#17 - Global, Rule Substitution

[Administrator]

Please post your questions below!

[mscrisbrown]

I chose A for question 17 . We someone please explain why D is the correct answer? Thank you

[Dave Killoran]

I chose A for question 17 . We someone please explain why D is the correct answer? Thank you

Good news, answer choice (D) is not correct! (A) is the correct answer so you got it right

[lsat_2020]

Hello -- Can someone explain why A is correct? On a redo, I was down to A and B, and A "looked" more correct, but I couldn't justify to myself why that would be.

Also, any general advice you have about how one would have done this quickly and efficiently on the test would be much appreciated. I have started to think I should give up on the idea that I will ever have enough time for a Rule Sub question on an actual exam...

Thank you!

[Adam Tyson]

I'll tackle the second part first, lsat_2020, and deal with the "how" of Rule Substitution questions. The goal in a question like this is to find the answer that would have the same overall effect on the game as the rule that was removed. If it helps, think of it as "which of these would result in the same exact diagram?" We are looking for something that creates all the same constraints on the game, while at the same time does not create any new constraints.

One approach is to consider what inferences came out of the original rule that is being removed. For example, imagine a game that had a rule that "If J is in Group 1, K must be in Group 3." Now imagine that in that game, that rule allowed you to make an inference that if J was in Group 1, L would have to be in Group 2 - probably because of some other rule about how K and L interact. If you were asked to remove the rule about J and K and find an answer that had the same effect, you might want to consider whether the inference about J and L would do the job. Perhaps a rule that said "if J is in Group 1, L is in Group 2" would also force K into Group 3? If it did, then you would be looking at a great contender, and probably the correct answer!

Another approach is to focus on what has been lost in removing the rule. In this game, what is lost is everything we know about M, because it is the only rule that has anything to do with M. Without that rule, M becomes a random variable, so the correct answer is going to have to do something with M in order for it to be returned to its original constrained status. That should help us to eliminate answers B and C, because adding them back to the game does nothing to M, leaving it unconstrained in any way.

From there, you have to consider how other rules will interact with the answer choice, and whether those interactions end up recreating the original rule. Look at answer E, for example - if M stays open, N must close. That would then trigger the first rule, that N and R cannot both close, and would force R to stay open. Putting those two things together in a conditional chain, we would get "If M is open, R is open," and that is a Mistaken Reversal of the rule we removed! That didn't put us back exactly where we started, and so it is not the correct answer.

But now look at answer A - if L closes, M stays open. I like this because it has the same Necessary Condition as the rule we got rid of (M staying open). If we apply the last rule, that L and R cannot both stay open, we would get "if R stays open, then L closes, and then M must stay open." Thus, following that conditional chain, if R stays open, M stays open - exactly what we were looking for!

Rule Substitution questions are tricky and can be very time consuming, so it is understandable that some people will choose to simply guess and move on when they encounter one. But consider these two approaches - a focus on inferences and on what was lost - and the idea that you are trying to recreate the original diagram, and you may find that they are often much easier and faster to solve than they at first appear. As always, practice, practice, practice!

[Littletiger1888]

I'm still not 100% sure about A. I get it that since L and R can't both be open, therefore R being open means L being closed. However, L and R CAN both be closed, right? In that case, since R is closed, then M can be either open or closed (hence M doesn't have to stay open). In other words, just from the fact that "L is closed" from option A, we can't deduce that R is open. Therefore, we can't get "M must stay open" from "L is closed". Am I wrong?

[Rachael Wilkenfeld]

It's a combination of rules that gets us there, tiger. Take a look at the rule that N and R cannot both close. So at least one of N and R is open. If N is open, L is open and R would close. If N is closed, R cannot be closed. So R would be open. R and L cannot both be open together. They also cannot both be closed together.

Let's start with the sufficient condition of answer choice (A). L closes. If L is closed, N has to close. N and R cannot both close. So if N is closed, R has to be open.

So starting with the sufficient condition of answer (A), we have L is closed, therefore R is open, and M is open. That has the same effect as if R is open, M is open.

Hope that helps!
Rachael

[JocelynL]

Hello,
On this I chose answer D and was so sure of it.
My logic was based on what happens with R is open
R M N closed L closed

I took the contrapositive of the above and got
L N M closed R closed
which led me to answer choice D) if L is open, then M must be closed. Which would give me the same diagram.

Am I linking these conditional chains incorrectly?

[Adam Tyson]

My logic was based on what happens with R is open
R M N closed L closed

You're starting with a chain that is not correct, JocelynL, in that M being open isn't sufficient to tell us anything about either N or L. If R is open, we know two things:

1) M is open, per the third rule
2) L is closed, per the last rule

And because L is closed, we also know that N is closed, via the contrapositive of the second rule.

But M being open didn't trigger anything else. L is closed in this scenario because R is open - that's from the last rule, not from any rule about M.

To prove that D does NOT have the same effect, let's see what we know must happen when L is open under the original set of rules:

1) R is closed, per the last rule
2) N is open, because of the first rule that N and R cannot both close

At this point, we know nothing about M, so it could be either open or closed. Answer D, then, in forcing M to close in this scenario, is changing the original outcome. It has a different effect than the rule that was removed, not the same effect. Thus, answer D is a loser.

[JocelynL]

My logic was based on what happens with R is open
R M N closed L closed

You're starting with a chain that is not correct, JocelynL, in that M being open isn't sufficient to tell us anything about either N or L. If R is open, we know two things:

1) M is open, per the third rule
2) L is closed, per the last rule

And because L is closed, we also know that N is closed, via the contrapositive of the second rule.

But M being open didn't trigger anything else. L is closed in this scenario because R is open - that's from the last rule, not from any rule about M.

To prove that D does NOT have the same effect, let's see what we know must happen when L is open under the original set of rules:

1) R is closed, per the last rule
2) N is open, because of the first rule that N and R cannot both close

At this point, we know nothing about M, so it could be either open or closed. Answer D, then, in forcing M to close in this scenario, is changing the original outcome. It has a different effect than the rule that was removed, not the same effect. Thus, answer D is a loser.

::bangs head on desk::

thank you Adam!