Resistivity and magnetoresistance measurements have been performed on insulating icosahedral AlPdRe quasicrystal (QC) bar samples. At temperatures in the range 300 K ≥ T ≥ 50 K, the resistivities follow a simple inverse temperature law: ρ(T) = ρ0/T(1.0±0.1). Below 1 K, the resistivity of a weakly insulating sample exhibited a simple inverse temperature law where ρ(T) = ρ0/T0.33 and not an activated variable-range hopping (VRH) law. Strongly insulating samples exhibit saturation of their resistivities to finite values as T → 0 K. These saturation resistivity values are believed to arise from the presence of a second metallic phase located within the quasicrystal's structure. By extrapolating the measured resistivities at 22 mK to absolute zero, the saturation conductivity values were estimated at T = 0 K and subtracted from the conductivity data points. These 'corrected' data, corresponding only to the QC phase, were found to follow activated VRH laws, having hopping exponents y that vary in the range 0.18 ≤ y ≤ 0.43. The activated VRH behaviours are observed only below 1 K. The magnetoresistances (MRs) of these samples are also anomalous. The MRs can be explained by including contributions from both the saturation conductivity values and from the QC MR ratios, estimated using the wavefunction shrinkage model.