Q25 - All actors are exuberant people

[ali.charania]

Could someone please walk me through how to solve this problem?

[giladedelman]

Sure! Thanks for posting.

We have two conditional statements:

Actor --> Exuberant
Exuberant --> Extrovert

These hook together pretty easily to give us

Actor --> Exuberant --> Extrovert

We also get another bit of information: some shy people are actors. Based on the chain we just put together, this means some shy people are exuberant and extroverted.

Now, we're looking for the one statement that does not have to be true.

(A) has to be true because like we just said, if some shy people are actors, and all actors are extroverts, then some shy people are extroverts.

(C) has to be true because if some shy people are actors, then some shy people are exuberant actors. And if that's true then we can say the reverse is also true: some exuberant actors are shy.

(D) has to be true because we know ALL actors are extroverts; so if you're not an extrovert, you can't be an actor.

(E) has to be true for the same reason as (A).

That leaves us with (B): some shy extroverts are not actors. This doesn't have to be true. We know that some shy people are actors and therefore extroverted, but we don't know whether there are shy people are extroverts, but not actors. Maybe there are, maybe there aren't. Therefore, (B) is correct.

Does that clear this one up for you, or are you still confused?