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# Grouping setup | Given info–must be true 1 | Worked example

Watch a demonstration of one way to approach a "Given info: must be true" question on a mixed setup. Created by Annie Hollister.

## Want to join the conversation?

• I understand skipping around on test day, but as a tutorial, I think it's important to go in sequence through the answers than skipping around to show the process. Even if you say "I can't prove this quickly" before moving on, it's still helpful to keep track as the audience and better understand the technique.
(14 votes)
• Just because the answer has been found , it isn't wise to skip explaining the other options especially since this is a tutorial and we're all trying to figure out how and when. So can you explain properly all the available options as in why it wont be the answer.
(2 votes)

## Video transcript

- Which one of the following must be true? With this type of question, we should be able to find the answer from what we already know or from any inferences we can make from the rules of the setup. So let's just rehash the information we already have. Any costume that has indigo in it must also have yellow in it, and any costume that has yellow in it, must also have indigo in it. So indigo and yellow are a pair. That means that at least one of the costumes has both indigo and yellow in it. Any costume that has red in it can't have either indigo or green in it. We also know that any costume that has indigo in it has yellow in it. So any costume that has red in it also can't have yellow. Which means that red can only be together with white and orange. Since every costume has three colors, that means that one costume is red, white and orange. And since no two costumes can have the same color combination, exactly one costume is red, white and orange. Which means that red only appears in one costume. So that gives us a lot of information and might let us find the answer. Let's look through the choices to see if anything stands out as something that must be true. D days at least one of the costumes has both orange and red in it. Well, we already figured out that one of the costumes is red, white and orange. So, that's the answer. At least one of the costumes has both orange and red in it. Let's double check the rest of the choices to make sure that isn't not the case that any of them must be true. A says at least one of the costumes has both green and orange in it. Well, that could be false. For instance, if green is here and the third costume is indigo, yellow, and white, that doesn't violate any of the rules of the setup. But it also doesn't have any costume that has both green and orange in it. So we can cross that off. B says at least one of the costumes has both green and yellow in it. Again, this isn't necessarily true. If one of the costumes is indigo, yellow and orange, one of them is red, white and orange, and the third one is green, white and orange, then no costume has both green and yellow in it. So we can cross that off. At least one of the costumes has both indigo and orange in it. Well, this comes up against the same problem as B. If one of the costumes is red, white and orange, one of them is indigo, yellow and green, and the third one is green, white and orange, then none of the costumes has both indigo and orange in it. But it doesn't violate any of the rules of the setup. Finally, at least two of the costumes have both indigo and white in them. Not only is it not the case that this must be true, it's actually not possible for this to be true. We know that one of the costumes is red, white and orange. At least one of them has indigo and yellow in it. But since no two costumes can have the same color combination, it's not the case that two costumes could have both indigo and white. If two costumes have indigo in them, then two costumes have both indigo and yellow in them. Which means that the third color in both of those costumes can't match, in order to avoid violating the first rule. So if two costumes have indigo in them, one of them could have white, but the other one would have to be either green or orange. So not only is it not the case that two costumes must have both indigo and white in them, it's actually not possible for two costumes to have both indigo and white. So the answer is D. According to the rules of the setup, at least one of the costumes has both orange and red in it.