I picked E, and this is my reasoning:
the show will begin and will continue for as long as the interest lasts.
The verbs begin and continue must be parallel. Both are the verbs for the subject show.
Between Until and As long as - I picked as long as. Until is used for showing finality, while as long as shows continuity of the action.
A. will begin at 6 p.m. and continue until audience interest lasts
until suspicious, better check for the other answer choices first.
B. begins at 6 p.m., continuing until audience interest lasts
this answer choice changes the verb continue into a ing modifier.
ING modifier, separated by a comma, modifies the preceding clause, and if used correctly, it will either present reasoning behind the clause, or the result.
Let's see the entire sentence:
I use: The show begins at 6 because it continues until audience interest lasts - non-sense.
II use: The show begins at 6 by continuing until audience interest lasts - non-sense.
Since neither use of the ING modifier is correct here, B is incorrect.
C. will begin at 6 p.m. and, until audience interest lasts, will continue
First of all, this one is wordy since it repeats "will". This is unnecessary. Until - suspicious.
D. begins at 6 p.m. and, as long as audience interest lasts, it continues
this choice is incorrect even if the 2 verbs are "parallel". Nevertheless, if you look closely, you see that begins and continues have different time frames. While it is ok to use present simple for future events, in the second part of the sentence: It continues - this is an incorrect use for describing a future event that will happen after another future event. Moreover, the pronoun "it" brings another error in the sentence. Since the sentence is not connected properly (e.g. comma+and), we have a run-on sentence. Subject+Verb and Subject+Verb. This is incorrect.
E. will begin at 6 p.m. and continue as long as audience interest lasts
will begin and continue - both verbs ||
continue as long as - looks better than until.
E is thus the best answer.