Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 09:54

### 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 |12x − 3| = |3x + 15|, what is the value of x?

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56275
If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

### Show Tags

10 Aug 2018, 03:47
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:55) correct 41% (01:49) wrong based on 101 sessions

### HideShow timer Statistics

If |12x − 3| = |3x + 15|, what is the value of x?

(1) x > 0
(2) x is an integer

_________________
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

### Show Tags

Updated on: 10 Aug 2018, 05:18
Bunuel wrote:
If |12x − 3| = |3x + 15|, what is the value of x?

(1) x > 0
(2) x is an integer

Given, |12x − 3| = |3x + 15|
Squaring both the sides,
$$(12x-3)^2=(3x+15)^2$$
Or, $$144x^2-72x+9=9x^2+90x+225$$
Or, $$135x^2-162x-216=0$$
or, $$x=-\frac{4}{5}\quad \mathrm{or}\quad \:x=2$$

Another way, 12x-3=3x+15 Or, x=2
and 12x-3=-(3x+15) or, x=-$$\frac{4}{5}$$
St1:- x > 0
Only acceptable value is 2.
Sufficient.

St2:- x is an integer
Only acceptable value is 2.
Sufficient.

Ans. (D)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine

Originally posted by PKN on 10 Aug 2018, 04:48.
Last edited by PKN on 10 Aug 2018, 05:18, edited 1 time in total.
Senior Manager
Joined: 18 Jun 2018
Posts: 267
Re: If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

### Show Tags

10 Aug 2018, 05:14
Bunuel wrote:
If |12x − 3| = |3x + 15|, what is the value of x?

(1) x > 0
(2) x is an integer

OA:D
If |12x − 3| = |3x + 15|, what is the value of x?

Case 1 :$$x<\frac{-15}{3}$$ or $$x<-5$$
$$-(12x-3)=-(3x+15)$$
$$9x=18, x = \frac{18}{9} = 2$$
Not possible as $$x<-5$$ whereas $$2>-5$$

Case 2 :$$-5≤x≤\frac{3}{12}$$

$$-(12x-3)=(3x+15)$$

$$15x=-12, x = \frac{-12}{15} = -\frac{{4}}{5}$$

Case 3: $$x>\frac{3}{12}$$

$$(12x-3)=(3x+15)$$
$$9x=18, x = \frac{18}{9} = 2$$

What is value of $$x$$? Given $$x=-\frac{4}{5}$$ or $$x= 2$$

Statement 1 : $$x>0$$

Out of $$-\frac{4}{5},2$$; Only 2 is greater than 0
So $$x=2$$
Statement 1 alone is sufficient

Statement 2 : $$x$$ is an integer
Out of $$-\frac{4}{5},2$$; Only 2 is integer
So $$x=2$$
Statement 2 alone is sufficient
Retired Moderator
Joined: 30 Jan 2015
Posts: 805
Location: India
Concentration: Operations, Marketing
GPA: 3.5
Re: If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

### Show Tags

10 Aug 2018, 05:15
Bunuel wrote:
If |12x − 3| = |3x + 15|, what is the value of x?

|12x − 3| = |3x + 15|
Case 1:
12x − 3 = 3x + 15
9x = 18
x = 2

Case 2:
12x − 3 = -3x - 15
15x = -12
x = -12/15

Therefore x = 2 or -12/15

(1) x > 0
Which means it has to be 2 and not -12/15
Sufficient

(2) x is an integer
Which means it has to be 2 and not -12/15
Sufficient

Hence, D.
_________________
The few, the fearless !

Thanks
Intern
Joined: 02 Mar 2017
Posts: 16
GMAT 1: 680 Q44 V38
Re: If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

### Show Tags

19 Apr 2019, 00:17
1
Bunuel wrote:
If |12x − 3| = |3x + 15|, what is the value of x?

(1) x > 0
(2) x is an integer

|x| = \sqrt{x}

|12x-3| = |3x+15|
\sqrt{12x-3}=\sqrt{3x+15}
squaring both sides
(12x-3)^2=(3x+15)^2 ---> (12x-3)^2 - (3x+15)^2 = 0
(12x-3+3x+15)(12x-3-3x-15)=0
x=-12/15 or x= 2

Statement 1: sufficient since x can only be 2
Statement 2: sufficient since x can only be 2

Re: If |12x − 3| = |3x + 15|, what is the value of x?   [#permalink] 19 Apr 2019, 00:17
Display posts from previous: Sort by

# If |12x − 3| = |3x + 15|, what is the value of x?

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

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