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

Conclusion > People like opera nowadays because 45 schools opened in the last 30 years.

A - No one cares
C - Again no one cares
D - The size of the average audience could have gone from 1 to 20000000000000, but yet again no one cares because the average size of the audience
is not the criteria used to advance the conclusion. The criteria is based on the # of opera companies not the amount of monacle wearing gentleman who attend operas.
E - This means zilch because the companies have already been founded, so wether or not the companies were founded because I was enthused doesn't matter at this point. Again, enthusiasm does nothing to advance the conclusion because it only talks about a "part" of a potential audience. That potential audience could be 1 billion people or you and your dog.

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

Imagine If there were 1 billion opera companies, and now there are 70 opera companies.
Now imagine that only 45 opened during the 30 years that 1 Billion opera companies closed. (+45) + (-1Billion) = wrecks this argument

IMO B

(A) All of the 70 professional opera companies are commercially viable options.
The argument doesn't mention the "commericial" aspect, this adds informations and the conclusion cannot be based on added information in the answer.
(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.
Correct (IMO)
(C) There has not been a corresponding increase in the number of professional companies devoted to other performing arts.
This is a good one... but since the passage doesn't mention any other art, I discard this and pick B.
(D) The size of the average audience at performances by professional opera companies has increased over the past three decades.
This option mention the "average", not the "number". Moreover the text links the increase of the number of bands to the explosion of public interest, and does not say anything about the audience.
(E) The 45 most recently founded opera companies were all established as a result of enthusiasm on the part of a potential audience.
The word "all" makes this answer too extreme

i think the answer must be B.
E is close but it just strengthens the fact that "Public likes the operas established in the last three decades or Operas are bound to make good profit or Opera is making a good business" But we are asked to find an assumption or support for the fact that it is against the public interest on the basis of an evidence that 45 out of 75 operas are founded in the last 3 decades." So the gap is "How can there be explosion of public interest if more number of operas are opened in that particular decade."
If we weaken the fact that all these operas in discussion are opened in the last three decades and not carried fwd frm previously running operas.
Than we can protect our conclusion.

Consider Kudos If my post helps!!

Archit

be flexible. Do not rely always on the negation technique: though is the most powerful tool for assumption questions, try to understand the question itself, too

this is what is our conclusion and what lead to it

The evidence of this explosion is that of the 70 or so professional opera companies currently active in North America, 45 were founded over the course of the last 30 years.


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


As you can see is completely unrelated to our conclusion.

Basically it says that NOW still exist more than 45 companies founded over the course of the last 30 years.

In E we see that something is RECENTLY founded due to the ENTHUSIASM of POTENTIAL audience. This is completely incosistent with our argument.

B must be the answer.

Hope is clear

Source : LSAT PrepTest February 1997, Q20 AnthonyRitz

EXPLANATION FROM KAPLAN

Assumptions link evidence and conclusion. Never forget that!

In arguing that North American public interest in and enjoyment of opera has skyrocketed over the last three decades, the author points to the fact that 45 out of the 70 active professional opera companies were founded during that time. He must see a link between the companies’ founding and audience enthusiasm over that time period, but this answer may be hard to predict, so let’s just examine each choice in turn.

(A) Do all 70 have to be “commercially viable” for the argument to work? No, because commercial viability isn’t a term in the discussion. Some, or even many, of the companies may be having a rough time commercially right now, but they still could have been founded by way of 30 years’ worth of audience enthusiasm. Eliminate.

(B) This one speaks to the implied comparison between the last three decades and earlier years. Suppose, for the moment, that (B) is wrong: Suppose that 30 years ago there were exactly 45 professional opera companies that went bust at some point thereafter. If so, then over the last 30 years there’s been no net gain in the number of companies that could support the notion of greater audience enthusiasm for opera. (The defunct 45 would just have been supplanted by the new 45.) Indeed, if things were worse, if 46 or 48 or 50 or more vintage companies have gone belly-up, that would represent a net loss of North American opera in the decades when the author claims that opera’s popularity has exploded! No, for the argument’s arithmetic to support the conclusion about audiences, (B) has to be true as written; over the last three decades there have to have been fewer companies dying than were born.

That’s the necessary assumption, as shown by the Kaplan Denial Test. Of the remaining choices:

(C) Theater, orchestral music, and ballet are outside the scope.

(D) Larger audiences might be read as a sign of greater public interest in opera, but they’re not necessary for this argument to work, since this argument draws its conclusion from the number of new companies, not from their overall health.

(E) asserts that the 45 new companies were all founded on the potential audience’s enthusiasm. Not necessarily. Many if not all of them may have been founded simply on the performers’ and impresarios’ desires to create opera, in the hope (rather than the expectation) that audiences would be enthusiastic. (E)’s firm cause-and-effect isn’t an integral part of the author’s logic.

GMATNinja, Could you please share your thought on this question? What is the logic to resolve? It is too complicated. Why answer choice (E) is incorrect?

The negation of (D) is
The size of the average audience at performances by professional opera companies has NOT increased over the past three decades.

Our conclusion can still hold even if this is true and therefore, (D) is not an assumption.

Conclusion: Over the last 30 years, there has been an explosion of interest in Opera.

We are given that 45 new companies were founded in this time. The size of the audience may not have increased because the new companies attracted the new following or size of the audience may have stayed the same because of capacity issues at the opera houses.

Also, absolute number of people visiting a place doesn't give you much info about the increase/decrease in popularity. You need to know the % of population that visits a place over a period of time. Opening up of many such new places hints at increase in popularity because it means that people see profit in the business and believe that it will do well provided they are not replacing the old dying companies and hoping to pull their clientele.

There is a small jump of assumption here - that the interest and no.of companies are directly correlated (and this assumption is not unjustified as such - it is not practical that when the public interest explodes, more companies would shut down than would open).

But strictly thinking, your point is valid - option B is a strengthening statement (very close to, if not is, an assumption).

Ziyuen, +1 for identifying the source of the question! LSAT used to license their questions to GMAT test-prep companies, but they stopped doing that a year or two ago, interestingly.

Anyway, on to your question. There are plenty of pretty good explanations already on this thread, so I'm not going to rehash all of them here -- but I do think that Tommy Wallach's explanation is spot-on, though I guess he could have said more about (E).

Remember that in an assumption question, you're looking for something that's necessary to draw the conclusion. It might not be 100% satisfying, or 100% airtight. It may not be the ONLY thing you need to draw the conclusion. But without it, the conclusion wouldn't work.

So... (E):



This sounds nice and everything, but you definitely don't want to confuse "enthusiasm on the part of a potential audience" with an explosion in the actual audience. It's fine if the 45 companies were founded when potential audience members were excited, but that does nothing to convince us that there has been a real explosion "of public interest in, and enjoyment of, opera over the past three decades." The enthusiasm (of a merely "potential" audience) when the companies were founded has little to do with any "explosion" of general public interest over a period of 30 years.

More importantly, (E) simply isn't necessary. You don't need to know anything about the enthusiasm levels when the companies were founded in order to show that there's been an explosion in public interest in opera. If you assume the opposite -- i.e., that there was little enthusiasm when the companies started -- it would still be possible that there was an explosion of interest later. (Real example: Starbucks was founded in 1971. Nobody gave a crap until the mid-1990s.)

But (B) is absolutely necessary, as others here have indicated. If the opposite of (B) is true -- that more opera companies closed than opened in the 30-year period -- then the argument falls apart in a big hurry.

I hope this helps!

(B) does not negate the premise.

Premise: Of the 70 currently active companies, 45 were founded over the course of the last 30 years.

Currently 70 companies are active. Of these 45 were founded over the last 30 years (say 1989 to now). So the argument seems to be saying that many companies were founded in the last 30 years so interest in opera has gone up in this time.

(B) There were fewer than 45 professional opera companies that had been active 30 years ago (before 1989) and that ceased operations during the last 30 years.

This option says that fewer than 45 companies were active before 1989 and ceased operations in the last 30 years. If this were not true, think what happens.
Say 60 companies which were active before 1989 ceased operations and are not active now. 45 new companies started after 1989 and are active now. Can we say that there has been an explosion of interest in opera? No. Even if 45 new companies started, 60 old companies shut down. So overall there are fewer companies now, perhaps because there are fewer opera lovers now.

Yes, previous companies means those that were founded more than 30 years ago and were active 30 years ago.
Yes, the 25 companies were founded more than 30 years ago and are still active.

I read somewhere that there is an assumption negation technique. Can I use that here?

Thanks Karishma for explaining the ANT.
I understand the above explanation given for ANT. I have read in the Veritas CR book that after Negate the choice in such a manner that newly created choice should be logically opposite of the original choice.

I tried this ANT for choice E.
Original Choice -
The 45 most recently founded companies were all established as a result of enthusiasm on the part of a potential audience.

As per me, after applying ANT, choice E becomes,
The 45 most recently founded companies were NOT all established as a result of enthusiasm on the part of a potential audience.
However, as per your below explanation, the ANT should be focusing on the number 45, not on verb = were established.
Can you discuss this in detail. I understand the below quoted reasoning, nonetheless.

Your negation is correct. You have negated the 45 as well. "All" stands for the 45 companies. "were not all" (it means not all 45) established as a result of enthusiasm...

I could have negated the correct option as
"There were not fewer than 45 ..." which is awkward. So instead, I made it "more than (or equal to) 45"

The giveaway word is ALL. If E were framed in this way "SOME of the 45 most recently founded companies were all established as a result of enthusiasm on the part of a potential audience" that response would be a stronger contender for a correct assumption than E is.

Negating B, the correct answer, basically rips the argument because it would imply that having 70 active professional opera companies is nothing spectacular or historic and thus cannot be used an indicator of a recent boom in operatic interest.

Karishma/OldFritz

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

how did you eliminate option D

if I negate D it will look like

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

This weakens the conclusion that there has been a explosion of interest

came down to b and e when you negate E, it doesn't really tie that well into the conclusion....IMO.

All,

I also thought about D as a viable answer choice after negating
Would someone please clarify what is wrong with this answer choice

Thanks
Cheers
J