The electrically variable transmission family of the present invention provides low-content, low-cost electrically variable transmission mechanisms including first, second and third differential gear sets, a battery, two electric machines serving interchangeably as motors or generators, and three selectable torque-transfer devices (two clutches and one brake. The three selectable torque transfer devices are engaged singly, in combinations of two, or singly along with a selectively braked motor/generator to yield an EVT with a continuously variable range of speeds (including reverse) and four mechanically fixed forward speed ratios. Alternatively, the three torque transfer devices may be disengaged while both motor/generators are braked to provide a fixed speed ratio. The first, second and third torque transfer devices and the first and second motor/generators are operable to provide five operating modes in the electrically variable transmission, including battery reverse mode, EVT reverse mode, reverse and forward launch modes, continuously variable transmission range mode, and fixed ratio mode.