12 jurors must be picked from a pool of n potential jurors. It m of

Question

12 jurors must be picked from a pool of n potential jurors. It m of the potential jurors are rejected by the defense council 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

Archit3110 · Answer

pool size is n
and m are rejected
pool size n-m
total to choose 12
ways to choose 
n-m C 12
#1
(1) If one less potential juror had been rejected, it would be possible to create 13 different juries
when n-m is 13 we get 13 c 12 ; 13 
12c12 ;1

sufficient

#2
n=m+12
n-m=12
12c12 ; 1
sufficient
option D

gmatophobia · Answer

Statement 1

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

n-m+1 C 12 = 13

n - m + 1 = 13

n - m = 12

Hence we have 12 jurors left and we need 12 jurors. They can be selected in 1 way.

Statement 1

n = m + 12

n - m = 12

Hence we have 12 jurors left and we need 12 jurors. They can be selected in 1 way.

Option D

Wai22 · Answer

would you kindly elaborate how you deduced n-m+1 to be 13 from (n-m+1)C(12) =13.... ?

pudu · Answer

How it is possible to take statement 1 like this? there is no information about the size of the jury... then how we can assume each jury contains 1 juro?

HarshavardhanR · Answer

GMAT-Club-Forum-fvq0ea8t.png Harsha

Abhijeet089 · Answer

could you please tell how we take n-m+1 =13 here after we get (n-m+1) C 12 = 13 ?
thank you

HarshavardhanR · Answer

Think: C 12 yields 13? Say, xC12 = 13. - Can x be <12? Nope. Mathematically not possible to select 12 jurors from a number of jurors less than 12. - Can x be 12? Nope. 12C2 = 1, not 13. - Can x be 13? Yes. 13C12 = 13. - Can x be 14? Nope. 14C12 = 14 x 13 / 2 = 91. - Can x be 15? Nope. 15C12 = an even bigger number (455) Observe. x cannot be lesser than 12. As x goes above 13, xC12 keeps increasing beyond 13. The only legit x value is x = 13. x can only be 13. i.e., n-m+1 = 13. Here is another way to figure out that n-m+1 = 13. https://gmatclub.com/forum/download/file.php?id=85733 --- Harsha GMAT-Club-Forum-arptcxe9.png

12 jurors must be picked from a pool of n potential jurors. It m of

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12 jurors must be picked from a pool of n potential jurors. It m of

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