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# X/|X|<X. Which of the following must be true for X?

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CEO
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X/|X|[#permalink]  21 Oct 2007, 21:41
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X/|X|<X. Which of the following must be true for X?

X > 1
X > -1
|X| < 1
|X| = 1
|X|^2 > 1
CEO
Joined: 29 Mar 2007
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Kudos [?]: 234 [0], given: 0

[#permalink]  21 Oct 2007, 21:45
I said A for this.

I narrowed my choices to A or B. Im confused why B is correct.

if x>-1. Then we can say X = 1/2

1/2/|1/2| < 1/2 ---> 1<1/2 This is not true.

However, from what I gathered. We can say that x>1 or 0>x>-1.
But when we say x>-1, doesn't that leave the first possiblity open?

But for A. Any positive value divided by itself will yield 1. Since X>1 we won't have 1/1<1 to deal w/

Thx.

Last edited by GMATBLACKBELT on 21 Oct 2007, 22:02, edited 1 time in total.
Senior Manager
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[#permalink]  21 Oct 2007, 21:54
Another A,

B is incorrect since 0 is not possible asnwer,

Ans: A
VP
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Re: PS - Challenges prob. [#permalink]  22 Oct 2007, 04:25
GMATBLACKBELT wrote:
X/|X|<X> 1
X > -1
|X| <1> 1

Since |X| is positive for any value of X (should be wary of 0)

we can have the eq set up as X<X>1

hence A
CEO
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[#permalink]  22 Oct 2007, 08:18

-.5/.5 = -1
-1<5>x>-1 and x>1.

but when u just say x>-1 then you include values such as -1/2,0 which do not make the inequality true.

So again, I can't see how B is correct according to the challenges.
VP
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[#permalink]  22 Oct 2007, 17:41
flood wrote:

-.5/.5 = -1
-1<-.5

Given X/|X|<X> X <X> X-X|X| <0> X(1-|X|) <0> X<0 OR 1< |X|

we dont have X<0 so it not the answer but we have

1<X> |X| > 1

=> X> + 0R -1

So X is surely > -1 and

HENCE B IS THE ANSWER
VP
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[#permalink]  22 Oct 2007, 17:41
flood wrote:

-.5/.5 = -1
-1<-.5

Given X/|X|<X

X < X|X|
X-X|X| <0
X(1-|X|) < 0
which is
X<0 OR 1< |X|

we dont have X<0> 1

X> + 0R -1

So X is surely > -1 and

HENCE B IS THE ANSWER
Intern
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[#permalink]  22 Oct 2007, 18:49
But the equation is satified for all values of X>1

Shouldn't A be the answer.
Intern
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[#permalink]  22 Oct 2007, 19:17
Ok when we use X> -1

then we can use the value x = 1

so acc. to the equation

1/|1| = 1

this doesn't satisfy the equation X/|X| < 1 . So ans is A.

Sorry but what am I missing....thanks
CEO
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[#permalink]  22 Oct 2007, 20:35
trivikram wrote:
flood wrote:

-.5/.5 = -1
-1<-.5

Given X/|X|<X

X < X|X|
X-X|X| <0
X(1-|X|) < 0
which is
X<0 OR 1< |X|

we dont have X<0> 1

X> + 0R -1

So X is surely > -1 and

HENCE B IS THE ANSWER

But what about fractions??? 1/2/1/2<1/2??????? this isnt true!

Im just tempted to say that this question is faulty.
[#permalink] 22 Oct 2007, 20:35
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# X/|X|<X. Which of the following must be true for X?

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