The quark model is used to predict various sum rules for limiting fragmentation. In particular, the ratio of the cross section of p --+ p to that of n --+ n is found to be 9 : 4. An initial combination of the quark model with the generalized optical theorem is found to produce results which violate the quark-model selection rules and differ from experimental values by a factor of 103-106 ? A possible modification is proposed and further tests are suggested.