If the mean of set S does not exceed

guerrero wrote:If the mean of set S does not exceed mean of any subset of set S, which of the following must be true about set S?

I. Set S contains only one element

II. All elements in set S are equal

III. The median of set S equals the mean of set S

A)II only
B)III only
C)II and III only
D)I, II, and III
E)none of the three qualities is necessary

OAc

If the mean of set S does not exceed mean of any subset of set S
Another way to phrase this it to say that (the mean of any subset of set S) > (the mean of set S)

Let's think about what that means.
Notice that each single element in set S is a subset of set S.
So, if M = the mean of set S, then we're saying that (every single value in set S) is > M
This means that every element in set S is identical. Otherwise, there would be at least 1 value greater than the mean and 1 value less than the mean.

If every element in set S is identical, then statements II and III must be true.

What about statement I?
This need not be true.
For example, set S could equal {1, 1}

So, the correct answer is C

Cheers,
Brent