CSASHISHPANDAY wrote:What is the value of y?
(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11
Ans C
Somehow I can reach on right ans but want to know that in choice (1) how one can say that
absolute value expression |x^2 - 4| must be greater than or equal to 0.
|a-b| = the DISTANCE between a and b.
Thus, |x²-4| = the distance between x² and 4.
The distance between two values must be NONNEGATIVE.
Thus, |x²-4| ≥ 0.
Statement 1: 3|x^2 - 4| = y - 2
|x²-4| = (y-2)/3.
Since |x²-4| ≥ 0, it must also be true that (y-2)/3 ≥ 0.
Thus:
(y-2)/3 ≥ 0
y-2 ≥ 0
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:
Only y=14 satisfies both statements.
SUFFICIENT.
The correct answer is
C.
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