Problem related to semiconductor?
Either this question is poorly phrased, or there is additional information related to it.

We know that increasing the voltage will increase the current through both the conductor and the semiconductor, therefore the question here is: which of the currents will increase more?

We know that the conductor's current increases linearly with voltage, but what behavior will semiconductor show?

This is the point where we can't say anything without additional information:

1) Are metal-semiconductor contacts ohmic or rectifying?

2) Is semiconductor intrinsic or extrinsic (is it doped)?

3) Should we consider second order effects (like conductivity change due to heating, mobility degradation under heavy bias, etc.)?

Assuming that there is no additional information provided with the question, I would guess that the contacts are ohmic and their resistance may be neglected, the semiconductor bulk is intrinsic and we should not consider second order effects. In this case, since the current is equal for the same bias, the resistances of semiconductor and conductor are equal, and the current-voltage characteristics will be the same, and the correct answer will be C.