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# Twelve jurors must be picked from a pool of n potential

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Manager
Joined: 05 Jun 2009
Posts: 87
Twelve jurors must be picked from a pool of n potential  [#permalink]

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20 Sep 2009, 01:32
1
5
00:00

Difficulty:

85% (hard)

Question Stats:

49% (01:30) correct 51% (01:51) wrong based on 263 sessions

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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
Manager
Joined: 11 Sep 2009
Posts: 129

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20 Sep 2009, 14:09
11
4

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
Intern
Joined: 18 Aug 2009
Posts: 12

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20 Sep 2009, 02:54
1
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?
Manager
Joined: 05 Jun 2009
Posts: 87

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20 Sep 2009, 07:24
the answer is D !! .and correction the second part of your explanation if n-m =12 ,so C(n-m,12) =C(12,12)=1 though not required to anwer . So we know that second is suff for answering ,but how is first suff for answering ?
Manager
Joined: 05 Jun 2009
Posts: 87

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22 Sep 2009, 01:02
thats gr8 expanation ,given +1
Intern
Joined: 29 Oct 2013
Posts: 15
Re: Twelve jurors must be picked from a pool of n potential  [#permalink]

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12 Feb 2014, 04:20
We need to find out (n-m)C12 = ?

From Stat 1: (n-m+1)C12 = 13 --> n-m+1 = 13 (nCn-1 = n)
so n-m = 12 --> suff
From Stat 2: n=m+12 --> n-m = 12 --> suff

Ans - D
Intern
Joined: 09 Aug 2014
Posts: 12
Re: Twelve jurors must be picked from a pool of n potential  [#permalink]

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30 Mar 2015, 05:38
AKProdigy87 wrote:

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.

Hi, thank you for the explanation. I still have troubles understanding why the first statement is sufficient. Could you please explain what do you mean by "our understanding of factorials"? I would highly appreciate it!

Thank you!
Senior Manager
Joined: 02 Mar 2012
Posts: 314
Schools: Schulich '16
Re: Twelve jurors must be picked from a pool of n potential  [#permalink]

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29 Jul 2016, 00:11
easy question

we actually need to find (n-m)C12 , or just value of n-m

2)n-m=12.wow this is what we need

1)converting the expression to algebraic form:
n-m+1=13
so n-m =12
suff

D
Intern
Joined: 18 Jul 2018
Posts: 30
Re: Twelve jurors must be picked from a pool of n potential  [#permalink]

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28 Oct 2018, 23:50
1
Can anyone please explain the statement 1 of the given question.I could not understand it.

Posted from my mobile device
Re: Twelve jurors must be picked from a pool of n potential &nbs [#permalink] 28 Oct 2018, 23:50
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