Abstract: If low energy supersymmetry is realized in nature, the apparent discovery of a Higgs boson with mass around 125 GeV suggests a supersymmetric mass spectrum in the TeV or multi-TeV range. Multi-TeV scalar masses are a necessary component of supersymmetric models with pure gravity mediation or in any model with strong moduli stabilization. The simplest model of pure gravity mediation contains only two free parameters: the gravitino mass and $tan beta$. Scalar masses are universal at some high energy renormalization scale and gaugino masses are determined through anomalies and depend on the gravitino mass and the gauge couplings. This theory requires a relatively large graviton mass (m_{3/2} gtrsim 300 TeV) and a limited range in tan beta simeq 1.7--2.5. By allowing for non-unversalities in the Higgs soft masses, the allowed range in tan beta is greatly increased which then permits smallers values of m_{3/2} and makes detection of the gluino at the LHC possible. Furthermore, if one adopts a no-scale or partial no-scale structure for the K"ahler manifold, sfermion masses may vanish at the tree level. It is usually assumed that the leading order anomaly mediated contribution to scalar masses appears at 2-loops. However, there are at least two possible sources for 1-loop scalar masses. These may arise if Pauli-Villars fields are introduced as messengers of supersymmetry breaking. We consider the consequences of a spectrum in which the scalar masses associated with the third generation are heavy (order $m_{3/2}$) with 1-loop scalar masses for the first two generations. A similar spectrum is expected to arise in GUT models based on $E_7/SO(10)$ where the first two generations of scalars act as pseudo-Nambu-Goldstone bosons. Explicit breaking of this symmetry by the gauge couplings then generates one-loop masses for the first two generations. In particular, we show that it may be possible to reconcile the $g_mu - 2$ discrepancy with potentially observable scalars and gauginos at the LHC.