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, 2000

Number theory Difficulty 2.0 Junior Find the answer Canada

The cookies in a jar contain a total of $1000$ chocolate chips. All but one of these cookies contains the same number of chips; it contains one more chip than the others. The number of cookies in the jar is between one dozen and three dozen. What is the sum of the number of cookies in the jar and the number of chips in the cookie with the extra chocolate chip?

(A) $65$ (B) $64$ (C) $63$ (D) $66$ (E) $67$

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