Let \(R\) be an \(n\)-Gorenstein ring, \(\mathcal L\) denotes the class of all \(R\)- modules of finite injective dimension, \({\mathcal L}^ \perp\) denotes the class of Gorenstein injective modules, i.e. the class of all modules \(K\) such that \(\text{Ext}^ 1 (N,K) = 0\) for all \(N \in {\mathcal L}\), whilst \(^ \perp {\mathcal L}\) denotes the class of Gorenstein projectives i.e. satisfying \(\text{Ext}^ 1 (K,N) = 0\) for all \(N \in \mathcal L\). In this paper the authors show that the measure of Gorenstein injectivity or projectivity of a module is concentrated in the zeroth term of the minimal resolutions in the sense that the resolutions of the first cosyzygy and syzygy are injective and projective resolutions respectively. This is then applied to results on \({\mathcal L}^ \perp\)- injective dimension and dually to \(^ \perp{\mathcal L}\)-projective dimension when \(R\) is commutative and local.