If x + y = k, where k is a constant, then the greatest possible value of xy occurs when x=y.
Example: x + y = 10
If x=5 and y=5, then xy = 25.
If x=4 and y=6, then xy = 24.
If x=3 and y=7, then xy = 21.
As the distance between x and y INCREASES, the product of x and y DECREASES.
Thus, the greatest possible value of xy occurs when x=y=5.
vipulgoyal wrote:22. Is xy < 1?
(1) x + y = 1
(2) x^2 + y^2 = 1
Statement 1: x + y = 1
Here, the greatest possible value of xy occurs when x = y = 1/2:
xy = (1/2)(1/2) = 1/4.
Thus, xy < 1.
SUFFICIENT.
Statement 2: x² + y² = 1
Here, the greatest possible value of x²y² occurs when x² = y² = 1/2:
x²y² = (1/2)(1/2)
(xy)² = (1/2)²
xy = 1/2.
Thus, xy < 1.
SUFFICIENT.
The correct answer is
D.
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