Let's check each options:-

(A) \(4^{(-2b)} = 4^{(-a)}\); a=2b, we can't conclude from here. DISCARD

(B) \(-4^b < 4^a\) or,\(4^a+4^b>0\);we can't conclude from here. DISCARD

(C) \(4^{(-b)} < 4^{(-a)}\) Or, \(4^b>4^a\) or, \(4^{b-a}>4^0\) or, b-a>0 or, b>a . This is our ANSWER.

Ans. (C)
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Regards,

PKN

Rise above the storm, you will find the sunshine

\(?\,\,\,\,:\,\,\,\,a\,\, < \,\,\,b\)

\(\left( {a,b} \right) = \left( {0,0} \right)\,\,{\text{satisfies}}\,\,\left( A \right),\left( B \right)\,\,{\text{and}}\,\,\left( E \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{they}}\,\,{\text{are}}\,\,{\text{out}}!\)

\(\left( {a,b} \right) = \left( {1,0} \right)\,\,{\text{satisfies}}\,\,\left( D \right)\,\,\,\,\, \Rightarrow \,\,\,{\text{out}}!\)


Alternative choice (C) is the only survivor, therefore it must be the right answer.


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

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net