following is true

[sanju09]

If x^2 < 9 and &#8722;2 < y < 1, then which of the following is true?

A. x < 3y
B. 3x < 2y
C. 2x > &#8722;3y
D. xy < 6
E. &#8722;xy > 6

[piyush_nitt]

If x^2 < 9 and &#8722;2 < y < 1, then which of the following is true?

A. x < 3y
B. 3x < 2y
C. 2x > &#8722;3y
D. xy < 6
E. &#8722;xy > 6

IMO D

[DanaJ]

One neeeds to analyze what x^2 < 9 actually means: it's that x is between -3 and 3. Now, you can easily eliminate options:
A. counterexample: x = 2 and y = -1
B. counterexample: x = 2 and y = -1
C. counterexample: x = -1 and y = -1
D. in order to eliminate this one, we consider the ends of the possible values for both x and y.
a. we pick the greatest positive values for x and y:
x < 3
y < 1
xy will be smaller than 3 in this case.
b. we pick the smallest possible values for x and y on the negative side:
x < -3
y < -2
xy will indeed be smaller than 6

E. xy < -6 is not valid: consider x = 1 and y = 0.5.

Answer D