If Paul comes to the party, Quentin leaves the party. If Quentin leave

Official Explanation

We can summarize the information, using capital letters to represent each statement:

If P, then Q.
If Q, then R or S.
If R or S, and if Q, then A.
If R or S and if not-Q, then not-A.

where P represents “Paul comes to the party,” Q represents “Quentin leaves the party,” R represents “Robert asks Alice to dance,” S represents “Steve asks Alice to dance,” (and conversely R represents “Alice is asked by Robert to dance” and S represents “Alice is asked by Steve to dance”), and A represents Alice accepts. If we have not-Q, then we can deduce notP from the first statement; thus, we have (D).

(A), (B), and (C) are incorrect since there is no necessity that Robert or Steve ask Alice to dance. (E) is incorrect since this statement is different from our other statements and must be assigned a different letter, perhapsX. Notice that “Alice will accept . . . ” tells us nothing about whether Alice leaves the party.

The correct answer is (D).