Dear krodin,

I'm happy to respond. This is a tricky one. If z were not mentioned in the first "if" statement, then the question would have a very different answer.

In statement #1, we find out that \(|x|=y\). Naively, this would leave two choices for (x, y), either x = y or x = -y. We might think that x = y is one possibility, but notice that this would make the numerator of the ratio zero, which means the ratio would equal zero, and the conditional statement at the very beginning of the question makes very clear that z cannot equal zero. Therefore, we cannot have x = y. The only possibility from this statement is that x = -y or -x = y. Then

z = (x-y)/(2x+y)
z = [x - (-x)]/[2x + (-x)]
z = (x + x)/(2x - x)
z = (2x)/(x) = 2

This statement leads directly to a numerical answer for z. This statement, alone and by itself, is sufficient.

Statement #2, by itself, tells us about x but not about y. This statement, alone and by itself, is insufficient.

Answer = (A)

Does this make sense?
Mike
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Thumbs up if you forgot that z is non-zero))

perse it looked easy..oh god...this was really tricky....mike can we get problems like this in actual GMAT...if yes, what would be the level?
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Dear Balajikarthick1990,

I'm happy to respond. I like your avatar with the picture of Srinivasa Ramanujam: he was one of the greatest mathematical geniuses of all time and I have tremendous respect for him.

Could you get a problem such as this on the GMAT? Yes. You see, all of math depends on precision, precision in the details. This applies to how one handles the numbers, but it also applies to each word of the text of the problem. In this problem, a very important detail was expressed verbally, in way that would usually convey only general conditions that most students tend to ignore. Never take anything for granted. Always be looking for any detail that can make a difference.

You see, sometimes in the business world, in a legal or contractual document, there could be one little detail that changes everything, perhaps even in the most unexpected place. The astute business man does not miss these details. That's why the GMAT would test detail management to this degree.

Hard to say the level of this. Many students are conscientious and pay attention to details, so I would estimate that a large percentage would get this right. This is not among the hardest questions on the test: in fact, when one notices the pertinent detail, the question is relatively straightforward.

Does all this make sense?
Mike
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Absolutely mike...I am from his place...Ramanujam serves as a gr8 source of inspiration to me especially for solving GMAT problems
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