For the given set n = {3, 6, 4, 6, 5, p}, is p > 2?

\(n = \left\{ { - 6, - 4,3,5,6} \right\} \cup \left\{ p \right\}\)

\(p\,\,\mathop > \limits^? \,\,2\)

\(\left( 1 \right)\,\,Me{d_n} > 2\,\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,p = 3\,\,\,\, \Rightarrow \,\,\,n = \left\{ { - 6, - 4,3,3,5,6} \right\}\,\,\,\,\left( {Me{d_n} = 3} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,p = 2\,\,\,\, \Rightarrow \,\,\,n = \left\{ { - 6, - 4,2,3,5,6} \right\}\,\,\,\,\left( {Me{d_n} = 2.5} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.\)

\(\left( 2 \right)\,\,\,Me{d_n}\,\, = \,\,\,\left\{ \matrix{\\
\,{{p + 3} \over 2} > 0\,\,\,{\rm{if}}\,\,2 < p \le 5\, \hfill \cr \\
\,{{3 + 5} \over 2} > 0\,\,\,{\rm{if}}\,\,\,p > 5 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( 2 \right)\,\,{\rm{contradicted}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,p > 2\,\,{\rm{is}}\,\,{\rm{false}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\)


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

Regards,
Fabio.