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20 Sep 2009, 02:32
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
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Question Stats:
58% (01:52) correct
42%
(02:12)
wrong
based on 489
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Twelve jurors must be picked from a pool of n potential jurors .If m of the potential jurors are rejected by the defense counsel and the prosecuting attorney ,how many different possible juries could be picked from the remaining potential jurors?
(1) If one less potential juror had been rejected, it would be possible to create 13 different juries.
(2) n = m + 12
(1) If one less potential juror had been rejected, it would be possible to create 13 different juries.
(2) n = m + 12
20 Sep 2009, 15:09
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The answer is D.
Essentially, there is an (n-m) pool of jurors to select a group of 12 from. As a result, the number of possible juries is equivalent to \(_{(n-m)}C_{12}\), or:
\(\frac{(n-m)!}{12!*(n-m-12)!}\)
For simplicity's sake, let's set X = n - m (the pool of jurors available after processing by the defense counsel). As a result the number of possible juries is equivalent to:
\(\frac{X!}{12!*(X-12)!}\)
Statement 1: If one less potential juror had been rejected ,it would be possible to create 13 different juries:
As a result, X increases to X + 1:
\(\frac{(X+1)!}{12!*(X+1-12)!} = 13\)
\(\frac{(X+1)!}{12!*(X-11)!} = 13\)
\(\frac{(X+1)!}{(X-11)!} = 13*12!\)
\(\frac{(X+1)!}{(X-11)!} = 13!\)
\((X+1)*(X)*(X-1)*...*(X-10) = 13!\)
Therefore, by using our understanding of factorials, we can determine X (or n-m) to be 12. The answer to the original question then becomes 1, and Statement 1 is proven to be sufficient.
Statement 2: n=m+12:
Rearranging the equation sets n-m = 12, which is enough to show that the answer to the original question is 1 possible jury, and Statement 2 also proves to be sufficient.
Therefore, both statements are sufficieint by themselves, and the answer is D.
Essentially, there is an (n-m) pool of jurors to select a group of 12 from. As a result, the number of possible juries is equivalent to \(_{(n-m)}C_{12}\), or:
\(\frac{(n-m)!}{12!*(n-m-12)!}\)
For simplicity's sake, let's set X = n - m (the pool of jurors available after processing by the defense counsel). As a result the number of possible juries is equivalent to:
\(\frac{X!}{12!*(X-12)!}\)
Statement 1: If one less potential juror had been rejected ,it would be possible to create 13 different juries:
As a result, X increases to X + 1:
\(\frac{(X+1)!}{12!*(X+1-12)!} = 13\)
\(\frac{(X+1)!}{12!*(X-11)!} = 13\)
\(\frac{(X+1)!}{(X-11)!} = 13*12!\)
\(\frac{(X+1)!}{(X-11)!} = 13!\)
\((X+1)*(X)*(X-1)*...*(X-10) = 13!\)
Therefore, by using our understanding of factorials, we can determine X (or n-m) to be 12. The answer to the original question then becomes 1, and Statement 1 is proven to be sufficient.
Statement 2: n=m+12:
Rearranging the equation sets n-m = 12, which is enough to show that the answer to the original question is 1 possible jury, and Statement 2 also proves to be sufficient.
Therefore, both statements are sufficieint by themselves, and the answer is D.
General Discussion
20 Sep 2009, 03:54
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The question essentially asks how many different juries of 12 jurors can be picked out of a pool of (n-m) jurors.
Statement 1 - Using the combinatinon formula - (n-m+1) C 12= 13
Even by expanding the equation, you still have 2 unknowns, n and m. Even if you know that the ultimate combination is 13 juries, the statement is insufficient.
Statement 2 - This means n-m=12, which should immediately tell you that this is sufficient as you now know that you need to find how many different juries of 12 can be picked from a pool of 12 jurors. Using the logic that you can arrange n number of items in n! ways, the answer is 12!
Statement 2 is sufficient.
IMO it's B. What is the answer?
Statement 1 - Using the combinatinon formula - (n-m+1) C 12= 13
Even by expanding the equation, you still have 2 unknowns, n and m. Even if you know that the ultimate combination is 13 juries, the statement is insufficient.
Statement 2 - This means n-m=12, which should immediately tell you that this is sufficient as you now know that you need to find how many different juries of 12 can be picked from a pool of 12 jurors. Using the logic that you can arrange n number of items in n! ways, the answer is 12!
Statement 2 is sufficient.
IMO it's B. What is the answer?
