Data Sufficiency

lheiannie07 wrote: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

Is statement 1 sufficient? Why?

OA D

The number of potential jurors left from which 12 jurors to be picked = n - m

Thus, the different possible juries could be picked from the remaining potential jurors = (n - m)C12; where n - m ≥ 12

If we get the value of n - m, we get the answer.

(1) If one less potential juror had been rejected, it would be possible to create 13 different juries.

=> The number of potential jurors had been rejected = n - m +1

Thus, the different possible juries could be picked from the remaining potential jurors = (n - m + 1)C12 = 13

Since 13 is a prime number, we can do a hit and trial. Say n - m + 1 = 13, thus, (n - m + 1)C12 = 13C12 = 13C1 = 13; note that nCr = nC(n - r)

n - m + 1 cannot be 14 or greater since if n - m + 1 were 14, then 14C12 = 14C2 = (14.13)/(1.2) = 98 ≠ 13.

At higher values of n - m + 1 than 14, we would move further away from 13. So n - m + 1 =13. Thus n - m = 12.

Thus, the different possible juries could be picked from the remaining potential jurors = (n - m)C12 = 12C12 = 12C0 = 1. Sufficient,

(2) n = m + 12

=> n - m = 12. This renders the same result as does the Statement 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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