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

 It is currently 22 Oct 2018, 11:55

### 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

# If |2x + 5| = |3x − 2|, which of the following is a possible value of

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

### Hide Tags

Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1211
Location: India
WE: Engineering (Other)
If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

Updated on: 21 Nov 2017, 01:24
2
3
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:42) correct 27% (01:37) wrong based on 251 sessions

### HideShow timer Statistics

If |2x + 5| = |3x − 2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

Source: Veritas Prep Mock

_________________

It's the journey that brings us happiness not the destination.

Originally posted by adkikani on 19 Nov 2017, 17:41.
Last edited by Bunuel on 21 Nov 2017, 01:24, edited 1 time in total.
Renamed the topic.
 Veritas Prep GMAT Discount Codes Optimus Prep Discount Codes EMPOWERgmat Discount Codes
CEO
Joined: 12 Sep 2015
Posts: 3028
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

19 Nov 2017, 18:10
Top Contributor
If |2x+5|=|3x−2|, which of the following is a possible value of x?

(a) -7
(b) -195
(c) -35
(d) 35
(e) 5

Source: Veritas Prep Mock

Did you transcribe the question (or answer choices) correctly?

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com

Sign up for our free Question of the Day emails

Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1211
Location: India
WE: Engineering (Other)
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

19 Nov 2017, 18:15
GMATPrepNow

Apologize for the same and corrected.
_________________

It's the journey that brings us happiness not the destination.

Senior Manager
Joined: 31 Jul 2017
Posts: 477
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

19 Nov 2017, 18:35
If |2x+5|=|3x−2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

Source: Veritas Prep Mock

2x+5 = 3x-2
x= 7
2x+5 = -3x+2
x=-3/5
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Math Expert
Joined: 02 Aug 2009
Posts: 6979
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

19 Nov 2017, 18:47
If |2x+5|=|3x−2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

Source: Veritas Prep Mock

Two ways..
Open the MOD..
|2x+5|=|3x-2|....
Square both sides...
$$(2x+5)^2=(3x-2)^2.......4x^2+20x+25=9x^2-12x+4....5x^2-32x-21=0.........(5x+3)(x-7)=0$$..
So x can be -3/5 or 7...

Second is substitution..
x=-3/5..
|2*-3/5+5|=|3*-3/5-2|........|5-6/5|=|-9/5-2|=19/5=19/5... Correct

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Senior SC Moderator
Joined: 22 May 2016
Posts: 2040
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

19 Nov 2017, 18:48
If |2x+5|=|3x−2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

Source: Veritas Prep Mock

After plugging in Answers A and E because the math was quick, and finding neither to be a solution, I took the case approach.
+LHS = +RHS
+LHS = -RHS

|2x+5|=|3x−2|

Case 1:
2x + 5 = 3x - 2
7 = x

Case 2:
2x + 5 = -(3x-2)
2x + 5 = -3x + 2
5x = -3
x = -3/5

_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

19 Nov 2017, 23:38
If |2x+5|=|3x−2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

Source: Veritas Prep Mock

When you open the mod take care to solve for both positive and negative situations i.e $$±$$

Here $$|2x+5|=|3x-2|$$. Now lets decide to open the LHS mod

so we will have $$2x+5=±|3x-2| => 2x+5=|3x-2|$$ and $$2x+5=-|3x-2|$$

Case 1: $$|3x-2|=2x+5$$, again we have a mod so we will have further two cases $$3x-2 =±(2x+5)$$

so $$3x-2=2x+5 => x=7$$

and $$3x-2=-(2x+5) => x= -\frac{3}{5}$$

Case 2: $$-|3x-2|=2x+5$$ or $$|3x-2|=-2x-5$$, again we have a mod so we will have further two cases $$3x-2=±(-2x-5)$$

so $$3x-2=-2x-5 => x=-\frac{3}{5}$$

and $$3x-2 = 2x+5 => x=7$$

So finally we have $$x=7$$ or $$\frac{-3}{5}$$

Hence Option C

Alternatively as Chetan had explained, you can square both sides to remove the mod. the only challenge in this method can be, if the equation is complex then it will lead to further complexity.
Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1211
Location: India
WE: Engineering (Other)
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

20 Nov 2017, 00:12
niks18

Thanks for your explanation. However I really found it a bit intimidating.

Is rahul16singh28 solution technically correct too?

He simply opened LHS modulus to take two cases of positive and negative terms of RHS.
But interestingly he probably assumed that LHS will be always be positive
ie no scope for -2x-5

Let me know your inputs
_________________

It's the journey that brings us happiness not the destination.

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

20 Nov 2017, 01:11
niks18

Thanks for your explanation. However I really found it a bit intimidating.

Is rahul16singh28 solution technically correct too?

He simply opened LHS modulus to take two cases of positive and negative terms of RHS.
But interestingly he probably assumed that LHS will be always be positive
ie no scope for -2x-5

Let me know your inputs

To be fail-safe, in my opinion, when we remove mod we need to consider both positive and negative scenarios for each expression

For this question squaring works best because the equation is linear and has only 1 variable x. Squaring should result in a simple quadratic equation. If the equation had been any other polynomial or had contained more than one variable, then squaring method would have been cumbersome.

Finally, you can always assume two scenarios for variables -

Case 1: if 2x+5>0 or x>-5/2, then |3x-2|=2x+5, solve this to get two values of x that satisfy x>-5/2

Case 2: if 2x+5<0 or x<-5/2, then |3x-2|=-(2x+5).....{because if x<0, then |x|=-x}, solve this to get two values of x that satisfy x<-5/2

then combine the values of x derived from the above two cases.

Would request other experts to chip-in with their thoughts
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8406
Location: Pune, India
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

21 Nov 2017, 01:20
2
If |2x+5|=|3x−2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

Source: Veritas Prep Mock

Method 1:

If I get this question in the test, I would just substitute options in the equation. That's the fastest way.

|2x+5|=|3x−2|
Try the integer values very quickly first. They don't satisfy

|2x + 25/5| = |3x - 10/5|
Now try 3/5, then -3/5.

-3/5 satisfies. Answer (C)

Method 2: |2x+5|=|3x−2|

2 * |x + 5/2| = 3 * |x - 2/3|

____________________ ( - 15/6) _________________________ ( 0 ) ____________ ( 4/6 )_____________________

This is a distance of 19 between them. Twice the distance from -15/6 should be equal to thrice the distance from 4/6.

So the point will be $$\frac{-15}{6} + (\frac{19}{6}*\frac{3}{5})$$

We get $$\frac{-3}{5}$$
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1211
Location: India
WE: Engineering (Other)
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

21 Nov 2017, 01:34
VeritasPrepKarishma

Quote:
Method 1:

If I get this question in the test, I would just substitute options in the equation. That's the fastest way.

|2x+5|=|3x−2|
Try the integer values very quickly first. They don't satisfy

|2x + 25/5| = |3x - 10/5|
Now try 3/5, then -3/5.

-3/5 satisfies. Answer (C)

I believe you also sensed that having 5 in denominator will help you ease the addition/ subtraction of fractions.
Super quick, thanks a ton.

Quote:
Method 2: |2x+5|=|3x−2|

2 * |x + 5/2| = 3 * |x - 2/3|

____________________ ( - 15/6) _________________________ ( 0 ) ____________ ( 4/6 )_____________________

This is a distance of 19 between them. Twice the distance from -15/6 should be equal to thrice the distance from 4/6.

So the point will be $$\frac{-15}{6} + (\frac{19}{6}*\frac{3}{5})$$

We get $$\frac{-3}{5}$$

I totally could not understand method 2. Can you elaborate?
_________________

It's the journey that brings us happiness not the destination.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8406
Location: Pune, India
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

21 Nov 2017, 09:35
1
VeritasPrepKarishma

Quote:
Method 1:

If I get this question in the test, I would just substitute options in the equation. That's the fastest way.

|2x+5|=|3x−2|
Try the integer values very quickly first. They don't satisfy

|2x + 25/5| = |3x - 10/5|
Now try 3/5, then -3/5.

-3/5 satisfies. Answer (C)

I believe you also sensed that having 5 in denominator will help you ease the addition/ subtraction of fractions.
Super quick, thanks a ton.

Quote:
Method 2: |2x+5|=|3x−2|

2 * |x + 5/2| = 3 * |x - 2/3|

____________________ ( - 15/6) _________________________ ( 0 ) ____________ ( 4/6 )_____________________

This is a distance of 19 between them. Twice the distance from -15/6 should be equal to thrice the distance from 4/6.

So the point will be $$\frac{-15}{6} + (\frac{19}{6}*\frac{3}{5})$$

We get $$\frac{-3}{5}$$

I totally could not understand method 2. Can you elaborate?

This post explains you what absolute value is:
http://www.veritasprep.com/blog/2011/01 ... edore-did/
And this one discusses how to use this concept:
https://www.veritasprep.com/blog/2011/0 ... s-part-ii/

In this question, we say that x is a point such that twice its distance from -5/2 is equal to thrice its distance from 2/3.

So x will divide the distance between the two points in the ratio 3:2. Hence, x will be at a distance 3/5th to the right from -15/6.

Does this help?
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

22 Nov 2017, 12:18
1
If |2x + 5| = |3x − 2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

First we can solve for when both 2x+5 and 3x−2 are positive:

|2x + 5| = |3x − 2|

2x + 5 = 3x - 2

-x = -7

x = 7

Next we can solve for when 2x+5 is positive and 3x−2 is negative.

|2x + 5| = |3x − 2|

2x + 5 = -(3x - 2)

2x + 5 = -3x + 2

5x = -3

x = -3/5

_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 30 Apr 2017
Posts: 84
Location: India
GMAT 1: 700 Q47 V39
GPA: 3.4
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of  [#permalink]

### Show Tags

23 Nov 2017, 10:23
niks18 wrote:
niks18

Thanks for your explanation. However I really found it a bit intimidating.

Is rahul16singh28 solution technically correct too?

He simply opened LHS modulus to take two cases of positive and negative terms of RHS.
But interestingly he probably assumed that LHS will be always be positive
ie no scope for -2x-5

Let me know your inputs

To be fail-safe, in my opinion, when we remove mod we need to consider both positive and negative scenarios for each expression

For this question squaring works best because the equation is linear and has only 1 variable x. Squaring should result in a simple quadratic equation. If the equation had been any other polynomial or had contained more than one variable, then squaring method would have been cumbersome.

Finally, you can always assume two scenarios for variables -

Case 1: if 2x+5>0 or x>-5/2, then |3x-2|=2x+5, solve this to get two values of x that satisfy x>-5/2

Case 2: if 2x+5<0 or x<-5/2, then |3x-2|=-(2x+5).....{because if x<0, then |x|=-x}, solve this to get two values of x that satisfy x<-5/2

then combine the values of x derived from the above two cases.

Would request other experts to chip-in with their thoughts

I am not an expert but would like to share my thoughts here.

When we have modulus on both side of the equality (=) sign and when we are trying the cases approach, we only need to consider two cases. First, both sides have same sign. Second, different sign on both sides.

One may try the other two cases as well, but the results will be the same as above.

Hope that helps. Let me know if you want more details.

Cheers,
Kabir
Re: If |2x + 5| = |3x − 2|, which of the following is a possible value of &nbs [#permalink] 23 Nov 2017, 10:23
Display posts from previous: Sort by

# If |2x + 5| = |3x − 2|, which of the following is a possible value of

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

 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®.