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

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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

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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]

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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)
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PKN

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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  D
Joined: 18 Jun 2018
Posts: 267
Re: If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

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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
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Re: If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

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

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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
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