Explanation

Creating a filter: in this sentence, there is a potential parallelism issue between "combat" and "administering." Should "administering" be "administer"? The intended meaning of the sentence will be the judge. We look closer at what it's trying to say. We're talking about a use of watercress and a different use hemlock. "Administering" is parallel with "using," and therefore is correct. That means that (A) might be right, so far, and we can take our observation to filter the other answer choices.

Applying the filter: based on our decision about (A), choices (B), (D), and (E) are defective. In (C), "administering" looks like it's parallel with "using," but it's preceded by "of" and therefore grammatically under the jurisdiction of "combating," which is contrary to the intended meaning. So (C) is wrong. That leaves (A) as the correct answer. We didn't have to worry about whether the "to combat" or "of combating" was better here, but the answer to that is that, when we are talking about a verb, the infinitive will be superior, whereas a preposition such as "of" is best used with a true noun, not a gerund. The correct answer is (A).