Final answer:
The default mode for a class declaration in Apex is system mode, but you can specify user mode using the without sharing keyword.
Step-by-step explanation:
In Apex, the with sharing and without sharing keywords are used to control the access level of the data in a class. By default, if the with sharing keyword is not used, the class runs in system mode, which means it can access all data in the organization regardless of user permissions. On the other hand if the without sharing keyword is used the class runs in user mode respecting the user's object and field-level permissions.
For example consider a scenario where you want to restrict access to certain information based on user permissions. In this case you can use the with sharing keyword to ensure that the class runs with the same access level as the calling user. This allows you to enforce the same data security rules for the user as if they were manually performing the operations. Therefore the statement that 'if you don't write the keyword with sharing, it runs in system mode' is true. To run a class in user mode and respect user permissions, you would use the without sharing keyword.