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# X/|X| < X. Which of hte following must be true about X?

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Intern
Joined: 27 Nov 2005
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X/|X| < X. Which of hte following must be true about X? [#permalink]

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09 Apr 2007, 04:03
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

6. X/|X| < X. Which of hte following must be true about X?

a) x>1
b) x>-1
c) |x| <1
d) |x| = 1
e) |x|^2>1

According to GMAT club's answer sheet, the answer is b. How is this possible? If X = 0 then the equation cannot be solve and if X=1 then 1=1, which breaks the all true rule about X. The answer should be A.

I don't know if the answer is wrong or the question is worded incorrectly.

If anyone from the GMAT Club is reading this, please clarify. Thanks!!!

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Intern
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09 Apr 2007, 12:10

if x = -0.1, it satisfies the true rule.

x=0, i think, is a bad example.

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SVP
Joined: 01 May 2006
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09 Apr 2007, 12:17
First of all.... Welcome to the GMATClub ! :D

(B) it is

X/|X| < X
<=> X < X*|X| as |X| > 0 and x must be different to 0.
<=> X - X*|X| < 0
<=> X*(1-|x|) < 0

implies that:
o x <0 and 1-|x| > 0 <=> |x| < 1
or
o x > 0 and 1-|x| < 0 <=> |x| > 1

so,
o -1 < x < 0
or
o x > 1

In other words, x must be superior to -1

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09 Apr 2007, 16:25

if x = -0.1, it satisfies the true rule.

x=0, i think, is a bad example.

But it fails for x=0.So the answer cannot be B

A makes sense.

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SVP
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09 Apr 2007, 23:42
goalsnr wrote:

if x = -0.1, it satisfies the true rule.

x=0, i think, is a bad example.

But it fails for x=0.So the answer cannot be B

A makes sense.

If -1 < x < 0 or x > 1, then x must be superior to -1. Even larger, it's the only answer choice that conveys all solutions and thus satisfies the "must be true".

Notice that it is not stated to find only the solutions. It says a condition that "must be true" about x. Here, x will be superior to -1, for sure.

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VP
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10 Apr 2007, 07:22
Fig wrote:
goalsnr wrote:

if x = -0.1, it satisfies the true rule.

x=0, i think, is a bad example.

But it fails for x=0.So the answer cannot be B

A makes sense.

If -1 < x <0> 1, then x must be superior to -1. Even larger, it's the only answer choice that conveys all solutions and thus satisfies the "must be true".

Notice that it is not stated to find only the solutions. It says a condition that "must be true" about x. Here, x will be superior to -1, for sure.

Thanks for making this clear.

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GMAT Club Legend
Joined: 07 Jul 2004
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10 Apr 2007, 08:51
Fig wrote:
goalsnr wrote:

if x = -0.1, it satisfies the true rule.

x=0, i think, is a bad example.

But it fails for x=0.So the answer cannot be B

A makes sense.

If -1 < x <0> 1, then x must be superior to -1. Even larger, it's the only answer choice that conveys all solutions and thus satisfies the "must be true".

Notice that it is not stated to find only the solutions. It says a condition that "must be true" about x. Here, x will be superior to -1, for sure.

Well said, I couldn't say it better

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SVP
Joined: 01 May 2006
Posts: 1794

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10 Apr 2007, 11:05
ywilfred wrote:
Fig wrote:
goalsnr wrote:

if x = -0.1, it satisfies the true rule.

x=0, i think, is a bad example.

But it fails for x=0.So the answer cannot be B

A makes sense.

If -1 < x <0> 1, then x must be superior to -1. Even larger, it's the only answer choice that conveys all solutions and thus satisfies the "must be true".

Notice that it is not stated to find only the solutions. It says a condition that "must be true" about x. Here, x will be superior to -1, for sure.

Well said, I couldn't say it better

Thanks

Kudos [?]: 166 [0], given: 0

10 Apr 2007, 11:05
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