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What is integer X? (1) X^X=|X| (2) X^2=|X^3|

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What is integer X? (1) X^X=|X| (2) X^2=|X^3| [#permalink]  05 Jun 2010, 20:00
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What is integer X?
(1) X^X=|X|
(2) X^2=|X^3|

[Reveal] Spoiler:
A
but I'm not so sure..
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Re: What is X? [#permalink]  05 Jun 2010, 20:25
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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Re: What is X? [#permalink]  06 Jun 2010, 01:18
statement one is true only for x=1.

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

Ans is A
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Re: What is X? [#permalink]  08 Jun 2010, 01:48
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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Re: What is X? [#permalink]  08 Jun 2010, 04:27
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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Re: What is X? [#permalink]  03 Aug 2010, 12:13
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 X?   [#permalink] 03 Aug 2010, 12:13
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