BTGmoderatorLU wrote:Source: Manhattan Prep
A sports team played 100 games last season. Did this team win at least half of the games it played last season?
1) The team won 60% of its first 65 games last season.
2) The team won 60% of its last 65 games last season.
$$\# \,{\rm{wins}}\,\,\,\mathop \ge \limits^? \,\,\,50$$
$$\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,39\,\,{\rm{wins}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{first}}\,65\,\,{\rm{games}}\,\,\,\,\left( {1{\rm{st}}\,\,{\rm{till}}\,\,65{\rm{th}}} \right) \hfill \cr
\,39\,\,{\rm{wins}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{last}}\,65\,\,{\rm{games}}\,\,\left( {36{\rm{th}}\,{\rm{till}}\,\,100{\rm{th}}} \right) \hfill \cr} \right.$$
$${\rm{If}}\,\,{\rm{wins}}\,\,{\rm{games}}\,\,\# \,\,\left\{ \matrix{
\,1,2,3, \ldots ,39\,{\rm{and}}\,\,62,63, \ldots ,100\,\,\,\,\,:\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\left( {78\,\,{\rm{games}}} \right) \hfill \cr
\,27,28, \ldots ,65\,\,{\rm{and}}\,\,36, \ldots ,74\,\,\, = \,\,\,27, \ldots ,74\,\,\,\,\,:\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\left( {48\,\,{\rm{games}}} \right) \hfill \cr} \right.$$
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
