The electrical resistivity ρ and Hall coefficient RH of the tetragonal single-layer cuprate La1.6-xNd0.4SrxCuO4 were measured in magnetic fields up to H=37.5 T, large enough to access the normal state at T→0, for closely spaced dopings p across the pseudogap critical point at p=0.23. Below p, both coefficients exhibit an upturn at low temperature, which gets more pronounced with decreasing p. Taken together, these upturns show that the normal-state carrier density n at T=0 drops upon entering the pseudogap phase. Quantitatively, it goes from n=1+p at p=0.24 to n=p at p=0.20. By contrast, the mobility does not change appreciably, as revealed by the magnetoresistance. Our data are in excellent agreement with recent high-field data on YBa2Cu3Oy and La2-xSrxCuO4. The quantitative consistency across three different cuprates shows that a drop in carrier density from 1+p to p is a universal signature of the pseudogap transition at T=0. We discuss the implication of these findings for the nature of the pseudogap phase.