In North America there has been an explosion of public interest in, an enjoyment of, opera over the last three decades. The evidence of this explosion is that the 70 or so professional opera companies currently active in North America, 45 were founded over the course of the last 30 years.

The reasoning above assumes which one of the following?

A. All of the 70 professional opera companies are commercially viable options.

B. There were fewer than 45 professional opera companies that had been active 30 years ago and that ceased operations during the last 30 years.

C. There has been a corresponding increase in the number of professional companies devoted to other performing arts.

D The size of the average audience at performances by professional opera companies has increased over the past three decades.

E. The 45 most recently founded opera companies were all established as a result of enthusiasm on the part of a potential audience.

Please give a detailed explanation of why each of the answers is correct or incorrect. Thanks!

Great question - this is one of my favorites, and a great example of a very difficult Assumption questions.

First, we need to understand the argument, which states that, because 45 new operas have been founded in the last 30 years, we can conclude that there has been an explosion of interest in opera over that time. Essentially, it concludes that the 45 new operas are proof that opera interest has increased.

If you use the Assumption Negation Technique, let's look at the correct answer, B, first. When negated, B would say that:

(B-negated): There were MORE than 45 opera companies that had been active 30 years ago and have since closed.

Well, with B negated, we'd have 45 new operas (from the stimulus) and more than 45 operas that have closed. Therefore, we'd have fewer operas than we did 30 years ago, and the conclusion that opera interest is up no longer holds - it's actually down.

If we negate the others:

(A-negated): NOT ALL of the current opera companies are commercially viable.

Here, it doesn't ruin the conclusion if not all of the operas are making money - if one or two were struggling, or publicly funded, we still have quite a few more than we did before, so we don't need this premise in order to prove the conclusion.

(C-negated): There has NOT BEEN a corresponding increase in the number of other art companies.

This one is out of scope - we're only concerned with opera companies, so the other arts have no bearing on our conclusion.

(D-negated): The size of the average audience has NOT increased over the past 30 years.

This also doesn't crush the conclusion - even if the average isn't higher, the fact that there are considerably more operas overall is still evidence that there is increased interest.

(E-negated): The 45 new operas were NOT ALL established as a result of enthusiasm of audiences.

Here, like in A, we don't need ALL of the operas to be the result of enthusiasm. A few may have simply replaced others that had closed, or were created by charitable organizations. As long as we have more operas than before, we can still make our conclusion, so A and E are out of scope because we don't need "ALL" of the operas to be profitable or in-demand...we just need an overall increase. B is the key element in this conclusion - if the 45 new operas don't represent an increase, then the argument fails.

Cheers,
Brian