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What is the value of (2^x + 2^x)/2^y ?

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What is the value of (2^x + 2^x)/2^y ?

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What is the value of (2^x + 2^x)/2^y ?

(1) x - y = 8
(2) x/y = -3

OA A

Source: Manhattan Prep

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BTGmoderatorDC wrote:
What is the value of (2^x + 2^x)/2^y ?

(1) x - y = 8
(2) x/y = -3

OA A

Source: Manhattan Prep
(2^x + 2^x)/2^y = 2*2^x /2^y = 2^(x - 1)/2^y = 2^(x - y +1)

If we get the value of x and y or (x - y), we get the answer.

Let's take each statement one by one.

(1) x - y = 8

Sufficient. We have the value of x - y.

(2) x/y = -3

Can't get the unique values of x and y. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorDC wrote:
What is the value of (2^x + 2^x)/2^y ?

(1) x - y = 8
(2) x/y = -3
Source: Manhattan Prep
$$? = {{2 \cdot {2^x}} \over {{2^y}}} = {2^{\left( {x + 1} \right) - y}} = {2^{x - y + 1}}$$
$$\left( 1 \right)\,\,x - y = 8\,\,\,\, \Rightarrow \,\,\,\,? = {2^{8 + 1}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,{x \over y} = - 3\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {3, - 1} \right)\,\,\,\, \Rightarrow \,\,\,\, ? = {2^5} \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( { - 3,1} \right)\,\,\,\, \Rightarrow \,\,\,\, ? = {2^{ - 3}} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$

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

Regards,
Fabio.

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