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Math Expert V
Joined: 02 Sep 2009
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What is the value of |x| ?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 54% (00:45) correct 46% (00:50) wrong based on 1998 sessions

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 59710
Re: What is the value of |x| ?  [#permalink]

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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.

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

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vinay911 wrote:
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
.

Hi,

Difficulty level: 600

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

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

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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GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: What is the value of |x| ?  [#permalink]

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1
Hi,

Difficulty level: 600

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

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

Regards,
Manager  Joined: 26 Dec 2011
Posts: 89
Re: What is the value of |x| ?  [#permalink]

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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.

Hi,

Difficulty level: 600

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

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

Regards,
Intern  Joined: 11 Apr 2012
Posts: 36
Re: What is the value of |x| ?  [#permalink]

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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
.

Hi,

Difficulty level: 600

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

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

Regards,
Manager  Joined: 26 Dec 2011
Posts: 89
Re: What is the value of |x| ?  [#permalink]

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Hi Bunuel, Can you please let me know where I have made the mistake to derive x<=0. It will be really helpful. Thanks.
Math Expert V
Joined: 02 Sep 2009
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Re: What is the value of |x| ?  [#permalink]

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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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GMAT 1: 620 Q43 V33 GMAT 2: 690 Q47 V38 Re: What is the value of |x| ?  [#permalink]

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

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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]

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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

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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3. Please vote for the questions themselves by pressing Kudos button;
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Stmt 1: no value,
stmt2: x = 2 or -2 and !x! = 2,
so answer i stmt B alone
Manager  Joined: 25 Jul 2012
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Re: What is the value of |x| ?  [#permalink]

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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
Intern  Joined: 05 Dec 2013
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Re: DS question from OG  [#permalink]

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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]

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

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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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janani28 wrote:
What is the value of |x|?

(1) x = -|x|
(2) x2 = 4

STAT1
x = -|x|
=> |x| = -x
It just tells us that x is a negative number or zero
So, INSUFFICIENT

STAT2
x^2 = 4
means x = +-2
So, |x| = 2
So, SUFFICIENT

Hope it helps!
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Re: What is the value of |x| ?  [#permalink]

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1
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
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Re: What is the value of |x| ?  [#permalink]

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Bunuel wrote:
What is the value of |x| ?

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

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.

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

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

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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

|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 $$\text{some expression} \le 0$$ then $$|\text{some expression}| = -(\text{some expression})$$. For example: $$|-5|=5=-(-5)$$;

When $$x \ge 0$$ then $$|x|=x$$, or more generally when $$\text{some expression} \ge 0$$ then $$|\text{some expression}| = \text{some expression}$$. 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

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________ Re: What is the value of |x| ?   [#permalink] 29 Aug 2017, 09:21

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