Last visit was: 19 Nov 2025, 14:35 It is currently 19 Nov 2025, 14:35
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
ITMRAHUL
User avatar
Joined: 10 Jan 2011
Last visit: 25 Aug 2011
Posts: 10
Own Kudos:
19
 [14]
Location: India
Schools:ISB, IIM-A
WE 1: 4 yrs in finance
Posts: 10
Kudos: 19
 [14]
Is x=square root of x^2? Updated on: 04 Dec 2012, 03:01
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.
3
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

68% (00:54) correct 32% (01:12) wrong based on 486 sessions

History

Date
Time
Result
Not Attempted Yet
Is \(x = \sqrt{x^2}\)?

(1) x = even
(2) 13 < x < 17
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
 [11]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
 [11]
Is x=square root of x^2? 23 Jan 2011, 08:51
8
Kudos
Add Kudos
3
Bookmarks
Bookmark this 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.

Answer: B.

Similar questions about this concept:
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.
General Discussion
User avatar
ITMRAHUL
User avatar
Joined: 10 Jan 2011
Last visit: 25 Aug 2011
Posts: 10
Own Kudos:
19
Location: India
Schools:ISB, IIM-A
WE 1: 4 yrs in finance
Posts: 10
Kudos: 19
Is x=square root of x^2? 23 Jan 2011, 10:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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???
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
 [1]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
 [1]
Is x=square root of x^2? 23 Jan 2011, 10:38
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
ITMRAHUL
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???
Show more

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.

Answer: B.
User avatar
ITMRAHUL
User avatar
Joined: 10 Jan 2011
Last visit: 25 Aug 2011
Posts: 10
Own Kudos:
19
Location: India
Schools:ISB, IIM-A
WE 1: 4 yrs in finance
Posts: 10
Kudos: 19
Is x=square root of x^2? 23 Jan 2011, 10:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
thanku very very much i got ur point more clearly nw
thx again
User avatar
shinbhu
User avatar
Joined: 29 Jul 2011
Last visit: 14 Oct 2013
Posts: 51
Own Kudos:
174
Given Kudos: 6
Location: United States
Posts: 51
Kudos: 174
Is x=square root of x^2? 03 Jan 2012, 11:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1. Insufficient since x can be negative
2. Sufficient, since here x is positive - irrespective of even or odd.

+1 for B
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 305
Own Kudos:
627
Given Kudos: 134
Posts: 305
Kudos: 627
Is x=square root of x^2? 19 Jun 2013, 11:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
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.

Answer: B.

Similar questions about this concept:
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.
Show more
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
77,000
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,000
 [1]
Is x=square root of x^2? 19 Jun 2013, 21:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WholeLottaLove
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?

Show more


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.
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 305
Own Kudos:
627
Given Kudos: 134
Posts: 305
Kudos: 627
Is x=square root of x^2? 20 Jun 2013, 08:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
WholeLottaLove
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.
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
Is x=square root of x^2? 20 Jun 2013, 10:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WholeLottaLove
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?
Show more

Have you read Karishma's response?

VeritasPrepKarishma
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.
Show more
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 305
Own Kudos:
627
Given Kudos: 134
Posts: 305
Kudos: 627
Is x=square root of x^2? 20 Jun 2013, 11:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
WholeLottaLove
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
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.
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
Is x=square root of x^2? 20 Jun 2013, 11:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WholeLottaLove
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!
Show more

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.
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 305
Own Kudos:
627
Given Kudos: 134
Posts: 305
Kudos: 627
Is x=square root of x^2? 28 Jun 2013, 12:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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)
User avatar
stonecold
User avatar
Joined: 12 Aug 2015
Last visit: 09 Apr 2024
Posts: 2,244
Own Kudos:
3,549
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Posts: 2,244
Kudos: 3,549
Is x=square root of x^2? 21 Nov 2016, 00:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
CEdward
User avatar
Joined: 11 Aug 2020
Last visit: 14 Apr 2022
Posts: 1,203
Own Kudos:
272
Given Kudos: 332
Posts: 1,203
Kudos: 272
Is x=square root of x^2? 03 Feb 2021, 12:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is x=√x^2?

We're being asked if x = | x |? i.e. is x > 0?

(1) x = even
Insufficient.
x = 2, -2

(2) 13 < x < 17
Sufficient as x >0

Answer is B.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
Is x=square root of x^2? 07 Apr 2022, 13:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
Is x=square root of x^2? 19 Jun 2023, 09:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105390 posts
kingbucky
496 posts