A search is performed for heavy particle pairs produced in root s = 7 TeV proton-proton collisions with 35 pb(-1) of data collected by the CMS experiment at the LHC. The search is sensitive to squarks and gluinos of generic supersymmetry models, provided they are kinematically accessible, with minimal assumptions on properties of the lightest superpartner particle. The kinematic consistency of the selected events is tested against the hypothesis of heavy particle pair production using the dimensionless razor variable R, related to the missing transverse energy E-T(miss). The new physics signal is characterized by a broad peak in the distribution of M-R, an event-by-event indicator of the heavy particle mass scale. This new approach is complementary to E-T(miss)-based searches. After background modeling based on data, and background rejection based on R and M-R, no significant excess of events is found beyond the standard model expectations. The results are interpreted in the context of the constrained minimal supersymmetric standard model as well as two simplified supersymmetry models.