Statement 1: |(z-2)²| > 4Vincen wrote:Is z > 2?
1) |(z-2)^2| > 4
2) |8x - 4k| = z, where x , k are variables
Since the square of a value cannot be negative, the expression in blue represents a NONNEGATIVE value:
(z-2)² ≥ 0.
As a result, the absolute values here have no effect: the left side of the inequality will be nonnegative even if the absolute value symbols are removed, as follows:
(z-2)² > 4.
The inequality in red will hold true if z-2 > 2 or if z-2 < -2.
Case 1: z-2 > 2, implying that z>4
In this case, the answer to the question stem is YES.
Case 2: z-2 < -2, implying that z<0
In this case, the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statement 2: |8x - 4k| = z
Since an absolute value cannot be negative, |8x - 4k| ≥ 0.
Since z = |8x - 4k| and |8x - 4k| ≥ 0, we get:
z ≥ 0.
Since it's possible that 0≤z≤2 or that z>2, INSUFFICIENT.
Statements combined:
Of the two cases that satisfy Statement 1, only Case 1 satisfies the constraint in Statement 2 that z≥0.
In Case 1, z>4.
Thus, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is C.
