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10 Sep 2013, 15:39
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:45) correct
37%
(02:28)
wrong
based on 558
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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 15:12:8. 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
For a discussion of ratios & proportions on the GMAT, further practice problems, and a solution of this problem, see:
https://magoosh.com/gmat/2013/gmat-quant ... oportions/
Mike
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
For a discussion of ratios & proportions on the GMAT, further practice problems, and a solution of this problem, see:
https://magoosh.com/gmat/2013/gmat-quant ... oportions/
Mike
10 Sep 2013, 21:57
Kudos
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Given, ratio of Base B: Basket B: Foot B = 15:12:8 and non of them play all three games.
Each form of game will have players who plays only that game and two games.
((Only Base B)+(Base B+Basket B)+(Base B+Foot B)) : ((Only Basket B)+(Basket B+Base B)+(Basket B+Foot B)) : ((Only Foot B)+(Foot B+Base B)+(Foot B+Basket B)) = 15:12:8
1) ((Only Base B)+(Base B+Basket B)+ 40 ) : ( 75 + 40 +(Foot B+Basket B)) = 15:8
from the provided information, we can't deduct the total number of base ball players. Hence, insufficient.(Options A and D can be eliminated)
2) from the provided information, we can't deduct the total number of base ball players. Hence, insufficient. (Option B can be eliminated)
Both 1 & 2 : (60 +(Base B+Basket B)+ 40 ) : ( 75 + 40 +(Foot B+Basket B)) = 15:8
From the provided information, we still can't deduct the total number of base ball players. Hence, insufficient. (Option C also can be eliminated)
Hence the answer is
/SW
Each form of game will have players who plays only that game and two games.
((Only Base B)+(Base B+Basket B)+(Base B+Foot B)) : ((Only Basket B)+(Basket B+Base B)+(Basket B+Foot B)) : ((Only Foot B)+(Foot B+Base B)+(Foot B+Basket B)) = 15:12:8
1) ((Only Base B)+(Base B+Basket B)+ 40 ) : ( 75 + 40 +(Foot B+Basket B)) = 15:8
from the provided information, we can't deduct the total number of base ball players. Hence, insufficient.(Options A and D can be eliminated)
2) from the provided information, we can't deduct the total number of base ball players. Hence, insufficient. (Option B can be eliminated)
Both 1 & 2 : (60 +(Base B+Basket B)+ 40 ) : ( 75 + 40 +(Foot B+Basket B)) = 15:8
From the provided information, we still can't deduct the total number of base ball players. Hence, insufficient. (Option C also can be eliminated)
Hence the answer is
/SW
31 Oct 2018, 14:47
Kudos
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Quote:
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.
