Final answer:
RE/MAX is the company with a balloon logo that claims to sell more real estate than anyone else, recognized by its network and brand identity.
Step-by-step explanation:
The company with a familiar balloon logo that claims to sell more real estate than anyone else is RE/MAX. This brand is easily recognizable by its hot air balloon emblem and is known for its extensive network of independent real estate agents and franchises. The strong brand identity, along with their vast network, has contributed to RE/MAX's ability to sell a large volume of properties worldwide.