Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 30 Mar 2017, 16:09

### 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

# Mod roots PS

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
Followers: 5

Kudos [?]: 769 [0], given: 22

### Show Tags

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 : )

Intern
Joined: 28 Jul 2009
Posts: 4
Schools: HEC Paris, Essec, ESCP Paris, Insead
Followers: 0

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

### Show Tags

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.
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 230

Kudos [?]: 1671 [0], given: 235

### Show Tags

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

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

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 26

Kudos [?]: 451 [0], given: 11

### Show Tags

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!

_________________

Impossible is nothing to God.

Re: Mod roots PS   [#permalink] 20 Dec 2012, 22:19
Similar topics Replies Last post
Similar
Topics:
PS 0 28 Mar 2016, 05:19
Evaluating Mods/Absolute Values Quicker 2 19 Jun 2013, 19:16
5 Solving Mods using diagrams 15 18 Apr 2012, 03:01
16 Inequalities and Roots 24 09 Aug 2011, 12:56
3 How to calculate range of x in inequality equations with MOD 4 11 Jun 2011, 15:43
Display posts from previous: Sort by