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# what is the value of |x| (1) x=-|x| (2)x^2=4

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Manager
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what is the value of |x| (1) x=-|x| (2)x^2=4 [#permalink]  12 Oct 2009, 23:45
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hi friends ,

the problem is as follow:-

what is the value of |x|

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

please explain in details ,please provide some information on absolute value concept . i face difficulty with such
Manager
Joined: 06 Sep 2009
Posts: 115
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Re: absolute value [#permalink]  13 Oct 2009, 02:33
sacmanitin wrote:
hi friends ,

the problem is as follow:-

what is the value of |x|

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

please explain in details ,please provide some information on absolute value concept . i face difficulty with such

Hi sacmanitin

This is a tricky question.
First, paraphrase what is being asked:

"What is the value of |X|?" means "What is the absolute value of |x|?"
I mean, what is the distance of X from zero? (This means you can disregard the signal, whatever it is)

Let's go through the information:

(1) x = -|x|
This information alone says nothing about the distance, right?
INSUFFICIENT

(2) Xˆ2 = 4

Take the square root:
sqrt (xˆ2) = sqrt(4)

x = +- 2
You still do not know whether it is either 2 or -2
It does not matter, because both have the distance of 2 from the origin.
SUFFICIENT

Got it?

If not, PM me
Manager
Joined: 07 Jun 2009
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Re: absolute value [#permalink]  13 Oct 2009, 03:02
Absolute value or Modulus is the numerical value without the sign. Therefore modulus of -3 and 3 is 3.

1. x= -$$mod x$$
That means, since $$mod x$$ is always positive and -$$mod x$$ will be negative, therefore x is a negative number.
This is not sufficient to answer the question of, what is the value of $$mod x$$.
2. $$x^2$$= 4. this means either $$-2^2$$= 4 or $$2^2$$=4. Again we are getting 2 values of x= 2 and -2.

Now combine 1 and 2. Since x is a negative number and it has to be either 2 or -2, then x = -2

I would go for option C.
_________________

Manager
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Re: absolute value [#permalink]  13 Oct 2009, 04:46
this is the explanation given :-
from (1) all that can be determined is that x is negative (or 0) since |x|,the absolute value of x ,is always positive
(or 0) ,thus , (1) alone is not sufficient ,from (2) it can be detrmined that x=+/- 2 in either case |x|=2 ,sufficient
OA is B

but still if someone can explain more about explanation for statement (1) would be helpful
Director
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Re: absolute value [#permalink]  13 Oct 2009, 04:53
Typical DS concept this is.
Whenever a question asks, what is the value of x ( or any variable for that matter ), it is asking what is a numeric value of that variable. So if the variable cannot have any value or if it has more than one value then we cannot answer this question.

stmt1 says that x is -ve ...x can be -1,-2,-3...but WHAT is x ? we can't say anything..so this is insuff.

stmt 2..x can be 2 or -2...but |x| will always be 2. suff.
Manager
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Re: absolute value [#permalink]  13 Oct 2009, 06:18
Agree with B

This is a tricky DS question.

Statement 1 - tells us nothing about the value, except that x is a negative number

Statement 2 - tells us x is +/- 2 normally this is insufficient but reread the original question!
Since we are looking for the absolute value it doesn't matter if 2 is +/- We know that the absolute value will be 2 regardless of the sign. So SUFFICIENT
Manager
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Re: absolute value [#permalink]  14 Oct 2009, 00:46
hi friends ,thanks for precise explanation ..
Re: absolute value   [#permalink] 14 Oct 2009, 00:46
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