If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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

Beginning of reading passage.

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.
End of reading passage.

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.

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?
  • 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
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
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.
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
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.
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.

Want to join the conversation?

  • blobby green style avatar for user Brandie Farmer
    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?
    (6 votes)
    Default Khan Academy avatar avatar for user
  • mr pink orange style avatar for user Nicole
    For the last question, when evaluating answer option (B), how do we know that Xavier can't be in Production?
    (1 vote)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user amnah.haque
    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)
    (4 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user a a
    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
    (2 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user IndiGCR89
      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.
      (1 vote)
  • blobby green style avatar for user Alex DeJarnett
    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?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user fortressmt
    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!
    (1 vote)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Annette Rousseau
    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.
    (1 vote)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user shauntelkblack
    At 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.
    (1 vote)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user April Lombardi
    Why can’t Xavier be in production in this scenario?
    (1 vote)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user robens101
    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.
    (1 vote)
    Default Khan Academy avatar avatar for user