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#39215
Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=12911)

The correct answer choice is (D)

This question asks us to determine which cannot be the colors of the two solid rugs, assuming a 3-1-1 distribution. Neither O nor W can be used in any of the solid rugs, as discussed earlier; however, this inference proves inadequate in attacking this question, because none of the answer choices contains either O or W.

To plug-and-chug five pairs of variables in an attempt to prove which pair does not work would be inefficient. To minimize the time spent on this task, first review your prior work! Every local diagram based on the 3-1-1 distribution can be used to show a pair of colors that could be used to create the two solid rugs, potentially eliminating one or more answer choices. Consider, for instance, the local setup for Question #13. It is immediately apparent that the two solid colors could be P and T, or else P and F. This eliminates answer choices (C) and (A).

With only three remaining contenders, the process of elimination should not take an exceptionally long time. An even more efficient approach would be to skip this question altogether, and work through the last two local questions first. The goal is to assemble a larger collection of local diagrams in the hopes of eliminating additional answer choices. This strategy proves quite useful here, as the local setup for Question #15 shows that T and Y could be the colors of the two solid rugs, additionally eliminating answer choice (E).

Answer choice (A) is incorrect, because P and F could be the colors of the two solid rugs, as shown in the local setup for Question #13.

Answer choice (B) is incorrect, because F and Y could be the colors of the two solid rugs, as long as P and T are not used together in the multicolored rug to avoid violating the fourth rule. Since P must always be among the colors used, it follows that T cannot be used in any of the rugs:
PT74 - Game_#3_#14_diagram 1.png
Answer choice (C) is incorrect, because P and T could be the colors of the two solid rugs, as shown in the local setup for Question #13.

Answer choice (D) is the correct answer choice. If P and Y were the colors of the two solid rugs, then O cannot be used in any of the rugs, because O requires P to be used together with it. With O out, we need to use the remaining three colors to create the multicolored rug:
PT74 - Game_#3_#14_diagram 2.png
This solution is in clear violation of the third rule, which forbids T and F from appearing in the same rug. Therefore, answer choice (D) is the correct answer choice to this Cannot Be True question.

Answer choice (E) is incorrect, because T and Y could be the colors of the two solid rugs:
PT74 - Game_#3_#14_diagram 3.png
This answer choice would be even easier to eliminate using the local diagram for Question #15, if you opted to attack Question #15 first.
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