I would go for A, because if the median and average are equal then of of the numbers has to equal to x. and question stem and st1 can only be true if fifth number is x. hence yes the average of 5 number will aslo be x.

for st 2
we can say yes all the five numbers are equal otherwisse not.We cannot be sure if all are equal

ketkoag wrote:A set has 5 numbers and the average of 4 of them is x. Is the average of the 5 numbers x also?
1) The median of the 5 numbers is x.
2) The fifth number is same to one of the 4 numbers.

[spoiler]IMO : E please confirm the answer.[/spoiler]

consider x, x+1, x+2, x-3, average is x

Statement 1: median is x, therefore at max we can say that fifth number would be less than or equal to x

as in x-3,x-1,x,x+1,x+2 median x but average not x
or x-3,x,x,x+1,x+2 median x and average also x Insufficient

Statement 2: if 5th number is same as one of the numbers

x-3,x,x,x+1,x+2 average x
x-3,x-3,x,x+1,x+2 average not x Insufficient

Combining 1 and 2

as we can see from the following sequences, they are following st 1 and st 2

x-3,x,x,x+1,x+2 average x
x-3,x-1,x,x+1,x+2 average not x Insufficient

hence E