1. Every delegate to the convention is a party member
2. Some delegates are government officials
3. Every government official at the convention is a speaker at the convention
(C) concludes that some speakers are delegates. We know that some of the delegates are government officials and from this we know that some government officials are delegates. Couple that with the fact that every one of the government officials will speak and we can conclude that some of the speakers will be delegates. Bingo!
Incorrect Answer
(A) is unsupported by the statements. Knowing our inference rules here is useful. If every A is B, what can we conclude? The answer is that some B is A. For (A), we know every delegate is a party member, but we cannot conclude the reverse: that every party member is a delegate. Eliminate.
(B) concludes that some of the speakers are neither delegates nor party members. What do we know about the speakers? From the second statement, we know that some of them are government officials. Since government officials make up some of the delegates, we can also say that some of the speakers are delegates, and therefore party members. That’s as far as we can go though; eliminate.
(D) makes the same mistake as A. We know every government official is a speaker; we cannot conclude the reverse. We can’t conclude anything about all speakers. Eliminate.
(E) is unsupported by the statements. Can we conclude anything about every government official? Only that they’re all speakers. Elminate.
Note that A, D, and E all make strong inferences using words like every and all. To be clear, this doesn’t mean they’re wrong, but the most extreme part of any claim is the most likely to have overreached, so when we’re eliminating, it’s helpful to focus on those parts.
With these types of problems, sometimes a picture can be helpful. Ideally this will be a mental picture, but if there’s time and it’s necessary, we could draw a quick sketch out. Here’s an example of how a picture may have looked:

When using this image, we must be careful to remember we’re looking at all of the delegates, but government officials, speakers, and party members are not necessarily completely represented; there could be member of those groups not at the convention. Using the diagram, we could eliminate (A) because there could be other party members out there, (D) because there could be other speakers out there, and (E) because there could be other government officials out there. The diagram doesn’t support (B)’s contention but certainly supports (C).
