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CEMC Gauss (Grade 7), 2011

Number theory Difficulty 2.0 Junior Find the answer Canada

Steve begins at $7$ and counts forward by $3$ , obtaining the list $7, 10, 13,$ and so on. Dave begins at $2011$ and counts backwards by $5$ , obtaining the list $2011, 2006, 2001,$ and so on. Which of the following numbers appear in each of their lists?

(A) $1009$ (B) $1006$ (C) $1003$ (D) $1001$ (E) $1011$

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