$$Statement\ 1:\ 3\left|x^2-4\right|=y-2$$
Make y the subject of the formula
$$y=\ 3\left|x^2-4\right|+2$$
$$x^2-4\ is\ a\ quadratic\ equation\ that\ is\ equal\ to\ 0.\ $$
S, x, being in a modulus can be positive or negative but y will always be positive.
$$So,\ y\ge2$$
This only tells that y is positive but it doesn't provide the exact value of y, so, statement 1 is NOT SUFFICIENT.
$$Statement\ 2:\ \left|3-y\right|=11$$
$$\pm\left(3-y\right)=11$$
For the positive, y = 14; for the negative y=-8.
Since the answer is not definite, statement 2 is NOT SUFFICIENT.
Combining both statements together
$$From\ statement\ 1:\ y\ge2$$
Statement 2: y = -8 or y = 14
Since y is positive, then the value of y=14; both statements together are SUFFICIENT.
ANSWER = C
What is the value of \(y?\)
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Source: Beat The GMAT — Data Sufficiency |
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deloitte247
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