If Mayer is not interviewed, which one of the following must be true?

BenMingov on November 28, 2019

Hi Farnoushsalimian, thanks for the question.

Unusual game indeed, let's try to break this down.

I treated this game like an in/out game with the key difference being that everything that is in group H (hired), is immediately known to be in group I (interviewed). This is the case because the scenario tells us that "only applicants who are interviewed will be hired". This constraint is conditional and signifies the following:

H - > I
NOT I - > NOT H

From there we are given a set of conditional rules and one obvious placement rule.

Rule 1: G(I) - > J(I)
Contrapositive: NOT J(I) - > NOT G(I)

Rule 2: J(I) - > L(I)
Contrapositive: NOT L(I) - > NOT J(I)

We can combine these two conditional rules even if we don't typically like to make long chains, just because of how clearly it is telling us A - > B - > C.
This becomes:

G(I) - > J(I) - > L(I)
NOT L(I) - > NOT J(I) - > NOT G(I)

Rule 3: Just place F into the I group.

Rule 4: F(H) - > K(I)
Contrapositive: NOT K(I) - > NOT F(H)

Rule 5: K(H) - > M(I)
Contrapositive: NOT M(I) - > NOT K(H)

Rule 6: Make sure to note that the two sufficient conditions are M(H) and L(I) respectively.
M(H) and L(I) - > O(H)
NOT O(H) - > NOT M(H) or NOT L(I)

We can't really do much with these rules because they only give us information once a sufficient condition is triggered. So just having F placed in group I is good for now and we can get into the questions. Because you asked about questions 7 and 8, let's focus on those.

Question 7:

Any list that is missing F in the group will be wrong. We can immediately remove A from contention.

Answer choice B: If F, J, and K are the only ones interviewed, then that's not possible because if J(I) - > L(I). Recall rule 2

Answer choice C: It cannot G interviewed plus one other, because if G(I), then we have to have J(I) + L(I) and don't forget about the F(I) that is always in.
Therefore, if G is interviewed, it is G + 3 others. Not 1.

Answer choice D: Wrong for the same reason as C, and this leaves us with answer choice E for the reason stated above.


Question 8:

If NOT M(I) - > NOT K(H)

It also triggers the initial rule we mentioned about H - > I

If NOT M(I), then NOT M(H).

Answer choice E is the only one that reflects what we know has to be true. That F(I) (always) and NOT K(H) now.

Let me know if this was helpful. Please let me know if you have any other questions.

farnoushsalimian on November 28, 2019

Yes
That made sense.
So we cannot infer that F is hired because if something is interviewed it doesn't mean that it's hired.


Thank you

Ravi on November 29, 2019

@farnoushsalimian, that's correct. We know that if someone was hired, they were definitely interviewed, but if we just know that someone was interviewed, we do not know that they were necessarily hired. Let us know if you have any other questions!