Traditionally the term “blue moon” does not refer to the second full

OFFICIAL EXPLANATION


MAGOOSH OFFICIAL ANSWER

Split #1: the Inside/Outside rule

The construction in this sentence is Not X But Y.

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.
Both are correct: that is, once outside or twice inside is correct.
[Be careful.] 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.
[In closed pairs, the preposition does not "carry over" from the X to the Y element. You must restate it.]

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 “refers 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).