A ballast tank is one-third full when additional ballast is added until it is two-thirds full. The increased amount of liquid in the tank will have the greatest influence on the __________.

Correct Answer: Option D — transverse stability

Adding ballast water to lower double-bottom tanks adds low weight to the vessel, significantly lowering the vertical center of gravity ($KG$) and increasing the transverse metacentric height ($GM$), which has the greatest direct influence on transverse stability.