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# PS: Absolute values

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Manager
Joined: 13 Jan 2009
Posts: 170

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21 Jan 2009, 05:12
I still don't get it. any number >-1 but 0 and 1 can be true in this equation - Understood! But why 1 is out of scope, GT? I don't get it. It doesn't even mentioned in the question.
I believe 1 is still bigger than -1 . I think the question stated incorrect.

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SVP
Joined: 07 Nov 2007
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Location: New York

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21 Jan 2009, 08:41
IanStewart wrote:
chicagocubsrule wrote:
so can we all agree that the correct answer is A?

kevin0118 wrote:

The answer is B. Those who think the answer is A are misunderstanding the question. The question is *not* asking for the solution set for x. It is simply asking what must be true of x. I think we can agree that if x/|x| < x, then either -1 < x < 0, or 1 < x. If that's true, then no matter what x is, x is certainly greater than -1; that must be true. B.

It is of no importance that x cannot equal 0.5. If you think that's relevant to the question, you're not answering the question that's being asked -- you're answering the question "under what conditions will x/|x| always be true?" Notice that's the precise opposite question to the one being asked.

It should be clear, in any case, that A is incorrect; it does not need to be true that x > 1, because x could be -0.5, for example.

I explained, with a different example, here for anyone who remains unconvinced (scroll way down):

http://www.beatthegmat.com/xs-good-one-t27185.html

agreed!! great explanation.

+1
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Intern
Joined: 11 Jan 2009
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Schools: Oxford, Cambridge, LSE

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22 Jan 2009, 19:12
X/|X| < X.

Which of the following must be true about X? (X does not equal 0)

X>1
X>-1
|X|<1
|X|=1
|X|^2>1

I tried plugging in numbers, and got the answer incorrectly.

after reading through all the posts, i finally got it. The answer is B because of the unique way the question is asked. I will categorize this as a "must be true" question.

I will not go into the details of solving the inequality. But the solution is -1<X<0 and X>1.

Now, let us consider a simpler question first. Assuming that John has more than 3 apples, which of the following statement MUST BE TRUE?
A) John has more than 5 apples
B) John has more than 2 apples
the answer is clearly B. The reason is that if John has more than 3 apples, thus he MUST have more than 2 apples.
A is wrong because it may not be true in all circumstances (e.g. John has 4 apples)

Going back to our question, we need to first solve the inequality to get -1<X<0 and X>1. Then, based on the solutions, we can transform the question into a simpler form:
assuming that -1<X<0 and X>1, which of the following statement MUST BE TRUE?
A) X>1
B) X>-1
Answer is B. The reason is that if the value of X is either -1<X<0 or X>1, then the value of X must be greater than X>-1.
A is wrong because it may not be true in all circumstances (e.g. X=-0.5)

Hope this helps

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Re: PS: Absolute values   [#permalink] 22 Jan 2009, 19:12

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