BTGmoderatorLU wrote:Source: GMAT Prep

If the drama club and music club are combined, what percent of the combined membership will be 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.

The OA is E

Clearly, neither statement alone is sufficient.
Statements combined:

Case 1: No one is a member of both clubs
Total males = 15+10 = 25.
Total members = 16+20 = 36.
Resulting fraction:
(total males)/(total members) = 25/36.

Case 2: Every male in the music club is also in the drama club, but no females belong to both.
Males in both clubs = 10.
Males in only the drama club = (total males in drama) - (males in both) = 15-10 = 5.
Total males = males in both + males in only drama = 10+5 = 15.
Total members = total music + total drama - males in both = 16 + 20 - 10 = 26.
Resulting fraction:
(total males)/(total members) = 15/26.

Since different fractions are possible, the two statements combined are INSUFFICIENT.

The correct answer is E.

1) 15 are male and 1 female in Drama club. Tells nothing about music club. Not sufficient.
2) 10 are male and 10 female in the Music club. Tells nothing about drama club. Not sufficient.

Combining both;

25 Males out of 36 members; % of male found.
Sufficient.

BTGmoderatorLU wrote:Source: GMAT Prep

If the drama club and music club are combined, what percent of the combined membership will be 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.

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

Now I believe the (1+2) bifurcation viability is trivially seen, hence the answer is (E), indeed.


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

Regards,
Fabio.

We need to know the total sum of drama and music club.
number and total sum of male or female member of both drama and music club

Statement 1
Of the 16 members of the drama club , 15 are male
16 = 100%
$$15=\left(16\cdot\frac{100}{10}\right)=93.9\%=94\%$$
94% are male in the drama club but there is no information about the music club.
Hence statement 1 is INSUFFICIENT.

Statement 2
Of the 20 members in the music club, 10 are male
20 = 100%
$$10=\frac{\left(100\cdot10\right)}{20}=\ 50\%$$
50% are male in the music club but there are no information about members of the drama group.
Hence statement 2 is INSUFFICIENT.

Combining statement 1 and 2 together
Statement 1 gives information about drama club
Statement 2 gives information about the music club

Total combined club = drama + music = 16 + 20 = 36 combined members.
Total combined males =Male in dance club + Male in music club = 15 + 10 = 25 combined male
% of combined members that are male =

$$=\frac{25}{36}\cdot100=\ 69.4\%\ =\ 69\%$$
Both statements combined together are SUFFICIENT.

$$answer\ is\ Option\ B$$