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What is the value of |x| ?

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Re: What is the value of |x| ? [#permalink]
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What is the value of |x| ?

(1) x = –|x|
x + |x| = 0 means that x could be 0 or x <0. INSUFFICIENT!

(2) x^2 = 4
$$\sqrt{x^2}=|x|=2$$. SUFFICIENT!
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Re: What is the value of |x| ? [#permalink]
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Re: What is the value of |x| ? [#permalink]
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sandal85 wrote:
What is the value of |x| ?

(1) x = –|x|
(2) x^2 = 4

We need to determine the value of |x|.

Statement One Alone:

x = -|x|

If x = -|x|, then x must be either zero or negative. However, we still do not have enough information to determine the value of |x|.

Statement Two Alone:

x^2 = 4

If x^2 = 4, then x is either 2 or -2.

If x = 2, then |x| = |2| = 2. If x = -2, then |x| = |-2| = 2. Either way |x| = 2.

Statement two alone is sufficient.

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Re: What is the value of |x| ? [#permalink]
ScottTargetTestPrep wrote:
sandal85 wrote:
What is the value of |x| ?

(1) x = –|x|
(2) x^2 = 4

We need to determine the value of |x|.

Statement One Alone:

x = -|x|

If x = -|x|, then x must be either zero or negative. However, we still do not have enough information to determine the value of |x|.

Statement Two Alone:

x^2 = 4

If x^2 = 4, then x is either 2 or -2.

If x = 2, then |x| = |2| = 2. If x = -2, then |x| = |-2| = 2. Either way |x| = 2.

Statement two alone is sufficient.
I think according to statement 2, x can also be under root 4. why is it not the case?
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Re: What is the value of |x| ? [#permalink]
Asked: What is the value of |x| ?

(1) x = –|x|
x is negative but value can not be determined
NOT SUFFICIENT

(2) x^2 = 4
x = {2,-2}
|x| = 2
SUFFICIENT

IMO B

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Re: What is the value of |x| ? [#permalink]
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Poojita wrote:
ScottTargetTestPrep wrote:
sandal85 wrote:
What is the value of |x| ?

(1) x = –|x|
(2) x^2 = 4

We need to determine the value of |x|.

Statement One Alone:

x = -|x|

If x = -|x|, then x must be either zero or negative. However, we still do not have enough information to determine the value of |x|.

Statement Two Alone:

x^2 = 4

If x^2 = 4, then x is either 2 or -2.

If x = 2, then |x| = |2| = 2. If x = -2, then |x| = |-2| = 2. Either way |x| = 2.

Statement two alone is sufficient.
I think according to statement 2, x can also be under root 4. why is it not the case?

Response:

If by “under root 4” you mean √4, that is equal to 2 and we consider that in the first case.
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Re: What is the value of |x| ? [#permalink]
What is the value of |x| ?

(1) x = –|x|
(2) x^2 = 4

Here's how I understood this

(1) x = -|x|

now, let's assume x=6

then 6= -|6| will ultimately give us 6= -6 [which obviously is not possible]

now, let's assume x= -6

then -6= -|-6| will give us -6= -6 [which is a possibility]

And, another case where x=0
0= -|0| which gives 0=0 [also possible]

but now we have 3 cases with different possibilities but no certainty about |x|, hence, (1) not sufficient

(2) x^2 = 4

this gives x= +2,-2

for x=+2 we get |2| = 2
for x=-2 we get |-2|=2

in both the cases |x|=2 hence, (2) sufficient
Re: What is the value of |x| ? [#permalink]
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