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CEMC Gauss (Grade 8), 2005

Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

Pete is given three positive integers and is told to add the first two, and then multiply the result by the third. Instead, he multiplies the first two and adds the third to that result. Surprisingly, he still gets the correct answer of $14$ . How many different values could the first number have been?

(A) $5$ (B) $4$ (C) $6$ (D) $3$ (E) $7$

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