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Assumption. The correct answer choice is (B).
In Assumption questions, we look for gaps the author has left between the premises and conclusion. Here, the argument is structured as follows:
Premise: 45 of the 70 currently active opera houses were founded over the course of the last 30 years
Conclusion: Explosion of public interest in opera over the last 30 years
When prephrasing this answer choice, we can see that one of the major gaps in this argument has to do with the fact that the author is just considering the number of currently active opera companies and how many of those have been founded in the last 30 years, without considering how many opera companies may have in fact closed over this same time period. What if there were many more opera companies in existence over 30 years ago? Since the author believes their conclusion about an explosion of public interest in opera is correct, the author must assume that there were more opera companies that opened than closed.
Answer choice (A): This answer choice is too strong. It is not necessary that all 70 of the opera companies are commercially viable for there to have been an explosion of public interest in opera. Perhaps some of the companies are mismanaged and are therefore struggling commercially even though there is public interest.
Answer choice (B): This is the correct answer. This answer choice addresses the gap and potential weakness we identified in our prephrase. The author is assuming that more opera houses opened than closed, meaning that there were fewer than 45 opera companies (the number that have opened) that have closed during the last 30 years. If we negate answer choice (B) to say that there were MORE than 45 opera companies that have closed during the last 30 years, that would attack the argument that the opening of 45 opera companies in the last 30 years indicates an explosion of public interest in opera.
Answer choice (C): This argument is only about opera and so it makes no assumptions about other performing arts.
Answer choice (D): The author does not make any assumptions about the size of the average audience at specific performances. The average audience size could remain the same but if there are more performances that could indicate more people actually going to the opera.
Answer choice (E): This answer choice is somewhat tempting but ultimately too strong to be necessary. It is not necessary that ALL of the 45 most recently founded opera companies were established as a result of enthusiasm on the part of a potential audience. What if some of them were established as pet projects by extremely wealthy benefactors who did not care whether they would attract a large audience? Most of the opera companies could have still been created to meet audience demand. If we negated this to say that NOT all of the 45 most recently founded opera companies were established as a result of enthusiasm on the part of a potential audience, it would not attack the conclusion above because it could still be the case that many of those newly founded companies were created due to public interest.