The electrically variable transmission family of the present invention provides low-content, low-cost electrically variable transmission mechanisms including first, second and third (and possibly fourth) differential gear sets, a battery, two electric machines serving interchangeably as motors or generators, five, six or seven selectable torque-transfer devices and possibly a dog clutch. The selectable torque transmitting devices are engaged to yield an EVT with a continuously variable range of speeds (including reverse) and up to six mechanically fixed forward speed ratios. The torque transmitting 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.