#11 - Local, Cannot Be True, False to True

[Dave Killoran]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=6424)

The correct answer choice is (B)

The question stem stipulates that exactly four applicants are hired, which means that at least four applicants are interviewed:

O97_Game_#2_#11_diagram 1.png

From the contrapositive of the last rule, when O is not hired, then M is not hired or L is not interviewed (or hired, then). But, consider what would happen if L is not interviewed: from the contrapositives of the first two rules, J could not be interviewed, and G could not be interviewed. That would mean that O could not be hired, L could not be hired, J could not be hired, and G could not be hired, leaving only three applicants available to be hired, violating the stipulation in this question that exactly four people are hired. Thus, L must be interviewed, and, correspondingly (to meet the contrapositive of the sixth rule) M cannot be hired. Thus answer choice (B), M is hired, cannot be true and is the correct answer.

[rka2224]

Hi there!

Could you walk me through the best way to approach Question 11 please?

Thanks!

-R

[Nikki Siclunov]

Hi R,

If O is not interviewed, by the contrapositive of the last rule we know that either M is not hired, or else L is not interviewed:

• O(i) M(h) OR L(i)

We must also ensure, however, that exactly four applicants are hired in accordance with the local condition of the stem. I'd worry about complying with this condition if the second of the two options (above) is true, i.e. if L is not interviewed. This is because if L is not interviewed, then J cannot be interviewed (second rule), and if J is not interviewed, then G is not interviewed (first rule):

• L(i) J(i) G(i)

Clearly, none of these people could be hired if L is not interviewed, leaving us with only F, K, and M to interview (and possibly hire). This violates the condition stipulating that exactly four applicants are hired. Clearly, then, L must be interviewed.

Since the second option presented by the contrapositive of the last rule is impossible to satisfy, we have no choice but to conclude that the first option must be satisfied, i.e. that M is not hired. The stem asks us to determine what must be false. Since M cannot be hired, answer choice (B) must be false and is therefore correct.

Hope this clears it up!

[emilym]

Hello,

I'm a little confused about this. If the contrapositive states that if O is not L is not interviewed, how can you violate that rule and state that L can be interviewed?

[Jeremy Press]

Hi emily,

The contrapositive of the last rule would actually be this:

Screen Shot 2020-04-13 at 12.58.43 PM.png

Remember that with multiple sufficient or necessary conditions, when we derive the contrapositive, the "and" changes to an "or" (and vice-versa).

So, when O is not interviewed, it could be that L is not interviewed. But it could also be that M is not hired.

From a logical perspective that's true because all we know that triggers O being hired (and thus being interviewed) is that both M's hiring and L's being interviewed (together) will do that. We don't know that one of those occurrences by itself will trigger O being hired (and interviewed).

I hope this helps!

Jeremy

[menkenj]

Hi there, I am working on recognizing next steps in the moment that is less time consuming than brute force. I immediately recognized that solving the problem would require attacking the contrapositive of the 6th rule, however I wasn't sure which element to start with Mh or Li.


Would an appropriate plan of action in these cases be to start with the most restrictive element? In this case, L is way more restrictive than M because of how the first two rules combine. So looking at how L not being interviewed plays out leads to the answer faster than starting with M not being hired. Does this thinking make sense beyond this particular game?

[Adam Tyson]

I don't think it's about where to start, menkenj, because you should diagram the entire contrapositive. The branch on which M is not hired stops right there, because that isn't sufficient for anything else. We don't have to choose where to go next, because this branch has nowhere else to go!

The branch of L not being interviewed, however, plays out a lot and should be followed to the end, showing that none of L, J, or G get interviewed and therefore none of them get hired. That would mean 4 of our 7 (including O) would not be hired, and that conflicts with the local restriction that exactly 4 people are hired.

Seeing that this branch conflicts with what we were given, we should conclude that L must be interviewed to avoid this problem, and that means M cannot be hired. No brute force required - it's all the result of just diagramming the chain while being cognizant of the local restriction!

In other games with similar situations, my advice would be to start by diagramming the entire chain that results from the local restriction. You never know where in that chain the answer will come from, so play it all out and see where it takes you!