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At a certain high school, there are three sports: baseball,

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by AAPL » Wed Oct 31, 2018 5:51 am

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A

B

C

D

E

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Magoosh

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?

1) 40 athletes play both baseball and football, and 75 play football only and no other sport.
2) 60 athletes play only and no other sport.

OA E.
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by fskilnik@GMATH » Wed Oct 31, 2018 1:39 pm
AAPL wrote:Magoosh

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?

1) 40 athletes play both baseball and football, and 75 play football only and no other sport.
2) 60 athletes play only baseball and no other sport.
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).


Image


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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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