Do I need to claim the sale of my home that I acquired thru quit claim deed with rights of survivorship from my mom?

I lived in the home at the time of her death in 2013 until the time I sold the home in 2017. I believe my parents bought it for $32,000 in 1977 and I sold it for $287,000. Would it be reported as an inheritance or my primary residence?

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Since your mother gifted it to you through a quit claim deed, you would claim the method of acquiring it as a gift with date of acquisition as their purchase date, and the cost basis the same as their cost basis plus any costs of improvements over the years.

Since you meet the requirement for use of the house as a primary residence or 2 out of the 5 years prior to sale, if you are single, up to $250,000 of any gain would be exempt from tax, leaving very little in taxable gain at the long-term capital gains rate. By time you subtract selling costs from your sale price, you would likely pay no tax.