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Medicare eligibility is primarily determined by age and specific qualifying conditions, which makes the third option the most comprehensive and accurate answer. Individuals who are 65 years of age or older automatically qualify for Medicare, reflecting the program's aim to provide health coverage for seniors.

Additionally, individuals under the age of 65 can also qualify if they have certain disabilities, specifically those who have been receiving Social Security Disability Insurance (SSDI) for at least two years. This inclusion recognizes the healthcare needs of younger individuals facing severe health challenges that prevent them from working.

Therefore, the correct answer encompasses both groups: those who are 65 and older, and those under 65 with disabilities who have met the criteria for a minimum duration. The other choices either fail to account for one of these groups or impose conditions that do not accurately reflect the eligibility criteria for Medicare.