If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?

(1) The range of set S is less than 9.

(2) The average of x and y is less than the average of set S.


(1) INSUFFICIENT: Statement (1) tells us that the range of S is less than 9. The range of a set is the positive difference between the smallest term and the largest term of the set. In this case, knowing that the range of set S is less than 9, we can answer only MAYBE to the question "Is (x + y) <>

Consider the following two examples:Let x = 7 and y = 7. The range of S is less than 9 and x + y <>

Let x = 10 and y = 10. The range of S is less than 9 and x + y > 18, so we conclude NO.

Because this statement does not allow us to answer definitively Yes or No, it is insufficient.

(2) SUFFICIENT: Statement (2) tells us that the average of x and y is less than the average of the set S. Writing this as an inequality:

(x + y)/2 < (7 + 8 + 9 + 12 + x + y)/6 (x + y)/2 < (36 + x + y)/6 3(x + y) <>

2(x + y) <>

x + y <>

Therefore, statement (2) is SUFFICIENT to determine whether x + y <>