Understanding first what sentence fragment comes first. Sentence fragment, or just fragment itself, refers to parts of sentences that are separated and that they can't stand by itself. They might as well be referred to as phrases, but they are constructed as sentences. Some might even qualify to be a sentence by itself. It is important to remember that a fragment can't stand by itself unless it is joined together with the main clause. As for the options presented, options C. and D. would be out of the question since they are complete. B and A would be arguable as to which is the best answer. The most probable answer would be A. The one that is more annoying to me. The option B. would be a complete sentence. It is a little bit confusing because of the usage of the word "even".
