Final answer:
The three core brands historically part of Wyndham Worldwide are a) Wyndham Hotels, RCI, and WorldMark, which consist of the company's global hotel chain, timeshare exchange company, and a timeshare network respectively.
Step-by-step explanation:
The student is asking about the three core brands of Wyndham Worldwide. As of my knowledge cutoff in early 2023, Wyndham Worldwide, now known as Wyndham Hotels & Resorts after spinning off Wyndham Destinations, has a number of hotel brand portfolios. However, for the scope of the question, the three core brands that were historically part of Wyndham Worldwide are a) Wyndham Hotels, RCI, and WorldMark. These brands represent different aspects of Wyndham Worldwide's business:Wyndham Hotels refers to its global chain of hotels.RCI stands for Resort Condominiums International, which is a timeshare exchange company.WorldMark is also a timeshare program offering a network of resort locations.Option b Ramada, Days Inn, and Super 8; option c La Quinta, Microtel, and Wingate; and option d Howard Johnson, Travelodge, and Knights Inn are all hotel brands that were under the Wyndham umbrella, but they do not represent the core brands being referred to in the question.