Which directory must be mounted with read and write access if it resides on a dedicated file system?

The correct choice is based on the typical usage and requirements of the directories listed. The /var directory is designed to hold variable data files that are expected to change as the system operates. This includes log files, spool files, and transient state data for various system services. Since the content of /var can change frequently, it is essential that this directory is mounted with read and write access to allow the system and applications to update the necessary files.

Conversely, the other directories serve different purposes. For example, /tmp is used for temporary files but can often be mounted with specific settings that allow for writing, depending on the system policy. /usr contains user utilities and applications and is typically more static, although it needs to be readable and sometimes writable for updates. /etc holds configuration files, and while it must also be writable for changes, it does not change as frequently as /var.

Given that /var's primary function is to accommodate dynamic data, it necessitates read and write access when mounted, confirming its suitability as the correct choice.