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Using recent lattice data on the thermodynamics of QCD in the presence of a background magnetic field, we show that the ratio of transverse to longitudinal pressure exhibits, to good accuracy, a simple scaling behavior over a wide range of temperature and magnetic field, essentially depending only on the ratio T/B $$ T/\sqrt{B} $$. We compare this QCD response to the corresponding magnetoresponse in maximally supersymmetric Yang Mills theory. Given suitable calibrations defining the comparison, we find excellent agreement. This may be viewed as a further test of the applicability of holographic models for hot QCD.