Recent LHC data on Pb+Pb reactions at sqrt[s](NN) = 2.7 TeV suggests that the p/π is incompatible with thermal models. We explore several hadron ratios (K/π, p/π, Λ/π, Ξ/π) within a hydrodynamic model with a hadronic after burner, namely the ultrarelativistic quantum molecular dynamics model 3.3, and show that the deviations can be understood as a final state effect. We propose the p/π as an observable sensitive on whether final state interactions take place or not. The measured values of the hadron ratios do then allow us to gauge the transition energy density from hydrodynamics to the Boltzmann description. We find that the data can be explained with transition energy densities of 840 ± 150 MeV/fm(3).