Data Sufficiency

amirhakimi wrote:What is the value of y?

(1) 3|x² - 4| = y - 2
(2) |3 - y| = 11

Target question: What is the value of y?

Statement 1: 3|x² - 4| = y - 2
Tons of possible values for y. Here are two cases:
Case a: x = 0, in which case y = 14
Case b: x = 1, in which case y = 11
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |3 - y| = 11
If |something| = k (where k > 0), then something = k, or something = -k

So, we get two possible equations:
3 - y = 11, in which case y = -8
3 - y = -11, in which case y = 14
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that y equals EITHER -8 OR 14
Statement 1 tells us that 3|x² - 4| = y - 2
Since absolute values are always greater than or equal to 0, we know that y - 2 > 0
This means that y >2
If y >2, then we can rule out the possibility that y = -8, which means y MUST equal 14

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent