The first step in the magnet R&D of the U.S. LHC Accelerator Research Program (LARP) is fabrication of technology quadrupoles TQS01 and TQC01. These are two-layer magnets which use cables of same geometry made of 0.7 mm MJR Nb3Sn. Through strand billet qualification and tests of strands extracted from the cables, predictions of magnet performance are made. Measurements included the critical current, I-c, using the voltage-current (VI) method at constant field, the stability current, I-S, as the minimal quench current obtained with the voltage-field (VH) method at constant current in the sample, and RRR. Magnetization was measured at low and high fields to determine the effective filament size and to detect flux jumps. Effects of heat treatment duration and temperature on I-c and I-S were also studied. The Nb3Sn strand and cable samples, the equipment, measurement procedures, and results are described. Based on these results, strand specifications were formulated for next LARP quadrupole models.