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

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

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New post 13 Sep 2018, 08:53
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What is the value of x?

(1) |x + 3| = 3|x - 3|
(2) x > 3
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Re: What is the value of x? (1) |x + 3| = 3|x - 3| (2) x > 3  [#permalink]

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New post 13 Sep 2018, 09:07
divyajoshi12 wrote:
What is the value of x?
1) |x+3|=3|x-3|
2) x>3.

Posted from my mobile device


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.
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Re: What is the value of x? (1) |x + 3| = 3|x - 3| (2) x > 3  [#permalink]

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New post 13 Sep 2018, 12:03
divyajoshi12 wrote:
What is the value of x?
1) |x+3|=3|x-3|
2) x>3.


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

\(? = x\)


\(\left( 1 \right)\,\,\,{\text{dist}}\left( {x, - 3} \right) = 3 \cdot {\text{dist}}\left( {x,3} \right)\)

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.

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

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.
Attachments

13Set18_11z.gif
13Set18_11z.gif [ 5.13 KiB | Viewed 364 times ]


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Re: What is the value of x? (1) |x + 3| = 3|x - 3| (2) x > 3  [#permalink]

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New post 13 Sep 2018, 21:44
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.
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Re: What is the value of x? (1) |x + 3| = 3|x - 3| (2) x > 3  [#permalink]

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New post 14 Sep 2018, 02:36
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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.
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Re: What is the value of x? (1) |x + 3| = 3|x - 3| (2) x > 3 &nbs [#permalink] 14 Sep 2018, 02:36
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