w, x, y, and z are integers. If z > y > x > w, is |

[Anaira Mitch]

w, x, y, and z are integers. If z > y > x > w, is |w| > x^2 > |y| > z^2?

(1) wx > yz
(2) zx > wy

Please help with above data sufficiency problem.

[GMATGuruNY]

w, x, y, and z are integers. If z > y > x > w, is |w| > x^2 > |y| > z^2?

(1) wx > yz
(2) zx > wy

Constraint:
Integers w, x, y and z are integers such that w<x<y<z.

Statement 1: wx > yz
Case 1: w=-4, x=-3, y=-2, and z=-1, with the result that wx > yz
Plugging these values into |w| > x^2 > |y| > z^2, we get:
|-4| > (-3)² > |-2| > (-1)²
4 > 9 > 2 > 1.
Since the portion in red is not valid, the answer to the question stem is NO.

Case 1: w=-10, x=-3, y=-2, and z=-1, with the result that wx > yz
Plugging these values into |w| > x^2 > |y| > z^2, we get:
|-10| > (-3)² > |-2| > (-1)²
10 > 9 > 2 > 1.
Since the inequality above is valid, the answer to the question stem is YES.

INSUFFICIENT.

Statement 2: xz > wy
Neither Case 1 nor Case 2 satisfies Statement 2, indicating that it is not possible for all four values to be negative.

The least positive option for y is 1.

Case 3: w=-1, x=0, y=1, and z=2, with the result that xz > wy
Plugging these values into |w| > x^2 > |y| > z^2, we get:
|-1| > 0² > |1| > 2²
1 > 0 > 1 > 2.
Since the portion in red is not valid, the answer to the question stem is NO.

Other options for y:
If y=0, then xz = (negative)(positive) = negative and wy = 0.
As result, xz < wy, violating the constraint in Statement 2 that xz > wy.
If y<0 and z≥0, then xz = (negative)(positive) = negative or xz = 0, while wy = (negative)(negative) = positive.
Either way, xz < wy, violating the constraint in Statement 2 that xz > wy.
Implication:
To satisfy Statement 2, y must be POSITIVE, implying that 0 < y < z.

Is |w| > x² > |y| > z²?
Since 0 < y < z, and y and z are integers, the portion in red cannot be true.
Thus, the answer to the question stem is NO.
SUFFICIENT.

The correct answer is B.