Received a PM asking me to respond. There was an error on the flashcards a while back - I remember Eric asking me about it.
Okay, so multiple things going on.
The structure that you're describing in the flashcards is not a straight sub-verb main clause set-up. Here's the difference:
The cat is red. cat = sub, is = verb, main clause set-up
The cat which is red likes to eat fish. cat = sub, then TWO verbs: "is" and "likes". The main clause is: the cat likes to eat fish. The "which is red" bit is a modifier. It's a noun modifier, so it modifies the preceding noun: cat. that's why "is" is singular.
Now, on the initial problem listed, we open with "The group of students." subj = "the group" and prepositional phrase = "of students." The whole thing is not a prep phrase - just "of students."
A group <of students who have begun to clean of the park in NYC> believes that (etc.)
Noun modifier again - so match "have begun" with "students." The verb "believes," on the other hand, is not inside of a modifier. This is the main verb for the sentence. So what's the main noun? "group." Match those two.
That allows us to eliminate everything but A and C. Then we've got the idiom "not X but Y" - and we also need parallelism. C breaks this parallelism:
the park needs NOT <to be redesigned> BUT <could be returned>
A is parallel:
the park needs NOT <to be redesigned> BUT <to be returned>
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