Although she had studied diligently, Sarah found the advanced calculus exam to be incredibly challenging furthermore, she felt unprepared for some of the more obscure topics.
Correct: C
This sentence contains a run-on sentence or a comma splice if the original had a comma before 'furthermore'. The two clauses 'Sarah found the advanced calculus exam to be incredibly challenging' and 'she felt unprepared for some of the more obscure topics' are independent clauses. They cannot be joined by just a comma and a conjunctive adverb ('furthermore'). They require stronger punctuation. A semicolon or a period can separate them. Option C uses a semicolon, which is appropriate for connecting two closely related independent clauses joined by a conjunctive adverb. Option D would also be correct, but a semicolon emphasizes the close relationship between the ideas.