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How many 3-digit positive integers have exactly one even digit?

(A) $350$ (B) $450$ (C) $375$ (D) $75$ (E) $125$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.