It's a trick question. The question creates doubt because it asks you to choose between two wrong options. [Edit: no, it gives all three possibilities; I speed-

It's a trick question. The question creates doubt because it asks you to choose between two wrong options. [Edit: no, it gives all three possibilities; I speed-read through that. Thanks to others for pointing that out. However it then does predominantly focus on the question of "up or down?", which isn't the right question.] Ice is lower density than water, which is why it floats. As the ice melts, the runoff from the above-surface ice will raise the water level -- but the shrinkage from the below-surface ice will lower the water level. Assuming the above-surface and below-surface ice melts at the same rate, the water level will remain unchanged. (Note that if this were a glass of hot water in a cold room, then you'd get non-uniform heating of the ice. The subsurface ice would melt first, causing the level of the water to lower, until the above-surface ice melted, at which point the water level would return to its original level. On the other hand, a glass of cold water in a hot room would initially overflow while the above-surface ice melted, and then its water level would lower when the subsurface ice melted. So the answer to the original question is, depending on context, either "neither" or "both".)