What is the value of y?
(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11
Statement 1: 3|x^2 - 4| = y - 2
No way to determine the value of y.
INSUFFICIENT.
Statement 2: |3 - y| = 11
Case 1: 3-y = 11
-y = 8
y = -8.
Case 2: -3+y = 11
y = 14.
Since it's possible that y=-8 or y=14, INSUFFICIENT.
Statements combined:
If y=-8 in statement 1, we get:
3|x^2 - 4| = -8 - 2
|x^2 - 4| = -10/3.
Not possible: an absolute value expression cannot be equal to a negative value.
Thus, the only value that satisfies both statements is y=14.
SUFFICIENT.
The correct answer is
C.
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