Setup and Rule Diagrams

[Kellyg]

Could you please explain the set up for this game. I simply wrote a few scenarios in which some variables would go into open/closed groups based on some of the rules that give insight such as putting N into open (because that would put L there and R in closed). However, this didn't yield many inferences which i felt hurt me later on in the game, specifically question 16 and 17.

[Jonathan Evans]

Hi, Kelly!

This game benefits from two basic templates:

PT83 Dec 2017 Game 3 Setup.png

Notice that R, N, and L are all connected to each other. Let's explore a couple possibilities. As you mention, if N is open, so is L. Then R is closed. I used this for the first template. I stipulated that in this scenario we do not know where P, Q, or M go. These three are our randoms in this template.

In the second scenario, I've put R into the open group instead of N. R open means M is also open. R open means that L is closed. L closed means that N is also closed. In this second template, only P and Q are randoms.

For question #16, we are asked which station must close if exactly two stay open. Either one of our templates would work in this scenario. The breakdown would be as follows:

• Question # 16
  
  Template 1 Open: N L, Closed: R P Q M
  
  Template 2 Open: R M, Closed: N L P Q

In both scenarios, both P and Q must be closed. Therefore, the correct answer will be P or Q. That's how we get the correct answer, (D).

For question #17, you don't really need the templates. What you have to do is try to replicate the effect of the substituted rule. The original rule is:

• R M

We need to make a replacement rule that would have the same result. In other words, we need to make R open sufficient to guarantee M open. Let's ask ourselves what else R open does. We can look for any other R open sufficient condition. There is one other R open sufficient condition:

• R L

Since R open also means L closed, we can make a chain conditional to replicate the original rule. We do this by making L closed the new sufficient condition to guarantee M open:

• L M

Now altogether we have a new chain conditional:

• R L M

The implication is that if R is open, M is open too. This is identical to the original rule.

I hope this helps!

[T.B.Justin]

Hi Jonathan,

I appreciate the breakdown - very helpful.

[lsatbossintraining]

Hi -

I understand that the last rule creates a double-not arrow. Does the double-not always imply that one of the two variables must occupy a slot in the “in” or “out” slots? I’m pretty sure the only inference we can make is the two can’t go together but just want to confirm.

Additionally, does the first rule imply that one of the variables must be in, and is there where you split the board into two templates?

Just looking for a refresher before my test next Monday.

Thanks so much.

Kyle

[Jeremy Press]

Hi Kyle,

In this game, it's crucially important to be clear about what you mean by the "in" group and the "out" group. It doesn't much matter which you decide for this game, but you have to make the decision up front and stick to it absolutely as you consider each rule. Personally, I'd select the "open" stations as the "in" group, and the "closed" stations as the "out" group, because "closed" has a negative connotation and will match well with what we generally mean when we negate variables in conditional rules (that they are "out").

Treating the "open" stations as the "in" group, and the "closed" stations as the "out" group, then the first rule in the game implies what you stated: that one of the variables must be in. Keep in mind that such a rule (by itself) allows for the possibility that both variables are in. The last rule also implies a "double-not arrow," as you stated. That means at least one of those variables must be out. But, it would ordinarily be possible under such a rule to leave both variables out.

The templates Jonathan created in his post above aren't coming from either the first rule by itself, or the last rule by itself, and I ordinarily wouldn't treat those kinds of rules (by themselves) as indicative of a templating approach. The templates Jonathan noted arise from the fact that, because of the way the rules interact, L and N are permanently linked (and thus always dictate where R goes).

How do you know L and N are linked? The first and last conditional rules combine to produce this inference:

L ~R N (i.e. L N).

We also know from the second rule that N L.

So, L and N are in a "double arrow" relationship (they're either both in, or they're both out). If L and N are both in, R must be out, because of the last rule. If L and N are both out, R must be in, because of the first rule. It's the double-arrow relationship between L and N that is "driving" the templates in this game.

I hope this helps!

Jeremy

[lsatbossintraining]

Thanks for clearing that up!

[Ari]

Hello,

I have seen other LSAT Prep sites will suggest a logic chain for simple in/out grouping. I attempted to do one with this, but it did not work well because R is connected to three different variables and it got messy. Do you guys ever suggest using logic chains, and if so, when? I feel like they could be helpful because sometimes I feel like I waste time trying to connect rules, but also with time and practice that will get faster, so I am not sure if they are worth the time.

[Rachael Wilkenfeld]

Hi Ari,

I'm not completely sure what you are referencing by logic chains. If you mean a conditional reasoning chain, then absolutely you should use one when the rules indicate. Not all conditional statements can be connected though, so you do need to be careful with that. Just because two rules share a common variable doesn't mean they connect in a chain. If you mean something else, it might help to diagram what you are describing so that we can comment on it more directly.

Hope that helps!
Rachael

[SGD2021]

Hello, it is ever possible for a variable not to show up in a game like this? Why can we just assume all variables will in fact show up?

[Adam Tyson]

You should never assume anything about a game, SGD2021! Most games will tell you that all the variables have to be included, but when they don't tell you that, sometimes you can still infer it. That's not making an assumption - that's determining something that must be true based on the information provided.

In this game, the operator is going to close at least one of the stations. If they don't close a station, it still exists somewhere, so we can't ever say that a variable here just disappears and is not in the game. It's either closed, or it's not closed; there is no other option! So whether you think of the variables as being "in" and "out," or "open" and "closed," or "selected" and "not selected," every solution will have to account for all of the variables. It's the nature of the scenario that everything has to be in the group (the stations the operator chooses to close) or not in the group (the other ones).