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# What is integer x?

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Manager
Joined: 06 Apr 2010
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05 Jun 2010, 19:00
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Difficulty:

65% (hard)

Question Stats:

42% (01:02) correct 58% (00:56) wrong based on 159 sessions

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What is integer x?

(1) x^x = |x|
(2) x^2 = |x^3|
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Jul 2013, 05:46, edited 1 time in total.
Edited the question.

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Manager
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05 Jun 2010, 19:25
1. X=-1, 1
1^1=1=|1|

-1^-1=-1
DNA to |-1|=1

X=1

2. X=-1, 1
1*1=|1*1*1|
-1*-1=|-1*-1*-1|
X could be 1 or -1

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Intern
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06 Jun 2010, 00:18
statement one is true only for x=1.

statement two is true for x=-1,0,1

Ans is A

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Manager
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08 Jun 2010, 00:48
1) X^X=|X|
0^0=|0|
so the statement should be true for x=0 and 1. Am I wrong?

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08 Jun 2010, 03:27
Eden wrote:
What is integer X?
(1) X^X=|X|
(2) X^2=|X^3|

[Reveal] Spoiler:
A
but I'm not so sure..

Eden wrote:
1) X^X=|X|
0^0=|0|
so the statement should be true for x=0 and 1. Am I wrong?

0^0, in some sources equals to 1, some mathematicians say it's undefined. Note that the case of 0^0 is not tested on the GMAT. (But anyway $$0^0\neq{0}$$)

Given: $$x=integer$$. Q: $$x=?$$

(1) $$x^x=|x|$$ --> $$x=1$$. Sufficient.
(2) $$x^2=|x^3|$$ --> $$x=1$$ or $$x=-1$$ or $$x=0$$. Not sufficient.

Hope it helps.
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03 Aug 2010, 11:13
sid4674 wrote:
What is integer X?
(1) X^X=|X|
(2) X^2=|X^3|

For 1) x^x=|x|

X =1, 1*1=|1|=>1=1
X=-1, -1*-1=|-1|=>1=1

hence A is not sufficient, could anyone please explain how statement one alone is sufficient.

Statement (1) is: $$x^x=|x|$$, so if $$x=-1$$, then $$(-1)^{-1}=\frac{1}{(-1)^1}=\frac{1}{-1}=-1\neq|-1|=1$$.
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Re: What is integer x? [#permalink]

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14 Apr 2014, 12:58
Is it valid if for statement 2 we divide both sides by x^2, hence obtaining

x = abs (x)

Therefore any >=0 number will do

Thanks
Cheers
J

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Re: What is integer x?   [#permalink] 14 Apr 2014, 12:58
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