing that Y in leads to G and O out, as well as the contrapositives.

Step 5

Since we know we must have at least one Y, and we know, per that third rule, that Y can’t be with G, we can place Y into one of our other window groupings, and, per that third rule, cross out O and G from beneath the group that Y is in. We can also cross out Y from underneath the G, P group.

Step 6

Note the conditional relationship between P and O in the fourth rule by showing that when P is out O must be in, and the contrapositive (if O is out, P must be in).

Step 7

That fourth rule leads to an inference that every window must have O, P, or both. Since the window with Y can’t have O, it must have a P. And per this inference we can put an O/P into one of the boxes for the final window as well.

Game 3 (Option 1)

Step 1

Per the given scenario and rules, we can write out two of each element to be placed, and lay out two positions each for each for the five talks, with an understanding that not all slots will be filled.

Step 2

Per the first rule, cross out Q from beneath F and H.

Step 3

Per the second rule, cross out R from beneath G and H.

Step 4

Per the third rule, notate that S and T cannot go together.

Step 5

Per the fourth rule, group Q and T1.

Step 6

Per the fifth rule, group S with R1.

Game 3 (Option 2)

Step 1

Per the given scenario and rules, we can write out two of each element to be placed, and lay out two positions each for each for the five talks, with an understanding that not all slots will be filled.

Step 2

Per the first rule, cross out Q from beneath F and H.

Step 3

Per the second rule, cross out R from beneath G and H.

Step 4

Per the third rule, notate that S and T cannot go together.

Step 5

Per the fourth rule, group Q and T1.

Step 6

Per the fifth rule, group S with R1.

Step 7

Create frames off of the limited options we have for where to place our two Q’s. (Similarly, you could have framed around where to place the two R’s). Since Q can’t first or third, it can either go in 2 and 4, 2 and 5, or 4 and 5.

Step 8

For the first frame, if Q goes in 2 and 4, the S and R grouping can only go in 1.

Step 9

For the second frame, if Q goes in 2 and 5, the S and R grouping can either go in 1 or 4. We can further split the frame per these possibilities. When the S, R grouping goes in 4, the second R must go in 5.

In both of these frames, since, per the fourth rule the first T must be grouped with a Q, the first T must be together with the first Q.

Step 10

In the third frame, if Q goes in 4 and 5, which also forces T into 4 and 5.  The S and R group can only go in 1. However, there is now no place for the second R to go, since it can’t go in 2 or 3. Therefore, this third frame is not a viable option and thus we can cross it out.

Game 4

Step 1

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

Step 2

Notate the first rule involving S, T, and U using or notation.

Step 3

Notate the second rule by showing that U goes before R and W.

Step 4

Notate the third rule involving T, W, and M using or notation.

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.