Twelve jurors must be picked from a pool of n potential

Question

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

AKProdigy87 · Accepted Answer

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 .

ssy84 · Answer

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?

sacmanitin · Answer

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 ?

sacmanitin · Answer

thats gr8 expanation ,given +1

syamen · Answer

We need to find out (n-m) C 12 = ?

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

Ans - D

IonutCZ · Answer

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!

hsbinfy · Answer

easy question

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

lets start with statement 2
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

Srija221 · Answer

Can anyone please explain the statement 1 of the given question.I could not understand it.

Posted from my mobile device

ScottTargetTestPrep · Answer

Statement One Alone:

If one fewer potential juror were rejected, it would be possible to create 13 different juries.

From statement one, we can create the equation:

(n - m + 1)C12 = 13

And we need to determine the value of (n - m)C12.

Since 13 is a prime number, the only way that (n - m + 1)C12 = 13 is if n - m + 1 = 13 (notice that 13C12 = 13). So we have n - m = 12 and thus (n - m)C12 = 12C12 = 1. Statement one alone is sufficient.

Statement Two Alone: 
n = m + 12

If n = m + 12 and if m jurors did not show up, then only n - m = 12 jurors showed up. The number of ways to choose 12 jurors from 12 jurors is 12C12 = 1. Statement two alone is sufficient.

Answer: D

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Twelve jurors must be picked from a pool of n potential

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Twelve jurors must be picked from a pool of n potential

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards