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!
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(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.
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