Bunuel wrote:

Is A positive?

(1) A^6 < A

(2) A^5 < A

\(A\,\,\mathop > \limits^? \,\,0\)

\(\left( 1 \right)\,\,\underline {{A^6} < A}\)

\(\left. \begin{gathered}

A = 0\,\,\,\, \Rightarrow \,\,\,0 = \underline {{A^6} < A} = 0\,\,\,\, \Rightarrow \,\,\,{\text{impossible}}\,\,\,\, \hfill \\

A < 0\,\,\,\, \Rightarrow \,\,\,0 < \underline {{A^6} < A} < 0\,\,\,\, \Rightarrow \,\,\,{\text{impossible}} \hfill \\

\end{gathered} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle\)

\(\left( 2 \right)\,{A^5} < A\,\,\,\left\{ \begin{gathered}

\,Take\,\,A = \frac{1}{2}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\, \hfill \\

Take\,\,A = - 2\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\

\end{gathered} \right.\,\,\)

The above follows the notations and rationale taught in the GMATH method.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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