Question

Which sentence has a gerund functioning as the object of a preposition?

Answer 1

A.
Gerunds generally end in -ing, and the subject of the prepositional phrase "for meeting" is meeting, which means it is the object of a preposition.
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Answer 2

The sentence that has a gerund functioning as the object of a preposition is A: "They thanked us exuberantly for meeting with them to discuss the deal".

Words that are formed from verbs but do not act as verbs are called verbals. This is the case of gerunds since they are formed from verbs but act as nouns.   Therefore, they behave as subjects, direct objects, objects of prepositions, predicate nouns, and more.

In this case, the gerund is "meeting". It functions as the object of the preposition "for" and it also takes complements and modifiers ("meeting with them to discuss the deal").