Quote:
{x, y, 1, 2, 3}
If x and y are positive integers less than 10, what is the median of the list above?
(1) When one number is chosen at random from the list, the probability of selecting a multiple of 2 is less than the probability of selecting a non-prime number
(2) When one number is chosen at random from the list, the probability of selecting a multiple of 3 is greater than the probability of selecting a prime number
Arranging the terms in ascending order, the set can be:
case (i): x & y =1
{1,1,1,2,3} => Median = 1
case (ii): either x or y, or both x,y =2
(a) {1,1,2,2,3} => Median = 2
(b) {1,2,2,2,3} => Median = 2
case (iii): x,y >=3
{1,2,3,x,y} => Median = 3
Statement I: \(P(2n) < P(non-prime)\)
case (i) : \(P(2n) = 1/5 < P(non-prime) = 3/5 \) (1 is non-prime)
=> \(Median = 1\)
case (ii): (a)\( P(2n) = 2/5 = P(non-prime) = 2/5\)
(b) \( = 3/5 > P(non-prime) = 1/\)5
case (iii): Possible Case
e.g:{1,2,3,9,9} => \(P(2n) = 1/5 < P(non-prime) = 3/5\)
=> \(Median = 3\)
Thus Median can be 1 or 3 (case i/iii possible)
NOT SUFFICIENT
Statment II: \( P(3n) > P(prime)\)
case (i): \(P(3n) = 1/5 < P(prime) = 2/5 \) (2,3 are prime)
case (ii) (a) & (ii) (b): \(P(3n) = 1/5 < P(prime) = 2/5 \) or \(3/5\)
case (iii) Possible Case
e.g: {1,2,3,6,6} => \(P(3n) = 3/5 > P(prime) = 2/5\)
=> Median =3 (Only case iii is possible)
SUFFICIENT
Choice; B