1) Sufficient If the sum is the same but the average for S is smaller, there must be more terms in S. Think if numerator is the same (average = sum/#terms), then the denominator must be larger for the average to be smaller.

2) The median has no relationship to the number of items in a set.

Statement 1:
This statement talks about the mean or the average of S

Mean = Sum/No. of terms
So we can easily say that Mean is inversely proportional to No. of terms.
Here we are given that the sum is same for both S and T.

So by the proportionality, we can find out the relation between the number of terms and have a definite YES or a definite NO as the answer to statement 1.

Statement 2:
The information about median does not gives us any data point to conclude about number of items.

Hence the correct answer is A

NOTE: I did not solve for statement 1 fully. Because I came to know that an answer can be found out.
On the DS questions, you just have to figure out a definite YES or a definite NO as the answer.
If it can be obtained, no need to solve further as you are not asked to solve. This can save considerable amount of time on the GMAT.

In Statement 1 - Principle of this question Mean * Number of Elements = Sum of Elements
SUFFICIENT.

Statement 2 - NOT SUFFICIENT.
There is no relation of Median with number of elements.

Answer is A