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What is the value of x ?

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What is the value of x ?  [#permalink]

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New post 06 Feb 2019, 07:17
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A
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Question Stats:

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GMATH practice exercise (Quant Class 14)

What is the value of \(x\) ?

\(\left( 1 \right)\,\,\,x > 0\)
\(\left( 2 \right)\,\,\,{8^x} - 12 \cdot {4^x} = 64 \cdot {2^x}\)

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Our high-level "quant" preparation starts here: https://gmath.net

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Re: What is the value of x ?  [#permalink]

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New post 06 Feb 2019, 22:56
Shouldn't answer be c? option 2 is a cubic having 3 roots : -4,0,16. Thus only with point 1 can we narrow down the answer to 4.
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What is the value of x ?  [#permalink]

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New post 06 Feb 2019, 23:14
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Mai20 wrote:
Shouldn't answer be c? option 2 is a cubic having 3 roots : -4,0,16. Thus only with point 1 can we narrow down the answer to 4.


Mai20

It is indeed B,

have a look here

\(2^x * 2^x * 2^x - 2^2 * 3* 2^x = 64 * 2^x\)

take \(2^x\) common from LHS and cancel it

\(2^x * 2^x - 12 * 2^x = 64\)

\(2^x\)(\(2^x\) - 12) = 64

\(2^x\) - 12 =\(2^{6-x}\)

only x = 4 will satisfy the above

\(2^4\) - 12 = \(2^2\)

4 = 4

B
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Re: What is the value of x ?  [#permalink]

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New post 07 Feb 2019, 05:33
fskilnik wrote:
GMATH practice exercise (Quant Class 14)

What is the value of \(x\) ?

\(\left( 1 \right)\,\,\,x > 0\)
\(\left( 2 \right)\,\,\,{8^x} - 12 \cdot {4^x} = 64 \cdot {2^x}\)

\(? = x\)

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


\(\left( 2 \right)\,\,\,{\left( {{2^x}} \right)^3} - 12 \cdot {\left( {{2^x}} \right)^2} - 64 \cdot \left( {{2^x}} \right) = 0\,\,\,\,\,\mathop \Rightarrow \limits^{z\, = \,{2^x}\,\, > \,\,0} \,\,\,\,\,z\left( {{z^2} - 12z - 64} \right) = 0\,\,\,\,\,\left( * \right)\)

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


The correct answer is therefore (B).


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

Regards,
Fabio.
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Our high-level "quant" preparation starts here: https://gmath.net

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Re: What is the value of x ?   [#permalink] 07 Feb 2019, 05:33
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