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# if X ____ = X, Which of the following must be true for all

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if X ____ = X, Which of the following must be true for all [#permalink]  26 Aug 2008, 09:41
if
X
____ = X, Which of the following must be true for all X?
|X|

x>1
x (BELONGS TO) (-1,0)U(1,infinity)
|x|<1
|x|=1
|x|^2>1

i could not understand the meaning.. pls explain

OA is B.
Manager
Joined: 15 Jul 2008
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Re: dont understand meaning... [#permalink]  26 Aug 2008, 09:48
arjtryarjtry wrote:
if
X
____ = X, Which of the following must be true for all X?
|X|

x>1
x (BELONGS TO) (-1,0)U(1,infinity)
|x|<1
|x|=1
|x|^2>1

i could not understand the meaning.. pls explain

OA is B.

Are you sure you typed the question properly ?
If x/|x| = x then then it is satisfied by only two values of x. 1 and -1. I would think D is the answer.

Last edited by bhushangiri on 26 Aug 2008, 10:11, edited 1 time in total.
Current Student
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Re: dont understand meaning... [#permalink]  26 Aug 2008, 09:55
its a club question...
the q's right.
its X/|X|
SVP
Joined: 30 Apr 2008
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Location: Oklahoma City
Schools: Hard Knocks
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Re: dont understand meaning... [#permalink]  26 Aug 2008, 10:00
The U means UNION.

If you have 2 groups, then this is saying that x belongs to group that is shared by both, meaning where the groups are the same, also referred to as UNION, like in Venn Diagrams.

With b), You have the group of -1,0, and then 1,infinity.

It appears that B is saying that the only values that satisfy the question are 1, -1, 0, and infinity. It is a confusing question, but you can also arrive at the answer of B by process of elimination.

arjtryarjtry wrote:
if
X
____ = X, Which of the following must be true for all X?
|X|

a) x>1 Incorrect. MUST BE TRUE, but is x = 2, then 2/|2| = 1, not 2 which is X.
b) x (BELONGS TO) (-1,0)U(1,infinity)
c) |x|<1 This means |x| is a positive or negative fraction. Not true 1/2 divided by 1/2 = +1, not x which is 1/2 here
d) |x|=1 The question asks for "all X" meaning we must consider all possible values for x. |x| = 1 is one part of the answer, but it ignores -1 and 0. (and I guess infinity?) Since the question asks for "all X" this isn't a complete answer.
e) |x|^2>1 This looks like a filler answer where the authors just needed something for answer e). If the square of |x| is greater than 1, then x the following must be true. x < -1 or x > 1. If we eliminated d because it was an incomplete answer, then there are multiple reasons to exclude this one. -1 and 1 satisfy the question stem, but it also appears to say that x > 1 would satisfy the question also, but this isn't true. x = 2 and we already know 2 is not a valid value of x.

i could not understand the meaning.. pls explain

OA is B.

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings SVP Joined: 07 Nov 2007 Posts: 1824 Location: New York Followers: 29 Kudos [?]: 565 [0], given: 5 Re: dont understand meaning... [#permalink] 26 Aug 2008, 10:13 Allen, I believe question wording need to be changed. something like this.. Find the range/all possible values of X if X/|X|=X. _________________ Your attitude determines your altitude Smiling wins more friends than frowning Manager Joined: 15 Jul 2008 Posts: 208 Followers: 3 Kudos [?]: 31 [0], given: 0 Re: dont understand meaning... [#permalink] 26 Aug 2008, 10:14 But the point is that for any x other than 1 or -1, the eqution will not be satisfied. eg. x=-0.5 LHS = x/|x| = -.05/0.5 = 1 <> -0.5=RHS eg. x= 3, LHS=1, RHS=3 LHS<>RHS Only 1 and -1 satisfy. x=1 then LHS=1= RHS x=-1 then LHS=-1 = RHS. I dont know how/why B could be the answer. SVP Joined: 30 Apr 2008 Posts: 1889 Location: Oklahoma City Schools: Hard Knocks Followers: 35 Kudos [?]: 473 [0], given: 32 Re: dont understand meaning... [#permalink] 26 Aug 2008, 10:22 is this a GMATClub challenge? _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

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Re: dont understand meaning... [#permalink]  26 Aug 2008, 11:50
This is a gmatclub question and the original poster did not post the right question.

The question states:

If $$\frac{X}{|X|} \lt X$$ . Which of the following must be true for all $$X$$ ?

* $$X > 1$$
* $$X \in (-1,0) \cup (1,\infty)$$
* $$|X| < 1$$
* $$|X| = 1$$
* $$|X|^2 > 1$$

For this inequality, you can multiply by |X|, because we know it's positive

So,
X < X*|X|
X - X*|X| < 0
X*(1-|X|) < 0

In order for the expression to be negative, the two components must be of opposite signs and/or not 0.
This is not true when 0< X < 1 or x < -1
Manager
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Re: dont understand meaning... [#permalink]  26 Aug 2008, 12:13
zoinnk wrote:
This is a gmatclub question and the original poster did not post the right question.

The question states:

If $$\frac{X}{|X|} \lt X$$ . Which of the following must be true for all $$X$$ ?

* $$X > 1$$
* $$X \in (-1,0) \cup (1,\infty)$$
* $$|X| < 1$$
* $$|X| = 1$$
* $$|X|^2 > 1$$

For this inequality, you can multiply by |X|, because we know it's positive

So,
X < X*|X|
X - X*|X| < 0
X*(1-|X|) < 0

In order for the expression to be negative, the two components must be of opposite signs and/or not 0.
This is not true when 0< X < 1 or x < -1

Now it makes perfect sense. < and = are two totally different ball games.
Re: dont understand meaning...   [#permalink] 26 Aug 2008, 12:13
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# if X ____ = X, Which of the following must be true for all

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