If the average (arithmetic mean)...

From the original, we know that the sum of the numbers is 120. However, we don't know anything about the individual terms.

(1) all terms are < 60

Well, we could have {27, 28, 29, 36) or {27, 28, 32, 33}, so we can get more than 1 answer: insufficient.

(2) 9, 10 are in the set

Well, we could have {9, 10, 50, 51} or {9, 10, 11, 90}, so we can get more than 1 answer: insufficient.

Together:

From (2), we know that the sum of the 2 missing terms is 120-19 = 101.

If all terms are < 60, and the last two terms sum to 101, then even if we make 1 term as big as possible (59.9999), the 2nd term will still be > 30.

Therefore, with both statements, we know that exactly 2 of the 4 terms will be greater than 30: sufficient, choose (C).

The answer should be (C).

Given: Sum of the four numbers = 4 * 30 = 120

(1) is not sufficient.
Choosing 31,31,31, 27 gives 3 numbers.
Choosing 59,59,1,1 gives 2 numbers

(2) is not sufficient.
120 - (9+10) = 101.
Choosing 100, 1 gives one number greater than 30
Choosing 31,70 gives two numbers.

Combining (1) and (2) gives 120 - (9+10+X+Y). X,Y has to be greater than since X <=60 and Y <=60.