Statement (1):
x^2 - 9 > 0
Using critical points method for x < 0
x < -3
(You will get the same answer even by plugging-in numbers)
SUFFICIENT

Statement(2):
x^3 + 9 < 0
Plug-in negative values. The inequality does not hold true for -1 and -2. It holds true first when x^3 = - 9.
x = - (9)^1/3
Since (-2)^3 = - 8 and (-3)^3 = - 27, and
-27 < - 9 < - 8,
x is between -2 and -3 and slightly less than - 2.
x = - 2.1 (approx)
Below this value, the statement will always hold true.

x < - 2.1

i.e., x can be less than - 3 or even greater than it (for the values between - 2.1 and - 3).

INSUFFICIENT.

[spoiler](A)[/spoiler] is the answer.

Traps in this problem:
(1)The problem does not mention that x is an integer, so some people will fall into the trap of assuming x as an integer and go with (D)
(2) x is negative. If you don't notice this you will go with (C).

What is the Critical Points method?
Read here:
https://www.beatthegmat.com/critical-poi ... tml#465861