Okay, quick way to the answer. 1/2 of the volume of the cork is submerged in water. Now in mercury, which is *13 times as dense* as water, how much is submerged? Well, realize that how much of the object is submerged depends on the density of the object relative to the liquid it's floating in. Say the density is like 0.7 g/mL (the math doesn't necessarily work out - I just made up a number). You know that it will float in water because it is less dense than 1.0 g/mL. Now put it in something that's 13 times as dense, or 13.0 g/mL. Okay, now the differential is even larger! So if it floats okay in water, it will float amazingly well in the denser liquid!

Now look at the answer choices. If it will float very well, very little of it will be submerged. So that rules out B and C. D can then be ruled out because it's only a little smaller than 1/2 - you can't have a 13-fold change in density of the liquid and only a minute difference in submersion.