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 [ 5.13 KiB | Viewed 364 times ]

_________________

Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)

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