GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Oct 2018, 11:04

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

What is the value of x? |x+2|+|x−3|=|2x+3|

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

Hide Tags

Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1381
Location: Viet Nam
GMAT ToolKit User Premium Member
What is the value of x: |x+2|+|x-3| = |2x+3|?  [#permalink]

Show Tags

New post 29 Nov 2016, 03:52
1
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:29) correct 20% (01:36) wrong based on 231 sessions

HideShow timer Statistics

Most Helpful Community Reply
Intern
Intern
avatar
B
Joined: 28 May 2017
Posts: 26
Location: India
GMAT 1: 750 Q50 V42
GPA: 3.03
WE: Management Consulting (Consulting)
Re: What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

Show Tags

New post 25 Oct 2017, 07:33
4
3
div10 wrote:
What is the value of x?
|x+2|+|x−3|=|2x+3|

A. -5
B. -2
C. 1
D. 4
E. 7


The ideal way to get the answer is by solving for different ranges of x. The above equation will take 4 different forms for the following ranges:
1. Greater than 3
2. From -1.5 to 3
3. From -2 to -1.5
4. Less than -2

Solving for each range separately, only one range gives a valid answer, which is 1.

A much easier way to solve this - substitute the options!

Hope this helps!




Sent from my iPhone using GMAT Club Forum mobile app
General Discussion
Intern
Intern
avatar
Joined: 24 Apr 2016
Posts: 3
Location: India
GMAT ToolKit User
Re: What is the value of x: |x+2|+|x-3| = |2x+3|?  [#permalink]

Show Tags

New post 29 Nov 2016, 04:27
C

Simply substitute the options

Sent from my ONE A2003 using GMAT Club Forum mobile app
Manager
Manager
User avatar
S
Joined: 25 Mar 2013
Posts: 248
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
GMAT ToolKit User Reviews Badge
Re: What is the value of x: |x+2|+|x-3| = |2x+3|?  [#permalink]

Show Tags

New post 08 Jan 2017, 14:57
On substituting options
3+2 = 5
C
But on removing bar and considering two cases could not match with options
Case 1 and 2
( x + 2 ) + ( x-3) = 2x + 3
2x - 1 = 2x + 3
2x - 2x = 4
?
Can anyone explain. Thanks
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2033
Premium Member CAT Tests
What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

Show Tags

New post 25 Oct 2017, 10:10
1
2
div10 wrote:
What is the value of x?
|x+2|+|x−3|=|2x+3|

A. -5
B. -2
C. 1
D. 4
E. 7

Using the answer choices is the fastest.

If you do not know how to use critical values and intervals, see this post, below, with links to excellent material on complex absolute value questions.
_________________

The only thing more dangerous than ignorance is arrogance.
-- Albert Einstein

Intern
Intern
avatar
B
Joined: 14 Jul 2017
Posts: 15
Re: What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

Show Tags

New post 06 Jan 2018, 12:47
@genxer123 Can you explain how you go 1 in case 4?? isn't

Case 4
|x+2|+|x−3|=|2x+3|

−x−2−x+3=−2x−3
-2x+1 = -2x-3
1=-3

which is invalid???
PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1218
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

Show Tags

New post 06 Jan 2018, 13:02
1
RashmiT wrote:
@genxer123 Can you explain how you go 1 in case 4?? isn't

Case 4
|x+2|+|x−3|=|2x+3|

−x−2−x+3=−2x−3
-2x+1 = -2x-3
1=-3

which is invalid???


Hi RashmiT

Yes you are correct in your observation. Case 4 by generis is incorrect.

This question is best solved through options. if you go for any other approach then you will have to work through multiple ranges.
Another option to remove mod is to square both sides but it will result in a complex polynomial equation.
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2033
Premium Member CAT Tests
What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

Show Tags

New post 06 Jan 2018, 13:59
1
RashmiT wrote:
@genxer123 Can you explain how you go 1 in case 4?? isn't

Case 4
|x+2|+|x−3|=|2x+3|

−x−2−x+3=−2x−3
-2x+1 = -2x-3
1=-3

which is invalid???

RashmiT , you are correct.
My brain clearly was not working well. :dazed :?
Nice catch, +1, thank you, and my apologies.

With two absolute value terms in an equation, you can open mods.

With more than two mods?

If, as here, the answers are before you, use them.

If answers are not before you, use

"Critical Method" see chetan2u, Absolute Modulus, A Better Understanding

and Bunuel , "3-steps approach for complex problems," Absolute Value Modulus, 3-steps approach

And "Graphical Method," chetan2u , Absolute Modulus, A Better Understanding

(You probably know what to do when there are more than two absolute value expressions. I post these links just in case you might need them, but mostly to help people who have not seen the excellent posts to which the links refer.)
_________________

The only thing more dangerous than ignorance is arrogance.
-- Albert Einstein

GMAT Club Bot
What is the value of x? |x+2|+|x−3|=|2x+3| &nbs [#permalink] 06 Jan 2018, 13:59
Display posts from previous: Sort by

What is the value of x? |x+2|+|x−3|=|2x+3|

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.