Fossilized remains of a horn though to be of

subject is "remains" - plural; so A & B are out.
"dated to be" is incorrect idiom, C is out
"dated as being" conveys incorrect meaning. Also parallelism is missing in "and thus". so D is out.

Hence E is the correct answer

fossilized remains is the main subject - plural, so 'has been' (singular) is eliminated. This leaves us with C, D, and E. dated takes the preposition "at", so C and D are invalid. This leaves us with E. Hence, E is the correct answer.

Correct idiom is "dated at" A,C,D eliminated. Between B and E. B is singular, and subject is remains.

Official Explanation

Creating a filter: in the original sentence, we can pause at "dated to be." That sounds funny. And if it doesn't sound funny to you, make a note of this specific idiom. We'll eliminate (A) and look for a replacement of "to be."

Applying the filter: in the other choices, the option "dated at" may sound funny as well. Perhaps we can evaluate the answer choices solely on other grounds.

Finding objective defects: all of the answer choices contain the word "thus," so that word won't be a factor. There are some verb differences at the end of the choices: "is," "are," and no verb. Omitting the verb at the end would create a sentence fragment. The grammatical subject of this verb, and the verb at the beginning of the underlined portion, is "remains," which is grammatically plural. "Horn" is a noun, but it's the object of the preposition "of," so it can't be the grammatical subject. That narrows our options to (C) and (E). We must decide between "to be" and "at." Indeed, in this question, we must know the idiom. The proper English idiom is "at."

The correct answer is (E).