Measurements of jet production rates in association with W and Z bosons for jet transverse momenta above 30 GeV are reported, using a sample of proton-proton collision events recorded by CMS at root s = 7 TeV, corresponding to an integrated luminosity of 36 pb(-1). The study includes the measurement of the normalized inclusive rates of jets sigma(V+ >= n jets)/sigma(V), where V represents either a W or a Z. In addition, the ratio of W to Z cross sections and the W charge asymmetry as a function of the number of associated jets are measured. A test of scaling at root s = 7 TeV is also presented. The measurements provide a stringent test of perturbative-QCD calculations and are sensitive to the possible presence of new physics. The results are in agreement with the predictions of a simulation that uses explicit matrix element calculations for final states with jets.