High mobility and high on/off ratio thin-film transistors are fabricated using solution-based deposition of purified semiconducting carbon nanotubes. A comprehensive spectrum of the density starting from less than 10 tubes mu m(-2) to the high end of around 100 tubes mu m(-2) is investigated. This study provides the first important roadmap for the trade-offs between mobility and on/off ratio in nanotube-based semiconducting inks.