Final answer:
In OSPF, an area border router advertises a Type 3 LSA for summarizing routes between areas within the same OSPF domain.
Step-by-step explanation:
In OSPF (Open Shortest Path First), an area border router advertises a Type 3 LSA (Link State Advertisement). The role of the Type 3 LSA, often called a summary LSA, is to summarize the routes from one area to routers in another area within the same OSPF domain. This allows for scalability by minimizing the number of routes that have to be processed by routers in different areas.
Type 1 and Type 2 LSAs are used within a single OSPF area. A Type 1 LSA is sent by each router and contains information about directly connected links and the state of those links. The Type 2 LSA is generated by the designated router on a multi-access network segment and includes the list of routers on that segment.
The Type 4 LSA is used to convey external route information by specifying the route to an autonomous system boundary router (ASBR). Therefore, the correct answer to the student's question is C) Type 3, as area border routers use Type 3 LSAs to advertise summary information of the networks to other areas.