Questions & Answers about Tek bir oda kaldı.
Yes, they are closely related, but they do different jobs here.
- bir = one / a
- tek = single / only / sole
So tek bir oda does not just mean one room. It adds emphasis:
- bir oda = a room / one room
- tek bir oda = only one room / a single room
Using both together is very common in Turkish when you want to stress that there is just one.