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Bunuel
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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 29 Nov 2018, 01:42
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67% (01:31) correct 33% (01:38) wrong based on 543 sessions

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If x ≠ 0, what is the value of x?

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


M36-34

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Bunuel
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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 18 Oct 2021, 04:39
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Bunuel
If x ≠ 0, what is the value of x?

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


M36-34
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Official Solution:


If \(x ≠ 0\), what is the value of \(x\)?

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

Square to get rid of the absolute value (note here that we can safely do that since both sides of the equation are non-negative):

\(x^2+4x+4=x^2\);

\(x=-1\). Sufficient.

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

If \(x^x > 0\), then we'd get \(x^x = 1\), which gives \(x = 1\);

If \(x^x < 0\), then we'd get \(x^x = -1\), which gives \(x = -1\).

Not sufficient.


Answer: A
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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 29 Nov 2018, 01:51
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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.

A is the answer.
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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 29 Nov 2018, 02:15
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Bunuel
If x ≠ 0, what is the value of x?

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

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

(A) is our answer.
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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 24 Dec 2018, 01:43
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Bunuel
If x ≠ 0, what is the value of x?

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

Par of GMAT CLUB'S New Year's Quantitative Challenge Set

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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 31 Dec 2018, 04:11
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DavidTutorexamPAL
Bunuel
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

(A) is our answer.
Show more

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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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 31 Dec 2018, 05:41
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DavidTutorexamPAL
Bunuel
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

(A) is our answer.

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
Show more

Hey GMATin, glad you found it helpful!
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... :) )
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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 02 Jan 2019, 07:30
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Hey GMATin, glad you found it helpful!
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! :)
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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 02 Jan 2019, 09:02
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GMATin
Hey GMATin, glad you found it helpful!
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... :) )
Show more


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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If x 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1 10 Jun 2023, 19:54
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