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1. Literally, very sharp, like a razor. Stand back, that tool is razor-sharp! Please be careful cutting those vegetables with such a razor-sharp knife.
2. Particularly clear, perceptive, and/or intelligent. Victoria may seem quiet, but she always has these razor-sharp insights on the texts we're reading. The think tank is known for razor-sharp analysis of world affairs. A lot of people are funny, but she has razor-sharp wit.