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What is integer x?

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Eden
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What is integer x? [#permalink] New post   Updated on: 03 Jul 2013, 06:46
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45% (01:21) correct 55% (01:18) wrong based on 188 sessions
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What is integer x?

(1) x^x = |x|
(2) x^2 = |x^3|
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A

Originally posted by Eden on 05 Jun 2010, 20:00.
Last edited by Bunuel on 03 Jul 2013, 06:46, edited 1 time in total.
Edited the question.
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estreet
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Re: What is X? [#permalink] New post   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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subratam99
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Re: What is X? [#permalink] New post   06 Jun 2010, 01:18
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statement one is true only for x=1.

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

Ans is A
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Eden
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Re: What is X? [#permalink] New post   08 Jun 2010, 01:48
1) X^X=|X|
What about x=0?
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] New post   08 Jun 2010, 04:27
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Eden wrote:
What is integer X?
(1) X^X=|X|
(2) X^2=|X^3|

Answer is
Show Spoiler
A
but I'm not so sure..


Eden wrote:
1) X^X=|X|
What about x=0?
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.

Answer: A.

Hope it helps.
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Re: What is X? [#permalink] New post   03 Aug 2010, 12:13
Expert Reply
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.


Your calculation is not correct.

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] New post   14 Apr 2014, 13:58
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
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Re: What is integer x? [#permalink] New post   22 Sep 2021, 14:34
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Re: What is integer x? [#permalink]
22 Sep 2021, 14:34
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