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Intern  Joined: 21 Jun 2008
Posts: 31
Schools: Harvard

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If $$\frac{X}{|X|} \lt X$$ , which of the following must be true about $$X$$ ? ( $$X \ne 0$$ )

(A) $$X \gt 2$$
(B) $$X \in (-1,0) \cup (1,\infty)$$
(C) $$|X| \lt 1$$
(D) $$|X| = 1$$
(E) $$|X|^2 \gt 1$$

Spoiler: :: OA
B

Source: GMAT Club Tests - hardest GMAT questions

Solution:

If X > 0, the inequality turns into X > 1,

If X < 0 , the inequality turns into X > -1

In each of the cases X > -1, therefore X > -1 is true for all possible X . Note that -10 and -0.5 can serve as counter-examples for other options.

___________________________

Isn't the correct answer -1<x<0 and x>1?
Using formula B with x=0.9 gives you 1<0.9 which doesn't work.
Intern  Joined: 10 Jan 2008
Posts: 29

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Hi Crush:

I agree that the solution is -1 < X < 0 OR X > 1.

I think the trick here is wording. Think about all the possible values of X.

They are all greater than -1. So, B doesn't define the set of possible values of X, but all the possible values of X are greater than -1. So it is ture.

HTH
Intern  Joined: 13 Oct 2008
Posts: 14

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Can anybody explain this in detail.

I did not understand this. guess I am dumbo X/|X| < X

if x is say -2 then

isn't it -2/2 < -2 ==> -1 < -2 hence cannot satisfy ?? Director  Joined: 04 Jan 2008
Posts: 581

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OA-B
just plug in -0.5 and you will get result
Intern  Joined: 21 Nov 2008
Posts: 10

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2
What if X=0.5?

In this case X>-1, but the inquality is violated.
Attachments 1.JPG [ 34.01 KiB | Viewed 8342 times ]

Director  Joined: 17 Jun 2008
Posts: 965

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The question is expecting the value of X and not necessarily for all values of X.

The answers are x > 1 and -1 < x < 0.

Hence, for any value of x within these ranges, x > -1.
Intern  Joined: 21 Nov 2008
Posts: 10

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scthakur wrote:
The question is expecting the value of X and not necessarily for all values of X.

The answers are x > 1 and -1 < x < 0.

Hence, for any value of x within these ranges, x > -1.

Actually the question stem states: which of the following MUST be true about X..

MUST means for any values, right? There is no limitations on the Value of X, so if one can find one case that doesn't satisfy our inequality, then the answer is wrong. And X>-1 includes values 0<x<1
For example if the stem had a note: X is an integer that would make the question clear.

IMHO the answer choices or the question stem should be reviewed.
CIO  Joined: 02 Oct 2007
Posts: 1179

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The questions stem is changed to:

$$\frac{X}{|X|} < X$$ . Which of the following must be true about integer $$X$$ ? ( $$X \ne 0$$ )

The first option changed to:

$$X > 2$$

Is the problem resolved now? Thanks for bringing up the issue. +1.
Intern  Joined: 12 Aug 2008
Posts: 40

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Can someone explain why |X|^2 > 1 is wrong?

If X is a non-zero integer and X has to be > -1, X has to be an integer greater than 1, as the other constraint says X>1, correct?

Am I missing something?

The explanation says, "Note that -10 and -0.5 can serve as counter-examples for other options." How can X be 0.5 or -10?
CIO  Joined: 02 Oct 2007
Posts: 1179

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You're right, guys. The question still needs revision. Here's what I've come up with. Is there any problem if we change the question stem and options to the following? I've removed the "integer" from the stem:

If $$\frac{X}{|X|} < X$$ , which of the following must be true about $$X$$ ? ( $$X \ne 0$$ )

(C) 2008 GMAT Club - m09#22

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

The explanation stays the same. -0.5 can serve as a counter example for A, D and E. If you plug -0.5 into the inequality from the stem, you will see that it holds true. -10 could be probably removed from the OE.
In order to answer the question, you have to solve the inequality from the question stem. The OE solves the modulus inequality. Is there anything wrong with the way the OE solves the inequality that I don't see?

What do you all think about the changes?
Manager  Joined: 29 Jul 2009
Posts: 200

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1
I've come across this question and the stimulus still contains "about integer". This is the question I saw

If $$\frac{X}{|X|} < X$$ , which of the following must be true about integer $$X$$ ? ( $$X \ne 0$$ )

(C) 2008 GMAT Club - m09#22

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

According to my understanding B cannot be the correct answer choice. As other members pointed out the solution is

The answers are x > 1 and -1 < x < 0. Since X is an integer x cannot take any values from -1 < x < 0 so the inequality only makes sense when x > 1 --> x >=2

IMO if you change option A for X >=2, I think it should be the correct answer choice. What do you think?
CIO  Joined: 02 Oct 2007
Posts: 1179

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The change should be visible now. Sorry.
Manager  Joined: 29 Jul 2009
Posts: 200

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I see the change but I still think that the correct answer cannot be B.

According to answer B, X can be 1 which is not a solution for the problem. Could someone explain me why I'm wrong?
CIO  Joined: 02 Oct 2007
Posts: 1179

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I see. The question is really tricky. What if we change the B option to $$X \in (-1, 1) \cup (1, \infty)$$? It's stated in the stem that $$X \not= 0$$, so this corrected B option should work.
Senior Manager  Joined: 01 Mar 2009
Posts: 295
Location: PDX

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dzyubam wrote:
I see. The question is really tricky. What if we change the B option to $$X \in (-1, 1) \cup (1, \infty)$$? It's stated in the stem that $$X \not= 0$$, so this corrected B option should work.

IMHO this should work but just wanted to clarify one basic question. Is the x x/|x| different from the X on the right side. I spent nearly 30 minutes trying to understand this.
CIO  Joined: 02 Oct 2007
Posts: 1179

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I'm not sure if I understand your question correctly. In the inequality from the stem, all three $$X$$ should be the same values when plugging in any number instead of $$X$$. All three are the same $$X$$.
I'll change the B option as stated above when some other people confirm that is a right move. Please tell me if it is the right move .
pleonasm wrote:
dzyubam wrote:
I see. The question is really tricky. What if we change the B option to $$X \in (-1, 1) \cup (1, \infty)$$? It's stated in the stem that $$X \not= 0$$, so this corrected B option should work.

IMHO this should work but just wanted to clarify one basic question. Is the x x/|x| different from the X on the right side. I spent nearly 30 minutes trying to understand this.
Manager  Joined: 29 Jul 2009
Posts: 200

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Hi dzyubam, I think that's the right move. I think that will make option B correct.
CIO  Joined: 02 Oct 2007
Posts: 1179

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Thank you. +1. I've edited the B option. Hope this question is OK now.
mikeCoolBoy wrote:
Hi dzyubam, I think that's the right move. I think that will make option B correct.
Senior Manager  Joined: 01 Mar 2009
Posts: 295
Location: PDX

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dzyubam wrote:
I'm not sure if I understand your question correctly. In the inequality from the stem, all three $$X$$ should be the same values when plugging in any number instead of $$X$$. All three are the same $$X$$.
I'll change the B option as stated above when some other people confirm that is a right move. Please tell me if it is the right move .
pleonasm wrote:
dzyubam wrote:
I see. The question is really tricky. What if we change the B option to $$X \in (-1, 1) \cup (1, \infty)$$? It's stated in the stem that $$X \not= 0$$, so this corrected B option should work.

IMHO this should work but just wanted to clarify one basic question. Is the x x/|x| different from the X on the right side. I spent nearly 30 minutes trying to understand this.

Yeah ok that's what I thought. Thanks for the clarification. It's the modulus tag that makes the x look a bit different.
Manager  Joined: 18 Aug 2009
Posts: 237

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dzyubam wrote:
I'm not sure if I understand your question correctly. In the inequality from the stem, all three $$X$$ should be the same values when plugging in any number instead of $$X$$. All three are the same $$X$$.
I'll change the B option as stated above when some other people confirm that is a right move. Please tell me if it is the right move .
pleonasm wrote:
dzyubam wrote:
I see. The question is really tricky. What if we change the B option to $$X \in (-1, 1) \cup (1, \infty)$$? It's stated in the stem that $$X \not= 0$$, so this corrected B option should work.

IMHO this should work but just wanted to clarify one basic question. Is the x x/|x| different from the X on the right side. I spent nearly 30 minutes trying to understand this.

Shouldn't the answer option B be:
$$X \in (-1,0) \cup (1,\infty)$$

Even the solution describes the same. If X falls in the range (0,1) the statement is not true. Re: m09 q22   [#permalink] 14 Nov 2009, 02:10

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# m09 q22

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