Data Sufficiency

What is the value of y?

(1) 3|x^2 - 4| = y - 2

(2) |3 - y| = 11

OA:C

Soln:
1)Statement does not provide a value of y but we know from the expression that y-2 is positive,
as y-2=3|x^2-4|
Insufficient

2)|3-y|=11 gives 2 solutions
y=-8 and y =14
Insufficient

1&2 combined:
we know that y-2 is +ve from stmt 1,therefore y=14 from stmt 2 is correct.C

Statement 2 gives us two values for y(14 and -8) so B and D are ruled out.
Statement 1 would also gives us many values for y, so A is ruled out as well.

From Statement 1, |x^2 - 4| = (y - 2)/3
Since modulus of any quantity always returns a positive number, (y - 2)/3 has to be positive.
From Statement 2, only y = -8 gives a negative value for (y - 2)/3 and hence y = - 8 is not possible.
y = 14 gives a positive value for (y - 2)/3 and thus is the only possible value.

We have a unique answer for y now.
(C) is the answer.