Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Apr 2015, 14:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is x=square root of x^2?

Author Message
TAGS:
Intern
Joined: 10 Jan 2011
Posts: 21
Location: India
Schools: ISB, IIM-A
WE 1: 4 yrs in finance
Followers: 0

Kudos [?]: 0 [0], given: 0

Is x=square root of x^2? [#permalink]  23 Jan 2011, 07:18
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:31) correct 28% (00:45) wrong based on 88 sessions
Is $x = \sqrt{x^2}$?

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

_________________

Rahul

Last edited by Bunuel on 04 Dec 2012, 02:01, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 27058
Followers: 4184

Kudos [?]: 40429 [0], given: 5421

Re: Root. Modulus question [#permalink]  23 Jan 2011, 07:51
Expert's post
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.
_________________
Intern
Joined: 10 Jan 2011
Posts: 21
Location: India
Schools: ISB, IIM-A
WE 1: 4 yrs in finance
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Root. Modulus question [#permalink]  23 Jan 2011, 09:21
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???
_________________

Rahul

Math Expert
Joined: 02 Sep 2009
Posts: 27058
Followers: 4184

Kudos [?]: 40429 [0], given: 5421

Re: Root. Modulus question [#permalink]  23 Jan 2011, 09:38
Expert's post
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 can not 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.

_________________
Intern
Joined: 10 Jan 2011
Posts: 21
Location: India
Schools: ISB, IIM-A
WE 1: 4 yrs in finance
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Root. Modulus question [#permalink]  23 Jan 2011, 09:58
thanku very very much i got ur point more clearly nw
thx again
_________________

Rahul

Manager
Joined: 29 Jul 2011
Posts: 111
Location: United States
Followers: 3

Kudos [?]: 41 [0], given: 6

Re: Is x = \sqrt{x^2} if (1) x = even (2) 13 < x < 17 [#permalink]  03 Jan 2012, 10:31
1. Insufficient since x can be negative
2. Sufficient, since here x is positive - irrespective of even or odd.

+1 for B
_________________

I am the master of my fate. I am the captain of my soul.
Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution.
PS - Always look at the answers first
CR - Read the question stem first, hunt for conclusion
SC - Meaning first, Grammar second
RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

Senior Manager
Joined: 13 May 2013
Posts: 475
Followers: 1

Kudos [?]: 78 [0], given: 134

Re: Root. Modulus question [#permalink]  19 Jun 2013, 10:35
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.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5429
Location: Pune, India
Followers: 1324

Kudos [?]: 6712 [1] , given: 176

Re: Root. Modulus question [#permalink]  19 Jun 2013, 20:47
1
KUDOS
Expert's post
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
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Senior Manager
Joined: 13 May 2013
Posts: 475
Followers: 1

Kudos [?]: 78 [0], given: 134

Re: Root. Modulus question [#permalink]  20 Jun 2013, 07:16
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.
Math Expert
Joined: 02 Sep 2009
Posts: 27058
Followers: 4184

Kudos [?]: 40429 [0], given: 5421

Re: Root. Modulus question [#permalink]  20 Jun 2013, 09:46
Expert's post
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: 475
Followers: 1

Kudos [?]: 78 [0], given: 134

Re: Root. Modulus question [#permalink]  20 Jun 2013, 10:04
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?

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
Joined: 02 Sep 2009
Posts: 27058
Followers: 4184

Kudos [?]: 40429 [0], given: 5421

Re: Root. Modulus question [#permalink]  20 Jun 2013, 10:40
Expert's post
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.
_________________
Senior Manager
Joined: 13 May 2013
Posts: 475
Followers: 1

Kudos [?]: 78 [0], given: 134

Re: Is x=square root of x^2? [#permalink]  28 Jun 2013, 11:40
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)
Re: Is x=square root of x^2?   [#permalink] 28 Jun 2013, 11:40
Similar topics Replies Last post
Similar
Topics:
3 If set M consists of the root(s) of equation 2-x^2 = (x-2)^2 3 19 Nov 2012, 01:49
1 Square root of X^2? 10 16 Jun 2011, 21:36
Is root(5-x)^2=5-x? 9 02 May 2010, 14:51
20 If x#0, then root(x^2)/x= 18 14 Dec 2009, 16:58
10 If x#0, then root(x^2)/x= 3 18 May 2008, 12:29
Display posts from previous: Sort by