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Xs good one.

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by rajataga » Sat Jan 03, 2009 3:37 am
thr r 3 overall possibilities,

x is positive
x is negative
x = 0


if x was positive or 0, x/|x| = x.....therefore x has to be negative...

now if x were < -1, then x/|x| > x, but since x/|x| < x, therefore x should be > -1

Therefore B
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by cramya » Sat Jan 03, 2009 7:53 am
The reason why B must be true is because it covers the maximum possible range for x/|x| < x condition to be true. IMO this does not mean all values >-1 this is true.

x=-1/2 x/|x| = -1 whereas x=-1/2 and -1 < -1/2 TRUE


Hope this helps!



Regards,
Cramya
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by gmatguy16 » Sun Jan 11, 2009 9:19 am
what happens when x=0.2 ,in that case x/|x|=1 ,so why must b be true
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by cramya » Sun Jan 11, 2009 11:04 am
what happens when x=0.2 ,in that case x/|x|=1 ,so why must b be true
Thats right .2> -1 so it covers the correct range of values in the question for ehich x/|x| = 1.
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Re: Xs good one.

by logitech » Sun Jan 11, 2009 12:49 pm
vittalgmat wrote:X / |X| < X.
Which of the following must be true about X ( X <> 0 )

A. X >1
B. X > -1
C. |X| < 1
D. |X| = 1
E. |X|^2 = 1

[spoiler]OA: B[/spoiler]
So

X / |X| can be either +1 if X is positive or -1 if X is negative

So X>1 and -1<x<0 are the two ranges we are talking about and clearly

0<X<1 will not satisfy this equation and B can not be the correct answer.

To test this, plug 1/2

1 < 1/2 ? I don't think so!
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by cramya » Sun Jan 11, 2009 12:58 pm
So X>1 and -1<x<0 are the two ranges we are talking about and clearly

0<X<1 will not satisfy this equation and B can not be the correct answer.

To test this, plug 1/2

1 < 1/2 ? I don't think so!

The reason why B must be true is because it covers the maximum possible range for x/|x| < x condition to be true. IMO this does not mean all values >-1 this is true

This question may be a little ambigous but out of the answer choices given x>-1 covers the maximum possible range. Again the question does not say that all x's that we choose in the answer choice have to satisfy this either so it really ambigous????.




Regards,
Cramya
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by logitech » Sun Jan 11, 2009 1:09 pm
cramya wrote:
So X>1 and -1<x<0 are the two ranges we are talking about and clearly

0<X<1 will not satisfy this equation and B can not be the correct answer.

To test this, plug 1/2

1 < 1/2 ? I don't think so!

The reason why B must be true is because it covers the maximum possible range for x/|x| < x condition to be true. IMO this does not mean all values >-1 this is true

This question may be a little ambigous but out of the answer choices given x>-1 covers the maximum possible range. Again the question does not say that all x's that we choose in the answer choice have to satisfy this either so it really ambigous????.




Regards,
Cramya
Cramya, this is a must be true question. So MUST is a MUST. I dont mess around when a question uses that term, so should not you! :)
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by rajataga » Sun Jan 11, 2009 1:23 pm
I agree with the OA.....

MUST BE true is used here to denote that the option selected must be true for all possible values of x that can be derived from the given equation.

Hence, if we choose A, there are values of x, such that -1 < x < 0, that are not satisfied by option A. Hence, option A would not hold true in the case where x was one of these values.

Option B on the other hand, is true for any value of x that is defined by the given equation. Hence, it satisfies the 'must be true' condition.


However i feel that this is far too ambigious and debatable question to appear on the GMAT. i remember that there was a similar question here about a month back, and a similar debate on it.

What is the source of this question?
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by cramya » Sun Jan 11, 2009 1:32 pm
Cramya, this is a must be true question. So MUST is a MUST. I dont mess around when a question uses that term, so should not you
I agree to a certain extent and may be the experts may weigh in on this and dismiss it.

The source would be GMATCLUB.

Again yes its a must be true question and we can exchange views about it for ever.

Like Raja explained the x>-1 is the one that must be true for x/|x| < x. Any other option we choose we will be excluding the -1 to 0 values.


I am sure in the real test there would be no room for such ambiguity or arguments in questions .

Regards,
CR
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by logitech » Sun Jan 11, 2009 1:35 pm
cramya wrote:

I am sure in the real test there would be no room for such ambiguity or arguments in questions .

Regards,
CR
Agreed!
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by Ian Stewart » Mon Jan 12, 2009 1:15 am
There is nothing ambiguous about the question, and I've seen questions with a similar type of logic on the real test. Let's look at a simpler question:

If 0 < x < 10, what must be true?

I) x > 5
II) x > -5
III) 2 < x < 10

The answer here is II) only. The question does *not* ask "which of the following gives all possible values of x, and only those values?" It only asks "what must be true?". If we know that x is greater than 0, we can be absolutely certain that x is greater than -5.

The same is true in the question in the original post, above. From the inequality given, X/|X| < X, we can determine that X is either between -1 and 0 or X is greater than 1. Well, regardless, X is certainly greater than -1; that must be true. It isn't important that X can't be equal to 0.5. What is important is that the only possible solutions for X are all larger than -1.

Even if we had been given different information and had reached the conclusion that X = 18, we'd still know that it must be true that X > -1, since 18 is greater than -1.
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by welcome » Mon Jan 12, 2009 5:00 am
Here is my solution.

X/|X| <X
=> 1/|X| < 1
=> 1<|X|
=> -1<x<1

=> Ans B.
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by Ian Stewart » Mon Jan 12, 2009 5:25 am
welcome wrote:Here is my solution.

X/|X| <X
=> 1/|X| < 1
=> 1<|X|
=> -1<x<1

=> Ans B.
You can't just divide both sides by x here, at least not without analyzing two cases; if x is negative, you'd need to reverse the inequality after you divide by x. In addition, you've made a mistake going from the second last line above to the last; if you ever do conclude that 1 < |x|, that means that x > 1 or x < -1.
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by logitech » Mon Jan 12, 2009 8:54 am
Ian Stewart wrote:There is nothing ambiguous about the question, and I've seen questions with a similar type of logic on the real test. Let's look at a simpler question:

If 0 < x < 10, what must be true?

I) x > 5
II) x > -5
III) 2 < x < 10

The answer here is II) only. The question does *not* ask "which of the following gives all possible values of x, and only those values?" It only asks "what must be true?". If we know that x is greater than 0, we can be absolutely certain that x is greater than -5.

The same is true in the question in the original post, above. From the inequality given, X/|X| < X, we can determine that X is either between -1 and 0 or X is greater than 1. Well, regardless, X is certainly greater than -1; that must be true. It isn't important that X can't be equal to 0.5. What is important is that the only possible solutions for X are all larger than -1.

Even if we had been given different information and had reached the conclusion that X = 18, we'd still know that it must be true that X > -1, since 18 is greater than -1.
Oh Ian..now you changed my entire paradigm for must be true question...hmm :shock:
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