Evidence for the decay mode X(3872) -> psi(2S)gamma in B+ -> X(3872)K+ decays is found with a significance of 4.4 standard deviations. The analysis is based on a data sample of proton proton collisions, corresponding to an integrated luminosity of 3 fb(-1), collected with the LHCb detector, at centre-of-mass energies of 7 and 8 TeV. The ratio of the branching fraction of the X(3872) -> psi(2S)gamma decay to that of the X(3872) -> J/psi gamma decay is measured to be B(X(3872) -> psi(2S)gamma)/B(X(3872) -> J/psi gamma) = 2.46 +/- 0.64 +/- 0.29, where the first uncertainty is statistical and the second is systematic. The measured value does not support a pure D (D) over bar* molecular interpretation of the X(3872) state. (C) 2014 CERN for the benefit of the LHCb Collaboration. Published by Elsevier B.V.