Diagramming Solutions for PrepTest 74

Utilizing methods taught in The LSAT Trainer.

Game 1

Step  1

Per the given scenario, we can write out the six elements to be placed - G, K, P, S, T, and V - and lay out the six positions to be filled, in order.

Step 2

Per the first rule, we can notate that G cannot be fourth.

Step 3

Per the third rule, we can notate that K must come after V and before G.

Step 4

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

Step 5

Per the fourth rule, we can split our existing diagram into two frames - one in which S comes after P and before T, and one where S comes before P and after T.

Game 2

Step 1

Per the given scenario, we can write out the four elements to be placed - F, G, H, and J, the four subsets - L, O, S, and W, and the four positions to be filled, in order.

Step 2

Per the first rule, we can notate that o and w must both go before l.

Step 3

Per the second rule, we can notate that F must go before o. We can connect this to our notation for the first rule.

Step 4

Per the third rule,we can infer that H must be one of the first two lecturers, and, from previous work, we can also infer that F must be one of the first two lecturers. That leaves G and J, in either order, for 3 and 4, which would satisfy this given rule. We can notate this on our diagram.

Step 5

We can mark that the subset s is not restricted by any of the rules.

Game 3

Step 1

Per the given scenario, we can write out the six elements to be placed - F, O, P, T, W, and Y.

Step 2

Per the given scenario and the first rule, we can set up two frames, one in which W is assigned and one in which W is not, and then we can lay out the assignments to be filled.

For the one which must include W, we know that the group W is in will have 3 total elements.  That means the other two groups must each have exactly one element assigned. We can also notate an “out” position for the one element not chosen.

For the frame without W, we can notate that each group must have at least one element, and tha W is the element that is out.

Step 3

Per the second rule, we can notate that if a rug uses O, it must use P.

For the first frame, we can infer from this that O cannot be the only element in either the second or third group, and P cannot be out by itself.

For the second frame, since we know both O and P must be used, we can place them into one of the groups together.

Step 4

Per the third rule, we can notate that F and T cannot be used together in a rug.

Step 5

Per the fourth rule, we can notate that P and T cannot be used together in a rug.

For the second frame, we can infer from this that T is on a separate rug from O and P and place it into our diagram.

Step 6

Per the fifth rule, we can notate that P and Y cannot be used together in a rug.

For the second frame, we can’t place Y because we don’t know where it goes relative to T, but we can notate that it cannot go in the same group as O and P.

Game 4 (Option 1)

Step 1

Per the given scenario, we can write out the six elements to be placed - F, G, H, K, L, and M - and we can lay out the assignments into two groups - S and T. For each group, we can notate that at least two elements will be assigned, and up to four total will be assigned.

Step 2

Per the first rule, we can notate that F and H must be assigned together.

Step 3

Per the second rule, we can notate that L and M cannot be assigned together.

Step 4

Per the third rule, we can notate that if G is assigned to S, L will be assigned to T, as well as the contrapositive.

Step 5

Per the fourth rule, we can notate that if K is not assigned to T, H and M must be assigned to T, as well as the contrapositive.

Game 4 (Option 2)

Step 1

Per the given scenario, we can write out the six elements to be placed - F, G, H, K, L, and M - and we can lay out the assignments into two groups - S and T. For each group, we can notate that at least two elements will be assigned, and up to four total will be assigned.

Step 2

Per the fourth rule, we can split up our diagrams into three frames, representing the three ways K, H, and M can be assigned respective to T: we can either have K assigned but not H and M, H and M assigned but not K, or H, M, and K assigned to T.

Step 3

Per the first rule, in the first frame, we can place F and H into group S. In the second frame, we can place F into the T group, and in the third frame, we can also place F into the T group.

In the third frame, T now has four elements, and there are only two elements left to fill the two required slots in S: G and L. We can place them into group S.

Step 4

Per the second rule, we can notate that L and M cannot be assigned together.

We can infer, for the second frame, that L cannot be in group T.

Step 5

Per the third rule, we can notate that if G is assigned to S, L must be assigned to T, as well as the contrapositive.

For the second frame, since we know that L cannot be assigned to T, we can infer that G cannot be assigned to S.

This rule creates problems for the third frame, which has both G and L in S. Thus, this rule makes the third frame invalid, and we can eliminate it.

Step 6

For the first frame, we can infer that since H and M cannot be in group T, the other required spot in T that must be occupied will be filled by G or L.

Step 7

For the second frame, we can infer that since G can’t be assigned to group S, the two spots in S that must be occupied must be occupied by the only two elements left: K and L.

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.