A search for supersymmetry or other new physics resulting in similar final states is presented using a data sample of 4.73 fb(-1) of pp collisions collected at root s = 7 TeV with the CMS detector at the LHC. Fully hadronic final states are selected based on the variable M-T2, an extension of the transverse mass in events with two invisible particles. Two complementary studies are performed. The first targets the region of parameter space with medium to high squark and gluino masses, in which the signal can be separated from the standard model backgrounds by a tight requirement on M-T2. The second is optimized to be sensitive to events with a light gluino and heavy squarks. In this case, the M-T2 requirement is relaxed, but a higher jet multiplicity and at least one b-tagged jet are required. No significant excess of events over the standard model expectations is observed. Exclusion limits are derived for the parameter space of the constrained minimal supersymmetric extension of the standard model, as well as on a variety of simplified model spectra.