PrepTest 59: Logic Game #4 Explanation, Cities

LSAT PrepTest 59 (December 2009 LSAT), Game 4, is a difficult linear game.

Below, I've written a complete explanation of this game, including the setup, diagrams, and questions.

If you haven't completed this PrepTest yet, save this blog post for later. You'll want to do this PrepTest as a full-length timed exam in the final week before you take the LSAT.

If you're taking the LSAT next week and you've already taken PrepTest 59, open your exam to this game and follow along. Otherwise, come back to this blog post in a few months or so.

Also see: Explanations for Recent LSAT Logic Games

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This is an especially difficult linear game due to the fact that V and L can be in either order, as can M and T.

The rules themselves do not lead to any major inference.

Here's an initial diagram that's very basic:











If you like, you can insert the simple inference that T cannot be 6th and L cannot be 1st:











Most people stop there and move directly on to the questions.

However, games usually have something more that you can do.

The following is the approach I take. It's not for everyone. You have to be able to think and sketch quickly. However, I believe it's the best way to approach this game.

By diagramming every possible scenario, or even a few main diagrams under which every valid scenario must fall, you ensure that you don't miss anything as you're going through the questions.

In other words, you ensure that you're going down every possible road.

In this blog post, I'll lay out how I draw every possible scenario, little by little, then use it to blaze through the questions like Wile E. Coyote.

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I use the V/L _ _ L/V rule to create my main diagrams because V is also involved in the rule that V and W must touch and because L is involved in the rule that T is before L.

I could've used the M/T _ _ T/M rule since T is also involved in the rule that T is before L.

However, I find a rule that imposes immediacy (in other words, a rule that forces certain variables to touch) to be more limiting. V and L are each involved in another rule (and the other rules they're involved in are not the exact same rule - they're involved in different rules).

On the other hand, only one of T and M involved in T before L rule ("T", of course).

As such, using L/V _ _ V/L is more powerful in creating multiple main diagrams because these variables relate well to the other variables. Their presence in particular spaces impacts the greatest number of variables. Using T and M as our starting point would not impact the other variables as much.

I start with the V/L _ _ L/V rule by creating 3 diagrams:

V on 1, L on 4
V on 2, L on 5
V on 3, L on 6

There's no more room to create diagrams with V before L with 2 spaces between them, so I then create 3 diagrams with:

L on 1, V on 4
L on 2, V on 5
L on 3, V on 6

This gives us:

















Yes, I know it looks crazy, but this is what I do. And it works.

"But wait!", you say. L can't go on 1.

Right you are. That diagram is invalid, so we can cross it off for good. Now there are only 5 main diagrams.

While we're at it, we can start applying the rule that V and W have to touch. In most of the diagrams, W could appear on either side of V, but not while V is on 1 or 6. As such, I put down W in the diagrams where it's limited to one specific space.

In the top diagram, where we put V on 1 and L on 4, W has to go on 2. T will have to go on 3, since T has to go before L.

Since T and M also have to be spaced apart with exactly 2 variables between them, M will have to go on 7, leaving N to go on 6. This diagram is now full.

Of course, I've also placed W on 5 in the bottom diagram. Focusing on the T before L rule does not automatically limit T to a specific space at the moment, so that's all for now.

All of this so far gives us the following:























Continuing, I focus on the bottom diagram since it is the most limited diagram not yet filled in. (I know it's limited because spaces 5 and 6 are determined already.)

T and M must have exactly 2 spaces between them, so they will have to go on spaces 1 and 4. Since T must go before L, T will go on 1, and M will go on 4. This leaves N to go on 2.

We now have the following:
























Now, the 5th diagram, the one directly above the one we just filled in.

L's on 2, so T's on 1, which forces M to be on 4. W and V have to touch, so W will go on 6. This leaves N to go on 3.

We now have:























Only 2 diagrams left, but there's an issue:

We don't know whether W comes before or after V in each of those diagrams. So we can break this open by creating 2 extra versions of each of those diagrams. This allows us to place W before V on one version of each diagram. We'll place W after V on the other version of each diagram...like so:















We can now approach the 4 remaining diagrams just like the others.

Notice that previously I've been placing N last since there are no rules about it. I'll continue to do the same. Since aside from N, the only variables I have are T and M, and there's a rule about them, I'll use them.

Given the nature of the rule involving T and M, I'm going to look for spaces that have exactly 2 slots between them.

Starting with the remaining diagram on the top-left (where W's on 1), I'm going to put T on 3 and M on 7. I can't put M on 3 and T on 7 because T must always go before L (another rule).

Therefore, N must go on 4, and this diagram is done:















On the top-right diagram (where W's on 3), T and M will have to go on 1 and 4, and they're interchangeable since both of those slots are before L.

It doesn't matter whether T goes on 1 or 4 - either way, it'll be before L.

N will go on 7, giving us:















On the bottom-left diagram (where W's on 2), T and M will go on 1 and 4. Again, they're interchangeable. N will go on 5:















Finally, in the bottom-right diagram (the only one remaining undone), T and M will go on 2 and 5, interchangeably. T will be before L whether it goes on 2 or 5. The only available space for N is on 1:















I'm lettering the diagrams for easy reference as I go through the questions. I obviously wouldn't do that on Test Day!














Now, the questions:

Question 17
There are two acceptable ways to approach this common opening question.

You can:

1. Take one rule at a time and apply it to all 5 choices, eliminate any violators, then take the next rule and do the exact same thing until you've exhausted all the rules and have the correct answer.

2. Check each choice against our complete list of possibilities.

Both ways are fine. In this particular situation, I like the 2nd option since the possibilities we have are pretty clear-cut and relatively simple. By this, I mean the diagrams don't contain too many slashes - only the 3 cases where T and M alternate like so: T/M _ _ M/T. This occurs in diagrams B2, C1, and C2.

I'd start by checking choice A, which starts with TVW. Only diagram B2 contains that possibility for the first 3 spaces, so I check the rest of Choice A to see if the rest of it complies with B2. It does, so we're finished. Circle A and move on. No need to go through the other choices.


Question 18
Since we have every possibility listed, we can easily eliminate wrong answers.

A) T's not always 1st. We have A, B1, and C2 to disprove it. Eliminated.
B) M's not always 4th. A, B1, B2, C1, and C2 don't have to have M 4th. Eliminated.
C) T's not always before M. Any of B2, C1, and C2 would be sufficient to disprove this choice. Eliminated.
D) N and V don't always touch. In fact, they never do. Eliminated.
E) By elimination, it must be our answer. Looking at it, are N and W 2 spaces apart? Yes, they are in every single one of our comprehensive list of scenarios. This is the answer.


Question 19
Now, they're asking us what would completely determine the layout of variables.

A) L on 5 occurs in both B1 and B2, so it can't be the answer. (Even if it had only occurred in B2, it wouldn't be the answer because B2 contains 2 possibilities.) Eliminated.

B) M on 6 occurs in both A and B1. Eliminated.

C) N on 5 occurs in both A and C1. Eliminated.

D) V on 1 occurs only in possibility A, where there are no slashes or ambiguities. Correct answer.


On Test Day, you should circle D on move on, but I'll explain E anyway:

E) W on 2 occurs in A and in C1. Eliminated.


Question 20
We want a complete list of places where W occurs. Let your eyes scan vertically across diagrams on each space, moving from space 1 to space 6 as you check through all the diagrams.

We have W on space:

1 in diagram B1
2 in diagrams A and C1
3 in diagram B2
4 in diagram C2
5 in diagram E5
6 in diagram D

Thus, choice E is our answer.


Question 21
If M is in the first year...this refers to diagrams B2 and C1.

A) W on 3 occurs in B2. Eliminated.
B) V on 3 occurs in C1. Eliminated.
C) T on 4 could occur in both. Eliminated.
D) N on 5 occurs in C1. Eliminated.
E) By elimination, it must be the answer. Looking at it, L on 5 occurs in neither. It's our answer.


Question 22

A) L on 1 does not occur in any diagram. Eliminated.
B) N on 2 occurs in diagram E. Pick B and move on.

The others never occur in any diagram either.


Question 23
In all 5 choices, they're asking which of the following pairs of variables could be consecutive (could touch).

A) L and N touch in all but 1 of the diagrams. You only need to find one case where they touch in order to eliminate this choice, of course, but they touch in A, B1, B2, C1, D, and E. Eliminated.

B) L and W never touch in any diagram. It's our answer, so pick it and move on.

However, I'll go through the other choices anyway, for learning purposes.

C) N and T touch in B1, C1, C2, and E. Eliminated.

D) T and V touch in B1, B2, C1, and C2. Eliminated.

E) T and W touch in A and B2. Eliminated.

Photo by sunsurfr / CC BY NC-SA