BTGmoderatorDC wrote:If the drama club and music club is combined, what percent of the combined membership is male?

(1) Of the 16 members of the drama club, 15 are male.

(2) Of the 20 members of the music club, 10 are male.
Source: GMAT Prep

$$? = {{\# \,{\rm{drama}}\,{\rm{males}}\,\,\, + \,\,\,\# \,{\rm{music}}\,{\rm{males}}\,\,\, - \,\,\,\# \left( {\,{\rm{drama}}\,{\rm{and}}\,{\rm{music}}\,\,\,{\rm{males}}} \right)} \over {\# \,{\rm{drama}}\,\,\, + \,\,\,\# \,{\rm{music}}\,\,\, - \,\,\,\# \left( {\,{\rm{drama}}\,{\rm{and}}\,{\rm{music}}} \right)}}$$

$$\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,\# \,{\rm{drama}}\,\, = \,\,16\,\,\,\,,\,\,\,\,\# \,\,{\rm{drama}}\,{\rm{males}}\,\,{\rm{ = 15}} \hfill \cr
\,\# \,{\rm{music}}\,\,{\rm{ = }}\,\,{\rm{20}}\,\,\,\,,\,\,\,\,\# \,\,{\rm{music}}\,{\rm{males}}\,\,{\rm{ = 10}} \hfill \cr} \right.$$

$$? = {{15\,\, + \,\,10\,\, - \,\,\# \left( {\,{\rm{drama}}\,{\rm{and}}\,{\rm{music}}\,\,\,{\rm{males}}} \right)} \over {16\,\, + \,\,20\,\, - \,\,\# \left( {\,{\rm{drama}}\,{\rm{and}}\,{\rm{music}}} \right)}}$$

Now the bifurcation viability is trivially seen, hence the answer is (E), for sure.

In explicit details:

Scenario 1: no one is in both drama and music club.
In this case our FOCUS would get the value 25/36

Scenario 2: there is just one person, a male, who is in both drama and music club.
In this case our FOCUS would get the value 24/25 , hence different from 25/36.


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.