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# Is x=square root of x^2?

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Is x=square root of x^2? [#permalink]

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23 Jan 2011, 08:18
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Is $$x = \sqrt{x^2}$$?

(1) x = even
(2) 13 < x < 17
[Reveal] Spoiler: OA

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Last edited by Bunuel on 04 Dec 2012, 03:01, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Root. Modulus question [#permalink]

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23 Jan 2011, 08:51
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Is $$x = \sqrt{x^2}$$?

Note that: $$\sqrt{x^2}=|x|$$, so the question basically asks whether $$x=|x|$$ or, which is the same, whether $$x\geq{0}$$ or whether $$x$$ is non-negative number.

(1) x = even --> not sufficient as x can be negative as well as a non-negative even number.
(2) 13<x<17 --> x is non-negative. Sufficient.

is-root-x-3-2-3-x-92204.html
if-x-0-then-root-x-x-is-81600.html
is-sqrt-x-5-2-5-x-100517.html
if-x-0-then-root-x-x-is-100303.html

Hope it helps.
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Re: Root. Modulus question [#permalink]

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23 Jan 2011, 10:21
what i understand abt properties of sqr. root that Sqrt(-ve) is not defined i.e
sqrt(x) => x has to be positive
stmt 2 says x is positive
Am i correct???
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Is x=square root of x^2? [#permalink]

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23 Jan 2011, 10:38
ITMRAHUL wrote:
what i understand abt properties of sqr. root that Sqrt(-ve) is not defined i.e
sqrt(x) => x has to be positive
stmt 2 says x is positive
Am i correct???

Even roots (such as square root) from negative numbers are undefined on the GMAT: $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$ (as GMAT is dealing only with Real Numbers);

Also square root function cannot give negative result: $$\sqrt{some \ expression}\geq{0}$$;

But in our original question we don't have $$\sqrt{x}$$ we have $$\sqrt{x^2}$$ and you should know that $$\sqrt{x^2}=|x|$$, so the question basically asks whether $$x=|x|$$ or, which is the same, whether $$x\geq{0}$$ or whether $$x$$ is non-negative number.

(1) x = even --> not sufficient as x can be negative as well as non-negative even number.
(2) 13<x<17 --> x is non-negative. Sufficient.

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Re: Root. Modulus question [#permalink]

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23 Jan 2011, 10:58
thanku very very much i got ur point more clearly nw
thx again
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Re: Is x = \sqrt{x^2} if (1) x = even (2) 13 < x < 17 [#permalink]

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03 Jan 2012, 11:31
1. Insufficient since x can be negative
2. Sufficient, since here x is positive - irrespective of even or odd.

+1 for B
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Re: Root. Modulus question [#permalink]

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19 Jun 2013, 11:35
x = \sqrt{x^2}

So basically, what this says is the following:

x = |x|

So, x = x or x = -x

Firstly, this means that, for example:

x=5 or x=-5

Correct?

I guess where I get tripped up is here:

Let's say x=14 and x=|x| so x=x or x=-x

so

x=14
OR
x=-14

With #2 we are told that x is positive and the stem tells us that x=|x|. But isn't that unnecessary? doesn't x=|x| imply that x is positive anyways? Or, if this makes any sense, if x=x or x=-x then couldn't 14=-x?

Bunuel wrote:
Is $$x = \sqrt{x^2}$$?

Note that: $$\sqrt{x^2}=|x|$$, so the question basically asks whether $$x=|x|$$ or, which is the same, whether $$x\geq{0}$$ or whether $$x$$ is non-negative number.

(1) x = even --> not sufficient as x can be negative as well as a non-negative even number.
(2) 13<x<17 --> x is non-negative. Sufficient.

is-root-x-3-2-3-x-92204.html
if-x-0-then-root-x-x-is-81600.html
is-sqrt-x-5-2-5-x-100517.html
if-x-0-then-root-x-x-is-100303.html

Hope it helps.

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Re: Root. Modulus question [#permalink]

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19 Jun 2013, 21:47
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WholeLottaLove wrote:
x = \sqrt{x^2}

So basically, what this says is the following:

x = |x|

So, x = x or x = -x

Firstly, this means that, for example:

x=5 or x=-5

Correct?

I guess where I get tripped up is here:

Let's say x=14 and x=|x| so x=x or x=-x

so

x=14
OR
x=-14

With #2 we are told that x is positive and the stem tells us that x=|x|. But isn't that unnecessary? doesn't x=|x| imply that x is positive anyways? Or, if this makes any sense, if x=x or x=-x then couldn't 14=-x?

I think you tripped up on what is given and what is to be found.

You are asked: Is $$x = \sqrt{x^2}$$?
You are asked: Is x equal to |x|?
The question doesn't tell us this. It wants us to answer whether it is true.

When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.
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Re: Root. Modulus question [#permalink]

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20 Jun 2013, 08:16
If x=|x| then don't we already know that x is positive? If that's the case then isn't #1) x=even irrelevant? Doesn't x HAVE to be positive?

VeritasPrepKarishma wrote:
WholeLottaLove wrote:
x = \sqrt{x^2}

So basically, what this says is the following:

x = |x|

So, x = x or x = -x

Firstly, this means that, for example:

x=5 or x=-5

Correct?

I guess where I get tripped up is here:

Let's say x=14 and x=|x| so x=x or x=-x

so

x=14
OR
x=-14

With #2 we are told that x is positive and the stem tells us that x=|x|. But isn't that unnecessary? doesn't x=|x| imply that x is positive anyways? Or, if this makes any sense, if x=x or x=-x then couldn't 14=-x?

I think you tripped up on what is given and what is to be found.

You are asked: Is $$x = \sqrt{x^2}$$?
You are asked: Is x equal to |x|?
The question doesn't tell us this. It wants us to answer whether it is true.

When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.

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Re: Root. Modulus question [#permalink]

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20 Jun 2013, 10:46
WholeLottaLove wrote:
If x=|x| then don't we already know that x is positive? If that's the case then isn't #1) x=even irrelevant? Doesn't x HAVE to be positive?

Have you read Karishma's response?

VeritasPrepKarishma wrote:
I think you tripped up on what is given and what is to be found.

You are asked: Is $$x = \sqrt{x^2}$$?
You are asked: Is x equal to |x|?
The question doesn't tell us this. It wants us to answer whether it is true.

When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.

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Re: Root. Modulus question [#permalink]

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20 Jun 2013, 11:04
Haha! Yes I did read it.

I understand that the question is asking IS x=√x^2 (i.e. x=|x|) but x HAS to be positive because x=|x|. That's what I don't get. I can't help but think both 1+2 are irrelevant because x HAS to be positive.

x=|x|
x=positive int.

Sorry for my mental stubbornness!

Bunuel wrote:
WholeLottaLove wrote:
If x=|x| then don't we already know that x is positive? If that's the case then isn't #1) x=even irrelevant? Doesn't x HAVE to be positive?

Have you read Karishma's response?

VeritasPrepKarishma wrote:
I think you tripped up on what is given and what is to be found.

You are asked: Is $$x = \sqrt{x^2}$$?
You are asked: Is x equal to |x|?
The question doesn't tell us this. It wants us to answer whether it is true.

When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.

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Re: Root. Modulus question [#permalink]

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20 Jun 2013, 11:40
WholeLottaLove wrote:
Haha! Yes I did read it.

I understand that the question is asking IS x=√x^2 (i.e. x=|x|) but x HAS to be positive because x=|x|. That's what I don't get. I can't help but think both 1+2 are irrelevant because x HAS to be positive.

x=|x|
x=positive int.

Sorry for my mental stubbornness!

The question asks: is $$x\geq{0}$$? So, the question asks whether x is more than or equal to zero.

(1) says that x IS even. Can we answer the question based on this statement? NO, because x is even does not imply that it's more than or equal to zero. For example, if x=-2, then the answer to the question is NO but if x=2, then the answer to the question is YES. We have two different answers, which means that this statement is NOT sufficient.

(2) says that 13 < x < 17, so x is some number from 13 to 17, not inclusive. Can we answer the question based on this statement? YES, because this statement implies that x IS indeed positive. Sufficient.

Therefore, the answer is B: statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Hope it's clear.
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Re: Is x=square root of x^2? [#permalink]

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28 Jun 2013, 12:40
Is x = √(x^2) ?

Is x = (x)
OR
Is x = (-x)

(1) x = even

X could be even but it may be positive or negative. x MUST be positive.
INSUFFICIENT

(2) 13 < x < 17

X is positive.
SUFFICIENT

(A)

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Re: Is x=square root of x^2? [#permalink]

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Re: Is x=square root of x^2? [#permalink]

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21 Nov 2016, 00:30
Great Question
Here in order for x=√x^2=> x must be positive as √x^2 is always positive
Hence what question is really Asking is that => If x≥0

Statement 1
x is even
x can be positive or negative
Hence insufficient

Remember => Negatives can be even too

Statement 2
This tells us that x is always positive
hence √x^2=> always equal to x
hence Sufficient
Hence B
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Re: Is x=square root of x^2?   [#permalink] 21 Nov 2016, 00:30
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