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

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X/|X| < X. Which of hte following must be true about X? [#permalink] New post 09 Apr 2007, 03:03
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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 [#permalink] New post 09 Apr 2007, 11:10
answer is b.

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

x=0, i think, is a bad example.
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 [#permalink] New post 09 Apr 2007, 11:17
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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 [#permalink] New post 09 Apr 2007, 15:25
saikadelik wrote:
answer is b.

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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 [#permalink] New post 09 Apr 2007, 22:42
goalsnr wrote:
saikadelik wrote:
answer is b.

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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 [#permalink] New post 10 Apr 2007, 06:22
Fig wrote:
goalsnr wrote:
saikadelik wrote:
answer is b.

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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 [#permalink] New post 10 Apr 2007, 07:51
Fig wrote:
goalsnr wrote:
saikadelik wrote:
answer is b.

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 :wink:
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 [#permalink] New post 10 Apr 2007, 10:05
ywilfred wrote:
Fig wrote:
goalsnr wrote:
saikadelik wrote:
answer is b.

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 :wink:


Thanks ;) :)
  [#permalink] 10 Apr 2007, 10:05
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