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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: 57238
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, 01:42
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35% (medium)

Question Stats:

65% (01:29) correct 35% (01:31) wrong based on 216 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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Joined: 18 Jul 2018
Posts: 1030
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, 01:51
1
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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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, 02:15
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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Math Expert
Joined: 02 Sep 2009
Posts: 57238
Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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24 Dec 2018, 01:43
Bunuel wrote:
If x ≠ 0, what is the value of x?

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

_________________
Manager
Joined: 24 Dec 2018
Posts: 91
Concentration: Entrepreneurship, Finance
GMAT 1: 710 Q47 V40
Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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31 Dec 2018, 04:11
DavidTutorexamPAL wrote:
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

Hey DavidTutorexamPAL

I really appreciate your elegant solution to the question. I do have a doubt regarding how you have solved statement 1, however. I see that many people square both sides when when both sides of an equation have a mod sign, is that the preferred way to solve the question or do you think the way you have discussed is better? Please shed some light on this.

Many thanks
_________________
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examPAL Representative
Joined: 07 Dec 2017
Posts: 1075
Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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31 Dec 2018, 05:41
GMATin wrote:
DavidTutorexamPAL wrote:
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

Hey DavidTutorexamPAL

I really appreciate your elegant solution to the question. I do have a doubt regarding how you have solved statement 1, however. I see that many people square both sides when when both sides of an equation have a mod sign, is that the preferred way to solve the question or do you think the way you have discussed is better? Please shed some light on this.

Many thanks

The short answer is that both ways are technically correct, I recommend the way I showed. squaring the sides is a bit dangerous, in that it can lead us to assume that the variable is positive, and forget the option that it's negative (the danger is turning |x| into x^2 and then solving for x, but forgetting that |x| can equal -x as well...)

More generally, the more important question is which method YOU find more intuitive and useful.
Our whole philosophy is that there is no one right tool or answer strategy in most cases, but several ones which we need to choose based on our own strengths and preferences. (We've built a whole course based on this idea... )
_________________
Manager
Joined: 24 Dec 2018
Posts: 91
Concentration: Entrepreneurship, Finance
GMAT 1: 710 Q47 V40
Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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02 Jan 2019, 07:30
The short answer is that both ways are technically correct, I recommend the way I showed. squaring the sides is a bit dangerous, in that it can lead us to assume that the variable is positive, and forget the option that it's negative (the danger is turning |x| into x^2 and then solving for x, but forgetting that |x| can equal -x as well...)

More generally, the more important question is which method YOU find more intuitive and useful.
Our whole philosophy is that there is no one right tool or answer strategy in most cases, but several ones which we need to choose based on our own strengths and preferences. (We've built a whole course based on this idea... )[/quote]

This is awesome. Thanks so much. I prefer your approach too!
_________________
Hit Kudos if you like my answer!
examPAL Representative
Joined: 07 Dec 2017
Posts: 1075
Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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02 Jan 2019, 09:02
GMATin wrote:
The short answer is that both ways are technically correct, I recommend the way I showed. squaring the sides is a bit dangerous, in that it can lead us to assume that the variable is positive, and forget the option that it's negative (the danger is turning |x| into x^2 and then solving for x, but forgetting that |x| can equal -x as well...)

More generally, the more important question is which method YOU find more intuitive and useful.
Our whole philosophy is that there is no one right tool or answer strategy in most cases, but several ones which we need to choose based on our own strengths and preferences. (We've built a whole course based on this idea... )

This is awesome. Thanks so much. I prefer your approach too! [/quote]

Very happy you like it! Always welcome to find more of our approach at exampal
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Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1   [#permalink] 02 Jan 2019, 09:02
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