Main content

## LSAT

### Course: LSAT > Unit 1

Lesson 3: Analytical Reasoning – Articles- Getting started with Analytical Reasoning
- How to approach ordering setups
- How to approach grouping setups
- How to approach mixed setups
- Given info: basic orientation | Quick guide
- Given info: could be true/false | Quick guide
- Given info: must/cannot be true/false | Quick guide
- New info: could be true/false | Quick guide
- New info: must/cannot be true/false | Quick guide
- Equivalent rule, min-max and completely determines | Quick guide
- Equivalent rule | Learn more
- Study plan for analytical reasoning | Getting more than 10 right
- How to use multiple scenarios in analytical reasoning setups
- Deductions in analytical reasoning | Introduction
- Deductions in analytical reasoning | Practice
- Diagram notation conventions for analytical reasoning setups

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# How to approach grouping setups

## Grouping setups overview

Grouping setups are common on Test Day. In this article, we’ll examine pure grouping setups (as opposed to mixed setups that include an ordering component), and share some tips to raise your game and boost your score.

**We recommend that you learn how to approach ordering setups before you move on to grouping setups.**

### How do we recognize grouping setups?

There are a few ways you can recognize simple grouping setups, but the most obvious way might be that there is

*no*ordering component to the task, and there’s only one kind of assignment that needs to be determined. Note that grouping setups, in comparison to ordering setups, have a bit more variety in how they’re presented to you.A few examples of grouping tasks:

- Determine which of 3 appetizers each of 7 people will eat.
- Determine whether each of 8 birds are in the forest or not in the forest.
- Determine in which of 2 seasons each of 10 employees will take a vacation.
- Determine which, and how many, of 3 upgrades each of 6 cars have.
- Determine which 5 of 7 people are selected to be on a committee.

Notice that order

*doesn’t*matter in*any*aspect of the tasks above; for example, selecting some of 7 people to be on a committee doesn’t imply any kind of*ordering*to the selection—it’s simply that five people will be on the committee and two will not. So the “groups” in that example are the “In” group and the “Out” group.Additionally, instead of putting elements

*into*subgroups, the task could ask you to*assign*elements to different groups, and those elements could repeat—for example, in the first example above, there are three appetizers and seven people. The “groups” are now the people, and the elements being assigned to them are the appetizers. It’s possible that*all*seven people eat the cheesy bread, for example. It’s also possible that*none*of the people eat bacon-wrapped dates.And if you see a grouping task, but you also see that order matters for some parts of the setup, then you’re looking at a

**mixed**setup.Ordering setups are covered in this article.

Mixed setups are covered in this article.

### What should we pay attention to in the passage?

In the passage for a grouping setup, you’ll be given a certain number of elements and told that they will be grouped in some way. Sometimes, the numbers will be simple: 9 people and 3 subgroups, for example.

*Sometimes*, however, the numbers won’t line up exactly that way; perhaps there will be 7 people for 3 groups and it’s possible that one group is empty. Always pay attention to how the number of elements could be split by group based on the restrictions provided!### What does the sketch look like for a grouping setup?

In general, it’s good to represent what’s happening in the setup with a diagram or sketch. The diagrams of grouping setups can be more varied than those of ordering setups, since grouping setups are more diverse in their tasks. We’ll show you a few different setups here, but the commonality is that elements are “grouped” into different categories.

**Elements assigned to different sub-groups:**

Suppose we have a task in which employees

**ABCDEF**are all traveling, each employee to exactly one of countries*,***X***, and***Y***. In addition, we learn that***Z***at least one*employee goes to each destination. Your empty diagram (before establishing any rules or deductions) might look like this:**Elements are either assigned to a group, or**

*not*assigned to that group (“In/Out”):Suppose we have a task in which employees

**ABCDEF**are either promoted or not promoted. Functionally, this isn’t too different from our first example, but the rules tend to be largely conditional in these types of setups—for example, “If**A**is not promoted, then**B**is promoted.” Since all employees must fall into one category or the other, we like to recommend an “In/Out” diagram.Here are two options that you can use—the first option can always be used, whereas the second option can only be used if you know exactly how many elements are “in” and how many are “out.”

### What kind of rules are typical in grouping setups?

Since grouping involves assignment, then some of the most common rules will involve how elements are—or are not—assigned. Let’s continue with the task we made up above, in which each of employees

**ABCDEF**will be traveling to exactly one of countries*,***X***, and***Y***. We will likely see rules that resemble the following:***Z**- Exactly one employee will travel to
.**X** **A**will not travel to.**X****A**and**B**don’t travel to the same country.**A**and**B**don’t travel to the same country, nor do either of them travel to.**X****A**and**B**travel to the same country.- There are fewer employees traveling to
than to**X**.**Y** - If
**A**travels to, then**X****B**travels to.**Z**

### What are some good ways to represent these typical rules, and what can I deduce from each one?

It’s a good idea to get into a habit of consistent rules notation. That doesn’t mean that any one notation is the “correct” one, though! Let’s talk through these rules, and we’ll give you one suggestion for each rule, and you can either use our suggestion or come up with your own. We’ll also let you know if there are any deductions that you can make for each rule, so that you can start to formulate deductions quickly and easily.

For these examples, we’ll imagine that the six employees

**ABCDEF**are traveling to countries*,***X***, and***Y***—each employee travels to only one country, and each country is traveled to by at least one employee.***Z**Exactly one employee will travel to

*.***X****Deductions:**

- We said that numbers are important in grouping (and mixed) setups. Always pay attention to what we can deduce from information regarding numbers!
- If exactly one employee travels to
, and we know that**X***at least one*employee travels toand to**Y**, then that leaves us with three spots to establish.**Z** - If the setup gives you a maximum of employees who can travel to each country, then that restricts the numbers more (and we like that!). For example, if the maximum of employees who can visit each country is three, and we have six employees in our list, then we know that one employee travels to
, two or three travel to**X**, and two or three travel to**Y**. In other words, the numbers will be 1:2:3 or 1:3:2.**Z** - If, however, the setup doesn’t give us a maximum of employees who can travel to each country, then the possibilities are more numerous. The numbers could be 1:1:4, 1:4:1, 1:2:3, 1:3:2.

**A**will not travel to

*.*

**X****Deductions:**

- Since
**A***doesn’t*travel to, we can deduce that**X****A**must travel to eitheror**Y**. If there were only two groups to pick from, then “not**Z**” would mean that**X****A***must*travel to the other group. - Since
**A**can only travel to two different countries, look for opportunities in the questions to build two scenarios around**A**—this is a helpful move only if doing so leads to*additional*deductions.

**A**and

**B**don’t travel to the same country.

**Deductions:**

- Since this rule tells us about something that
*can’t*happen, we can’t make any useful deductions from this rule alone. - What’s likely is that either:
- 1) this rule will lead to deductions when it’s combined with another rule (for example, a rule that states, “
**B**travels to” leads to the deduction that**Y****A***can’t*travel to), or**Y** - 2) this rule will lead to deductions when it’s combined with temporary rules in the questions (for example, a temporary rule might tell us, or allow us to determine, that the travelers to country
**X***don’t*include**A**or**B**, which would mean that*one*of**A**and**B**travels toand**Y***the other*travels to).**Z**

**A**and

**B**don’t travel to the same country, nor do either of them travel to

*.*

**X****Deductions:**

- Since
**A**and**B**both*don’t*travel to,**X***and*they can’t be a pair, that means that one of them travels toand the other travels to**Y**.**Z** - We don’t know which one goes where, but we
*can*“reserve” a spot for each of them under countriesand**Y**.**Z** - This allows us to account for
**A**and**B**and create a placeholder for them so that they are included in any applicable counts or possibilities.

**A**and

**B**travel to the same country.

**Deductions:**

- Since grouping setups have a limited number of groups, you
*may*be able to create scenarios around this**AB**pair. - For instance, you could draw three scenarios, one in which
**AB**travels to, to**X**, and to**Y**. If, for example, you were also told that each country has a maximum of two visitors, this would greatly restrict where all of the other elements can go.**Z**

There are fewer employees traveling to

*than to***X***.***Z****Deductions:**

- We can deduce that
must have**Z***at least*two employees, so we can add a blank directly to our initial diagram. - Note that we’re not necessarily done with
and**X**! We don’t know if**Z**has one employee and**X**has two employees, or if**Z**has two employees and**X**has three employees, or if**Z**has one employee and**X**has three employees.**Z**

If

**A**travels to*, then***X****B**travels to*.***Z****Deductions:**

- We’ll want to remember to note the logically equivalent rule: if we learn that
**B***doesn’t*travel to, then we’ll deduce that**Z****A***doesn’t*travel to.**X** - That means that if we learn that
**B***does*travel toor**X**, then this rule triggers and we can deduce that**Y****A**travels to eitheror**Y**.**Z** - If you have
*multiple*conditional rules, it’s not necessary (or even recommended) to “chain” them all together the way we do in ordering setups. As long as you have all of the rules written out neatly on your page, you’ll be able to “follow the triggers” as you move through the questions. - In other words, if you have a rule stating that “if A is selected, then B is selected” and a separate rule that states, “if B is selected, then D is not selected”, don’t spend the time making a
*longer*rule from the two rules. Just keep the individual rules neat and lined up.

### Practice Example

Now, let’s take everything we’ve learned and apply it to an actual LSAT setup!

**What does the setup tell us?**

We have seven employees,

*some*of whom will be part of a volunteer group. Since it’s not necessarily true that all of the employees will be volunteers, then that’s a grouping scenario—either an employee volunteers, or that employee doesn’t volunteer. There is no ordering component to this task, since there’s no arrangement or sequence of any kind. Go ahead and make a basic sketch based on this information before we look at the rules!**What do the rules tell us?**

Go ahead and note the rules, making sure to take the time to understand them, and to get them right the first time!

**What can we deduce?**

Now it’s time to make deductions! Can you use what we covered in this lesson in order to deduce what must be true beyond what’s presented to us at face value?

We’re in a really great spot to move on to the questions! With this diagram, we won’t have to use much (if any) time-consuming “trial and error”, and we'll gain points on Test Day.

Which one of the following could be a complete and accurate list of the volunteers?

(A) Felicia, Salman

(B) Masatomo, Rochelle

(C) Leah, Salman, Terry

(D) Salman, Rochelle, Veena

(E) Leah, Salman, Terry, Veena

(B) Masatomo, Rochelle

(C) Leah, Salman, Terry

(D) Salman, Rochelle, Veena

(E) Leah, Salman, Terry, Veena

If Veena volunteers, then which one of the following could be true?

(A) Felicia and Rochelle also volunteer.

(B) Felicia and Salman also volunteer.

(C) Leah and Masatomo also volunteer.

(D) Leah and Terry also volunteer.

(E) Salman and Terry also volunteer.

(B) Felicia and Salman also volunteer.

(C) Leah and Masatomo also volunteer.

(D) Leah and Terry also volunteer.

(E) Salman and Terry also volunteer.

If Terry does not volunteer, then which one of the following CANNOT be true?

(A) Felicia volunteers.

(B) Leah volunteers.

(C) Rochelle volunteers.

(D) Salman volunteers.

(E) Veena volunteers.

(B) Leah volunteers.

(C) Rochelle volunteers.

(D) Salman volunteers.

(E) Veena volunteers.

If Masatomo volunteers, then which one of the following could be true?

(A) Felicia volunteers.

(B) Leah volunteers.

(C) Veena volunteers.

(D) Salman does not volunteer.

(E) Terry does not volunteer.

(B) Leah volunteers.

(C) Veena volunteers.

(D) Salman does not volunteer.

(E) Terry does not volunteer.

If Felicia volunteers, then which one of the following must be true?

(A) Leah volunteers.

(B) Salman volunteers.

(C) Veena does not volunteer.

(D) Exactly three of the employees volunteer.

(E) Exactly four of the employees volunteer.

(B) Salman volunteers.

(C) Veena does not volunteer.

(D) Exactly three of the employees volunteer.

(E) Exactly four of the employees volunteer.

Which one of the following pairs of employees is such that at least one member of the pair volunteers?

(A) Felicia and Terry

(B) Leah and Masatomo

(C) Leah and Veena

(D) Rochelle and Salman

(E) Salman and Terry

(B) Leah and Masatomo

(C) Leah and Veena

(D) Rochelle and Salman

(E) Salman and Terry

### Takeaways

- Order and arrangement
*don’t*matter in grouping scenarios. In other words, you could list elements in any order and it wouldn’t change the dynamics of the task. - Numbers can be very important in grouping tasks. Pay attention to minimums and maximums (if there are any) per group, and look for ways that you can make deductions based on those numbers.
- Know how to manage conditional rules! You’ll want to be very adept at forming the logical equivalent of conditional rules (sometimes known as the “contrapositive”).

### Next steps

head over to the practice area

Then, once you've finished your diagnostics and created a practice schedule, head over to the practice area and try some grouping setups on your own!

## Want to join the conversation?

- From rule 3 or 4 alone, isn't there still a possibility for both R & L or S & V to be volunteers? When one is absent, the other must volunteer. However, there is no requirement that they both cannot be volunteers. In other words at least one should volunteer. Please correct me if I'm wrong!(24 votes)
- I second this question. I thought from rule 3 if S is out then V is in meant that Sand V being in is not an option. Please clarify.(34 votes)

- #2 - If Veena volunteers, how could Salman also volunteer? B, the chosen answer, isn't right in that case.

#4 - If M volunteers, R and T would also volunteer. If R volunteers, L cannot. Therefore, B isn't the right answer again.

Please clarify #2 and #4. Thanks!(16 votes)- In question 2 , if salman does not volunteer then veena must volunteer, does not says anything as to what happens if salman volunteers. So the conclusion that if salman volunteers then veena can also volunteer is not contradicted.

However , option B still is wrong because since Rochelle is not volunteering Leah has to.(4 votes)

- How are the "equivalent rules" on Rule 3 and Rule 4 correct? With Rule 3, Veena and Salman could both be in. Similarly, with Rule 4, Leah and Rochelle could both be in.

Rule 3: If Salman is out, then Veena is in. The equivalent rule is that if Veena is out, then Salman is in.

Rule 4: If Rochelle is out, then Leah is in. The equivalent rule is that if Leah is out, then Rochelle is in.

These "equivalent rules" seem to commit the grave error we are warned against (creating rules that are not actually rules).(14 votes) - For the question: If Veena volunteers, then which one of the following could be true?

How could the answer be (2) Felicia and Salmon could volunteer.

If Veena volunteers, Salmon cannot, so how could he volunteer? Thus how can number (2) be the answer?(13 votes) - (We can then cross off (A), because three questions ago, it was possible for both Felicia and Terry to be out!)

I am confused on how Felicia and Terry could both be OUT if T is out that means F is IN. Am I missing something?(9 votes)- The rule says if T is in F is out. Nothing is mentioned about what happens to F if T is out(1 vote)

- Is there an error in the first practice problem? For "Which one of the following could be a complete and accurate list of the volunteers?," the explanation for the right and wrong answers do not make sense to me. Please let me know if I am just misunderstanding the question, answer and explanation. I thought the answer could be either A (F&S) or C (L,S,T). When looking at the fast approach to solving this problem, your explanation states that A cannot be the correct answer because of "Rule 4: If Rochelle is out, then Leah is in. We can cross off (A)." However, option A does not mention Rochelle or Leah at all... It mentions Felicia and Salaman, so I'm not sure how they arrived at that conclusion.(8 votes)
- #1

Which one of the following could be a complete and accurate list of the volunteers?

(A) Felicia, Salman

(B) Masatomo, Rochelle

(C) Leah, Salman, Terry

(D) Salman, Rochelle, Veena

(E) Leah, Salman, Terry, Veena

The given answer is C. But isn't it already given that If R is present, M has to be present and if M is present T has to be present? How can the answer be a "complete and accurate list of volunteers" then?

R,M,T,S could be a complete and accurate list of volunteers right? But it's not given in any of the options.

According to the article on Contrapositives, If A is absent when B is present, then, A cannot be present if B is present. Is that correct or have i misunderstood contrapositives?(7 votes) - How do I do the last problem with the pairs?

Which one of the following pairs of employees is such that at least one member of the pair volunteers?

(A) Felicia and Terry

(B) Leah and Masatomo

(C) Leah and Veena

(D) Rochelle and Salman

(E) Salman and Terry(6 votes)- The question is asking for you to determine which pair is such that at least one of the two employees MUST volunteer or else a rule gets broken. The fastest way to check for the answer, then, is to plop the answer choice pairs into the "out" column. If that pair necessarily breaks one of the rules, then you have the answer.

The answer is B because if M is out then so is R, but L and R cannot both be out, so the rule about "if R is out then L is in" gets broken. It must be true that, between the two of them, either L or M volunteers.(1 vote)

- In the question where the temporary rule that Veena must volunteer, why is Salman not put in the out list? The rules state that if Veena volunteers, then Salman does not.(4 votes)
- I was confused about that as well. Our rule states that "If Salman does not volunteer, then Veena volunteers," so the contrapositive/logically equivalent statement is "If Veena does not volunteer, then Salman volunteers." With that, it made sense to me at first that "if V volunteers, then S doesn't." However, I took a look back at the Sufficiency and Necessity section of the Logic Toolbox that gave some good examples why making the logical leap to "If V volunteers, then S doesn't" is actually not accurate. It might be helpful in understanding why we can't assume "if V does, then S doesn't"?

https://www.khanacademy.org/test-prep/lsat/lsat-lessons/modal/a/logic-toolbox--article--if-x-then-y--sufficiency-and-necessity(4 votes)

- What's another way to solve the question - which one of the following pairs of employees is such that at least one member of the pair volunteers - without referring back to diagrams made for previous questions?(3 votes)