Grouping setup | New info–could be true 1 | Worked example

- [Narrator] This question asks if only one of the costumes has both yellow and orange in it, then which one of the following could be true? So we wanna add the new information that one of the costumes has both yellow and orange to the set-up we already have, and cross out choices that could not be true, given this new information. Well, if one of the costumes has both yellow and orange in it, what else do we know? Rule two and three together tell us that yellow and indigo are together, so if a costume has both yellow and orange in it, that costume is yellow, indigo and orange, so we can add that here. We also figured out from rule four and the fact that indigo and yellow are a pair, that red can only be paired with white and orange, so one of the costumes is red, white and orange. This means that if yellow and orange are together in a costume, two of the costumes are fully determined. Since each of the colors has to appear in at least one costume, the third costume must have green in it somewhere. It can't have red, but we don't know anything else about it. So let's look at the choices. A, exactly one of the costumes has yellow in it. Well we haven't learned anything that tells us that this has to be false, for instance if this costume that has green in it is green, white and orange, then exactly one of the costumes could have yellow in it, so let's leave this aside for now. B, exactly two of the costumes have green in them. Well, if one of the costumes has both yellow and orange in it, then the third color in that costume has to be indigo, because indigo and yellow are a pair. We know that under any circumstances, one of the costumes is red, white and orange, because red can only be paired with white and orange, and therefore has to be paired with white and orange, so only one of the costumes can have green in it. Exactly three of the costumes have white in them. Well, if one of the costumes has both yellow and orange in it, then the third color in that costume has to be indigo because indigo and yellow are paired, so it can't be the case that three of the costumes have white in them. At least one of the costumes has both indigo and white in it. Well we figured out that two of the costumes are red, white and orange, and indigo, yellow and orange, so if one of the costumes has both indigo and white in it, it must be the third costume. Because each color has to appear at least once, the third costume has to include green, and that means that if the third costume also includes indigo, the third color in that costume has to be yellow because indigo and yellow are always paired together. That means that the third costume cannot contain both indigo and white, so none of the costumes contains indigo and white, so we can cross that off. At least two of the costumes have both green and white in them. Well we already figured out that only one of the costumes has green in it, so we can rule that out. And that leaves the answer is A, exactly one of the costumes has yellow in it, which is possible if the third costume is green, white and orange.