This presents a valid argument. Mismatches with the stimulus are in bold:

English
If we collect enough funds, we’ll build the theater.
We did collect the funds.
________
We will construct the theater.

Logic
Funds → Theater
Funds
________
Theater

This presents a valid argument. You can translate “unless” a few different (logically equivalent) ways – these summaries present the argument in the contrapositive form. Mismatches with the stimulus are in bold:

English
To reduce flights, we must collect higher fares.
We can’t collect higher fares.
________
We can’t reduce flights.

Logic
Reduction → Fares
/Fares
________
/Reduction

This argument displays a different flaw – it affirms the necessary condition instead of denying the sufficient condition. There’s also a structural mismatch – (C) introduces an additional necessary condition. The first of these differences is more important than the second. Mismatches with the stimulus are in bold:

English
To start the project, we must have 1) council approval, and 2) mayoral approval.
We have mayoral approval.
________
The project will start.

Logic
Project → Council and Mayor
Mayor
________
Project

(D) mirrors the stimulus in denying the sufficient condition. Here’s the English:

Stimulus
If people complain, we’ll need an exterminator.
People aren’t complaining.
________
We won’t need an exterminator.

(D)
If the band plays, people will attend*.
The band won’t play.
________
People won’t attend.

And here’s the logic:

Stimulus
Complaints → Exterminator
/Complaints
________
/Exterminator

(D)
Band → Attend*
/Band
________
/Attend

*Notice how I’ve cut the term “most” out of these summaries. It does in fact appear on the other side of the arrow than the word “majority” in the stimulus. But that doesn’t matter. See the footnote in the analysis for more detail.

(E) differs from the stimulus in two important ways. First, it attempts valid contrapositive reasoning, negating a necessary condition. Second, it introduces an additional necessary condition. (E) fails to negate that condition, which makes it a flawed argument, but it’s flawed in a different way than the argument in the stimulus. Mismatches are in bold:

English
To change the code, we must have 1) principal approval, or 2) PTA approval.
We don’t have principal approval.
________
We won’t change the code.

Logic
Change Code → Principal or PTA
/Principal
________
/Change Code