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# What is the value of x? (1) |x|=−x (2) |x|^2 = −x^2

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Intern
Joined: 21 Mar 2013
Posts: 41
GMAT Date: 03-20-2014
What is the value of x? (1) |x|=−x (2) |x|^2 = −x^2 [#permalink]

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06 Mar 2014, 22:17
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What is the value of x?

(1) |x| = −x

(2) $$|x|^2$$ = −$$x^2$$
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43901
Re: What is the value of x? (1) |x|=−x (2) |x|^2 = −x^2 [#permalink]

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06 Mar 2014, 22:58
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What is the value of x?

(1) |x| = −x. This implies that x is less than or equal to zero. Not sufficient.

(2) $$|x|^2= -x^2$$ --> $$x^2=-x^2$$ --> $$2x^2=0$$ --> $$x=0$$. Sufficient.

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Re: What is the value of x? (1) |x|=−x [#permalink]

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25 Oct 2015, 14:44
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dina98 wrote:
What is the value of x?
(1) |x|=−x
(2) |x|^2=−x^2

As for the question, x=?

Per statement 1, |x|=-x ---> x<0. Not sufficient.

Per statement 2, |x|^2=−x^2 ---> a positive quantity = negative quantity, only possible when x=0. Sufficient.

Hope this helps.
Manager
Joined: 14 Jul 2014
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Re: What is the value of x? (1) |x|=−x [#permalink]

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25 Oct 2015, 14:57
Engr2012 wrote:

Per statement 1, |x|=-x ---> x<0. Not sufficient.

.

This statement threw me off. I can now see that x < 0. Thanks!
SVP
Joined: 06 Nov 2014
Posts: 1904
Re: What is the value of x? (1) |x|=−x (2) |x|^2 = −x^2 [#permalink]

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25 Oct 2015, 19:44
dina98 wrote:
Engr2012 wrote:

Per statement 1, |x|=-x ---> x<0. Not sufficient.

.

This statement threw me off. I can now see that x < 0. Thanks!

Modulus of any value is always positive or is the absolute value

If a number is positive, we open the modulus by the positive sign
Eg: |5| = 5

If a number is negative, we open the modulus with a negative sign:
Eg: |-5| = - (-5)

In this case, since we are opening the modulus with a negative sign, the number should be less than 0
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Posts: 1747
Re: What is the value of x? [#permalink]

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14 Jan 2017, 07:26
roastedchips wrote:
(1) |x|=−x

(2) |x|2=−x2

FROM 1

x could be any -ve number or 0 ... insuff

from 2

x^2 is +ve by default and so is /x/ thus for this to happen x must be = 0... suff

OR

/X/^2 = X^2 thus /x/^2 = -x^2 is = to x^2 = -x^2 thus 2x^2 = 0 thus surely x = 0

B
Math Expert
Joined: 02 Sep 2009
Posts: 43901
Re: What is the value of x? (1) |x|=−x (2) |x|^2 = −x^2 [#permalink]

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14 Jan 2017, 08:47
roastedchips wrote:
What is the value of x?

(1) |x|=−x

(2) |x|^2=−x^2

Similar question: what-is-the-value-of-x-221441.html
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Re: What is the value of x? (1) |x|=−x (2) |x|^2 = −x^2 [#permalink]

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24 Jan 2018, 11:44
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Re: What is the value of x? (1) |x|=−x (2) |x|^2 = −x^2   [#permalink] 24 Jan 2018, 11:44
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