Q24 - Downtown Petropolis boasted over

[christine.defenbaugh]

ywan1990, I'm so glad you posted! You raise an excellent question, which reveals an often misunderstood aspect of the negation test for Necessary Assumptions.

You already know that negating a necessary assumption should destroy the argument, but what exactly does that mean? It means destroying the link between the evidence and the conclusion. This does not necessarily force the conclusion to become false. Rather, it makes the conclusion invalid - in other words, it makes the conclusion something you can't validly conclude!

Let's take a simple core to illustrate:

Premise: All boys like sports.
Conclusion: Andy likes sports.
Necessary Assumption: Andy is a boy.

If we negate the necessary assumption, we get "Andy is not a boy". If Andy isn't a boy, then we have no idea whether Andy likes sports or not. We can't say for sure that Andy doesn't, but claiming Andy does would be silly! That would be wholly unsupportable.

That's exactly how the negation test is supposed to work. So, you are 100% correct that negating (E) leaves you with the idea that "some number that is not significantly fewer than 60 buildings have been built". And that does leave open the possibility that that number is still less than 60 - just not significantly so. Maybe 58 buildings have been built, and that's not considered to be "significantly fewer than 60."

If 58 buildings were built, that doesn't prove the conclusion definitely false. You're right, it's still possible that Downtown Petropolis is in a serious state of decline for some other reason, but that conclusion isn't supported by the number of demolished buildings anymore. Why not? Because now we know that whatever the net decrease in buildings is, it is not significant. Maybe a net decrease of 2 buildings could support a conclusion that there's a non-serious economic decline - but a decrease we know to be insignificant can't support the idea of an economic decline that is serious.

To finish things off, let's take a quick spin through the wrong answer choices:
(A) It doesn't matter exactly when during the five years the buildings were demolished, just that they were.
(B) The argument IS assuming that there weren't significantly more than 100 large buildings 5 years ago! But it's not assuming there were never significantly more than 100 large buildings. Maybe there were 10,000 buildings 50 years ago, but only 100 5 years ago - in that case, a loss of 60 buildings is still pretty bad, and the conclusion would still be supported.
(C) It doesn't matter why the buildings were demolished, just that they were.
(D) We don't need this to be true. What if all the large buildings were replaced instead with flower gardens? That doesn't hurt or help the argument.


Does that help clear things up a bit? The difference between proving a conclusion false and destroying the support for a conclusion is a critical issue, but one that can be difficult to master. The negated assumption only has to do the latter!

Please let me know if this completely answers your question!


#officialexplanation

[LSAT-Chang]

Hello!
I had trouble with this question since I thought we had to assume (B) for the conclusion to hold..
So the author is concluding that the downtown Petropolis is in a serious state of economic decline. Why? Because it boasted over 100 large buildings 5 years ago, but since then, 60 have been demolished. So I thought if we negated (B), "there HAVE been significantly more than 100 large buildings in downtown Petropolis" the conclusion would be destroyed since, it seems like the author is assuming that there were only 100, and so 60 have been demolished, so there is only a few left. But what if there wasn't 100 to start with? Maybe there were 1000000+ and only 60 have been demolished, so it wouldn't make sense that the downtown is in a serious state of economic decline. Does this make sense? Could someone help me understand why (B) is not necessary and (E) IS necessary? How would you negate (E)?

[gilad.bendheim]

Lets make sure we get the stimulas down pat first, because I think you might be misinterpreting it.

- FACT: 5 years ago Downton Petropolis used to have at least 100 buildings
- FACT: in the past 5 years, 60 of those buildings have been demolished
- PREMISE: the number of large buildings in a downtown area is an indicator of economic health
- CONCLUSION: Downtown Petropolis is in a serious econ. decline

So the argument is that the number of buildings signifies the economic health, and because 60 buildings have recently been destroyed, the economic health of the downtown area must now be less than it was 5 years ago.

The gap in the logic here is that it must be assumed that these buildings were not replaced by an equal number or more buildings. Maybe they were torn down because they were old and too small to support the thriving economy and exploding job growth, and are now replaced by taller, newer, all glass buildings that are environmentally friendly etc etc. The stimulas DID NOT say that there used to be 100 buildings and now there are 40. It said that there were at least 100 and 60 were demolished - leaving open the question of whether they were replaced or not.

So back to choice (B). (1) The reason that it is incorrect is because the argument in the stimulas makes a RELATIVE point. As you correctly pointed out, the number 100 is somewhat arbitrary. The stimulas never said that 100 buildings means a healthy economy, only that more buildings=healthier, fewer=less healthy. So we dont really care about whether the figure of 100 was correct. All we care about is if the new figure is lower than the old one.

(E) on the other hand nails the gap. It says that the only way we could reasonably assume that there is a SIGNIFICANT decline is if many of the 60 demolished buildings have not been replaced. If this is the case, then we know there are fewer large buildings now then before, and, based on the premise of the argument, can say with confidence that there has been a serious economic decline.

PS - I think your point about 10,000 buildings is a valid one, in the sense that losing 60 buildings - even if all were not replaced - does not seem significant if you still have 99,940 left. Nonetheless, the logic that would even allow one to attempt to claim that there was a decline, still requires that there be a net loss of buildings, which is what (E) accomplishes. Whether or not we are convinced by the argument is another story altogether.

Hope this helps!

[ywan1990]

I still have some problem with (E).

The reason I was put off is the word 'significantly'. I think it is rather NOT necessary.

So applying the negation to the choice, I got 'not significantly fewer than...', which leaves open the possibility that 'fewer than 60 new buildings, even though not significantly fewer than 60, have been built'. In this case, still more buildings would have been demolished than built. It follows that the downtown P could still be in a serious state of economic decline. So negating (E) does not necessarily weaken the conclusion.

Does anyone know where I have got wrong here? Is it because the conclusion says the decline is 'serious' (so significantly fewer could be built)?

[timsportschuetz]

@ywan1990: I used to do the same when negating until I learned (from tons of PT's) to be more flexible with SOME of the logical terms being used on the LSAT. I kindly suggest that you look at answer choice (E) in a slightly different way: Instead of attempting to negate "significantly fewer", extrapolate the logical MEANING of the phrase. "Significantly fewer" than 60 buildings means what? Well, you DON'T really know exactly! However, it always helps to fall back on some of the concrete quantity indicator words that every LSAT test-taker should know:

Any quantity from 1 to 100 (out of a total of 100 "widgets"): Some, few, many, sometimes, at least one, at least some, more than one, a number, and several (please keep in mind that this list is by no means absolute - they are only the most common words for this particular category, and memorizing these, will suffice for the test); It should be noted that the aforementioned terms CAN mean 1, 45, 65, 50, 99, and even 100 out of a total of 100. However, they CANNOT be interpreted to mean 0 (out of 100)!

The other major category denotes quantities from 51 to 100 (out of 100): Most, typically, usually, more often than not, almost all, a majority, etc. These indicator words CAN mean 51, 55, 80, 99, and 100 out of a total of 100! However, they cannot be interpreted to mean 50 and/or anything below 50 out of 100.

In summary, you should note an important lesson: Both of the above categories CAN be used to mean 100 out of 100!

OK, now, let's look at the answer choice. "Significantly fewer" does NOT specifically mean category 2 from above. It COULD mean category 2, but we cannot reasonably infer this! Next, we would HAVE to make the correct logical leap that "significantly fewer MUST be something LESS than 60 AND that it CANNOT be 0 (since the answer rules this out by using the past participle of "build", thus denoting that at least one building must have been built). Next, when negating answer choice (E), we would get "NOT significantly fewer than 60...". Therefore, the number of large buildings that have been built in the last 5 years is NOT zero! The next part is rather tricky to grasp. Since the conclusion is categorical in nature and states that "Petropolis is in a serious state of economic decline", EVEN IF we take the LOWEST POSSIBLE NUMBER (ie: most conservative inference - which means that if the weakest interpretation of the evidence destroys the argument, then it MUST be the correct answer choice since higher numbers of buildings would only create an even better answer choice!) from the negation of answer (E),
and infer that ONLY ONE new large building was built in the last 5 years, then the argument is destroyed! If even one large building was built, we CANNOT conclude that Petropolis is "clearly" in a serious state of economic decline!

I apologize for going on for such a long time! Especially regarding the discussion of indicator words. However, I felt that it was a pertinent to the discussion that followed. Let me know if you have any further questions!

[christine.defenbaugh]

timsportschuetz, I'm afraid I find your reasoning here somewhat difficult to follow.

Some/Most

The definitions you post of some and most are mostly correct, but not relevant to this question. While it's always good to be reminded that "some" and "most" could possibly mean "all", applying these definitions to this question may be unnecessarily confusing.

Use of "built"

The fact that the answer uses the past participle of the word "build" does not indicate that at least one building was built. The phrase "Zero buildings were built" proves that you can use that verb form and still mean zero.

Since zero is a number, the phrase "some number significantly fewer than 60" will absolutely include zero, as long as zero is considered to be 'significantly fewer than 60' (and most people would probably agree that it is). Similarly, the negation "a number not significantly fewer than 60" would include zero if zero were considered not to be significantly fewer than 60.

So what does all that mean? It means that zero isn't a very useful benchmark for this question in any case!

Negation

I'm afraid I don't follow your negation of (E) that seems to mean "any number greater than 0" buildings were built (since you test it by using 1). By doing that you've completely dropped the "not significantly less than 60" notion. You're only allowed to use 1 building built as a test case for the negation, if 1 building fits the criteria of "a number not significantly fewer than 60." Now, if it does, then you're right that it destroys the conclusion. But if you've dropped the notion of "significance" altogether, then you can't conclude that even 1 building being built would undermine the conclusion.

If 1 is considered, for instance, to be "significantly fewer than 60" (which most reasonable people would likely agree with), then building only one new building would still mean that the net decrease in buildings was "significant", which would still support a conclusion that we have a "serious economic decline."

This is all a bit convoluted. I would encourage you to stay a bit closer to the actual text of the question. The negation of (E) is literally "Some number that is not significantly fewer than 60 new large buildings have been built in downtown Petropolis during the past 5 years." No one knows precisely what that means, numerically. What it must mean, however, is that the net decrease in buildings is an insignificant decrease. As an insignificant decrease (whatever that is), it can no longer support a conclusion of serious decline.

I hope this makes things a bit clearer. Please don't hesitate to let me know if you have any questions on any of this!