Data Sufficiency

I will solve the question first and you can then leave your questions if you are still not happy.

Q) K is a set of numbers such that if x is in K, then -x is in K, and if each of x and y is in K, then xy is in K.

Is 12 in K?

(1) 2 is in K

If 2 is in K, -2 is in K
If 2 and -2 are in K then -4(xy) is in K.
If -4 is in K, 4 is in K
If -4 and 2 are in K then -8(xy) is in K and so on.
For the integer 12 to be in the set, there should be a 3(3*4 = xy, since you already know that there is an integer 4) in the set or a -12(if X(-12)is present -X(12) is also present) in the set or the integer 12 itself or few other cases.
Since we don't have a definitive answer to the question, statement I is insufficient to answer the question.

(2) 3 is in K

If 3 is in K, -3 is in K
If 3 and -3 are in K then -9(xy) is in K.
If -9 is in K, 9 is in K
If -9 and 3 are in K then -8(xy) is in K and so on.
For the integer 12 to be in the set, there should be a 4(3*4 = xy, since you already know that there is an integer 3) in the set or a -12(if X(-12)is present -X(12) is also present) in the set or the integer 12 itself or few other cases.
Since we don't have a definitive answer to the question, statement II is insufficient to answer the question.

From I + II

2 is in K and 3 is in K
If 2 is in K, then -2(-X) is in K
If 2 and -2 are in K, then -4(XY) is in K
If -4 is in K, then 4(-X) is in K
If 3 and 4 are in K, then 12(XY) is in K.
So, we are sure that the integer 12 is present in the set K.

Answer C

I don't understand why statement (1) and (2) aren't sufficient since they both show 12 not being in the set.

Answer) 2 is in K, doesn't mean that 12 isn't in K. Similarly, it also doesn't mean that 12 is in K.