Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Undefined game.

This game is difficult for two primary reasons. First, the number of applicants interviewed and hired is Undefined. As mentioned elsewhere, Undefined grouping games are generally harder than Defined grouping games because Undefined games have a relatively greater number of solutions, and the lack of certainty in the setup forces the test taker to remember extra elements throughout the game. Second, the two groups are linked. Generally, Grouping games feature separate groups with no true interrelation. For example, a game might feature children in separate canoes. Once a child has been placed in one canoe, he or she is then prevented from being in the other canoe and can be taken out of the variable pool. In this game, however, applicants who are hired must first “pass through” the interview group. Thus, an applicant who is placed into the interview group may or may not proceed to the hiring group. This effectively keeps variables “alive” even though they have already been placed once.

The basic scenario for the game appears as follows, with the relationship between Hired and Interviewed shown with an arrow indicating if an applicant is hired, they must have been interviewed first.

Thus, to be hired, an applicant must be interviewed. The contrapositive of that rule indicates that if an applicant is not interviewed, then they cannot be hired. So, any Not Law that appears under the Interviewed group will automatically result in the same Not Law appearing under the Hired group.

The third rule establishes that F is interviewed, which can be shown directly on the diagram:

The remaining rules are conditional in nature. When diagramming these rules, use subscript designations for interviewing (I) and hiring (H):

The first two rules can also be combined to form a conditional chain:

Note the importance of L in the above chain: if L is not interviewed (and thus not hired), then neither G nor J can be interviewed or hired.

It is also important to keep in mind the contrapositive of each rule. For example, the contrapositive of the fifth rule would state that “if M is not interviewed then K is not hired.” Thus, in a question like #8, where M is not interviewed, you immediately know that K cannot be hired. Remember, when conditional statements are presented in a form that is in any way unusual, always take the contrapositive.

The information above can be used to form the final diagram for the game:

[Basia W]

Hello,

I had the right set-up for this but I was wondering if this game would constitute a two value system due to the "interviewed" and "hired" duality?

very best,

Basia

[David Boyle]

Hello,

I had the right set-up for this but I was wondering if this game would constitute a two value system due to the "interviewed" and "hired" duality?

very best,

Basia

Hello,

Not really, since there isn't really a duality. You have to be interviewed to be hired, instead of "interviewed" being any kind of an opposite category from "hired". "Hired" may be considered a subset of "interviewed", which all is not really a duality.

David

[Sherry001]

Hello hello !
For this game there is a conditional rule in the stimulus that I had trouble diagraming . I was wondering if you could show me how I could avoid such an error in the future.

The rule : only applicants who are interviewed will be hired.

I originally diagramed it like this : interviewed --> hired
**I just thought from reading the bibles that the necessary condition indicator "only" is interrupted by the sufficient indicator "people who" that's why I diagramed it like so.

Thanks so much
Sherry

[Robert Carroll]

Sherry,

It's excellent for you to be so aware of conditonal indicator words and phrases like "only" and "people who." One thing to keep in mind, though, is that "only" is a pretty reliable indicator of a necessary condition no matter what words come along with it. This is most evident in combination with "if" - "if" alone is a sufficient condition indicator, but "only if" is always a necessary condition.

In this particular case, we can confirm that "only" indicates the necessary condition by imagining two candidate interpretations of the rule, and then seeing which one matches the English sense of the rule itself:

Candidate rule 1: interviewed hired

Candidate rule 2: hired interviewed

Because each rule is the reversal of the other, one of these is the Mistaken Reversal, so we really need to make sure we have the order right!

If the first interpretation is correct, the rule says something like "You must be hired in order to be interviewed." In other words, everyone interviewed is hired. This does not match the rule as stated in the scenario - in the rules as stated on the test, all hires come from interviewed people, and no one else. Thus, the real sense of the rule is that "You must be interviewed in order to be hired" - our second candidate above.

"Only" thus indicates the necessary condition.

It may be useful to imagine which group can be larger - the hires or the interviews. There is, in this situation, no problem having the groups be equal in size, so we'll just speculate - if you had an extra person or extra people in one group, which group could it be? If there is an extra person in the hire group, so that there is someone hired who isn't interviewed, that would violate the rule that "Only applicants who are interviewed will be hired" - if someone is hired without being interviewed, that doesn't work. A sufficient condition group can never be larger than the necessary condition group. It's not as if you must think this way every time you have such conditionals, but if identifying the conditions based on indicator words is not clear, this is another way to view the issue.

I hope this has helped!

Robert Carroll

[Echx73]

Hello,

I was curious, the first rule in the game states "If G is interviewed, J is interviewed." My question: Is there any way the contrapositive would be anything else beside J not interviewed, then G is not interviewed? I know above you talk about subscripts and I just want to make sure you cannot work hiring into the contrapositive somehow. Also, do know of another preptest that exhibits a rule like Interview <--------Hiring. I understand this test, but I would like to see this rule in a different form. Thank you!

Eric

[Echx73]

Hello Team!

Can you draw the contrapositive to the rule: "K is not hired, unless M is interviewed" thank you!

Eric

[Emily Haney-Caron]

Hi Eric,

Here your diagrams are:
K hired M interviewed
M not interviewed K not hired

[rka2224]

Hi there!

Would you be able to walk us through the full setup for the game? I'm not sure I made all of the needed inferences to tackle the game. In 11 minutes, I only got through the first 4 questions.

I have:

GI JI LI
FH FI & KI
KH MI & KI
MH & LI OH OI

Is there anything critical I'm missing? Also, did I interpret it correctly if I have 3 groups: H, I, Out? After working through a few of the problems, it seemed as though the "Out" group was superfluous, as it didn't have too much of an impact on the problems, save for the last one maybe.

Thanks!

- R

[Nikki Siclunov]

Hey R,

Yes, you understood the game correctly. I probably would omit the "out" group in this case. Technically, we have three groups of people: people who are neither interviewed nor hired; people who are interviewed but not hired; and people who are both interviewed and hired. For simplicity's sake, I'd keep track of only two groups: people who are interviewed (whether or not they are hired); and people who are hired (having also been interviewed).

When diagramming the rules, it is important to use subscript designations for interviewing and hiring (you seem to have done that). It is also important to keep in mind the contrapositive of each of the rules. For example, the contrapositive of the fourth rule would state that “if K is not interviewed, then F is not hired.”

The only thing missing from your setup is the rule stating that F is interviewed. Put F in the "Interviewed" group.

The setup in this game should not be terribly time-consuming, as the game does not generate a lot of inferences. Instead, spend the bulk of your time answering the questions that follow.

Thanks,