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

2

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

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.

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

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

Expert's post

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.

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

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

Re: What is the value of |x| ? [#permalink]
29 Jul 2012, 07:10

2

This post received KUDOS

Expert's post

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 \(x\leq{0}\).

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

Re: What is the value of |x| ? [#permalink]
17 Aug 2012, 05:17

Expert's post

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.

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Stmt 1: no value, stmt2: x = 2 or -2 and !x! = 2, so answer i stmt B alone

Re: DS question from OG [#permalink]
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

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

Re: What is the value of |x| ? [#permalink]
30 May 2014, 10:04

1

This post received KUDOS

Expert's post

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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