Is xy < 1? (1) x + y = 1 (2) x^2 + y^2 = 1

Yes. The property you are referring to is: for given sum of two numbers, their product is maximized when they are equal.

Hope it helps.

Questions about this concept:
if-x-2-y-2-100-and-x-0-and-y-0-the-maximum-value-of-x-147064.html
if-the-population-of-city-a-is-increased-by-a-in-year-130222.html
the-discreet-charm-of-the-ds-126962-20.html#p1039634
is-x-2-y-108343.html
maxmize-an-ear-of-a-right-triangle-128319.html

Maybe another approach which is a bit visual:

F.S 1:Imagine the straight line on the x-y axis : Omitting the x/y intercepts where anyways the value of xy = 0 ,any point on the line in the 2nd quadrant will always have the sign of (x,y) as (-,+)--> The product xy<0 and hence xy<1. Similarly for any point on the line in the 4th quadrant, where (x,y) will always be (+,-) and xy<1. For any point on the line in the first quadrant except (1,0) or (0,1), 0<x<1 and 0<y<1 --> 0<xy<1. Sufficient.

F.S 2:Similarly, for the circle, the same analogy for different sign of (x,y) would be in place for the 2nd and 4th quadrant. IN the 1st and 3rd quadrant,for the reason given above, the value of xy can never be greater than 1 as they are individually less than 1.Sufficient.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.