There are 6 US Post Offices in Quay County serving a total of 8,949 residents equating to 1,492 residents per post office. It's estimated that approximately 14,284 packages are handled across the 6 county post offices annually. Quay County (pronounced \"kway\") is a county located in the state of New Mexico. As of the 2010 census, the population was 9,041. Its county seat is Tucumcari. The county was named for Pennsylvania senator Matthew Quay, who supported statehood for New Mexico. It is west from the Texas state line.