Is the median of set S even?

1. Set S is composed of consecutive odd integers

2. The mean of set S is even

Oa is

I think there is some problem with OA here.

Using only statement II we can solve this Q as follows:

Assuming

I. the set as {2,4,6} -------statement II required

Mean = 4 , even

Median = 4 even

II. Set as {2,4,6,8}

Mean = 5

Median = 5

III. Set {1,3,5,7} -------statement II required

Mean = 4

Median = 4

Hence we do not require the info provided in statement I and we can solve with statemetn II only. Can anybody comment on this ?

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 \(median=1.2\neq{integer}\).

(1) Set S is composed of consecutive odd integers --> set S is evenly spaced --> for every evenly spaced set \(mean=median\). But still insufficient.

(2) The mean of set S is even. Insufficient as shown above.

(1)+(2) From 1: \(mean=median\) and from 2: \(mean=even\) --> \(mean=median=even\). Sufficient.

Answer: C.