Which of the following symptoms is associated with tertiary syphilis if untreated?

Tertiary syphilis represents the late stage of syphilis infection that can occur years after the initial infection if left untreated. One of the hallmark symptoms of tertiary syphilis is the development of destructive granulomas known as gummas. These gummas can form in various tissues, including the skin, bone, and internal organs, leading to significant damage and disruption of tissue integrity. The presence of these granulomas is a key feature that differentiates tertiary syphilis from earlier stages of the disease.

In contrast, clear skin and vitality, mild headaches, and routine infections do not characterize tertiary syphilis. Clear skin and vitality imply a state of good health, which is not consistent with the severe consequences of untreated tertiary syphilis. Mild headaches could occur in various conditions but are not specific or indicative of this advanced stage of syphilis, and routine infections are also not a direct symptom of tertiary syphilis. Thus, the presence of destructive granulomas is a definitive indicator of the severe complications that can arise during this late stage of syphilis.