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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] New post 15 Feb 2012, 19:46
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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%
[Reveal] Spoiler: OA
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Re: Of all the players in a professonal baseball league, 1/2 are [#permalink] New post 15 Feb 2012, 21:18
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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] New post 16 Feb 2012, 01:33
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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
Baseball.PNG [ 4.63 KiB | Viewed 1478 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%.

Answer: A.

Hope it helps.
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Re: Of all the players in a professional baseball league, 1/2 [#permalink] New post 23 Oct 2013, 04:47
Fantastisc question, I got into the trap, and picked E.
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Re: Of all the players in a professional baseball league, 1/2 [#permalink] New post 20 Jan 2014, 20:02
Bunuel wrote:
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:
The attachment Baseball.PNG is no longer available
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%.

Answer: A.

Hope it helps.



Hi Bunuel

Please check and correct me if I am wrong.....

As per the matrix diagram 6/6=100%

Ans-A..

Rgds
Prasannjeet
Attachments

Picture1.jpg
Picture1.jpg [ 15.1 KiB | Viewed 548 times ]

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Re: Of all the players in a professional baseball league, 1/2 [#permalink] New post 22 Jan 2014, 00:04
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%



Assume that the total number of players is 100.

1/2 are foreign born, so 50 are foreign born. 75 players are pitchers out of which 1/3 are foreign born. 25 players are foreign born and pitchers. The other 25 who are foreign born are thus not pitchers.

Thus out of 25 non pitchers, 25 are foreign born. Answer: A - 100%
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Re: Of all the players in a professional baseball league, 1/2 [#permalink] New post 22 Jan 2014, 03:20
Let total number of players be 100.

3/4 are pitchers => 75 pitchers + 25 non-pitchers. ---(1)
1/2 are foreign born and include 1/3 of the pitchers. So 50 are foreign born of which 75/3 =25 are pitchers.
Out of 50 foreign born 25 are pitchers and 25 are non-pitchers. ---(2)

There are total 25 non-pitchers from (1)
and 25 foreign born non-pitchers from (2).

so 100% are foreign born non-pitchers. A is the answer.
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Re: Of all the players in a professional baseball league, 1/2   [#permalink] 22 Jan 2014, 03:20
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