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Setup and Rule Diagrams

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Setup and Rule Diagram Explanation

This is a Grouping Game: Defined-Fixed, Unbalanced: Underfunded.

When you create the setup, it is critical that the correct base be selected. There are two choices: the four researchers or the four languages. Since the researchers can learn one to three languages but it is uncertain exactly how many languages each researcher learns, the researchers seem a poor choice for the base. On the other hand, the number of researchers learning each language is clearly specified in the rules and as such the languages are the best choice for the base:


pt28_j99_g2_1.png
pt28_j99_g2_1.png (632 Bytes) Viewed 74 times


The distribution of researchers to languages is thus fixed at 1-2-2-3, and since there are only four researchers, it is clear that at least two researchers will have to learn more than one language (in fact, at least two researchers and at most three researchers will learn more than one language). Using the above base, we can set up the game as follows:


pt28_j99_g2_2.png
pt28_j99_g2_2.png (3.54 KiB) Viewed 74 times


Because G appears in both the non-numerical rules, it is clear that G is a power variable. The key inference involving G comes with Yoruba. Because Yoruba must be learned by exactly three researchers, and G cannot be selected with either L or P, it can be inferred that G cannot learn Yoruba, and the other three researchers must learn Yoruba. Additionally, since when G is selected H must also be selected, it is not possible for G to learn Rundi, as there is no room for H to be selected. Consequently, since G must learn at least one language, G (in the form of a GH block) must learn either Swahili or Tigrinya or both. From this inference it follows that neither L nor P can learn both Swahili and Tigrinya.
deana
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I am completely lost on the set up of this game. Not sure what to use as a base etc...
I set the bottom line up as RSSTTYYY but I literally missed every question.
Adam Tyson
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Deana, as I look at this game, what stands out to me are the numerical rules - 1 learns R, two learn S, etc. When I see numerical rules like that, I tend to think of setting those variable up as my groups, because I will have a fixed number for each group. Try setting it up like this (and I hope this looks right when I post it!) (Okay, it looked all wrong when I tried the first time, so I am doing it again, and setting up my groups vertically instead of horizontally as I normally would, just to make it look right):

R __
S __ __
T __ __
Y __ __ __

After that, your rules are two not-blocks blocks: [L/G], [P/G];
and one conditional rule leading to a block: G --> [HG].

Keep in mind that nobody can be in all four groups.

Try starting there and see what inferences you can draw. I think you'll find that there are some big ones.

Adam M. Tyson
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Adam M. Tyson
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deana
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Oh my gosh! Thanks so much. Just by changing my base I got every problem right in 5 minutes! The vertical setup was so much better than horizontal. How will I know in the future to use that? I know that seems like a ridiculous questions but I am really having trouble quickly knowing these types of set up difference.

Thanks so much!
Dave Killoran
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Hi Deana,

There really is no difference between the vertical and horizontal setup; functionally, they are identical. So, use the one that feels best to you :D Just make sure to represent the rules according to the direction of your setup.

Of course, some games--such as a game about a building--makes more sense to be set up vertically, whereas a game about houses on a street would typically make more sense as a horizontal game.

Thanks!
Dave Killoran
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cornhusker37
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Hello,

I am having some trouble with the formal logic aspect of this game. As I understand it, the fifth condition would suggest that L :dblline: G and P :dblline: G . If this were true, combined with the sixth condition of G :arrow: H , I would expect to infer that L :dblline: H and P :dblline: H . However, this is clearly not the case. Can you please help me figure out where I am going wrong? Thank you very much!
Dave Killoran
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Hi Cornhusker,

You are close, but the connections aren't correctly aligned to produce the inferences you are looking at. To be specific, the arrow that points from G towards H needs to be pointed in the other direction.

What you have here is:


    L :dblline: G :arrow: H
    P :dblline: G :arrow: H

Those produce the following two inferences:


    H :some: L
    H :some: P

If you had the following initial relationships instead:


    H :arrow: G :dblline: L
    H :arrow: G :dblline: P

Then that would yield the inferences you were looking for:


    H :dblline: L
    H :dblline: P

But see how the arrow now points away from H instead of towards it as in the first set of diagrams? That changes the inference dramatically in these two cases.

Please let me know if that helps. Thanks!
Dave Killoran
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Angelic414
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I am not sure how to approach this game. I simply created a board where the researchers are the players and the languages are where the researchers are placed.

My board looks like this:

___
___ ___ ___
___ ___ ___ ___
R S T Y

PLEASE HELP!
Lucas Moreau
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Hello, Angelic,

This game requires a bit of an unconventional setup. Here's what I came up with:

(1) R ___ ___ ___ ___
(2) S ___ ___ ___ ___
(2) T ___ ___ ___ ___
(3) Y ___ ___ ___ ___
.......L....G...P....H
(periods for spacing)

This diagram allows for all four researchers and all four languages to be represented in a gridlike manner that also demonstrates all the rules. The numbers to the left of the languages indicate how many times that language will appear among the four researchers.

L and G have :dblline: between them, as do G and P (I just couldn't get the formatting right to have it like that here :ras: ). You could add G :arrow: H off to the side if you like, or you could put a long arrow that curves underneath P connecting G and H, whichever you prefer. Just make sure it's not a double arrow - what G knows, H knows, but not necessarily the other way around! ;)

From here you should be ready to start making inferences. Good luck! :-D

Hope that helps,
Lucas Moreau
Echx73
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Hey Team,

I have question! Why do you not suggest just "Templating" the setup out? GH can only go in S or T and altogether there is four languages. Therefore, GH can go in S or T, or both. The question is so so much easier this way then in the book. This leads me to feel like I am missing something, but I get 100% on the question when I template out! Can't wait to here your thoughts!

Eric