A quick glance through all the option, we will see that

option D which is $u + 3v > 0$ is not possible, so might be the answer, however lets look at the remaing option

option A :: $\frac{u}{3} < -v$ - This is possible if we divide by 3 on both sides

Option B:: $\frac{u}{v} > -3$ - This is possible, since -3v > 0 so v < 0

Option C:: $\sqrt{\frac{u}{-v}} < \sqrt{3}$ - It is possible by dividing $\sqrt{-v}$ on both sides

Option E:: $u < -3v$ - It is also possible by squaring on both sides.

** When the GRE writes a root sign, they are indicating a nonnegative root only**