"universities may collect student activity fees even with students' objections to particular activities"
it sounds like the universities are collecting both fees and objections together - collecting fees with objections, like collecting dolls with special dresses. But that doesn't make any sense, right?
So I scanned down to see what my other options are. "universities may collect student activity fees even..."
A) with objections
B/C) if they (have objections / object)
D) from students who object
E) though students have an objection
A just repeats the original - eliminate.
B and C use the pronoun "they" so I've got to scan back and see whether "students" (the logical antecedent) is in the sentence. It's not, so "they" has no antecedent (ie, noun to which "they" refers). Eliminate B and C.
"student" isn't in possessive form, so it's not possessive poison, but "student" is an adjective here. "Student activity fees" - the noun is "fees" and "student" is just describing the type of fee. So you still couldn't use even a singular pronoun to refer to the word "student" because "student" isn't a noun in the original sentence.
a pronoun has to work both structurally and logically. If you use a subject pronoun in a later clause, then you would structurally expect the noun antecedent to be the subject of an earlier clause. If the pronoun points to one noun structurally but logically it points to a different one, that's ambiguous - and therefore wrong.
So let's look at B: "universities may collect student activity fees even if they have objections to particular activities..." In this part, "they" is a subject pronoun, so the structural antecedent is "universities" - but logically that doesn't make sense. Logically, "they" should refer to students who object to the activities (and that noun is not even in the sentence!). So that's a mismatch and B is wrong.
E has multiple problems. This opening bit that we've been looking at changes the meaning: instead of saying "I can collect money from everyone, even from those students who object," it's saying "I can collect money even though (all) students object." The word "but" later in the sentence also changes the intent - the stuff after the comma is supposed to indicate the rule that the universities have to follow in order to collect money from everyone. The word "but" introduces a contrast, which isn't the right meaning. There are other problems with this one, but that's enough to eliminate!
That leaves us with D.
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