What fact must a property manager disclose when showing a single-family rental home?

The correct answer highlights the importance of maintaining transparency regarding the condition of a property, especially when health and safety issues are concerned. When a property manager is showing a single-family rental home, they have a duty to disclose any significant issues that could affect a tenant's decision to rent the property.

In this case, if the former owner sold the home due to a recurring mold problem, that is a critical fact that could directly impact the health and safety of future occupants. Mold can cause serious health issues, and it is crucial for prospective tenants to be aware of any history of such a problem, as it influences their living environment and well-being.

The other options, while they may be relevant in different contexts, do not pertain to health and safety concerns to the same extent. A burglary incident, while unfortunate, does not necessarily indicate an ongoing risk, and disclosure of a previous owner’s medical condition as in the case of AIDS is typically protected by privacy laws. Additionally, the presence of a registered sex offender in the neighborhood does not constitute a direct hazard linked to the property itself, though it may be a factor for potential residents to consider in their decision-making process.