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Intern  Joined: 10 Jan 2011
Posts: 14
Location: India
Schools: ISB, IIM-A
WE 1: 4 yrs in finance
Is x=square root of x^2?  [#permalink]

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2
9 00:00

Difficulty:   25% (medium)

Question Stats: 66% (00:56) correct 34% (01:05) wrong based on 345 sessions

### HideShow timer Statistics Is $$x = \sqrt{x^2}$$?

(1) x = even
(2) 13 < x < 17

_________________
Rahul

Originally posted by ITMRAHUL on 23 Jan 2011, 08:18.
Last edited by Bunuel on 04 Dec 2012, 03:01, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 56260

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5
1
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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##### General Discussion
Intern  Joined: 10 Jan 2011
Posts: 14
Location: India
Schools: ISB, IIM-A
WE 1: 4 yrs in finance

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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???
_________________
Rahul
Math Expert V
Joined: 02 Sep 2009
Posts: 56260
Is x=square root of x^2?  [#permalink]

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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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Intern  Joined: 10 Jan 2011
Posts: 14
Location: India
Schools: ISB, IIM-A
WE 1: 4 yrs in finance

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thanku very very much i got ur point more clearly nw
thx again
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Rahul
Manager  Joined: 29 Jul 2011
Posts: 81
Location: United States
Re: Is x = \sqrt{x^2} if (1) x = even (2) 13 < x < 17  [#permalink]

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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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Senior Manager  Joined: 13 May 2013
Posts: 414

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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.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9446
Location: Pune, India

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1
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.
_________________
Karishma
Veritas Prep GMAT Instructor

Senior Manager  Joined: 13 May 2013
Posts: 414

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56260

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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?

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.

_________________
Senior Manager  Joined: 13 May 2013
Posts: 414

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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?

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56260

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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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Senior Manager  Joined: 13 May 2013
Posts: 414
Re: Is x=square root of x^2?  [#permalink]

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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)
Current Student D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: Is x=square root of x^2?  [#permalink]

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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]

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_________________ Re: Is x=square root of x^2?   [#permalink] 04 Jan 2019, 07:11
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