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Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x|

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GMATinsight
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Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x| [#permalink] New post   25 Jun 2020, 04:33
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Find the value of x?


(1) \(|x|^{|x|} = |x|\)

(2) \(x ≠ |x|\)


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C
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yashikaaggarwal
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Re: Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x| [#permalink] New post   25 Jun 2020, 04:48
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Find the value of x?

1) |x|^|x| = |x|

Case 1: |1|^|1| = |1|
=> 1 = 1
=> Satisfying

Case 2: |-1|^|-1| = |1|
=> 1 = 1
=> Satisfying
We have 2 values for x (Not satisfying)

2) x ≠ |x|
X is not equal to |x|
Therefore x is negative.
So x ≠ |x| is true for all negative values.
(Insufficient)

Statement 1&2: X is negative and according to statement 1, X is -1 (sufficient)

Answer is C

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Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x| [#permalink] New post   25 Jun 2020, 10:44
GMATinsight wrote:
Find the value of x?


(1) \(|x|^{|x|} = |x|\)

(2) \(x ≠ |x|\)




S1: x could equal 1 or -1. NOT SUFFICIENT.

S2: x could equal any negative number. NOT SUFFICIENT.

S1+S2: We know from S2 that x must be negative and since S1 only has one negative solution, we can conclude that x = -1. SUFFICIENT.

ANSWER: C
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Re: Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x| [#permalink] New post   26 Jun 2020, 09:37
GMATinsight wrote:
Find the value of x?


(1) \(|x|^{|x|} = |x|\)

(2) \(x ≠ |x|\)


Source: https://www.GMATinsight.com


#1
\(|x|^{|x|} = |x|\)
possible value of x = +/-1
insufficient
#2
\(x ≠ |x|\)
means value of x is -ve but can be any value so insufficient
from 1 &2
x = -1
sufficient
OPTION C
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Re: Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x| [#permalink] New post   26 Jun 2020, 10:01
GMATinsight wrote:
Find the value of x?


(1) \(|x|^{|x|} = |x|\)

(2) \(x ≠ |x|\)


Source: https://www.GMATinsight.com


Asked: Find the value of x?


(1) \(|x|^{|x|} = |x|\)
x = 1 or -1
NOT SUFFICIENT

(2) \(x ≠ |x|\)
x <=0
NOT SUFFICIENT

(1) + (2)
(1) \(|x|^{|x|} = |x|\)
x = 1 or -1
(2) \(x ≠ |x|\)
x <=0
x = - 1
SUFFICIENT

IMO C
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Re: Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x| [#permalink] New post   24 Sep 2020, 10:25
yashikaaggarwal wrote:
Find the value of x?

1) |x|^|x| = |x|

Case 1: |1|^|1| = |1|
=> 1 = 1
=> Satisfying

Case 2: |-1|^|-1| = |1|
=> 1 = 1
=> Satisfying
We have 2 values for x (Not satisfying)

2) x ≠ |x|
X is not equal to |x|
Therefore x is negative.
So x ≠ |x| is true for all negative values.
(Insufficient)

Statement 1&2: X is negative and according to statement 1, X is -1 (sufficient)

Answer is C

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If we take x= -2 for case 1... then it will not hold true...
since 2^2 = 4 cannot be equal to 2.....

Ans should be E..

Why only 1 is taken into consideration?
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Re: Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x| [#permalink] New post   24 Sep 2020, 10:32
ShubhiChauhan wrote:
yashikaaggarwal wrote:
Find the value of x?

1) |x|^|x| = |x|

Case 1: |1|^|1| = |1|
=> 1 = 1
=> Satisfying

Case 2: |-1|^|-1| = |1|
=> 1 = 1
=> Satisfying
We have 2 values for x (Not satisfying)

2) x ≠ |x|
X is not equal to |x|
Therefore x is negative.
So x ≠ |x| is true for all negative values.
(Insufficient)

Statement 1&2: X is negative and according to statement 1, X is -1 (sufficient)

Answer is C

Posted from my mobile device





If we take x= -2 for case 1... then it will not hold true...
since 2^2 = 4 cannot be equal to 2.....

Ans should be E..

Why only 1 is taken into consideration?

Exactly, that's why we took 1&-1 as X value because they hold the constraint true.
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Re: Find the value of x? (1) |x|^|x} = |x| (2) x ≠ |x| [#permalink]
24 Sep 2020, 10:32
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Bunuel
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