Last visit was: 24 Apr 2026, 12:04 It is currently 24 Apr 2026, 12:04
Home
Messages
Tests
Schools
Events
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
prinits
User avatar
Joined: 10 May 2009
Last visit: 27 Aug 2012
Posts: 34
Own Kudos:
308
 [143]
Given Kudos: 11
Posts: 34
Kudos: 308
 [143]
How many roots does the equation || x +2 | - 2 | = 2 have? Updated on: 15 Mar 2014, 05:38
Originally posted by prinits on 07 Jun 2009, 02:13.
Last edited by Bunuel on 15 Mar 2014, 05:38, edited 2 times in total.
Renamed the topic and edited the question.
12
Kudos
Add Kudos
131
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

62% (01:34) correct 38% (01:37) wrong based on 2715 sessions

History

Date
Time
Result
Not Attempted Yet
How many roots does the equation || x +2 | - 2 | = 2 have?

A. 0
B. 1
C. 2
D. 3
E. 4

M13-02

Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,051
 [33]
Given Kudos: 105,873
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: 109,818
Kudos: 811,051
 [33]
How many roots does the equation || x +2 | - 2 | = 2 have? 29 Apr 2013, 07:26
14
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
imhimanshu
Hi Experts,
I would like to understand what exactly the question is testing? What are we supposed to find in such questions.

Thanks
H
Show more

We should find the number of values of x that satisfy the given equation.

How many roots does the equation \(|| x +2 | - 2 | = 2\) have?

A. 0
B. 1
C. 2
D. 3
E. 4

Given: \(||x +2|-2|=2\). Two cases are possible:

1. \(|x +2|=0\). In this case \(x=-2\);

2. \(|x +2|=4\). In this case \(x=2\) or \(x=-6\).

So, the given equation has three roots: -2, 2, and -6.

Answer: D
User avatar
sondenso
User avatar
Joined: 04 May 2006
Last visit: 04 Dec 2018
Posts: 857
Own Kudos:
7,608
 [19]
Given Kudos: 1
Concentration: Finance
Schools:CBS, Kellogg
Posts: 857
Kudos: 7,608
 [19]
How many roots does the equation || x +2 | - 2 | = 2 have? 07 Jun 2009, 02:21
13
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
prinits
How many roots does this equation have?

||x+2|-2|=2

Please explain!
Show more

the same as:|x+2|-2 = + - 2

1. |x+2|-2=2 -->|x+2|=4, again, x+2=+ -4
1.1, x+2=4, x=2
1.2, x+2=-4, x=-6

2. |x+2|-2=-2 -->|x+2|=0, x=-2

So, x=-6,-2,2
General Discussion
User avatar
imhimanshu
User avatar
Joined: 07 Sep 2010
Last visit: 08 Nov 2013
Posts: 216
Own Kudos:
6,365
Given Kudos: 136
GMAT 1: 650 Q49 V30
Posts: 216
Kudos: 6,365
How many roots does the equation || x +2 | - 2 | = 2 have? 29 Apr 2013, 07:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Experts,
I would like to understand what exactly the question is testing? What are we supposed to find in such questions.

Thanks
H
User avatar
imhimanshu
User avatar
Joined: 07 Sep 2010
Last visit: 08 Nov 2013
Posts: 216
Own Kudos:
6,365
Given Kudos: 136
GMAT 1: 650 Q49 V30
Posts: 216
Kudos: 6,365
How many roots does the equation || x +2 | - 2 | = 2 have? 30 Apr 2013, 05:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel


We should find the number of values of x that satisfy the given equation.

Show more

Thanks Bunuel for the explanation. However, I would like to ask, Is it possible to solve it through graphs. Also, What does above equation mean in terms of graphical representation. i.e Do we need to find the number of points for line y=2 intersects the graph. Is it correct representation of the given equation.
Please clarify.

Regards,
H
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,051
 [4]
Given Kudos: 105,873
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: 109,818
Kudos: 811,051
 [4]
How many roots does the equation || x +2 | - 2 | = 2 have? 30 Apr 2013, 06:26
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
imhimanshu
Bunuel


We should find the number of values of x that satisfy the given equation.


Thanks Bunuel for the explanation. However, I would like to ask, Is it possible to solve it through graphs. Also, What does above equation mean in terms of graphical representation. i.e Do we need to find the number of points for line y=2 intersects the graph. Is it correct representation of the given equation.
Please clarify.

Regards,
H
Show more

Possible? Yes.
Good approach? No.

As for the graph itself:
Attachment:
graph.png
graph.png [ 5.93 KiB | Viewed 41860 times ]
Hope it helps.
User avatar
WoundedTiger
User avatar
Joined: 25 Apr 2012
Last visit: 03 Jan 2026
Posts: 520
Own Kudos:
2,584
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Products:
My Reviews
Posts: 520
Kudos: 2,584
How many roots does the equation || x +2 | - 2 | = 2 have? 15 Mar 2014, 02:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Q. How many roots does the equation ||x+2|−2|=2 have?

a. 0
b. 1
c. 2
d. 3
3. 4

I am okay with the solution given for the above problem but I tried solving by solving algebraically and I missed out on one of the roots.

||x+2|−2|=2----->>Can be re-written as

\(\sqrt{({| {|x+2|}−{2}|)^{2}}\) = 2
Squaring both sides we get
(||x+2|−2|)^2 = 4
Now |x+2| is positive so the expression can be written as ((x+2)-2)^2= 4 or x^2=4 or x=-2 or 2

How do I get -6 (another root) which should be there actually...Did I do anything wrong above.

PS: Looked on the forum before but could not find anything so posting it here.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,051
 [6]
Given Kudos: 105,873
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: 109,818
Kudos: 811,051
 [6]
How many roots does the equation || x +2 | - 2 | = 2 have? 15 Mar 2014, 05:50
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
WoundedTiger
Q. How many roots does the equation ||x+2|−2|=2 have?

a. 0
b. 1
c. 2
d. 3
3. 4

I am okay with the solution given for the above problem but I tried solving by solving algebraically and I missed out on one of the roots.

||x+2|−2|=2----->>Can be re-written as

\(\sqrt{({| {|x+2|}−{2}|)^{2}}\) = 2
Squaring both sides we get
(||x+2|−2|)^2 = 4
Now |x+2| is positive so the expression can be written as ((x+2)-2)^2= 4 or x^2=4 or x=-2 or 2

How do I get -6 (another root) which should be there actually...Did I do anything wrong above.

PS: Looked on the forum before but could not find anything so posting it here.
Show more

Yes |x+2| is positive but |x+2| = x+2, only when x>=-2. What you should have done is as follows:

Square: \(||x+2|-2|=2\):

\((x+2)^2-4|x+2|+4=4\);

\(x^2+4x+4-4|x+2|+4=4\);

\(x^2+4x+4=4|x+2|\);

\((x+2)^2=4|x+2|\);

\((x+2)^4=16(x+2)^2\);

\((x+2)^4-16(x+2)^2=0\);

\(((x+2)^2-4(x+2))((x+2)^2+4(x+2))=0\);

\((x^2-4)(x+2)(x+6)=0\);

\(x=2\), \(x=-2\), or \(x=-6\).

Hope it's clear.
User avatar
thorinoakenshield
User avatar
Joined: 03 Jan 2015
Last visit: 28 Mar 2015
Posts: 50
Own Kudos:
120
 [8]
Given Kudos: 223
Concentration: Strategy, Marketing
Schools: Insead July'17 Judge'17 ISB '17 Johnson '17 Oxford'17
WE:Research (Pharmaceuticals and Biotech)
Schools: Insead July'17 Judge'17 ISB '17 Johnson '17 Oxford'17
Posts: 50
Kudos: 120
 [8]
How many roots does the equation || x +2 | - 2 | = 2 have? 30 Jan 2015, 21:04
6
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
||x + 2 |-2| = 2
|x + 2| - 2 = 2 or |x + 2| - 2 = -2
|x+2| = 4 or |x + 2| = 0
x + 2 = 4 or x + 2 = -4 or x + 2 = 0
x = 2 or x = -6 or x = -2

ANSWER: D
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,777
Own Kudos:
13,047
 [5]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,777
Kudos: 13,047
 [5]
How many roots does the equation || x +2 | - 2 | = 2 have? 08 Oct 2015, 10:42
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi All,

Since this equation has an absolute value embedded inside another absolute value, the key to solving it is to work from the "outside" in…

We're given || X +2 | - 2 | = 2

Let's rewrite this as…

||something| - 2| = 2

Taking the "-2" and the "outside" absolute value into account, we need the left "side" of the equation to equal EITHER 2 or -2….

So….

|something| - 2 = 2
|something| - 2 = -2

In the first option, we need |something| to equal 4
In the second option, we need |something| to equal 0

Now we can deal with the inner absolute value….

|X + 2| = 4

This has two solutions: -6 and +2

|X + 2| = 0

This has one solution: -2

Thus, we have 3 solutions/roots.

Final Answer:
Show Spoiler
D

GMAT assassins aren't born, they're made,
Rich
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 24 Apr 2026
Posts: 5,986
Own Kudos:
5,859
 [3]
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,986
Kudos: 5,859
 [3]
How many roots does the equation || x +2 | - 2 | = 2 have? 06 Jun 2020, 23:43
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
prinits
How many roots does the equation || x +2 | - 2 | = 2 have?

A. 0
B. 1
C. 2
D. 3
E. 4

M13-02
Show more

Asked: How many roots does the equation || x +2 | - 2 | = 2 have?

Case 1: |x+ 2| - 2 = 2
|x+2| = 4
x = 2 or -6

Case 2: |x+ 2| - 2 = -2
|x+2| = 0
x = -2

x = {-6,-2,2}; 3 roots

IMO D
User avatar
Rishm
User avatar
Joined: 05 May 2024
Last visit: 24 Apr 2026
Posts: 244
Own Kudos:
22
Given Kudos: 67
Location: India
Schools: Johnson '27 LBS '27 IESE '27
GPA: 10
WE:Consulting (Consulting)
Products:
Forum Quiz
Schools: Johnson '27 LBS '27 IESE '27
Posts: 244
Kudos: 22
How many roots does the equation || x +2 | - 2 | = 2 have? 22 Apr 2026, 14:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I just solved it the simpler method of removing the | and you get two values x=-6 and x=2, moving ahead you also see that there is -2 which also satisfies the equation and it falls under the range -6 and 2. So you see there are 3 values which satisfies the equation.
Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts