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 Administrator
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#39213
Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=12911)

The correct answer choice is (B)

If F and P are used together in a rug, we can safely rule out the 2-2-1 distribution, because it requires P and O to be used together in a rug. This deduction helps eliminate answer choice (A).

If F and P are two of the three colors in a rug subject to the 3-1-1 distribution, the third color must be W or O. This is because neither W nor O can be used in any of the solid rugs, as discussed in the main setup:
PT74 - Game_#3_#15_diagram 1.png
PT74 - Game_#3_#15_diagram 1.png (1.5 KiB) Viewed 891 times
With no room for both W and O to be used in the multicolored rug, we need to ensure that one of them is not used in any of the rugs. The remaining two colors—T and Y—must be the colors of the two solid rugs:
PT74 - Game_#3_#15_diagram 2.png
PT74 - Game_#3_#15_diagram 2.png (1.79 KiB) Viewed 891 times
By focusing our attention to the uncertainty inherent in this setup (W/O), we can easily see that answer choice (B) could be true, and is therefore correct.

Answer choice (A) is incorrect, because the applicable distribution here is 3-1-1, not 2-2-1, as discussed earlier.

Answer choice (B) is the correct answer choice, because W can be excluded without violating any of the conditions governing the assignment of colors to the three rugs.

Answer choice (C) is incorrect, because Y must be the color of one of the two solid rugs.

Answer choice (D) is incorrect, because T and W cannot be used together in any of the rugs.

Answer choice (E) is incorrect, because T and Y are the colors of the two solid rugs, and cannot be used together in any of the rugs.
 ncolicci11
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#76061
Why can T and W never be together? I am not sure why that is the case. Is it not possible to have O out, P solid, F solid, and WYT?
 Frank Peter
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#76071
Hi ncolicci,
ncolicci11 wrote: Is it not possible to have O out, P solid, F solid, and WYT?
The problem with that setup is that it wouldn't comport to the setup for this local question, which requires F and P to be used together in a rug.

Frank
 angelsfan0055
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#86347
Can you explain why E is incorrect? What in the rules precludes T and Y from going together? It doesn't seem like there has to be a minimum of solid rugs
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 Ryan Twomey
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#86421
Hey Angels Fan,

Check out the drawing above. So essentially, W or O has to be out. And W or O has to be in the rug with F and P. If W is in it has to go with F and P because their aren't enough entities remaining to get to 3 colors which is what W requires. If O is in, it has to be with P.

So essentially Y and T will be in their own solid rugs because we need to have 3 rugs. We cannot have only two rugs in this game because they told us three rugs will be woven in the prompt.

The key to figuring out this deduction for this particular question if figuring out that W or O has to be out and that W or O has to be the third rug with F and P.

Hope this helps.

Best,
Ryan

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