Statement 1: x² + y² = 1
Generally:
When a SUM for x and y is given, the greatest possible PRODUCT will be yielded if x=y.
Here, if x=y=√(1/2), then xy = √(1/2) * √(1/2) = √(1/4) = 1/2.
No other combination for x and y will yield a greater product.
Thus, xy ≤ 1/2.
SUFFICIENT.
Statement 2: x² - y² = 1
If x=1 and y=0, then xy = 1*0 = 0, which is less than 1/2.
If x=2 and y=√3, then xy = 2√3, which is greater than 1/2.
INSUFFICIENT.
The correct answer is
A.
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