BTGmoderatorDC wrote:S is a set of n consecutive positive integers. Is the mean of the set a positive integer?
(1) the range of S is an even integer
(2) the median of S is a positive integer
Source: Magoosh
$$S\,\,\,:\,\,\,n\,\,{\rm{consec}}{\rm{.}}\,\,{\rm{posit}}{\rm{.}}\,\,{\rm{ints}}\,\,\,\,\,\,\left( { \Rightarrow \,\,\,{\rm{mean}} > 0} \right)$$
$${\rm{mean}}\,\,\mathop = \limits^? \,\,{\rm{int}}\,\,\,\, \Leftrightarrow \,\,\,\,n\,\,\mathop = \limits^? \,\,{\rm{odd}}$$
$$\left( 1 \right)\,\,\max - \min = {\rm{even}}\,\,\,\, \Rightarrow \,\,\,\,n\,\,{\rm{odd}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( 2 \right)\,\,{\rm{mean}}\mathop = \limits^{\left( * \right)} {\rm{median}} = {\mathop{\rm int}} \,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( * \right)\,\,{\rm{finite}}\,\,{\rm{arithmetic}}\,\,{\rm{sequence}}$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
