What is the value of (2^x + 2^x)/2^y ?
(1) x - y = 8
(2) x/y = -3
OA A
Source: Manhattan Prep
What is the value of (2^x + 2^x)/2^y ?
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(2^x + 2^x)/2^y = 2*2^x /2^y = 2^(x - 1)/2^y = 2^(x - y +1)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
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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$$? = {{2 \cdot {2^x}} \over {{2^y}}} = {2^{\left( {x + 1} \right) - y}} = {2^{x - y + 1}}$$BTGmoderatorDC wrote:What is the value of (2^x + 2^x)/2^y ?
(1) x - y = 8
(2) x/y = -3
Source: Manhattan Prep
$$\left( 1 \right)\,\,x - y = 8\,\,\,\, \Rightarrow \,\,\,\,? = {2^{8 + 1}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,{x \over y} = - 3\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {3, - 1} \right)\,\,\,\, \Rightarrow \,\,\,\, ? = {2^5} \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( { - 3,1} \right)\,\,\,\, \Rightarrow \,\,\,\, ? = {2^{ - 3}} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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