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

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4487
At a certain high school, there are three sports: baseball,  [#permalink]

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10 Sep 2013, 15:39
3
10
00:00

Difficulty:

85% (hard)

Question Stats:

55% (02:42) correct 45% (02:32) wrong based on 278 sessions

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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:
http://magoosh.com/gmat/2013/gmat-quant ... oportions/

Mike

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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Re: At a certain high school, there are three sports: baseball,  [#permalink]

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10 Sep 2013, 21:57
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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.

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)

/SW
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
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At a certain high school, there are three sports: baseball,  [#permalink]

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31 Oct 2018, 14:47
1
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.
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At a certain high school, there are three sports: baseball,   [#permalink] 31 Oct 2018, 14:47
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