Which of the following is a potential symptom of TB that warrants examination?

A persistent cough lasting longer than 2 weeks is indeed a potential symptom of tuberculosis (TB) that warrants further examination. This symptom is particularly significant because TB primarily affects the lungs, leading to chronic respiratory symptoms such as a prolonged cough. When a cough extends beyond two weeks, it raises concern for underlying conditions, including infectious diseases like TB, and prompts healthcare providers to investigate further through testing and diagnostic imaging.

The other options, while they can indicate health issues, are less specific or definitive for TB. Sudden weight gain is not typically associated with TB and may suggest different health concerns. Skin rashes alone do not indicate TB and could be related to various dermatological conditions. General fatigue, while a common symptom of many illnesses, is also not specific to TB and can be caused by a wide range of factors unrelated to this infection. Thus, while all these symptoms can be important in their own right, the persistent cough is the most closely linked to TB and warrants prompt examination.