It is currently 23 Nov 2017, 02:39

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Mod roots PS

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Director
Director
User avatar
Joined: 07 Jun 2004
Posts: 610

Kudos [?]: 952 [0], given: 22

Location: PA
Mod roots PS [#permalink]

Show Tags

New post 24 Jul 2010, 03:46
How many roots does the following equation have?


|| x +2 | - 2 | = 2

can some one explain how to do this algebraically

OA is 3 roots
_________________

If the Q jogged your mind do Kudos me : )

Kudos [?]: 952 [0], given: 22

Intern
Intern
avatar
Joined: 28 Jul 2009
Posts: 4

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

Schools: HEC Paris, Essec, ESCP Paris, Insead
Re: Mod roots PS [#permalink]

Show Tags

New post 24 Jul 2010, 04:26
I think it shud go like this -->

|| x +2 | - 2 | = 2 , from this take off the outermost || sign .
This will result in the following two equations :

|x+2| -2 = 2 -- 1)
and |x+2|- 2 = -2 -- 2)

Now take 1) and solve it as |x+2| = 4
Again take the || off to get
x+2 = 4 ... 3)
and x=2 = -4 ... 4)

Solve 3) to get x = 2 and solve 4) to get x = -6

Also solve 2) to get
|x+2 | = 0 , this gives us x=-2

So u have 3 values --> x= 2, -2, -6 as the 3 roots of the equation.

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

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2756

Kudos [?]: 1912 [0], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: Mod roots PS [#permalink]

Show Tags

New post 24 Jul 2010, 09:30
|| x +2 | - 2 | = 2 two cases are possible

1. | x+2 | = 0 which is only possible when x= -2

2. | x+2 | = 4 => x+2 = 4 or x+2 = -4

=> x = 2 or x = -6
hence total 3 solutions
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Kudos [?]: 1912 [0], given: 235

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 558 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: Mod roots PS [#permalink]

Show Tags

New post 20 Dec 2012, 22:19
rxs0005 wrote:
How many roots does the following equation have?
|| x +2 | - 2 | = 2


Let |x+2| = y...

\(|y-2|=2\)
\(y-2=2\) and \(-y+2=2\)
\(y=4\) and \(y=0\)

y=|x+2|=4
\(|x+2|=4\)
\(x+2=4\) and \(-x-2=4\)
\(x=-2\) and \(x=-6\) 2 Roots!

y=|x+2|=0
What value of x has 0 distance from -2? Only the number itself! 1 Root!

Answer: 3 Roots!
_________________

Impossible is nothing to God.

Kudos [?]: 558 [0], given: 11

Re: Mod roots PS   [#permalink] 20 Dec 2012, 22:19
Display posts from previous: Sort by

Mod roots PS

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.