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How to use multiple scenarios in analytical reasoning setups

What are multiple scenarios, and how do I use them to my advantage?

Sometimes you’ll be able to narrow Analytical Reasoning situations down to just two or three possibilities, or what we call “Scenarios”. Scenarios can be used in any type of Analytical Reasoning task. If you need to refresh on the three types of tasks:
When you choose to approach a setup using scenarios, you’ll sketch out diagrams for the 2-3 versions, instead of creating just one master diagram.
In this article, we’ll show you how to recognize when the use of multiple scenarios might be helpful.

When not to use scenarios – two examples

Multiple scenarios aren’t always efficient or helpful! Novice LSAT students often want to build scenarios in cases in which doing so would actually slow them down. So, before we get into how to recognize where scenarios can be useful, let’s talk about where scenarios aren’t useful.
Example 1: A rule that restricts a single element to only two spots
  • R can only be placed on Monday or Friday.
Many students immediately feel an urge to build scenarios in response to a rule like this, with one diagram in which R is on Monday and another diagram in which R is on Friday:
Two ordering diagrams. An ordering diagram labeled 1 includes 5 horizontal bars. Bar entries read as follows. Bar 1. R. An ordering diagram labeled 2 includes 5 horizontal bars labeled from left to right as follows. M, T u, W, T h, F. Bar entries read as follows. Bar F. R.
There’s no benefit in splitting this rule into scenarios, when the following notation (or something to the same effect) would work just as well and take less time:
An ordering diagram includes 5 horizontal bars labeled from left to right as follows. M, T u, W, T h, F. Above the bars is R. A left arrow extends from R to bar M. A right arrow extends from R to bar F.
Plus, imagine that you later get to the last rule, which tells you that R is placed on the day after S. Suddenly, you would have drawn that second scenario for nothing, since we could now deduce that R is definitely placed on Friday.
Scenario-making doesn’t make sense unless you can make other deductions cascade from the split.
So, when single elements are restricted to only two positions, that alone isn’t enough to warrant scenarios. When groups are restricted to only two (or three) positions, then we have a case to make for scenarios!

Example 2: Conditional rules that don’t tell the whole story
Here’s another place where you shouldn’t immediately jump into scenario-making:
  • If R is on Friday, then M is on Tuesday.
We must not make false inferences here. The logically equivalent rule is:
  • If M is not on Tuesday, then R is not on Friday.
So, we know what happens if R is on Friday, but we don’t know what happens if R is not on Friday. Therefore, we cannot build scenarios! We can only create scenarios when we know that every acceptable situation fits into one of the scenarios. That’s the entire point of laying out the multiple scenarios to begin with.

When to use scenarios

1. Pairs and groups

This is probably the most common path to Scenarios of the three we’re going to discuss. Let’s take a look at why pairs and groups are more amenable to building scenarios than are the single elements we discussed above.
We saw why we wouldn’t want to build multiple scenarios given only a single rule that “R can only be placed on Monday or Friday”—but what about if R were part of a group?
Example: X_RM
  • In other words: X is two spots earlier than R, and R is immediately before M.
If we were working with ten spots, then we would have too many scenarios to make it worth our time to build them. But if we only had five spots, then there would only be two ways in which this group could be placed:
Two ordering diagrams. An ordering diagram labeled 1 includes 5 horizontal bars. Bar entries read as follows. Bar 1. X. Bar 2 is blank. Bar 3. R. Bar 4. M. Bar 5 is blank. An ordering diagram labeled 2 includes 5 horizontal bars labeled from left to right as follows. 1, 2, 3, 4, 5. Bar entries read as follows. Bar 1 is blank. Bar 2. X. Bar 3 is blank. Bar 4. R. Bar 5. M.
This is high-impact for our deductive opportunities. Why? In each scenario, we’ve already placed three out of the five elements. For each of the new info questions, you’ll only need to determine which scenario applies, and then go from there!
For example, if you were given a question that read, “If C is earlier than X, which of the following must be true?”, you would quickly see that Scenario 1 doesn’t apply, and our answer will come from Scenario 2—it’s the only Scenario in which an element could be placed earlier than X.

2. Arithmetic

Sometimes, you’ll be able to build scenarios around the arithmetic of the game.
Example: Let’s say we have a grouping setup in which seven people (ABCDEFG) use a coupon for either breakfast, lunch, or dinner on a certain day. We also know that each meal has at least one person participating in it. Now, consider the following rule:
  • Exactly twice as many people use a coupon for lunch as for breakfast.
Don’t just hastily note the rule and move on! We only have seven people to place in this setup. Could the numbers be restricted enough to warrant creating scenarios?
  • If one person uses a coupon for breakfast, that means that two people use a coupon for lunch and therefore four people use a coupon for dinner. 1:2:4 is one arithmetic possibility here.
  • What if two people use a coupon for breakfast ? That means that four people use a coupon for lunch and therefore one person uses a coupon for dinner. 2:4:1 is our second arithmetic possibility.
  • What if three people use a coupon for breakfast? This can’t happen—that would mean that six people use a coupon for lunch, and we only have seven people to place! We’re at the end of our possibilities.
Because we only have two scenarios, we should build them:
Two grouping diagrams. A grouping diagram labeled 1 includes three columns labeled b r e, l u n, d i n. Below column b r e is one horizontal line. Below column l u n are two horizontal lines. Below column d i n are four horizontal lines. All lines are blank. A grouping diagram labeled 2 includes three columns labeled b r e, l u n, d i n. Below column b r e are two horizontal lines. Below column l u n are four horizontal lines. Below column d i n is one horizontal line. All lines are blank.
We may not know anything about specific elements and where they go yet, but we have a concrete framework for each column instead of open-ended numbers. Every acceptable situation will conform to one of these two scenarios; therefore, if you encounter a rule such as, “A and B use a coupon for the same meal”, you’d know that it can’t be for breakfast in Scenario 1 and it can’t be for dinner in Scenario 2.

3. Paired rules

Finally, you’ll sometimes encounter rules or pairs of rules that work together in such a way that only two or three scenarios are possible.
Example 1
  • R is on Friday if and only if M is on Tuesday.
Wait a minute...this sounds very similar to the rule above for which we told you not to make scenarios. But "if" (in the previous example) is very different than the "if and only if" that we see here. Look at what this "if and only if" means:
  • If R is on Friday, then M is on Tuesday.
  • If R is not on Friday, then M is not on Tuesday.
The logically equivalent rules are:
  • If M is not on Tuesday, then R is not on Friday.
  • If M is on Tuesday, then R is on Friday.
The simplest way to state the rule is, therefore: “Either R is on Friday and M is on Tuesday, or R isn’t on Friday and M isn’t on Tuesday. No other scenario besides these two is possible! We could diagram the scenarios this way:
Two ordering diagrams. An ordering diagram labeled 1 includes five horizontal bars. Bar entries read as follows from left to right. Bar 1 is blank. Bar 2. M. Bars 3 and 4 are blank. Bar 5. R. An ordering diagram labeled 2 includes 5 horizontal bars labeled from left to right as follows. M, T u, W, T h, F. Notations below the bars read as follows from left to right. Bar T u. M is crossed out. Bar F. R is crossed out.
Example 2
  • If Rose performs in the choir, then it’s true that in the orchestra, Jorge performs earlier than Boris, who performs earlier than Aileen.
  • If Rose performs in the orchestra, then both Tylissa and Vu perform in the choir, and Tylissa performs sometime earlier than Vu.
If there are no other groups besides the choir and the orchestra, and each student has to perform in one or the other, then we could build multiple scenarios here. That’s because Rose performing in the choir allows more information to follow, and Rose performing in the orchestra likewise leads to more information. Since there aren’t any possibilities besides these two for Rose, then Rose is our pivot point for the scenarios:
Two grouping diagrams. A grouping diagram labeled 1 includes two columns labeled c h o, o r c. In column c h o is R. In column o r c , a chain diagram is a grouping of initials linked in sequence by solid lines. The chain reads as follows. J is before B. B is before A. A grouping diagram labeled 2 includes two columns labeled c h o, o r c. In column c h o, a chain diagram is a grouping of initials linked in sequence by a solid line. The chain reads as follows. T is before V. In column o r c is R.

Takeaways

  • Look for an opportunity to build Scenarios when you have 1) groups of elements that break down into only 2 ways, 2) arithmetic that breaks down into only 2 or 3 ways, or 3) a certain pairing of rules that creates a pivot point for scenarios.
  • A good rule of thumb: Build multiple scenarios when you can see more from the scenarios than if you only had one—for example, when building the two scenarios means that you can make more deductions cascade from the split.
  • Making multiple scenarios is never compulsory, and creating multiple scenarios almost always takes more initial setup time than using just one diagram; however, when done correctly, the scenarios save more time in the questions than they take in the setup.

Want to join the conversation?

  • blobby green style avatar for user helloEenap
    In the first example, is there a typo in this paragraph?

    "Plus, imagine that you later get to the last rule, which tells you that R is placed on the day after S. Suddenly, you would have drawn that second scenario for nothing, since we could now deduce that R is definitely placed on Friday."

    Did the write mean to say that "you would have drawn the FIRST scenario for nothing"? Because the first scenario drawn in the example is the one that's not applicable.
    (2 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user nicolez.gaitan
      This is not a typo. The second scenario was "drawn for nothing" because it wasted time to draw an entire second diagram (which is the point of the article) with the scenario of R being last since you would have gotten to that deduction anyway with the additional/last rule that R comes after S. And since the rules say that R is either first or last, you would deduce that it would have to be last (since it can't be first), and therefore you don't need two diagrams.

      I hope that helps.
      (1 vote)
  • blobby green style avatar for user Michael Damyanovich
    Hi!
    I see this written above at Part 3. Example 1:

    "R is on Friday if and only if M is on Tuesday."
    =
    If R is on Friday, then M is on Tuesday.
    =
    If R is not on Friday, then M is not on Tuesday.

    Doesn't that last line break the switch-and-negate rule for making contrapositives?

    Thanks!
    (0 votes)
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    • piceratops seed style avatar for user b t
      You are looking at the equivalency wrong.

      "R is on Friday if and only if M is on Tuesday"
      =
      ("If R is on Friday, then M is on Tuesday." AND "If R is not on Friday, then M is not on Tuesday.")

      That is, the first rule (the if and only if) is equivalent to both of the following two rules being true. It is not drawing any equivalence between the latter two rules.
      (5 votes)
  • blobby green style avatar for user aliciaa.dyck
    In 3. Paired rules in example 1, it says that "If R is not on Friday, then M is not on Tuesday", but I don't understand this. If R is not on Friday, why does it affect M? Is it because of the "if and only if"? I can't seem to understand it.
    (1 vote)
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  • blobby green style avatar for user ebpurdy
    I'm confused about this part:
    "Scenario 1: R is on Monday
    Scenario 2: R is NOT on Monday
    Either R is on Monday, or R is not on Monday, and therefore there's no other day that R could be."

    If R is on Monday in scenario 1 and NOT on Monday in scenario 2, how can there be no other day for R to be on? If it is NOT on Monday then there is 6 other days it could be on...
    (1 vote)
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  • blobby green style avatar for user Andree Comeau
    If in the same exercise, one rule says that M is directly before S....and a second rule says T is before K. Can we assume that there is at least one spot between T and K. In other words, does the ommission of directly mean that it is NOT directly?
    (1 vote)
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