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Re: a GWD math (6) , which hasn't been discussed [#permalink]
20 Aug 2011, 16:15
Rephrase the question: "\(x = y?\)"
Statement 1: \(x^2 = y^2\) implies that \(|x| = |y|\). In the xy-plane this looks like an X (two lines) straight through the origin with slopes of 1 and -1. For \(xy < 0\) (quadrants II and IV), \(y = -x\). For \(xy > 0\) (quadrants I and III), \(y = x\).
If \(|x| = |y|\), x does not have to equal y, it could equal -y. Insufficient.
Statement 2: \(xy > 0\) means that any point occupies either quadrant I or III. x and y could take on any coordinate in these quadrants, such as (4,3), (1000000000000,1), (-452, -2), or (1,1), (-55,-55) etc. We do not know whether x and y are equal. Insufficient.
Combined: |x| = |y| and xy > 0, so x = y. Sufficient.