Diagramming Solutions for PrepTest 65

Utilizing methods taught in The LSAT Trainer.

Game 1

Step 1

Per the given scenario, write out the five elements - F, G, H, J, and K - to be placed, and five positions to be occupied.

Step 2

Per the first and third rules, notate that H and F must be immediately next to one another (in either order), and that G must come before this duo.

Step 3

Per the second rule, notate that K must come before H and J. We can connect this to the H we already have written down.

Game 2

Step 1

Per the given scenario, we can lay out six positions to be filled. We can also list out the six subjects - N, O, P, S, T, and W-as the elements to be assigned, and use subscript to represent the teacher connected to that subject: Nj, Oj, Pk, Sk, Tk, WL.

Step 2

Per the first rule, we can notate that we cannot have two consecutive K’s.

Step 3

Per the second rule, we can notate that Sk must be before Oj.

Step 4

Per the third rule, we can notate that Tk must be before WL.

Game 3 (Option 1)

Step 1

Per the given scenario, we can write out the eight items to be placed: desserts F and G (Fd, Gd), main courses N, O, and P (Nm, Om, Pm), and side dishes T, V, and W (Ts, Vs, Ws), notate the three dishes that are hot (with an h before F, N, and T), and we can lay out the five positions to be selected and the three positions for those who won’t be selected.

Step 2

Per the first rule, notate that we must have at least one of each subset. A small inference that can be made is that since we only have two desserts total (F and G), at least one of those two must be selected. We can place an F/G on the board, and notate conditionally that if either of them are out, the other must be in.

Step 3

Per the second rule, notate that at least one hot dish must be selected.

Step 4

Per the third rule, notate that P and W must always be together.

Step 5

Per the fourth rule, we can notate conditionally that if G is selected, O must be as well, and the contrapositive. We can add this notation to the conditional information we’ve already notated about G.

Step 6

Per the fifth rule, we can notate conditionally that if N is selected, V cannot be, and the contrapositive. We can make and notate a small inference that this means at least one of the two -- either N or V -- must be out.

Game 3 (Option 2)

Step 1

Step 2

Per the third rule, we can create two frames, one where P and W are both selected, and another where neither is selected.

Step 3

In the second frame, when neither are selected, we only have one remaining out slot. Looking down at the fifth rule, we know that that final spot must be occupied by either N or V. Thus, in the second frame, all other elements must be selected, and we can draw them in. Testing the selections against the rules, we don’t violate any of the rules, and so we know that the frame is viable.

Step 4

Returning the first frame, per the first rule, notate that we must have at least one of each subset. A small inference that can be made is that since we only have two desserts total (F and G), at least one of those two must be selected. We can place an F/G on the board, and notate conditionally that if either of them are out, the other must be in.

Step 5

Per the second rule, notate that at least one hot dish must be selected.

Step 6

Step 7

Game 4

Step 1

Per the given scenario, write out the elements to be placed - G, R, S, T, and W - and indicate that G takes up two :30 slots while the rest of the elements take up just one. Also, lay out six slots for the six positions that begin at 1:00.

Step 2

Per the first rule, split the board into three frames, representing the three times where the G (or G’s, per how we’ve notated it) can be placed: at 1:00, 2:00, and 3:00.

Step 3

Per the second rule, notate on each frame that T must go on the half hour rather than the hour.

Step 4

Per the third rule, notate that R must be before S.

Step 5

Per the fourth rule, notate conditionally that if W is before T, it must be immediately before T, and the contrapositive (if W is not immediately before T, W must be after T.)

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

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