Statement 1:VJesus12 wrote:Is xy < 6?
(1) x < 3 and y < 2.
(2) 1/2 < x < 2/3 and y^2 < 64.
If x=0 and y=0, then xy = 0, so the answer to the question stem is YES.
If x=-10 and y=-10, then xy=100, so the answer to the question stem is NO.
INSUFFICIENT.
Statement 2:
y² < 64 implies that -8 < y < 8.
xy ≥ 6 only if x and y have the SAME SIGN.
Since 1/2 < x < 2/3 implies that x is positive, test positive values for x and y to see whether it's possible that xy ≥ 6.
If x=2/3 and y=8, then xy = 16/3 = 5.33.
Since any positive value for x must be LESS than 2/3 and any positive value for y must be LESS than 8, we know that xy < 5.33.
Thus, xy < 6.
SUFFICIENT.
The correct answer is B.
