Data Sufficiency

Would someone please explain to me how to do this problem?

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.