Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and

S = {2, 4, 6, 8, x, y}
x and y are both prime numbers and 0 < x < 40 and 0 < y < 40
I. The maximum possible range of the set is greater than 33.
The biggest prime number < 40 is 37 . To obtain the max possible range either x or y has to be 37
Range = 37-2 = 35
True
II. The median can never be an even number.
S = {2, 4, 6, 8, x, y}
If x and y are prime numbers greater than 8 , then median will be (6+8)/2 = 7
If x and y are 3 and 5 , then set S = {2,3,4,5,6,8} , then median will be = 9/2
If x = 3 , then set S = { 2,3,4,6,8, y} , then median will be = 5
If x = 5 , then set S = { 2,4,5,6,8,y} , then median will be = 11/2
If x = 7 , then set S ={ 2,4,6,7,8,y} , then median will be = 13/2
Median will either be an odd number or a decimal .
True
III. If y = 37, the average of the set will be greater than the median.
S = {2, 4, 6, 8, x, 37}
The average will be least when x is smallest
S = {2, 3, 4, 6, 8, 37}
If x=3 , then average will be 60/6 = 10 and median will be 5 .
The median will be highest when x>8 , median = 7 , now the average will be more than 10 .
True
Answer E