#12 - Local, Must Be True

[Dave Killoran]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=2316)

The correct answer choice is (E)

As H and I are already assigned to Y, and must therefore speak French or Turkish, M and N must also speak French or Turkish. Therefore, M and N must together be assigned to V or X:

• Possibility #1: M and N assigned to V (where both speak French)

J98_Game_#2_#12_diagram 1.png

• Possibility #2: M and N assigned to X (where both speak Turkish)

J98_Game_#2_#12_diagram 2.png

In each instance, H, I, M, and N speak the same language (French in Possibility #1, Turkish in Possibility #2). As shown in Possibility #2, answer choice (E) could be true and is correct.

[rachelgstevens]

Hi, I don't understand why there isn't possibility #3:
                         M          
                         I          
K      N          H          L
Vf     Xt,s     Yf,t     Zs,r

Wouldn't this still satisfy the requirements? M, I, H, and N could all speak turkish leaving K to speak French (which is the correct answer).

When I worked this problem, I had the two possibilities in the book and this one. I'm sure I am missing something obvious

Thanks!

[Jay Donnell]

Hi Rachel!

Good spot!

That would totally be an acceptable assignment of tourists to guides while following the additional constraint introduced by the Local question.

The 3-1-1-1 distribution is in line with the most extreme acceptable numerical possibility, and as long as we keep K out of Xerxes then M is free to speak any language, leaving Turkish wide open.

With the question being a Could Be True, this just provides another route to the same possibility that we discovered in allowing K to speak French in the correct response of E.

Great catch, take this a sign of some seriously impressive reasoning skills!

[Pat Mc]

Edit: The text is OK, but the diagrams are NOT what I intended. I guess I'll research how this works and come back and redo the diagrams later.
Hi, I think that in total there are 6 possibilities, which you can quickly tell by doing a template based on your only 2 choices (3 for when H, I, M and N all speak French, and 3 for when H, I, M and N all speak Turkish).

Note: This is the main diagram (universal diagram) I drew. I never explicitly came up with the numerical distribution, which would have made things easier. Gotta practice with a checklist so I don't miss these things.

≥2 of I
(K, M, N) H L
V X Y Z
F T F S
S T R

General Possibility #1: H, I, M and N all speak French
Then M-->(V/Y) and N-->(V/Y). Since (V and X) must be filled by 2 or more of (K, M, N), then since neither M or N is available for X, that means K must go to X. (Note: We were told that all guides (in other words, groups) must have 1-3 vars, so 0 is not allowed). Since we know KX is true, we need to worry in any template we make here whether it follows the KX --> MF rule is followed. But MF is already followed by the construction of this possibility (remember, M speaks French by assumption, and we have already made sure to follow that by limiting M to only V/Y), so on further thought, this rule will automatically be followed.

I Remaining vars: M and N
K H L M-->(V/Y)
V X Y Z N-->(V/Y)
F T F S
S T R

We now know where all the variables must go except for M and N. Since we have 2 options for each of them, we should have 4 possibilities. But M and N both going to Y is pretty easily seen to be not allowed, because Y would have 4 vars, and guides are only allowed 1-3. So we only have 3 possibilities: 1. M and N both in V, or 2. M in V and N in Y or 3. N in V and M in Y.

Sub-Possibility A:

M I
N K H L
V X Y Z
F T F S
S T R

Sub-Possibility B:

N
I
M K H L
V X Y Z
F T F S
S T R

Sub-Possibility C:

M
I
N K H L
V X Y Z
F T F S
S T R

All 3 rules are followed in all possibilities ( the first two because they're written in to the diagram and the third because of what I said above) and the group sizes rules are also met (don't forget about the rules which are not exactly listed as rules like this one!), so all 3 possibilities should be valid.

General Possibility #2: H, I, M and N all speak Turkish
Then M-->(X/Y) and N-->(X/Y). Since (V and X) must be filled by 2 or more of (K, M, N), then since neither M nor N is available for V, that means K must go to V. Since now we know K is not in X, we do not need to worry about checking whether the KX --> MV/Y rule is followed in any of these templates here, because the sufficient condition KX will never be fulfilled.

I Remaining vars: M and N
K H L M-->(X/Y)
V X Y Z N-->(X/Y)
F T F S
S T R

We now know where all the variables must go except for M and N. Again, since we have 2 options for each of them, it looks like we have 4 possibilities but we really only have 3 because one guide is empty, and the other has 2 already. The 3 possibilities are: 1. M and N in X, or 2. M in X and N in Y or 3. N in X and M in Y.

Sub-Possibility A:

N I
K M H L
V X Y Z
F T F S
S T R

Sub-Possibility B:
N
I
K M H L
V X Y Z
F T F S
S T R

Sub-Possibility C:
M
I
K N H L
V X Y Z
F T F S
S T R

Personally, the way I did this was slightly different; I only diagrammed what I knew for sure. I made the 2 templates, and noted that in the M - French one, K must go to X, no others can go to X or Z (those lines represent caps, though I draw them differently) and M/N must go to V, though I left the options open for the second to go on V or Y.
_ I _
M/N K H L
V X Y Z

M-->(V/Y) N-->(V/Y)

In the M - Turkish one, I noted K must go to V, no others can go to V or L, and M/N must go to X, again leaving the options open for the second one.

_ I _
K M/N H L
V X Y Z

M-->(X/Y) N-->(X/Y)

[Rachael Wilkenfeld]

Hi Pat,

Note: we typically cannot review posted setups since it's so time-consuming, but we'll go ahead and do just this one Anyone else is always free to comment though!

Please let me know if I'm understanding your basic structure. You have two main scenarios. In one, where the four speak French, you have K in X, IH in Y, and at least one of M/N in V (with the other also able to go in Y). In the other main scenario, you have K in V, at least one of M/N in X, IH in Y (with possibly one of M/N).

That represents fairly well what was in the explanations above. You can have either K or M/N in either X or V, with either M/N together or one in X/V and the other in Y. I personally just drew out the 2 main possibilities because they represented what I needed. It gave me a good idea of what could be true, and I didn't need to draw out all 6 options. In each of the two main scenarios, I drew three slots for M/N. One in IH, and two in either X or V depending on the scenario.

Good work!
Rachael