We present the electrical properties of GaAs/In x Ga1-x As core/shell nanowires (NWs) measured by ultrafast optical pump-terahertz probe spectroscopy. This contactless technique was used to measure the photoconductivity of NWs with shell compositions of x = 0.20, 0.30 and 0.44. The results were fitted with the model of localized surface plasmon in a cylinder in order to obtain electron mobilities, concentrations and lifetimes in the In x Ga1-x As NW shells. The estimated lifetimes are about 80-100 ps and the electron mobility reaches 3700 cm2 V-1 s-1 at room temperature. This makes GaAs/InGaAs NWs good candidates for the realization of high-electron-mobility transistors, which can also be monolithically integrated in Si-CMOS circuits.