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What is the value of x ?

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Source: — Data Sufficiency |
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by fskilnik@GMATH » Thu Feb 07, 2019 5:19 am

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fskilnik@GMATH wrote:Image

GMATH practice exercise (Quant Class 14)
$$? = x$$

$$\left( 1 \right)\,\,\,x > 0\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,? = 1 \hfill \cr
\,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,? = 2 \hfill \cr} \right.$$

$$\left( 2 \right)\,\,\,{\left( {{2^x}} \right)^3} - 12 \cdot {\left( {{2^x}} \right)^2} - 64 \cdot \left( {{2^x}} \right) = 0\,\,\,\,\,\mathop \Rightarrow \limits^{z\, = \,{2^x}\,\, > \,\,0} \,\,\,\,\,z\left( {{z^2} - 12z - 64} \right) = 0\,\,\,\,\,\left( * \right)$$
$$\left( * \right)\,\,\,\, \Rightarrow \,\,\,z\left( {z - 16} \right)\left( {z + 4} \right) = 0\,\,\,\,\,\mathop \Rightarrow \limits^{z\, > \,0} \,\,\,\,\,z = 16\,\,\,\,\, \Rightarrow \,\,\,\,\,{2^x} = 16\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$


The correct answer is therefore (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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