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What is the value of |x| ?

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What is the value of |x| ? [#permalink] New post 23 Jul 2012, 03:43
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Re: What is the value of |x| ? [#permalink] New post 23 Jul 2012, 03:43
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SOLUTION

What is the value of |x| ?

(1) x = - |x| --> |x|=-x. This equation holds true for any x which is less than or equal to zero, so all we know from this statement is that x\leq{0}. Not sufficient.

(2) x^2 = 4 --> |x|=2. Sufficient.

Answer: B.
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Re: What is the value of |x| ? [#permalink] New post 23 Jul 2012, 04:47
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Hi,

Difficulty level: 600

Using (1),
x = -|x|
or x \leq 0, Insufficient.

Using (2),
x^2 = 4
or |x| = 2. Sufficient.

Answer (B)

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Re: What is the value of |x| ? [#permalink] New post 25 Jul 2012, 01:27
Please confirm if this is right logic to prove x<=0?

from condition 1: x=-|x|

thus, if x>0 ==> x=-x ==> 2x=0 ==> x=0
and if x<0 ==> x=-(-x) ==> x=x...however x<0, then for this condition x will be always less than zero to satisfy x=x

Thus in combination x<=0.



cyberjadugar wrote:
Hi,

Difficulty level: 600

Using (1),
x = -|x|
or x \leq 0, Insufficient.

Using (2),
x^2 = 4
or |x| = 2. Sufficient.

Answer (B)

Regards,
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Re: What is the value of |x| ? [#permalink] New post 27 Jul 2012, 06:31
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SOLUTION

What is the value of |x| ?

(1) x = - |x| --> |x|=-x. This equation holds true for any x which is less than or equal to zero, so all we know from this statement is that x\leq{0}. Not sufficient.

(2) x^2 = 4 --> |x|=2. Sufficient.

Answer: B.
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Re: What is the value of |x| ? [#permalink] New post 29 Jul 2012, 05:58
Cyberjadugar/Bunuel,
is Pavan puneets approach right to confirm stmt ( 1) leads us to x<=0 ?
can you just break stmt 1 down for us a little please ?
pavanpuneet wrote:
Please confirm if this is right logic to prove x<=0?

from condition 1: x=-|x|

thus, if x>0 ==> x=-x ==> 2x=0 ==> x=0
and if x<0 ==> x=-(-x) ==> x=x...however x<0, then for this condition x will be always less than zero to satisfy x=x

Thus in combination x<=0
.



cyberjadugar wrote:
Hi,

Difficulty level: 600

Using (1),
x = -|x|
or x \leq 0, Insufficient.

Using (2),
x^2 = 4
or |x| = 2. Sufficient.

Answer (B)

Regards,
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Re: What is the value of |x| ? [#permalink] New post 29 Jul 2012, 06:29
Expert's post
vinay911 wrote:
Cyberjadugar/Bunuel,
is Pavan puneets approach right to confirm stmt ( 1) leads us to x<=0 ?
can you just break stmt 1 down for us a little please ?
pavanpuneet wrote:
Please confirm if this is right logic to prove x<=0?

from condition 1: x=-|x|

thus, if x>0 ==> x=-x ==> 2x=0 ==> x=0
and if x<0 ==> x=-(-x) ==> x=x...however x<0, then for this condition x will be always less than zero to satisfy x=x

Thus in combination x<=0
.



cyberjadugar wrote:
Hi,

Difficulty level: 600

Using (1),
x = -|x|
or x \leq 0, Insufficient.

Using (2),
x^2 = 4
or |x| = 2. Sufficient.

Answer (B)

Regards,



From (1) we can conclude that x\leq{0} (check this: what-is-the-value-of-x-136195.html#p1108170), though the approach you are referring to is not precise enough.
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Re: What is the value of |x| ? [#permalink] New post 29 Jul 2012, 06:50
Hi Bunuel, Can you please let me know where I have made the mistake to derive x<=0. It will be really helpful. Thanks.
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Re: What is the value of |x| ? [#permalink] New post 29 Jul 2012, 07:10
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pavanpuneet wrote:
Hi Bunuel, Can you please let me know where I have made the mistake to derive x<=0. It will be really helpful. Thanks.


Sure. If we do the way you are proposing then we should consider two cases:

If x\leq{0}, then we would have that x=-(-x) --> x=x, which is obviously true. So, x=-|x| holds true for any x which is \leq{0};


If x>{0}, then we would have that x=-x --> 2x=0 --> x=0, which is not a valid solution since we are considering the range when x>{0}. So, if x>{0} then x=-|x| has no valid solutions.

Therefore, from the above we have that x=-|x| holds true only when x\leq{0}.

Now, you could conclude that right away, since we can rewrite x=-|x| as |x|=-x, which according to the properties of absolute value is true for x\leq{0}.

Hope it's clear.
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Re: What is the value of |x| ? [#permalink] New post 17 Aug 2012, 05:01
I understand the answer explanation, so thanks to everyone who contributed. But what I'm confused is when they use the term "value." Does that always mean they are looking for a single number?
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Re: What is the value of |x| ? [#permalink] New post 17 Aug 2012, 05:17
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bpdulog wrote:
I understand the answer explanation, so thanks to everyone who contributed. But what I'm confused is when they use the term "value." Does that always mean they are looking for a single number?


When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

Hope it's clear.
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Re: What is the value of |x| ? [#permalink] New post 16 May 2013, 08:27
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

What is the value of |x| ?

(1) x = - |x|
(2) x^2 = 4

Practice Questions
Question: 1
Page: 275
Difficulty: 600


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Stmt 1: no value,
stmt2: x = 2 or -2 and !x! = 2,
so answer i stmt B alone
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Re: What is the value of |x| ? [#permalink] New post 27 Aug 2013, 04:12
Hello,

I need help understanding and visualizing the absolute value concept of |x|=x

For example:

|x|=3 we know that on the number line x is exactly 3 units away from zero

x=3 or x=-3


How do we translate |x|=x? x is exactly x units away from zero?

x=x or x=-x?


So when I break statement one down in to further steps I get:

|x|=-x

+x=-x or -x=-x

x=-x or x=x? I think I am wrong here though? Because how can x\leq{0}?

I would really like to master this concept down. If you have similar questions with |x|=x being tested, please post

thanks
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Re: DS question from OG [#permalink] New post 30 Dec 2013, 11:07
seabhi wrote:
1. What is the value of |x| ?

(1) x = –|x|
(2) x2 = 4


Posting OG question, did not find in the search.


First off, this is a "value" DS question therefore in order to be sufficient, we must be able to calculate a specific value for x

S1: x could be a suite of numbers such as: any negative integer or fraction, and 0 --> not sufficient
S2: 2x = 4 - therefore x = 2 --> sufficient because we know the value of x, and can now answer the question stem |x| --> |2| = 2

Let me know if this helps!
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Re: What is the value of |x| ? [#permalink] New post 30 May 2014, 10:00
Hi,

I've got a big dilemma for this question.

For statement 2
x^2=4

I see 3 solution fitting:
i) x=2 >> 2^2=4
therefore abs(2)=2

ii) x=(-2) >> (-2)^2=4
therefore abs(-2)=2

BUT
iii) sx=qr(4) >>> sqr(4)^2=4. Am I not correct on this? The sterm/question does not say that x has to be an integer right? So sqr(4) can fit in here, isn't it?
therefore abs(sqr(4))=sqr(4)

Therefore statement 2 is insufficient.

Between the OG and Online explanations, I do not understand why sqr(4) could not fit in statement 2.

Thx
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Re: What is the value of |x| ? [#permalink] New post 30 May 2014, 10:04
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bdrrr wrote:
Hi,

I've got a big dilemma for this question.

For statement 2
x^2=4

I see 3 solution fitting:
i) x=2 >> 2^2=4
therefore abs(2)=2

ii) x=(-2) >> (-2)^2=4
therefore abs(-2)=2

BUT
iii) sx=qr(4) >>> sqr(4)^2=4. Am I not correct on this? The sterm/question does not say that x has to be an integer right? So sqr(4) can fit in here, isn't it?
therefore abs(sqr(4))=sqr(4)

Therefore statement 2 is insufficient.

Between the OG and Online explanations, I do not understand why sqr(4) could not fit in statement 2.

Thx


\sqrt{4}=2.

x^2=4 means that x=\sqrt{4}=2 or x=-\sqrt{4}=-2. Two solutions.
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Re: What is the value of |x| ? [#permalink] New post 30 May 2014, 10:09
Hmm I am tired... I should have seen that!
Thanks Bunuel
Re: What is the value of |x| ?   [#permalink] 30 May 2014, 10:09
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