BTGmoderatorDC wrote:The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?
(1) The integers are consecutive odd numbers
(2) Of these integers, the greatest is 6 more than the least.
Source: Official Guide
$$\sum\nolimits_{4\,\,{\rm{different}}\,\,{\rm{odds}}} {\,\, = \,\,\,64\,\,\,\,\left( * \right)} $$
$$? = \,\,{\rm{max}}\,\,{\rm{among}}\,\,{\rm{them}}$$
$$\left( 1 \right)\,\,\,{\rm{consecutive}}\,\,{\rm{and}}\,\,{\rm{sum}}\,\,64\,\,\,\left( {{\rm{from}}\,\,\left( * \right)} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{\rm{they}}\,\,{\rm{are}}\,\,{\rm{unique}}!\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{\rm{SUFF}}.\,\,\,\,$$
\[\left( 2 \right)\,\,\,{\text{must}}\,\,{\text{be}}\,\,{\text{consecutive}}\,\,\,\left[ {\,\,\underline {2M - 3} \,\,,\,\,2M - 1\,\,,\,\,2M + 1\,\,,\,\,\underline {2M + 3} \,\,} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,\left( 1 \right)\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{\text{SUFF}}.\,\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
