The simplest representations of SU(6) and U(12) which are capable of describing the low-lying positive-parity baryon resonances are the three-quark representations. All particle states in these multiplets are eigenstates of W spin and SU(6)W, the subgroup of U(12) and U(6)×U(6) which remains invariant for two-body decay processes, even when kinetic-energy terms and derivative couplings are included in the calculations. It is shown that SU(6)W leads to various selection rules and to definite branching ratios for the decays of these resonances. The branching ratios for the decays of the spin -32, SU(3)-octet resonances in the 70 representation of SU(6) and SU(6)W are calculated. An attempt is made to include SU(3) symmetry-breaking effects in a calculation of the decay rates of the 32+ decuplet within the 56 of SU(6)W.