The destruction of 7Be with neutrons represents the last possible standard avenue to reduce the predicted abundance of the primordial 7Li and in this way to attempt to solve the Cosmological 7Li problem. We discuss the results of an experiment performed at the Soreq Applied Research Accelerator Facility (SARAF) in Israel where we measured the Maxwellian Averaged Cross Sections (MACS) of the 7Be(n,p), 7Be(n,a), and 7Be(n,ga) reactions. Our MACS measured at 49.5 keV in the window of the Big Bang Nucleosynthesis (BBN), indicate the lack of standard nuclear physics solution to the Primordial 7Li Problem.