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does "expressing" in option "a" act as a gerund? Which noun does it modify? also, since there is no "to be" verb it can't act as a verb
It seems expressing is acting like a verb, can we eliminate a on basis of this fact?
Interesting question, but there are better reasons to eliminate (A) here. To see how the phrase, "end up + -ing" works, consider a simpler example:
If Tim remains their legal guardian, his kids will surely end up becoming sugar-addicted zombies.
Here "will... end up" seems to function as the main verb of that second clause. "Becoming" certainly isn't a verb, but whether we call it a gerund that functions as an object for "end up" or a participle that functions as an adverb isn't important here. All we care about is that there's no good reason to argue that the construction is wrong.
Now take another look at (A):
The tourism commission has conducted surveys of hotels in the most popular resorts, with the ultimate goal of reducing the guests who end up expressing overall dissatisfaction with the service in the hotels.
The phrase "who end up expressing" is functioning as a modifier for "the guests." Within the modifier, "who" is the subject, and "end up" is the verb. I wouldn't worry too much about what to call "expressing," but there's no reason to believe it's an error.
It's more useful to recognize that "reducing the guests" is illogical. Are they making the guests physically smaller? It makes far more sense to write that they're reducing the
number of guests. Because (A) has a nonsensical meaning, it's out.
Put another way, if a sentence is illogical, there's no reason to agonize over the grammar. So if you're unsure about one element of a sentence, look for others you're more confident about.
I hope that helps!