#20 - In North America there has been an explosion of public interest in,

[ikim10]

Hello, I just wanted to confirm my reasoning for this question and make sure I understood why (B) is the correct answer and (D) is incorrect.

Negating (B), I paraphrased it "There were 45 or more opera companies that had been active 30 years ago and closed within the past 30 years."

This hurts the argument, because it is assuming that there was an increase in the number (specifically, by 45) of professional opera companies in the past 30 years. However, the negation of (B) tells us that at least the same number or more opera houses closed within the past 30 years than opened, meaning that the number of opera houses compared between 30 years ago and now is either the same or is lower than what it was. This hurts the argument, since it is saying we can use the increase in the number of opera houses as evidence of its increase in popularity/enjoyment with the public.

(D) is incorrect because (D) negated is "The size of the average audience at perfromances by professional opera companies has not increased over the past three decades."

This does not hurt the argument; if the average audience size stayed the same, then combined with the premise that implies that there has been an increase in the number of opera houses, it could potentially mean that more people are going to the opera. This doesn't hurt the argument, so it is not a necessary assumption and is incorrect.

[Luke Haqq]

Hi ikim10!

Yes, it looks like you've applied the Assumption Negation technique correctly. Your paraphrases and reasoning all look good--well done!

[BrainDrain15]

Hi all! I'm getting confused about assumption questions. Would someone be able to help me with an explanation of why (D) is incorrect and (B) is correct?

[Jeff Wren]

Hi BrainDrain,

First, if you haven't done so already, I'd recommend reading the first post in this thread (Post #1), as this student did a very good job of explaining both Answer B and D.

The conclusion of this argument is the first sentence. The argument concludes that there has been a significant increase in public interest in opera in the past 30 years. This conclusion is based on the fact that 45 of the 70 currently active professional opera companies in North America were founded in the past 30 years.

For assumption questions, it can actually be quite helpful to first think about any weaknesses or flaws in an argument, as many assumptions protect the argument by eliminating these weaknesses. (We refer to these assumptions as Defenders.)

In this argument, we are missing important data about the number of professional opera companies in North America thirty years ago and how that number compares to the number today. Just because 45 of the 70 currently active professional opera companies in North America were founded in the past 30 years, that does not mean that there has been a net increase in the number of professional opera companies in North America in the past 30 years, which is what the argument is assuming.

For example, what if more opera companies closed in the past 30 years than new ones opened? What if 30 years ago, there were 100 professional opera companies in North America? If that were true, that would suggest that public interest in opera has been decreasing in the past 30 years rather than increasing. In other words, the fact that 45 professional opera companies were founded in the past 30 years would not indicate an increase in public interest in opera; it could simply reflect routine turnover as opera companies periodically close and new ones open.

Negating Answer B, if "there were more than 45 professional opera companies that had been active 30 years ago and that ceased operations during the last 30 years," this would directly attack the conclusion that interest in opera has been increasing in the past 30 years. (Technically, the logical opposite of "fewer" would be "equal or more," but this would still attack the argument. I often simplify the negation to "more" for the sake of clarity.)

While Answer D would help the argument, it is not required of the argument. The size of the average audience could still remain the same as long as there are more performances taking place. The important thing is that there are more people interested in opera overall rather than needing specific information about average performance sizes.