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# Of all the players in a professional baseball league, 1/2

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Of all the players in a professional baseball league, 1/2 [#permalink]  15 Feb 2012, 20:46
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Of all the players in a professional baseball league, 1/2 are foreign-born, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreign-born?

A) 100%
B) 75%
C) 66 2/3%
D) 50%
E) 25%
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Re: Of all the players in a professonal baseball league, 1/2 are [#permalink]  15 Feb 2012, 22:18
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I assigned numbers to figure this one out:

24: total number of players
12: foreign born players (1/2 foreign born)
12: non-foreign born players (24-12)
18: pitchers (3/4 are pitchers)
6: foreign born pitchers (incl. 1/3 of pitchers)
12: non-foreign born pitchers (18 total pitchers - 6 FB pitchers) -THIS IMPLIES ALL NON-FOREIGN BORN PLAYERS ARE PITCHERS (since there are only 12 total), and hence, that 100% of non-pitchers are foreign born
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Re: Of all the players in a professional baseball league, 1/2 [#permalink]  16 Feb 2012, 02:33
Smita04 wrote:
Of all the players in a professional baseball league, 1/2 are foreign-born, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreign-born?

A. 100%
B. 75%
C. 66 2/3%
D. 50%
E. 25%

There are 4 main approaches to solve overlapping sets problem:
1. Pure logic and simple math;
2. Direct formulas (check the following link for the formulas of 3 overlapping sets: formulae-for-3-overlapping-sets-69014.html#p729340);
3. Venn diagram (check this: how-to-draw-a-venn-diagram-for-problems-98036.html);
4. Double-set matrix.

It depends on the problem, as well as on one's personal preferences to pick which approach to apply to some particular problem.

Also notice that when there are some percents and ratios involved, it's almost always a good idea for plug-in method.

For example, for this problem I'd use double-set matrix method along with plug-in method. Pick some smart number for total players, so that all subsets will be integers: as there are 1/2, 1/3 and 3/4 involved pick 12 (the lowest common denominator). Next, fill the matrix step by step:
Attachment:

Baseball.PNG [ 4.63 KiB | Viewed 595 times ]
Question asks: what percentage of the players who are not pitchers are foreign-born? So basically we need the ratio of yellow cells, which is 3/3=1, so the answer is 100%.

Hope it helps.
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Re: Of all the players in a professional baseball league, 1/2   [#permalink] 16 Feb 2012, 02:33
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