An 850 level question if I ever saw one! Still, there's enough information in the prompt to be able to make sense of this problem. First off, the fact that the question is asking us about the relative values of squares and absolute values is a hint that we will be making all of the variables into a positive number, so the question is testing us on positive and negative properties. The second hint is that z goes from being the largest integer in the first inequality to the smallest part of the inequality in the question. Since we are dealing with integers, squaring z would make it a larger number (unless it were 0), meaning that z doesn't get smaller... all the other numbers must get larger than z^2 if the answer to the question is yes. Finally, with the idea that the question is dealing with positives & negatives and given the inequality z > y > x > w, we can make a chart showing the possible signs of the different variables:
Now rather than thinking about the entire chart, let's just focus on the variables z and y. Which of these five scenarios would allow |y| > z^2? Only when y is negative- scenarios 4 and 5. In those two scenarios, the value of the variables will determine whether the answer to the question is yes, no, or maybe. So our chart looks like:
This is the key to a LOT of 700+ Data Sufficiency questions. Being able to take the question and translate it into something that's workable before even looking at the statements. If one or both statements eliminate scenarios 4 & 5, we will have sufficient information to answer the question.
(1) wx > yz
Using the chart, this statement is never true in scenario 1 (smaller < larger) or 2 (neg < pos), always true in scenario 4 (pos > neg), and may be true in scenario 3 or 5 (pos ? pos). This leaves us with scenarios 3, 4, or 5, which is insufficient information.
(2) zx > wy
Using the chart, this statement is never true in scenario 4 (neg < pos) or 5 (smaller < larger), always true in scenario 1 (larger > smaller) or 2 (pos > neg), and may be true in scenario 3 (neg ? neg). But the key thing is that Statement 2 eliminates the possibility of scenarios 4 or 5 and provides us sufficient information to answer the question- is |w| > x^2 > |y| > z^2 ? No.
The correct answer is B.
Note: Even if any of the variables were zero, this would not change the approach or answer. Instead of (pos > neg) it would be (zero > neg) or (pos > zero).
