We discuss implications of recent experimental data for B decays into two pseudoscalar mesons, with emphasis on those with η and η' in the final states. Applying a U-spin argument, we show that tree and penguin amplitudes, both in B^+ →π^+ η and in B^+ →π^+ η', are of comparable magnitudes. Nontrivial relative weak and strong phases between the tree-level amplitudes and penguin-loop amplitudes in the B^±→π^±η modes are extracted. We predict possible values for the averaged branching ratio and

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... asymmetry of the B^±→π^±η' modes. We test the assumption of a singlet-penguin amplitude with the same weak and strong phases as the QCD penguin in explaining the large branching ratios of η' K modes, and show that it is consistent with current branching ratio and CP asymmetry data of the B^+ → (π^0, η, η') K^+ modes. We also show that the strong phases of the singlet-penguin and tree-level amplitudes can be extracted with further input of electroweak penguin contributions and a sufficiently well-known branching ratio of the η K^+ mode. Using SU(3) flavor symmetry, we also estimate required data samples to detect modes that have not yet been seen.