What is the purpose of protected variables in a class?

The purpose of protected variables in a class is to allow derived classes access to the data while hiding it from other parts of the program. In object-oriented programming, the access modifier 'protected' serves a specific function; it enables a class and its subclasses (derived classes) to interact with certain data members, while restricting access from other classes that are not in the hierarchy.

This behavior is crucial for maintaining encapsulation within a software design. By using protected variables, a base class can provide essential data to its derived classes without permitting the broader application or other unrelated classes to interact with that data directly. This ensures that the integrity of the data is maintained and that any modifications or access can be controlled.

The other answer choices highlight concepts that do not accurately reflect the functionality of protected access. For instance, some options suggest that access is either completely open or entirely restricted, which is not consistent with the defined purpose of protected access in programming languages such as C# or Java.