  The following is a long-standing open question: "If the zero-framed surgeries
on two knots in the 3-sphere are integral homology cobordant, are the knots
themselves concordant?" We show that an obvious rational version of this
question has a negative answer. Namely, we give examples of knots whose
zero-framed surgeries are rational homology cobordant 3-manifolds, wherein the
knots are not rationally concordant (that is not concordant in any rational
homology S^3 x [0,1]). Specifically, we prove that, for any positive integer p
and any knot K, the zero framed surgery on K is Z[1/p]-homology cobordant to
the zero framed surgery on its (p,1) cable. Then we observe that most knots are
not rationally concordant to their (p,1) cables.
