**Quote:**

At a certain high school, there are three sports: baseball, basketball, and football. Some athletes at this school play two of these three, but no athlete plays in all three. At this school, the ratio of (all baseball players) to (all basketball players) to (all football players) is 15:12:18. How many athletes at this school play baseball?

Statement (1): 40 athletes play both baseball and football, and 75 play football only and no other sport

Statement (2): 60 athletes play only baseball and no other sport

Obs.: my solution is for the "15:12:

18" version, slightly different that the original (first) post presented in this topic. Obviously the reasoning is identical.

Nice example of the

Venn diagrams ("overlapping sets") and the

k technique together!

\(15:12:18 = 5:4:6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{

\,{\rm{Baseball}} = 5k \hfill \cr

\,{\rm{Basketball}} = 4k \hfill \cr

\,{\rm{Football}} = 6k \hfill \cr} \right.\,\,\,\,\,\,\,\left( {k > 0} \right)\)

\(? = 5k\,\)

We go straight to (1+2): a

BIFURCATION will guarantee that the correct answer is (E).

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!