Thus, Vlad [could, and did, refer]to himself as "Dracula" and even signed official documents with that sobriquet.

A. NO CHANGE
B. could, and did refer
C. could and did, refer
D. calls and refers

The answer key says: If you look at (C) and (D), you will see that they change the meaning or create sentence fragments, so you can eliminate them. This question is testing commas. You could pull out the stuff between the commas and the sentence would still be correct, so you need the pair in (A), not the single comma in (B).

I don't understand how there are sentence fragments when using choice C and D?
P.S. Is the placement of the colon after the word says correct?

1. Yes, the answer key is right that the answer is A. Both commas are needed for the very reason given -- that the words between the commas can be pulled out and the rest of the sentence would read just fine and there'd be no significant change in meaning. All the other choices (B, C, and D) would result in changing the meaning of the sentence or causing confusion in the reader's mind. (I, too, don't understand how there'd be sentence fragments in C or D.)

2. A colon should not be used after any verb, including "says" -- http://grammar.ccc.commnet.edu/grammar/marks/colon.htm -- the information and the examples in the box explains this.

Let's analyze the options for this question and address your concerns.

Option A: "Thus, Vlad [could, and did, refer] to himself as 'Dracula' and even signed official documents with that sobriquet."

Option B: "Thus, Vlad could, and did refer to himself as 'Dracula' and even signed official documents with that sobriquet."

Option C: "Thus, Vlad could and did, refer to himself as 'Dracula' and even signed official documents with that sobriquet."

Option D: "Thus, Vad calls and refers to himself as 'Dracula' and even signed official documents with that sobriquet."

First, let's focus on the sentence fragments you mentioned. In option C, if we remove the phrase "and did" between "could" and "refer," the sentence becomes "Thus, Vlad could and refer to himself as 'Dracula' and even signed official documents with that sobriquet." This sentence is grammatically incorrect because it lacks a verb after "could." Therefore, option C contains a sentence fragment.

Similarly, in option D, the phrase "calls and refers" doesn't have a subject. Without a subject, the sentence becomes a fragment: "Thus, Vad calls and refers to himself as 'Dracula' and even signed official documents with that sobriquet." Again, this is grammatically incorrect because it lacks a proper subject-verb agreement.

Now, regarding the placement of the colon, it should come after the word "says" when used in a sentence like "The answer key says:" followed by an explanation or continuation of the sentence. So, the placement of the colon in your statement is correct.

In summary, options C and D are eliminated because they either create sentence fragments or lack a subject. The correct choice, as mentioned in the answer key, is option A.