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Statement 1 is sufficient. Any number squared will be positive. If z^2 is less than 4, the absolute value of Z must be less than 2. Therefore - 2<z<2
Statement 2 is insufficient. Z can be any number. For instance, Z=3 or - 3, z^2=9. Alternatively, z =1, z^2 =1. Both satisfy the equation , but don't tell us if Z is in the desired range.
Statement 1. z^2 < 4 implies that: -2 < z < 2 This statement directly answers the question with YES. So Sufficient.
Statement 2. z^2 > -4. All squares are either 0 or positive. So no matter what the value of z, its square will be > -4. This doesn't answer whether -2 < z < 2 or not. So Insufficient.
Simplifying the inequality in statement one, we have:
√z^2 < √4
z < 2
or
-z < 2
z > -2
Thus, -2 < z < 2, so statement one is sufficient to answer the question.
Statement Two Alone:
z^2 > −4
The information in statement two is not sufficient to answer the question. The square of every real number is non-negative and therefore greater than -4; so, statement two is satisfied by every real number. Thus, z could be any real number. Statement two alone is not sufficient to answer the question.