Final answer:
Damage to the olives of the medulla oblongata typically results in difficulty with balance and coordination. This is related to the role of the olives in providing sensory input to the cerebellum and their involvement in motor coordination processes.
Step-by-step explanation:
The olives of the medulla oblongata are structures that are significant for their role in motor coordination and balance. Damage to these structures can result in various neurological symptoms. The superior olivary complex, for example, is involved in the ability to localize sound, and the medial and inferior olives work closely with the cerebellum, aiding in the regulation of body movements and coordination. When considering the options provided, damage to the olives would typically manifest as difficulty with balance and coordination due to their input to the cerebellum and the role they play in the processing of sensory feedback. Specifically, the inferior olive sends sensory information to the cerebellum through pathways like the inferior cerebellar peduncle (ICP), and thus injuries to these structures might lead to a symptom profile characterized by motor and balance difficulties, which fits the description of a movement disorder known as ataxia.
The other symptoms mentioned, such as an inability to track moving objects with the eyes, hypersensitive vomiting reflex, and difficulty forming memories, could result from damage to other areas of the brain, but they are not primarily associated with the function of the olives of the medulla oblongata.