Choice 1 is not clear from your post.
But nevertheless since we need to solve for y and there is another variable x choice 1 is not sufficient.

Choice 2
|3 - y| = 11 has two equations

3-y = 11 and
3 -y = -11
This gives two values for y -8 and 14
Hence 2 is not sufficient either

Together they are not sufficient either.
So answer is E.

Sorry for not writing it clearly.

Choice 1 should be this: (1) 3|x^2 – 4| = y – 2

So from choice (1), you can tell that y>2. Since 3|x^2 – 4| must be positive.


So if you combine what this with what you wrote for (2), you get C.


Thanks for your help!

There is no special way for this question.
As Bourne told there is nothing to do with statement 1 alone given there is x and nothing simplifies.
Statement 2
Result is either -8 or 11

With statement 1 and 2 you need to chose a positive one number so it's 11