The razor approach to search for R-parity conserving supersymmetric particles is described in detail. Two analyses are considered: an inclusive search for new heavy particle pairs decaying to final states with at least two jets and missing transverse energy, and a dedicated search for final states with at least one jet originating from a bottom quark. For both the inclusive study and the study requiring a bottom-quark jet, the data are examined in exclusive final states corresponding to all-hadronic, single-lepton, and dilepton events. The study is based on the data set of proton-proton collisions at root s = 7 TeV collected with the CMS detector at the LHC in 2011, corresponding to an integrated luminosity of 4.7 fb(-1). The study consists of a shape analysis performed in the plane of two kinematic variables, denoted M-R and R-2, that correspond to the mass and transverse energy flow, respectively, of pair-produced, heavy, new-physics particles. The data are found to be compatible with the background model, defined by studying event simulations and data control samples. Exclusion limits for squark and gluino production are derived in the context of the constrained minimal supersymmetric standard model (CMSSM) and also for simplified-model spectra (SMS). Within the CMSSM parameter space considered, squark and gluino masses up to 1350 GeV are excluded at 95% confidence level, depending on the model parameters. For SMS scenarios, the direct production of pairs of top or bottom squarks is excluded for masses as high as 400 GeV.