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Hey TJ,
Good question - the tricky thing with absolute values is that each has two solutions, so to do them algebraically you have to consider both. As an example, for statement 1:
abs[z] > abs[y]
means either that a positive value of z is greater than a positive value of y or that a negative value of z is less than a negative value of y.
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The pure algebra is tough given that there are so many possibilities, so that's why plugging in numbers can be helpful so that you can make it more tangible. And I know that another of your posts this week mentioned that you felt plugging in numbers was time-consuming, so that's probably something you'll want to work on. For data sufficiency, I personally prefer to use algebra whenever possible, but plug in numbers primarily when:
1) My goal is to "prove insufficiency" by finding numbers that give me two different answers to the main question.
2) I know that a question asks more about the types of numbers (conceptual) than for specific numbers ("calculational") - for example, if the question stem asks "is x < 0", I know that they're asking whether x is negative, and I may just plug in numbers to see if x has to be negative, or if it could be positive or 0.
3) The terms are nebulous (like this one...too many possibilities with absolute variables, inequalities, and multiple variables) and I want to make the problem more concrete.
Practice using numbers to your advantage and I think you'll find it a useful part of your strategic arsenal.
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In this case, plugging in numbers to prove insufficiency, you'll find that, even given both statements, you could have:
x = -1, y = 0, z = -2
abs[-1 -(-2)] = abs [-1 - 0] (1 = 1) ---> NO
x=-1, y = 0, z = 2
abs [-1 -(2)] > abs [-1 - 0] (3 > 2) ----> YES
Therefore, the correct answer is E.
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