#16 - Local, Could Be True

[Dave Killoran]

This game is also discussed in our Podcast: LSAT Podcast Episode 70: The May 2020 LSAT-Flex Logic Games Section

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=33051)

The correct answer choice is (B).

If T hosts two meetings, then we know that T hosts in both semesters and that T is the sole doubled city; every other city can then appear only a single time. Thus, T occupies a spot in each semester, and then M and V must each host in a different semester to satisfy the third rule. This leaves H and O to rotate between semesters as well:

• _H/O_ _O/H_
  
  __T__       __T__
  
  _M/V_ _V/M_
  Fall      Spring

The information above eliminates answer choices (C) and (E)—since M and V must host meetings in different semesters—but it is not enough to narrow the answers down to a single response, so you must go further.

Since M and V are split, look at the two possibilities that exist when M hosts in the fall, and then when V hosts in the fall:

Solution #1: T hosts twice, M hosts in the fall

Under this scenario, each of the first two rules is already satisfied no matter where H and O are placed. Thus, H and O can continue to rotate. This scenario does allow us to prove answer choice (B) correct, however, since M and O both hosts meetings in the fall.

• _H/O_ _O/H_
  
  __T__       __T__
  
  __M__ __V__
  Fall      Spring

Solution #2: T hosts twice, V hosts in the fall

Just for academic purposes, let's look at the other scenario. In this case, H cannot host in the fall since from the first rule that would force M to host in the fall, which cannot occur here. Thus, H must host in the spring, leaving O to host in the fall.

• __O__ __H__
  
  __T__       __T__
  
  __V__ __M__
  Fall      Spring

Answer choice (A): H and V cannot both host meetings in the fall since there is no way for M to also host a meeting in the fall per the first rule.

Answer choice (B): This is the correct answer choice. As shown in Template #1 above, M and O can both host meetings in the fall.

Answer choice (C): This answer choice is incorrect because M and V cannot host in the same semester in this question due to the combination of the numerical constraints and the third rule.

Answer choice (D): M and O cannot both host meetings in the spring since that forces H to host in the fall, and then there is no way for M to also host a meeting in the fall per the numerical limitations in this question.

Answer choice (E): This answer choice is incorrect because M and V cannot host in the same semester in this question due to the combination of the numerical constraints and the third rule.

[cmorris32]

Hi PowerScore,

I'm really confused by this question. I thought this game was a two-values system so I diagrammed the rules like this:

H in F M in F
(contrapositive: M in S H in S)

V in S T in S
(contrapositive: T in F V in F)

M or V or Both in each semester

This question is asking if Tampa hosts two meetings, which one of the following could be true. I set up this situation using a hypothetical:
Fall: T
Spring: T

Because of the contrapositive of the second rule, I thought that since T was in F, V must also be in F. Therefore, I eliminated answer choice B because there wouldn't be enough room for T, V, M, and O to all host meetings in the fall.

I'm not sure if my contrapositives are incorrect in this game. I got the rest of the questions right in this game using the set-up I have with the contrapositives, but I just cannot figure out this question.

[Jeremy Press]

Hi there!

You got tripped up by the two-value assumption. It's not a true two-value system, because there are three options for any given variable: (1) meeting in Fall (but NOT in Spring), (2) meeting in Spring (but NOT in Fall), and (3) meeting in both. So, the contrapositives should be: M(Fall) H(Fall); and T(Spring) V(Spring).

Since T actually is in the spring for this question, the contrapositive doesn't trigger and V can be either in Spring or in Fall (though not both, since only one city can be both).

I hope this helps!

[cmorris32]

Hi Jeremy,

Thank you so much, that makes sense! I had a feeling that when I came to this question that the two-value assumption might have not been correct. I guess I just got lucky with getting the questions right, since I had the contrapositives of these conditional statements wrong.

Do you have any tips for avoiding this wrong assumption in the future? I am taking the Nov 2020 test in a couple days and want to make sure I don't make this assumption again. Do two-value systems only work when there are two base variables, and the other variable set can only go in one of two base sets?

Thank you again!

[legalbeagle99]

I made the same mistake regarding the two value assumption. Are there any previous games that are similar to this one that I could practice avoiding that mistake again?

[Adam Tyson]

There are plenty of games out there with conditional rules that could be mistaken for two-value systems if we aren't careful, beagle, but the first one that comes to my mind is fairly recent - PT 84, June 2018, Game 4, the Corporate Bonds game. There, two of the variables have to repeat, and so saying that a company offers a 5-year bond is not the same as saying it does not offer a 10-year bond. Check that game out and see if you can avoid that error. Good luck!

[Kelly R]

Just to clarify,

If a game scenario seems to establish a two-value system but includes variables that can repeat, then a true two-value system isn't present? In that case, it would be best to represent the contrapositive of conditional rules as their simple negations, correct (e.g. A-->B and NOTB-->NOTA)?

[Rachael Wilkenfeld]

Absolutely correct, Kelly. If it's not a true two-value system, you need to diagram it with the clear negation, instead of diagramming the contrapositive as just one of the potential three (or more) options in the system.

It's really easy to see when all three (or more) values are completely independent and separate. Ie John will go to either New York, Boston, or Miami. If we know he doesn't go to New York, we'd never conclude just from that that he goes to Boston. We'd leave both as possible, and make sure the diagram reflected it.

Here it's much easier to assume it's a two value because things occur in either the fall or the spring. But because of our distribution (6 slots for 5 cities), we know that one of those 5 cities has to occur in fall and spring, giving us a third option. It's an easy thing to overlook. If you made this error, awesome! Now you will be careful of this sort of error in the future. As a note, it also comes up with sequencing games and potential ties, or games that have two groups, but don't require that all variables be used.

Hope that helps!

[Kelly R]

Super helpful, Rachael– thanks so much!