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Course: LSAT (DEPRECATED) > Unit 1

Lesson 5: Analytical Reasoning – Worked examples

Grouping setup | Given info–must be false | Worked example

Watch a demonstration of one way to approach a "Given info: CANNOT be true" question on a grouping setup on the analytical reasoning section of the LSAT. Created by Annie Hollister.

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  • piceratops seed style avatar for user Aleija
    I believe A could also be correct based on the setup of the question. In particular, rule 1 states that no two costumes can have the same color combination. If two costumes have indigo in them, then those same two costumes also have yellow, which would violate rule 1.
    (0 votes)
    Default Khan Academy avatar avatar for user

Video transcript

- [Narrator] Which one of the follow must be false? With this type of question we should be able to deduce the right answer from the information we already have, and any inferences we made in the setup. So, first let's think about what we already know. Rules two and three together tell us that indigo and yellow are a pair and always appear together. Rule four says that red can't be matched with indigo or green, and because indigo and yellow are paired that also tells us that red and yellow aren't together. That means that red can only be matched with white and orange, and since each costume has three colors in it that means that one costume must be red, white, and orange. It also means that because no two costumes have the same three colors, there's only one costume that has red in it. So, that gives us a lot of information to think about what must be false, but looking at the choices E says exactly two of the costumes have both green and orange in them. We worked out that one of the costumes is red, white, and orange which definitely doesn't have green in it, and we also know that another one is indigo and yellow and some third color. Well that costume can't have green and orange in it because the third color is either green or orange, and the other two are indigo and yellow. That means that only one costume could possibly have green and orange in it, and that is that third costume that doesn't have red or the indigo yellow pair in it. So, the answer is E. Exactly two of the costumes have both green and orange in them. This must be false given the rules of the setup. In the real exam you should just move on, but we might as well check that A-D could be true given the rules of the setup. For instance A, exactly two of the costumes have indigo in them. Well, that could be true if this third costume has indigo in it, which would also mean that third costume has yellow in it, which means that one of these costumes has green in it and the other has either orange or white. B says exactly two of the costumes have white in them. Let's also find, for instance, if this costume is red, white and orange, this one is indigo, yellow, and white, and this costume is indigo, yellow, and green. All three costumes have orange in them. Again, this is possible if the third color in this costume is orange, and this third costume is orange, green, and white. Finally, exactly one of the costumes has both yellow and white in it. That can be true if this costume is indigo, yellow, and white, and this costume is say indigo, yellow, and green. So all of these are possible, it's only E, exactly two of the costumes have both green and orange in them that must be false.