We present a set of conditions that an arbitrary pure tripartite state must satisfy in order that the Entanglement of Formation (EOF) becomes a monogamic measure. The monogamic relation derived is deeply connected to the discrepancy between classical and quantum correlations, embodying the possible negative signal of the EOF tangle whenever the quantum correlation is larger than the classical one. The estimated limits bound the possible amount of quantum conditional entropy in the system. We present general analytical results for a three- qubit system and give a simple numerical algorithm to calculate the EOF tangle for a system with dimension 2 × 2 × N. Those results are employed to elucidate features of the distribution of entanglement during a dynamical evolution. See more athttp://xxx.lanl.gov/abs/1110.1054