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

 It is currently 13 Oct 2019, 16:40

### 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

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

Author Message
TAGS:

### Hide Tags

Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1333
Location: Viet Nam
What is the value of x: |x+2|+|x-3| = |2x+3|?  [#permalink]

### Show Tags

29 Nov 2016, 03:52
2
1
7
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:35) correct 25% (01:39) wrong based on 265 sessions

### HideShow timer Statistics

What is the value of x?

\(|x+2|+|x-3| = |2x+3|\)

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

_________________
Current Student
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

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
Joined: 24 Apr 2016
Posts: 3
Location: India
Re: What is the value of x: |x+2|+|x-3| = |2x+3|?  [#permalink]

### Show Tags

29 Nov 2016, 04:27
C

Simply substitute the options

Sent from my ONE A2003 using GMAT Club Forum mobile app
Manager
Joined: 25 Mar 2013
Posts: 226
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: What is the value of x: |x+2|+|x-3| = |2x+3|?  [#permalink]

### Show Tags

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
Joined: 22 May 2016
Posts: 3536
What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

### Show Tags

25 Oct 2017, 10:10
1
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

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.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Intern
Joined: 14 Jul 2017
Posts: 25
Re: What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

### Show Tags

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???
Retired Moderator
Joined: 25 Feb 2013
Posts: 1182
Location: India
GPA: 3.82
Re: What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

### Show Tags

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
Joined: 22 May 2016
Posts: 3536
What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

### Show Tags

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.
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.)
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Manager
Joined: 25 Mar 2018
Posts: 72
Location: India
Schools: ISB '21, IIMA , IIMB
GMAT 1: 650 Q50 V28
GPA: 4
WE: Analyst (Manufacturing)
What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

### Show Tags

08 Jun 2019, 23:03
broall wrote:
What is the value of x?

\(|x+2|+|x-3| = |2x+3|\)

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

This is a very simple question should be solved in 1 min or else you can complete Quant session. You just write down the equation and start substituting values. Never ever think of solving by taking "x" greater than 3 , then x greater than -1.5, then x greater than -2.

So we start substituting ,

A . becomes 11 = 8 x is not equal to -5

B. Become 5 = 1. Not satisfies.

C. 5 = 5. So x =1 . Done.
_________________
Please give me +1 kudos if my post helps you a little. It will help me unlock tests. Thanks
Manager
Joined: 07 May 2018
Posts: 61
Re: What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

### Show Tags

16 Jun 2019, 18:54
parmeshwarsharma wrote:
C

Simply substitute the options

Sent from my ONE A2003 using GMAT Club Forum mobile app

Hi,

Manager
Joined: 07 May 2018
Posts: 61
Re: What is the value of x? |x+2|+|x−3|=|2x+3|  [#permalink]

### Show Tags

16 Jun 2019, 18:55
broall wrote:
What is the value of x?

\(|x+2|+|x-3| = |2x+3|\)

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

Re: What is the value of x? |x+2|+|x−3|=|2x+3|   [#permalink] 16 Jun 2019, 18:55
Display posts from previous: Sort by