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# If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1

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Math Expert
Joined: 02 Sep 2009
Posts: 51221
If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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29 Nov 2018, 00:42
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:20) correct 26% (01:15) wrong based on 43 sessions

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If x ≠ 0, what is the value of x?

(1) |x + 2| = |x|
(2) |x^x| = 1

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Director
Joined: 18 Jul 2018
Posts: 502
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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29 Nov 2018, 00:51
From statement 1:

|x+2| = |x|
Squaring on both sides
$$x^2+4+4x$$ =$$x^2$$

4+4x = 0
4(1+x) = 0
4 cannot be equal to 0. Hence x+1 = 0 or x = -1.
Sufficient.

From statement 2:

|x^x| = 1

x^x = +1 or -1

Either x = 1 or -1, Since $$1^1$$ = 1 or $$-1^{-1}$$ = -1
Insufficient.

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examPAL Representative
Joined: 07 Dec 2017
Posts: 841
Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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29 Nov 2018, 01:15
Bunuel wrote:
If x ≠ 0, what is the value of x?

(1) |x + 2| = |x|
(2) |x^x| = 1

We'll use basic properties of absolute value to simplify the equations.
This is a Precise approach

Recall that |a| = |b| implies a = b or a = -b.
Then:
(1) |x+2| = |x| implies x+2=x --> so 2 = 0 which is impossible, or x+2= -x --> 2x = -2 and x = -1.
Sufficient.

(2) |x^x| = 1 implies x^x = 1 in which case x = 1 or x^x = -1 in which case x = -1.
Insufficient

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Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 &nbs [#permalink] 29 Nov 2018, 01:15
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