$$Statement\ 1=>3\left|x^2-4\right|=y-2$$
Even though the value of x is not definite, the absolute value of |x^2 - 4| will always yield a positive value. $$So,\ y-2\ge0\ and\ y\ge2;\ y\ can\ be\ any\ value\ between\ 2\ and\ infinity.$$
Therefore, there is no definite value. Hence, statement 1 is NOT SUFFICIENT.
Statemet 2 => |3-y| = 11
$$\pm\left(3-y\right)=11$$
3 - y = 11 or - 3 + y = 11
y = -8 or y = 14
The answer is not definite, so, statement 2 is NOT SUFFICIENT.
Combining both statements together =>
$$From\ statement\ 1:\ y\ge2$$
$$From\ statement\ 2:\ y=-8\ or\ 14$$
$$Since\ y\ge2,\ the\ only\ possible\ value\ of\ y=14.$$
Therefore, both statements combined is SUFFICIENT.
Hence, answer = option 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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