Official Explanation:
This sentence is correct as written.
The underlined portion of the sentence contains the third-person pronoun they, so check whether the pronoun agrees in number with its referent. The plural they clearly refers to nutritionists. There appear to be no errors in the original sentence, so keep choice A. Because there are no errors in the original sentence, there are no obvious repeaters to look for. Evaluate the remaining choices individually, looking for reasons to eliminate each answer.
Choice B introduces a pronoun error by replacing the phrase these elevated levels with the pronoun them. These elevated levels clearly refers to cholesterol levels, but there are two plural nouns in the sentence to which the pronoun them might refer. Since the referent of the pronoun them is ambiguous, eliminate choice B. Choice C repeats the pronoun error introduced in choice B, replacing these elevated levels with the pronoun them. In addition, choice C introduces an idiom error by replacing not with neither. The word neither forms the first part of a correlative conjunction, neither…nor. Choice C pairs neither with or, which is not idiomatic. Eliminate choice C. Choice D creates a new error by employing the pronoun their, the referent of which is ambiguous. In addition, choice D creates a parallel construction error by introducing a list the elements of which represent different parts of speech. The first item, determined, is a verb, but the second item, how, is an adverb. Eliminate choice D. Choice E creates a subject-verb agreement error by introducing the clause levels is. In addition, the referent of the pronoun their is ambiguous. Eliminate choice E.
Choice A: Correct.
Choice B: No. The referent of the pronoun them is ambiguous. Pronoun ambiguity.
Choice C: No. The referent of the pronoun them is ambiguous, and the correct idiom is neither…nor. Pronoun ambiguity; Idiom.
Choice D: No. The referent of the pronoun their is ambiguous, and the items in the list, determined… and how…, do not represent the same part of speech. Pronoun ambiguity; Parallel construction.
Choice E: No. The singular verb is does not agree in number with the plural subject levels, and the referent of the pronoun their is ambiguous. Subject-Verb agreement; Pronoun ambiguity.
The correct answer is choice A.