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Of all the players in a professional baseball league, 1/2 [#permalink]
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15 Feb 2012, 20:46
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Of all the players in a professional baseball league, 1/2 are foreignborn, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreignborn? 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]
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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: nonforeign born players (2412) 18: pitchers (3/4 are pitchers) 6: foreign born pitchers (incl. 1/3 of pitchers) 12: nonforeign born pitchers (18 total pitchers  6 FB pitchers) THIS IMPLIES ALL NONFOREIGN BORN PLAYERS ARE PITCHERS (since there are only 12 total), and hence, that 100% of nonpitchers are foreign born



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Re: Of all the players in a professional baseball league, 1/2 [#permalink]
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16 Feb 2012, 02:33
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Smita04 wrote: Of all the players in a professional baseball league, 1/2 are foreignborn, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreignborn?
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: formulaefor3overlappingsets69014.html#p729340); 3. Venn diagram (check this: howtodrawavenndiagramforproblems98036.html); 4. Doubleset 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 plugin method. For example, for this problem I'd use doubleset matrix method along with plugin 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 3544 times ]
Question asks: what percentage of the players who are not pitchers are foreignborn? 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]
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23 Oct 2013, 05:47
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]
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20 Jan 2014, 21:02
Bunuel wrote: Smita04 wrote: Of all the players in a professional baseball league, 1/2 are foreignborn, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreignborn?
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: formulaefor3overlappingsets69014.html#p729340); 3. Venn diagram (check this: howtodrawavenndiagramforproblems98036.html); 4. Doubleset 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 plugin method. For example, for this problem I'd use doubleset matrix method along with plugin 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 foreignborn? 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% AnsA.. Rgds Prasannjeet
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Re: Of all the players in a professional baseball league, 1/2 [#permalink]
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22 Jan 2014, 01:04
Smita04 wrote: Of all the players in a professional baseball league, 1/2 are foreignborn, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreignborn?
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]
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22 Jan 2014, 04:20
Let total number of players be 100. 3/4 are pitchers => 75 pitchers + 25 nonpitchers. (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 nonpitchers. (2) There are total 25 nonpitchers from (1) and 25 foreign born nonpitchers from (2). so 100% are foreign born nonpitchers. A is the answer.
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