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Course: LSAT (DEPRECATED) > Unit 1

Lesson 5: Analytical Reasoning – Worked examples

Grouping setup | "Completely determines" | Worked example

Watch a demonstration of one way to approach a "completely determines" question on a grouping setup on the LSAT analytical reasoning section. Created by Annie Hollister.

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  • blobby green style avatar for user Sohum Buch
    I am a little confused on Answer Choice D in this question. Here is my diagram that I used.

    Initial
    Dress 1: Red, White, Orange
    Dress 2: Indigo, Yellow, Unknown
    Dress 3: Unknown

    If you implement answer choice D:
    Dress 1: Red, White, Orange
    Dress 2: Indigo, Yellow, Unknown
    Dress 3: White, Indigo, Yellow

    My reasoning for Choice D is this: If exactly 1 dress has Indigo and White, then it must also have Yellow. This can be dress three for example. Just as the narrator of the video assumed white can added in dress 2, that did not lead anywhere and left dress 3 empty. Therefore, the narrator crossed it out. However, why can't you assume that the Indigo and White combination is in Dress 3?

    If you look at it that way, then you see that Yellow has to be added to Dress 3, and then since Green hasn't been used yet, it would have to be in Dress 2 with Indigo and Yellow, solving the colors in each dress completely. This rationale contradicts choice A as well.
    (3 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user Andrew Mawdryk
      The question asks for which answer "completely determines" the colors of each of the three costumes. The problem with D is that although you can create a way for it to work as you have, there is also another way:

      1: Red, White, Orange
      2: Indigo, Yellow, White
      3: Green, Orange, White

      Because there is more than one possible scenario, this means that it doesn't completely predict the rest of the costumes whereas for A), there is only one set up that can be laid out.
      (10 votes)
  • blobby green style avatar for user tricedavis1989
    I chose (E)
    I am confused how it was not selected.

    The diagram drawn shows that there is only exactly one costume that has both orange and white, which goes with E.

    Answer (A) can't be true because it is not true that white is in all three, white could bd in just two. But answer (E) is a definitely if True

    Could you please explain this better for me?
    Thank you
    (1 vote)
    Default Khan Academy avatar avatar for user

Video transcript

- [Narrator] Which one of the following, if true, completely determines the colors each of the three costumes has? With this type of question, before we look at the choices, it's a good idea to take stock of what information we don't have. Rules two and three for instance tell us that indigo and yellow are a pair, so one of the costumes is going to have indigo and yellow together. We also figured out that because red can't be with indigo or green, and therefore can't be with yellow, because indigo and yellow are a pair, there are only two colors that red could be matched with, white and orange. Since each costume has three colors, that means that one of the costumes is red, white and orange. That gives us a lot of information. What we don't know is anything about the third costume, or what the third color is in the costume that has indigo and yellow. Those are some things to look out for in an answer that will tell us the complete grouping of the colors and costumes. Let's look at the choices and keep an eye out for things that will answer these specific questions. What's in the third costume? And what's the third color in the costume that has indigo and yellow? Let's look at the choices. A, all three of the costumes have white in them. This actually gives us a lot of information. If all three of the colors have white in them, then the third color in the costume with indigo and yellow is white. We already know that one of the costumes is red, white and orange, and it also tells us that white is one of the colors in the third costume. Each of the colors has to appear at least once, and neither of these two costumes has green in it, so another color in this costume has to be green. That means that we only need to know what the third color is in this costume. Well, we already figured out that it can't be red, and it can't be indigo or yellow, because indigo and yellow are always paired together. So it has to be orange. So it looks like right off the bat, if all three of the costumes have white in them, that completely determines the colors that each of the three costumes has. Just to make sure we have the right answer, let's check the other choices, even though on the real test you'll want to move on once you find the answer. B, exactly one of the costumes has green in it. If exactly one of the costumes has green in it, we actually don't know which one that is. Green could be here with indigo and yellow, or it could be here, and that doesn't tell us much about the rest of the colors. So that doesn't determine the colors of each of the costumes. If exactly one of the costumes has both green and orange, then it has to be this one. Which means that the third color in this costume has to be white, because it can't be indigo or yellow, but it doesn't tell us about the third color in this costume. So that's not the answer either. If exactly one of the costumes has both indigo and white, then we can add white here as the third color in this costume, which means that one of these colors is green, because green has to appear somewhere, but it doesn't tell us about the rest of this costume. This could be indigo and yellow, or it could be orange and white, we don't know which. So that's not the answer either. Finally, exactly one of the costumes has both orange and white in it. If exactly one of the costumes has both orange and white, it's this one, because we know that red, orange and white are together in one costume. That means that orange and white aren't both in this one, which actually means that indigo and yellow are both in this one, because there have to be three colors in the costume. But it doesn't tell us what the third color is in either of these costumes. In either of these, the third color could be green, orange, or white. So this doesn't give us the answer either. The answer is A, the colors of the three costumes are completely determined if all three of the costumes have white in them.