What is the value of x? (1) |x + 3| = 3|x - 3| (2) x 3

Question

What is the value of x?

(1) |x + 3| = 3|x - 3|
(2) x > 3

souvonik2k · Answer

S1 - |x+3|=3|x-3|
x+3=3x-9
2x=12
x=6
OR
-x-3=3x-9
4x=6
x= \frac{3}{2} 
Insufficient.

S2 - x>3
Insufficient.
Combining both,x=6 Sufficient.
Answer C.

fskilnik · Answer

Let´s solve this nice problem without ANY calculations, shall we?

? = x

\left( 1 ight)\,\,\,{	ext{dist}}\left( {x, - 3} ight) = 3 \cdot {	ext{dist}}\left( {x,3} ight)

In the image attached, I present a GEOMETRIC BIFURCATION that guarantees the insufficiency!

Note that it is easy to "graphically understand" the following:

We have EXACTLY two different real values of x that satisfy (1), one between -3 and 3, and the other greater than 3.

\left( 2 ight)\,\,\,x > 3\,\,\,\left\{ \begin{gathered}
 \,{	ext{Take}}\,\,x = 4 \hfill \
 \,{	ext{Take}}\,\,x = 5 \hfill \ 
\end{gathered} ight.

The insufficiency of statement (2) was asked for Ph.D candidates in Astrophyisics, correct? (Just joking!)

(1+2) Using the fact presented in blue (from statement (1)) and statement (2), we are sure we have a unique answer. Done!

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

KrishnakumarKA1 · Answer

Hi,

Just another point of view to solve this question.

Question: Value of x ?

Statement I is insufficient:

|x + 3| = 3|x - 3|

i.e., |x+3| = |3x - 9|

Since modulus function is a non-negative function, we know that both sides of the equality are positive and we can square on both sides.

(x+3)^2 = (3x - 9)^2

(x+3)^2 – (3x-9)^2 = 0

Using a^2 – b^2 = (a+b)(a-b)

(x+3+3x-9)* (x+3-3x+9) = 0

(4x-6)*(12-2x) = 0

So, x = 3/2 or x = 6

There are two value of x, hence not sufficient.

Statement II is insufficient:

x > 3

Clearly not sufficient.

Together it is sufficient.

x > 3 , so from statement I it has to be x = 6

So the answer is C. Together sufficient.

Hope this helps.

VodkaHelps · Answer

What is the value of x?

(1) |x + 3| = 3|x - 3|
(2) x > 3

In the first condition we will have 2 transition points (-3) and (3) and hence we will have 3 ranges to consider (-inf;-3); [-3;3) and [3;+inf). Hence we will have more than 1 answer for the value of x. Therefore, we can't have a UNIQUE answer. So Insufficient.

Second, condition just gives us x>3 which is not enough to find x.

1) + 2), the 2nd condition gives us the 3rd range which is (3; +inf) and hence we can find 1 unique value.

DavidTutorexamPAL · Answer

The answer is C.  
Logically, both 1) and 2) are insufficient - 2) gives un an infinite range, while 1), being an absolute value question, will have two different solutions. 
Let's try combining: 
We'll simplify the absolute value 1) into two separate equations:
a) x+3=3(x-3) ==> x+3=3x-9 ==> 2x=12 ==> x=6
b) x+3=3(3-x) ==> x+3=9-3x ==> 4x = 6 ==> x=1.5 
using 2), we know that x>3 -  so it can't be 1.5 and must be 6 ! sufficient!

amanvermagmat · Answer

(1) |x+3| = |x-(-3)|. This basically is the distance between x and -3 on the number line. And similarly 
|x-3| is the distance between x and 3 on the number line.

So as per this statement, distance between x and -3 must be three times of the distance between x and 3 on the number line. 
This will happen in two cases: one where x lies between -3 and 3 (but closer to 3) and two where x lies to the right of 3 on the number line. So there will be two answers for x.

Not sufficient.

(2) x > 3 is obviously not sufficient.

Combining the two statements, x can now only lie to the right of 3 on the number line and thus there will be only one unique value of x.

Sufficient.

Hence C answer.

Posted from my mobile device

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What is the value of x? (1) |x + 3| = 3|x - 3| (2) x > 3

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