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As more and more data become accessible, ranking query semantics such as ranked retrieval, possibly combined with Boolean query conditions, has gained a lot of attention lately. As the formulation of such queries is known to be difficult, we aim at providing quick approximate answers as cues for interactive query refinements. Toward the goal, we study approximate answering techniques for Boolean+ranking queries. While approximate query answering has been studied for Boolean-only queries, we observed that a straightforward extension of this work for advanced queries incurs prohibitive overheads. We thus propose a systematic framework which significantly outperforms such a naive extension. We also empirically validate the effectiveness and efficiency of our framework.