Most of Portugal's 250,000 university students boycotted classes in a

Hello Schachfreizeit,

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To answer your query, yes; if the "comma + present participle ("verb+ing")" construction is linked with a clause, it modifies the entirety of the clause and in doing so conveys that the subject of the clause took the action described in the participle.

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but then I don't understand your solution for A) "This answer choice incorrectly modifies "the cost of higher education" with "previously paying $7 per year""

Just a small doubt. Doesn't we use "noun" after 'instead of' not a phrase, verb, adverb or prepositional phrases. Using "instead of" isn't it incorrect here? If it was rather than then would have picked D. Am I getting rule wrong?

'instead of' is a preposition and needs a noun/noun phrase after it. In option (D), it is followed by a noun phrase 'the $7 per year.'
(A noun phrase is a noun + articles/modifiers)

Hello AndrewN MartyTargetTestPrep

I am unable to understand why option A is wrong. If "paying" refers back to "Most of Portugal's 250,000 university students boycotted ...." or "them to contribute ..", is the meaning nonsensical? Can you elaborate on that?

Yes, the meaning conveyed by the (A) version is nonsensical.

Here's the end of that version:

requires them to contribute $330 a year toward the cost of higher education, previously paying $7 per year.

It suggests that, in the process of contributing $330, they are "previously paying $7." Since they would not be paying $7 in contributing $330, that meaning is illogical.

Just to confirm that there is no way for the sentence to work, let's see whether "previously paying $7 per year" could instead modify the main clause of the sentence.

Most of Portugal's 250,000 university students boycotted classes ..., previously paying $7 per year.

Now the sentence conveys that, in the process of boycotting classes, the students were somehow "previously paying $7 per year," as if, by boycotting classes, they paid $7 previously. How would they do something previously by boycotting classes in the present? Do they have a time machine? Also, they would not pay $7 by boycotting.

The (A) version of the sentence is nonsensical no matter how we read it.

Most of Portugal's 250,000 university students boycotted classes in a one-day strike to protest a law that requires them to contribute $330 a year toward the cost of higher education, previously paying $7 per year.

Option Elimination -

A. year toward the cost of higher education, previously paying $7 per year - Comma + ING is adverbial. Here, "paying" is modifying "law requires" as if the law is making the payment. Wrong.

B. year toward the cost of higher education, for which was previously paid $7 per year - "which" modifying "higher education"? Moreover, depending on the context, "for which was ..." is a prepositional phrase that can be adjectival or adverbial. Here, "for which was ..." modifying "the cost"? The cost was paid? No. Or "higher education"? Higher education was paid $7. No. Can it be adverbial? "for which was ..." modifying "law requires"? No. So, this prepositional phrase doesn't make much sense.

C. year, compared to the previously $7 per year, toward the cost of higher education - "ed" verbals modify nouns. The nearest noun is "a year." Does it make sense? No. Moreover, "previously" is an adverb modifying the noun phrase "$7 per year" - wrong.

D. year toward the cost of higher education, instead of the $7 per year required previously - Two ways to look at it. First, X instead of Y. X is "contribute $330 a year," which is modified by the prepositional phrase "toward the cost of higher education," and Y is "the $7 per year" modified by "ed" verbal "required." Another way is "instead of" with a comma acts as an adverbial like any other prepositional phrase modifying the preceding clause.

E. year as opposed to the $7 per year required previously for the cost of higher education - This is a perfect deception. Let's dig deeper.
First, there is a difference between "as opposed to" and "instead of."
"as opposed to" highlights the contrast or difference between two things. E.g., "an approach that is theoretical as opposed to practical."
"instead of" indicates substituting or replacing one thing with another. E.g., She decided to have tea instead of coffee. RonTargetTestPrep shared this difference pretty well.
Let's also refresh "rather than" to put things in perspective. "rather than" indicates a preference or choice between two options. E.g., I would prefer to go for a walk rather than watch TV.

In this option, we aren't contrasting "$330 a year" and "$7 per year." The intended meaning is earlier "$7 per year" is substituted with "$330 a year," which is a substantial difference and thus boycotts.

Moreover, we are comparing "X," which is "$330 a year, with "the $7 per year required previously for the cost of higher education." As sayantanc2k also pointed out, its better to use ellipses to the latter than the former. Here the prepositional phrase "for the cost of higher education" is next "$7 per year" which it modifies and this preposition phrase is not linked to "$330 a year" which is wrong.

Additionally, let us also refresh our memories on the usage of the preposition "for."

1. Preposition of Purpose: "For" is often used as a preposition to indicate the purpose or intended use of something. It answers the question "Why?" or "What is the intended goal or benefit?" Example: I bought a laptop for work. Explanation: In this sentence, "for" indicates the purpose or intended use of the laptop, which is for work.

2. Preposition of Time: "For" can also be used as a preposition to indicate a duration of time. It answers the question, "How long?" Example: She studied for three hours. Explanation: Here, "for" indicates the duration of time, which is three hours.

3. Preposition of Exchange or Exchange Rate: "For" can be used to express an exchange or exchange rate when discussing currencies or trading. Example: I exchanged my dollars for euros. Explanation: In this sentence, "for" indicates the exchange of one currency (dollars) into another currency (euros).

4. Conjunction: Sometimes, "for" is a coordinating conjunction connecting two clauses or phrases. Example: She studied hard for she wanted to pass the exam. Explanation: In this sentence, "for" is a coordinating conjunction connecting the two independent clauses, indicating a cause-and-effect relationship.

Here, "for the cost" is a bit off as the cost is not the purpose.