Bunuel wrote:

Official Solution:

(1) No number in set A is less than the average (arithmetic mean) of set A.

Since no number is less than the average, then no number is more than the average, which implies that the list contains identical elements: \(A=\{x, \ x, \ x, \ ...\}\). From this it follows that (the average)=(the median). But we don't know the value of \(x\), thus this statement is NOT sufficient.

(2) The average (arithmetic mean) of set A is equal to the range of set A.

Not sufficient: if \(A=\{0, \ 0, \ 0, \ 0\}\), then (the median)=0, but if \(A=\{1, \ 2, \ 2, \ 3\}\), then (the median)=2.

(1)+(2) From (1) we have that the list contains identical elements. The range of all such sets is 0. Therefore, from (2) we have that (the average)=(the range)=0 and since from (1) we also know that (the average)=(the median), then (the median)=0. Sufficient.

Answer: C

Hi Bunuel

How can you derive the highlighted part above? (i.e. then no number is more than the average) - I think this is possible

Eg A= { 2 } - Here, Median = Mean = 2

A = { 2, 2, 2, 3} - Here, Median = 2, Mean = 2.25 ..... What Im trying to say is that we can have a number > Mean

Either ways, I agree that this is Insufficient.

Pls clarify my doubt

Thanks