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

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New post 29 Nov 2018, 01:42
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  45% (medium)

Question Stats:

64% (01:31) correct 36% (01:26) wrong based on 182 sessions

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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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New post 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.

A is the answer.
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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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New post 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

(A) is our answer.
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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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New post 24 Dec 2018, 01:43
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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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New post 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

(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
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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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New post 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

(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


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

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New post 02 Jan 2019, 07:30
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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Re: If x ≠ 0, what is the value of x? (1) |x + 2| = |x| (2) |x^x| = 1  [#permalink]

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New post 02 Jan 2019, 09:02
GMATin wrote:
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... :) )



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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