Is the median of set S even?

Your reasoning is not correct. Are you saying that all sets with even mean have even median? What about: {1, 1, 4} --> \(mean=2=even\) and \(median=1=odd\) OR {0.6, 1.2, 4,2, } --> \(mean=2=even\) and \(median=1.2\neq{integer}\).

Is the median of set \(S\) even?

(1) Set \(S\) consists of consecutive odd integers.

The above implies that set \(S\) is evenly spaced. For every evenly spaced set, the mean equals the median. However, we don't have any information about the actual value of the median, making this statement insufficient.

(2) The mean of set \(S\) is even.

On its own, this statement is insufficient.

(1)+(2) From (1), we have that \(mean=median\). From (2), we have that \(mean=even\). Hence, \(mean=median=even\). Sufficient.


Answer: C

Hope it helps.