Traditionally, the term blue moon does not refer to the second full

Magoosh Official Explanation:

Split #1: the Inside/Outside rule

One important rule about parallelism is the Once Outside, Twice Inside rule. This rule comes into effect when we have correlated conjunctions—that is, a coupled pair of conjunctions marking the two halves of the parallelism: examples include “both X and Y,” “neither X nor Y,” “not X but Y,” and “not only X but also Y.” When any of these are used, the parallelism has a clear start at the beginning of the first word. Anything that is within the “both X and Y” structure is “inside,” and anything that comes before or after it is “outside.” Now, suppose a preposition applies to words in both branches of the parallelism. We have two options:

Once Outside: to both X and Y

Twice Inside: both to X and to Y

In the first, the preposition “to” appears once “outside,” that is, before the parallelism begins. In the second, a “to” follows each of the correlated conjunctions, “inside” the parallelism.

Common mistake patterns are “once inside” or “once outside, once inside.”

In this question, it’s a verb, “refer,” that is the element that may fall inside or outside. In all five choices, the “to” falls inside the parallelism in the first branch and needs to be repeated.

Choice (A): the verb “refer” occurs only once inside; this choice is incorrect.

Choice (B): the structure “refer to” occurs only once inside; this choice is incorrect.

Choice (C): the verb “refer” occurs once outside, and “to” occurs twice inside; this is error-free

Choice (D): the verb “refer” occurs once outside, but “to” occurs only once inside; this choice is incorrect.

Choice (E): the structure “refer to” occurs once inside and once inside; this choice is incorrect.

On the basis of that single split, we have isolated a single correct answer. For the sake of understanding the grammar of other parts of the sentence, I will explore a second split.

Split #2: popular thought

What is the correct idiomatic way to talk about popular thought? Here are how these five answer choices handle it:

Choice (A): “as they popularly think”—the pronoun “they” has no clear antecedent, so this choice is incorrect.

Choice (B): “which is popularly thought”—the antecedent of pronoun “which” is the action of the preceding clause; a pronoun cannot refer to an action, so this choice is incorrect.

Choice (C): “as is popularly thought”—this elegant phrase is common in higher-quality writing; this is error-free.

Choice (D): “which is what is popularly thought”—repeats the pronoun mistake of (B); this choice is incorrect.

Choice (E): “as would be popularly thought”—this is grammatically correct, but illogically it is hypothetical, suggesting that it is speaking about something contrary-to-fact. This does not match the situation. This choice is incorrect.

As both splits have made clear, the only possible answer is (C).