Bunuel wrote:
Is 10m > 5n - k?
(1) n = 2m
(2) |k| = -k
\(10m\,\,\mathop > \limits^? \,\,5n - k\)
\(\left( 1 \right)\,\,\,n = 2m\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\,\left( {n,m,k} \right) = \left( {0,0,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\, \hfill \cr
\,{\rm{Take}}\,\,\,\left( {n,m,k} \right) = \left( {2,1,1} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\, \hfill \cr} \right.\,\)
\(\left( 2 \right)\,\,\,\,\left| k \right| = - k\,\,\,\, \Leftrightarrow \,\,\,\,k \le 0\)
\(\left\{ \matrix{
\,{\rm{Take}}\,\,\,\left( {n,m,k} \right) = \left( {0,0,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\, \hfill \cr
\,{\rm{Take}}\,\,\,\left( {n,m,k} \right) = \left( {0,1, - 1} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\, \hfill \cr} \right.\)
\(\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
10m\,\,\mathop > \limits^? \,\,5\left( {2m} \right) - k\,\,\,\,\, \Leftrightarrow \,\,\,\,k\,\,\mathop > \limits^? \,\,0 \hfill \cr
k \le 0 \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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Fabio Skilnik ::
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