What is the value of |x| ? (1) x = - |x| (2) x^2 = 4

Question

What is the value of |x| ?

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

Bunuel · Accepted Answer

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.

Bunuel · Answer

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.

cyberjadugar · Answer

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,

pavanpuneet · Answer

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.

GMATBaumgartner · Answer

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 ?

Bunuel · Answer

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.

bpdulog · Answer

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?

Bunuel · Answer

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.

bparrish89 · Answer

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!

bdrrr · Answer

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

Bunuel · Answer

\sqrt{4}=2 .

x^2=4  means that  x=\sqrt{4}=2  or  x=-\sqrt{4}=-2 . Two solutions.

BrushMyQuant · Answer

STAT 1: x = -|x|  
=> |x| = -x
It just tells us that x is a negative number or zero
So, INSUFFICIENT

STAT 2: x^2 = 4  
means x = +-2
So, |x| = 2
So, SUFFICIENT

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

EgmatQuantExpert · Answer

A few students above had difficulty in processing the first statement: x = -|x|

Here's how you can think through this statement visually:

|x| denotes the distance of an unknown number x from the zero point on the number line. Being the distance, |x| is always non-negative. (Please note that it will be wrong to say that the distance |x| is always positive, because the word 'positive' means 'strictly greater than zero'. It is possible that a point lies ON the zero point, thereby making its distance from the zero point equal to zero. )

So, x = (-)(a positive number) = (a negative number)

Or, x can be equal to zero (that is, on the number line, point x lies ON the point zero. Therefore, |x| = distance between 0 and x = 0 as well)

The important takeaway is that when processing equations of the type x = -|x| etc., start by first considering that |x| is non-negative, since it represents the distance of a number from the zero point on the number line.

Hope this helps!

Japinder

ScottTargetTestPrep · Answer

We need to determine the absolute value of x.

Statement One Alone:

x = -|x|

If x = -|x|, then x must be negative or 0. For example, if x = -3, -3 = -|-3|. However, since we do not have an exact value for x, statement one is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

x^2 = 4

We can simplify by taking the square root of both sides of the equation:

√x^2 = √4

|x| = 2

Since we have 2 as the value for |x|, this answers the question.

Answer: B

adkikani · Answer

HI  Bunuel

Can you validate my understanding?
(1) x = - |x|
|x| can be a positive or negative no. (based on x>0 or x<0) but since we do not have 
an unique value for x, st 1 is insufficient.

(2) x^2 = 4
We took square root on LHS and RHS to get
|x| = 2 (-2 is not possible on GMAT since square root of negative no shall yield complex no and 
we deal with only real nos)
Since we got an unique answer, st 2 is sufficient

Bunuel · Answer

|x| is an absolute value of a number, so it CANNOT be negative. |x| can be positive or 0. When x \le 0 then |x|=-x , or more generally when ext{some expression} \le 0 then | ext{some expression}| = -( ext{some expression}) . For example: |-5|=5=-(-5) ; When x \ge 0 then |x|=x , or more generally when ext{some expression} \ge 0 then | ext{some expression}| = ext{some expression} . For example: |5|=5 . (1) says that |x|=-x, thus x \le 0 . Not sufficient. (2) says that x^2 = 4, so x = 2 or x = -2. I any case |x| = 2. Sufficient. Check complete solution here: https://gmatclub.com/forum/what-is-the- ... l#p1106786 10. Absolute Value Theory Math: Absolute value (Modulus) Absolute Value: Tips and hints Properties of Absolute Values on the GMAT Absolute modulus : A better understanding GMAT Question Patterns: Abolute Value The Reason Behind Absolute Value Questions on the GMAT Questions Inequality and absolute value questions from my collection The E-GMAT Question Series on ABSOLUTE VALUE DS Questions PS Questions For more check Ultimate GMAT Quantitative Megathread Hope it helps.

wallstreet789 · Answer

Hi  Bunuel ,
if the question had asked, what is the value of X?
then would C be the answer,

thanks

Bunuel · Answer

Yes.

From (1) we have that  x\leq{0}  and from (2) we have that x = 2 or -2. So, when combining we can get that x = -2.

MasteringGMAT · Answer

Hi Bunuel I am trying to understand the statement 1, more from number line range POV. You said X could be 0 or any negative number. Could you please illustrate an example simplification of this statement taking a negative number and 0.

Thank you, Tilak

What is the value of |x| ? (1) x = - |x| (2) x^2 = 4

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What is the value of |x| ? (1) x = - |x| (2) x^2 = 4

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