Q21

[evelina.chang]

I don't understand how to arrive at the answer for this question. :/

[ohthatpatrick]

This is a crazy weird game -- a nice reminder of why we're lucky that the modern era mostly sticks to familiar game types.

Our initial inventory of people is
Partners - H, R
Associates - O
Assistants - G, J, L, S, T, W

The game is only concerned with whether the Associates and Assistants get promoted to the next highest level (with each year's review).

The rules that govern the promotion process are as follows:
- with each review, everyone has a chance of being promoted
- at least 1 Assoc and 1 Assist must be promoted each time (this guarantees that O must be promoted during the first year's review)
- you get promoted if a majority of the people above you vote for you

The way the game begins, only H and R will vote on O (but like we said, we know that O will have to get promoted, because at least one Associate is promoted each year).

H, R, and O will all vote on the Assistants (and at least one Assist. must be promoted).

It's probably helpful to sketch out a voting chart to organize the info we have:

G J L S T W
n n _ _ n _ (Olivos's votes)
_ _ n n _ _ (Rafael's votes)
_ n _ _ _ n (Wilford's votes)

(n = "no" vote)

Note that from this chart, we already know that Johnson is screwed. He has 2 votes against him, so he can't get promoted during the first review. In fact, he needs a minimum of 5 people above him to have a chance, since he would need 3 yes votes to override those 2 no votes.

Now that we kinda understand the rules of the game, let's look at #21.

It gives us some voting information for R and W (leaving open the question of O's votes). Let's make a new voting chart to incorporate that info:

G J L S T W O
n n _ _ n _ / (Olivos's votes)
y n n n n y y (Rafael's votes)
n n y y n n y (Wilford's votes)

Because it said "votes ONLY for", we know that the names not mentioned get a NO vote.

So do we know anyone who definitely is or isn't being promoted?

Definitely NOT being promoted: G, J, T

Let's get rid of any answers with G, J, or T. That gets rid of (A), (B), (C), and (E).

So (D) is our correct answer.

(Without doing any of the work for Q21, we would know that (B) and (E) are wrong --- our initial analysis of the setup/rules told us that in the first review Olivos MUST be promoted to partner, so E is wrong, and that Johnson CANNOT be be promoted to Associate, so B is wrong).

Hope this helps. Let me know if you have lingering questions.