For the last question, when evaluating answer option (B), how do we know that Xavier can't be in Production?

The last question states "If Xavier is NOT hired for one of the PRODUCTION positions. . ."

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Course: LSAT > Unit 1

Lesson 3: Analytical Reasoning – Articles

Deductions in analytical reasoning | Practice

Working with deductions in Analytical Reasoning setups

Before starting this article, you should have completed the article Introduction to AR Deductions. In a moment, we’re going to apply the skills we detailed in that introductory article, so it’s important that you feel well-versed in the foundations of making Analytical Reasoning deductions before heading into this exercise.

The setup

Seven job applicants—Feng, Garcia, Herrera, Ilias, Weiss, Xavier, and Yates—are hired to fill seven new positions at Chroma, Inc. One position is in the management department, three are in the production department, and three are in the sales department. The following conditions must apply:

Herrera is hired for a position in the same department as Yates.

Feng is hired for a position in a different department from Garcia.

If Xavier is hired for a sales position, then Weiss is hired for a production position.

Feng is hired for a production position.

What the setup tells us

We’re asked to determine which department each of seven job applicants will be assigned to. There are three departments, and we’re told exactly how many positions are in each department. There isn’t any kind of ordering component in this setup, so this is a pure grouping setup.

Since this article is focused primarily on making advanced deductions, we’ll let you set up a diagram instead of walking you through it step by step. Go ahead and sketch a basic diagram, then click below to compare your diagram with ours.

If you feel shaky on grouping setups in general, you could review how to tackle them before moving ahead: How to Approach Grouping Setups article

What do the rules tell us?

Take some time now to note the rules accurately—click below when you’ve finished! We’ll head to the deductions after this step.

Rule 1: Herrera and Yates are a pair in one of the departments.
Rule 2: Feng and Garcia are in different departments, in other words not a pair.
Rule 3: If Xavier is in sales, then Weiss is in production. The logically equivalent rule (sometimes known as the contrapositive) is that if Weiss is not production, then Xavier is not sales.
Rule 4: Feng is in production. We added this directly to the diagram.

What can we deduce?

Now, let’s head into our deductions! We’ll spend the most time on this, since it’s the focus of this article. Thinking about the GEARS acronym we gave you as a guide in the Intro to AR deductions article, we can focus our thinking instead of guessing at deductions.

Groups

Our most concrete group is the HY pair. Since Herrera and Yates are in the same department (Rule 1), we can deduce that HY can’t be in the management department. That’s because the management department only has one position, according to the passage.
We can mark that HY isn’t in management directly in the diagram.

Established Elements

The only element we’ve established is Feng. Looking at our rules, does Feng being definitively in production allow us to deduce anything?
As far as Rule 1 is concerned, nothing has changed. The HY pair must still be either production or sales regardless of Feng being established.
Rule 2 allows us to make an Established Element deduction! Since Feng and Garcia are not grouped together, then we can deduce that Garcia is not in production. Let’s add that directly to our diagram.
Finally, Rule 3 isn’t affected by Feng’s placement because Feng in production isn’t a trigger for Rule 3’s conditions.
We can move on!

Arithmetic

The only place in this setup in which numbers figure is in the assignment of concrete numbers to each group. Don’t take these number assignments for granted—they’re significant. See how only one person can be in management ? If we assign that spot at one point, that will dramatically reduce where employees can be placed.
We made a deduction earlier around numbers: we said that since management only has one spot, the HY pair can’t be placed there. This will end up being very important.
So while we can’t do anything concrete right now, it’s always good to look and ensure that the numbers framework doesn’t lead to any further deductions.

Repeats

Which elements repeat among the rules?
The only element who repeats from one rule to another is Feng, and we already made an Established Element deduction around Feng.
We can move on, now that we’ve confirmed that there are no other repeating elements.

Scenarios

When deciding whether we can make Scenarios, we want to ask ourselves if any of the rules or groups or numbers restrictions allows us to create only two or three scenarios, and
If creating those scenarios will lead to more deductions that we wouldn’t otherwise have been able to make.
The answer to these two questions is yes! Earlier, we said that the HY pair can’t be in management. Can we turn that negative into a positive?
We can deduce that the HY pair is in either production or sales. There are our two scenarios!
Can you draw two diagrams around HY’s placement and make deductions from there?

Scenario 1: HY is in production.

Since HY is in production and Feng was already in production, the production department is completely determined.
Looking for Repeats, we see that production is also mentioned in Rule 3. If Weiss is not in production, then Xavier is not in sales.
Since production is completely determined, then Rule 3 is triggered, and we can deduce that Xavier is not in sales.
And, if we continue to remind ourselves to turn negatives into positives, “not in sales” means—in this case—”in management”.
So, Xavier is in management.
The management department is now completely determined with Established Elements, so that means that the remaining elements—Garcia, Ilias, and Weiss—must make up the sales department.
This scenario is fully determined!

Scenario 2: HY is in sales.

In this case, we can’t determine anything beyond placing HY in sales.
Establishing that pair doesn’t trigger any of the other rules to provide deductions, and that’s how we know that we’re at the end of our deductions for this scenario:

Here is our initial diagram:

Notice that we have no further use for the HY pair rule nor the FG rule, since both are definitively indicated in the diagram. We’ll keep an eye on the conditional rule and how it applies in various questions.

That’s right; it does take more time, but it makes possibilities and truths much more apparent—and that’s what you’re being tested on! You’ll spend a little more time up front creating scenarios and save a lot more time on the back end in the questions. Try it both ways when you’re working in our practice area with a setup for which we present scenarios as a helpful deduction. Don’t take our word for it—see it for yourself!

Notice that when we built two scenarios, we had to run through deductions possibilities again. That’s because we Established Elements that we had not established before. That changes the playing field and allows for more deductions to be made.
For more in-depth practice with recognizing when Scenarios are helpful and worthwhile, please bookmark the article How to apply multiple scenarios in AR and review it when you can. It takes practice to become adept at creating scenarios, but the payoff is tremendous.

Takeaways

Be patient and methodical when looking for deductions, instead of trying to “get lucky.”
Each time you establish a new element, you’ll want to start the GEARS checklist all over again.
Turn negatives into positives where possible. The more you learn about where an element can’t go, the closer you get to determining where it does go.

Exercise Questions

To understand how helpful deductions are in tackling questions, we’ve included the questions and explanations for the grouping setup here so that you can practice. If you’d like to time yourself, we recommend setting a stopwatch (not a countdown timer) so that you can see how long you spent on each question.

For additional reinforcement after you’ve finished, you could try the setup again without the scenarios to see how different the experience of tackling questions is.

Good luck!

Which one of the following could be a complete and accurate matching of the applicants with the departments in which they were hired?

(A) management: Weiss; production: Feng, Herrera, Yates; sales: Garcia, Ilias, Xavier
(B) management: Weiss; production: Garcia, Ilias, Xavier; sales: Feng, Herrera, Yates
(C) management: Xavier; production: Feng, Garcia, Herrera; sales: Ilias, Yates, Weiss
(D) management: Xavier; production: Feng, Herrera, Ilias; sales: Garcia, Weiss, Yates
(E) management: Xavier; production: Feng, Ilias, Weiss; sales: Garcia, Herrera, Yates

One approach that tends to be very efficient might seem a little counterintuitive at first. Instead of looking at each choice and evaluating it against all of the rules, it makes sense to look at each rule one at a time and eliminate the choices that violate that rule. Think about it this way: if the answer is (E), then looking at each choice first means going through all of the rules five times. But if you start with the rules and eliminate choices after looking at each rule, then you only have to go through the rules once!

What choice(s) does each rule eliminate when you evaluate each rule one at a time? Let’s take a look at them together!

Rule 1: HY is a pair. (C) and (D) each break this rule, so we can eliminate (C) and (D).
Rule 2: Feng and Garcia aren’t a pair. None of the remaining choices violates this rule.
Rule 3: If Xavier is in sales, then Weiss is in production. We can eliminate (A) because it shows Xavier in sales but Weiss in management.
Rule 4: Feng is in production. We can cross off (B).

The only choice remaining is (E), so that’s our answer.

Which one of the following is a complete and accurate list of the applicants, each of whom CANNOT be hired for a production position?

(A) Feng, Ilias, Xavier
(B) Garcia, Herrera, Yates
(C) Herrera, Yates
(D) Garcia
(E) Ilias

Since we aren’t given any new information, we can use our initial diagram to see if one of our deductions allows us to quickly home in on the answer. What do we know about the production position?

We deduced that Garcia can never be in production. That means that Garcia must be in the answer.
We can eliminate (A), (C), and (E).
Now, left with (B) and (D), we only need to ask ourselves whether Herrera and Yates could ever be in production. They can, in Scenario 1!
Thanks to our multiple scenarios, we can quickly eliminate (B).

(D) is the answer. Garcia is the only applicant who can never be in production.

It can be determined in which department each of the seven applicants is hired if which one of the following statements is true?

(A) Feng and Weiss are both hired for production positions.
(B) Garcia and Yates are both hired for sales positions.
(C) Ilias and Weiss are both hired for sales positions.
(D) Ilias and Weiss are both hired for production positions.
(E) Ilias and Xavier are both hired for production positions.

Normally, for a completely determines question, we would need to test each choice out with our pencil and a new diagram. We would incorporate the choice’s condition into a blank diagram and make deductions based on that condition until we run out of deductions.

However, we made scenarios in this setup, and one of those scenarios is completely determined! It’s not a guarantee that the answer will be represented by Scenario 1, since we could also get a condition that would completely determine Scenario 2, but it’s a good starting point just in case.

Do you see any choices that are represented in Scenario 1, our completed scenario?

(C) is that Ilias and Weiss are both in sales. It’s the only choice that reflects a truth from Scenario 1, so let’s test it.

If IW is in sales, then the only place for the HY pair to go would be in production.
Since Rule 4 tells us that Feng is in production, production is now full.
Rule 4 tells us that if Weiss is not in production (which is true here), then Xavier cannot be in sales. That means that Xavier can only be in management.
Only one spot remains for Garcia, and that’s in sales.

(C) completely determines the placement of applicants and is the answer.

Each of the following could be an accurate partial list of the applicants hired for sales positions EXCEPT:

(A) Garcia, Ilias
(B) Garcia, Xavier
(C) Garcia, Yates
(D) Herrera, Weiss
(E) Herrera, Xavier

Since we aren’t given new information, using our initial diagram is usually a good first step. We’ll go through each choice and determine whether the two people listed can be in sales together. If they can, we’ll eliminate.

(A): Can GI work in sales? Yes, because GIW are the sales employees in Scenario 1.

(B): Can GX work in sales? It’s not possible in Scenario 1, because Xavier is in management. It’s also not possible in Scenario 2, because there isn’t enough room for HY and GX to work in sales.

(B) is the answer, because it lists two people who can’t be in sales together at any point. On Test Day, we would select this choice and move on.

Management: Xavier
Production: Feng Weiss Ilias
Sales: Herrera Yates Garcia

(D) could be true in Scenario 2. The assignment could be, for instance:

Management: Garcia
Production: Feng Xavier Ilias
Sales: Herrera Yates Weiss

(E) could be true in Scenario 2, for instance:

Management: Garcia
Production: Feng Weiss Ilias
Sales: Herrera Yates Xavier

If Feng is hired for a position in the same department as Xavier, then each of the following could be true EXCEPT:

(A) Garcia is hired for a sales position.
(B) Herrera is hired for a production position.
(C) Ilias is hired for a sales position.
(D) Weiss is hired for the management position.
(E) Weiss is hired for a production position.

This question gives us a new and temporary rule to apply. This temporary rule won’t conflict with any of our original rules. We’re meant to determine the consequences of considering this new rule.

Note that because we built scenarios in our initial deductions, we’ll want to start out by determining which of the scenarios allows the new condition to happen. It could be one, or it could be all of the scenarios.

The answer will be a statement that must be false, while the wrong choices will be those that could be true.

Remember, we’re looking for information that must be false. Let’s compare each choice against our new diagram for this question:

(A) Can Garcia be in sales? Yes. You might see that placing Garcia in sales doesn’t really affect anything, but for completion’s sake, here’s a possible acceptable scenario:

Management: Ilias
Production: Feng Weiss Xavier
Sales: Herrera Yates Garcia

(B) Can Herrera be in production ? No—this must be false! In Scenario 2, which we determined was the only scenario that can apply the new condition, Herrera is in sales.

On Test Day, we’d select (B) and move on. Here are the explanations for the remaining choices, in case you need them:

Management: Garcia
Production: Feng Weiss Xavier
Sales: Herrera Yates Ilias

(D) Weiss can be in management if the assignment is, for instance:

Management: Weiss
Production: Feng Ilias Xavier
Sales: Herrera Yates Garcia

(E) Weiss can be in production if the assignment is, for instance:

Management: Garcia
Production: Feng Weiss Xavier
Sales: Herrera Yates Ilias

(B) is the answer, and again—you wouldn’t evaluate the remaining choices on Test Day if you’re confident in your work. It’s a big time-waster to do so.

If Xavier is not hired for one of the production positions, then which one of the following could be true?

(A) Feng and Herrera are both hired for sales positions.
(B) Herrera and Weiss are both hired for sales positions.
(C) Feng and Yates are both hired for production positions.
(D) Garcia and Weiss are both hired for production positions.
(E) Herrera and Weiss are both hired for production positions.

The answer will be a statement that could be true, while the wrong choices will be those that must be false.

Remember, we’re looking for information that could be true. Let’s compare each choice against our new diagram for this question:

(A): Can FH be in sales? No. In Scenario 1, FH is in production, and in Scenario 2, they’re in different departments.

(B): Can HW be in sales? No, though we have to look carefully to see this. In Scenario 1, they’re in different departments. Let’s look at what happens in Scenario 2:

If HW were in sales, then sales would be full.
Since Xavier can’t be in production, that would force Xavier into management, and management would be full.
That would force Garcia and Ilias into production—but we know that Garcia can’t be in production !
That means that (B) must be false.

(C): Can FY be in production? Yes, because this happens in Scenario 1. We have our answer!

For your reference:

(D): GW can’t be in production, because Garcia can never be in production.
(E): HW can’t be in production because they’re separated in Scenario 1, and Herrera is in sales in Scenario 2.

(C) is the answer.

Want to join the conversation?

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Brandie Farmer
Posted 3 years ago. Direct link to Brandie Farmer's post “It can be determined in w...”
It can be determined in which department each of the seven applicants is hired if which one of the following statements is true?
(A) Feng and Weiss are both hired for production positions.
(B) Garcia and Yates are both hired for sales positions.
(C) Ilias and Weiss are both hired for sales positions.
(D) Ilias and Weiss are both hired for production positions.
(E) Ilias and Xavier are both hired for production positions.

Why can't the answer to the completely determines question be "D" IW in production?
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(6 votes)
Answer
Nicole
Posted 5 years ago. Direct link to Nicole's post “For the last question, wh...”
For the last question, when evaluating answer option (B), how do we know that Xavier can't be in Production?
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(1 vote)
Answer
- April Paris
  Posted 5 years ago. Direct link to April Paris's post “The last question states ...”
  The last question states "If Xavier is NOT hired for one of the PRODUCTION positions. . ."
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  (9 votes)
amnah.haque
Posted 4 years ago. Direct link to amnah.haque's post “For the last question ("I...”
For the last question ("If Xavier is not in prod..."), I think we can make the deduction in scenario 2 that "I" and "W" must be with Feng in production since all the other elements are unable to be in production. (H, Y are already in Sales, G can't be with F, X is not in production - this leaves only I and W)
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(4 votes)
Answer
a a
Posted 6 years ago. Direct link to a a's post “It can be determined in w...”
It can be determined in which department each of the seven applicants is hired if which one of the following statements is true?
(A) Feng and Weiss are both hired for production positions.
(B) Garcia and Yates are both hired for sales positions.
(C) Ilias and Weiss are both hired for sales positions.
(D) Ilias and Weiss are both hired for production positions.
(E) Ilias and Xavier are both hired for production positions.

Why isn't A the correct answer?

Management: G
Production: FWI
Sales: HYX
Button navigates to signup pageComment on a a's post “It can be determined in w...”
(2 votes)
Answer
- IndiGCR89
  Posted 5 years ago. Direct link to IndiGCR89's post “Because option C) Illias ...”
  Because option C) Illias and Weiss are both hired for sales positions; reveals where each employee will work.
  Since I and W are in Sales there is only one more sales slot open. If we look at the other letters we can quickly eliminate all but one for this sales position. We know it can't be F because it must always be in production, or H and Y since they must always be together and there is only 1 slot open in sales. That leaves G to fill in that vacant sales slot, because if X were in sales, then per the rule, Weiss would have to be in production instead.
  Therefore option C, best answers the question, by determining which department each of the seven applicants will be hired for.
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  (1 vote)
Alex DeJarnett
Posted 4 years ago. Direct link to Alex DeJarnett's post “I started out strong on t...”
I started out strong on this question but lost steam over time. It was difficult to refer back to the questions as scrolled down the page. Can the questions be made to "float" as the page is scrolled?
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(2 votes)
Answer
fortressmt
Posted 4 months ago. Direct link to fortressmt's post “In the last scenario wher...”
In the last scenario where "Xavier is not hired for one of the production positions," I quickly sketched a NEW #2 Scenario with Xavier in sales and was able to plot the positions of all the other employees. It made finding the answer painfully SIMPLE! This learning module helped me significantly. Thanx!
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(1 vote)
Answer
Annette Rousseau
Posted 6 months ago. Direct link to Annette Rousseau's post “first Q. is wrong. if X i...”
first Q. is wrong. if X is not in sales, W is not in production. answer E. X is in Mgt. W is in production. this breaks rule if X in s, then W in P. If x not in sales, then W is not in P.
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(1 vote)
Answer
shauntelkblack
Posted 4 years ago. Direct link to shauntelkblack's post “At 7:41 pm, Why can't the...”
At
7:41
pm, Why can't the answer to question 3 be B?
M: W
P: F, X, I
S: Garcia, Yates, H

If G and Y are assigned to sales, that means H also has to go to production (Rule 1). The contra rule to rule #3 was that if W was not assigned to production then X could not be assigned to sales. X cannot go to sales, so that means W cannot go to production (P), and must go to Management (M). That leaves X and I for production.
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(1 vote)
Answer
April Lombardi
Posted a year ago. Direct link to April Lombardi's post “Why can’t Xavier be in pr...”
Why can’t Xavier be in production in this scenario?
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(1 vote)
Answer
robens101
Posted 8 months ago. Direct link to robens101's post “Could you elaborate on th...”
Could you elaborate on the first question? The correct answer is E. I'm a bit confused.
The rules state:
if Xavier is in Sales
Weiss is in Production.
another way that I phrase it is:
if Xavier is not in sales, then Weiss is not in production. isn't that correct?

on choice E, Xavier is not in sales, and Weiss is in production. Doesn't that violate the rules?

To me, for choice E to be correct, Weiss shouldn't have been in production. This is because if Xavier is not on sale, Weiss is not in production.

I understand the concept as one needs to worry about the contra-conditional situation only when making the scenario? correct?
when answering the question, just simply read the rules and go from there.
E is correct when I read the rules and does not consider anything else.
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(1 vote)
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