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UKMT Intermediate Mathematical Challenge, 2019

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

When $5655$ is divided by a two-digit positive integer $N$ , the remainder is $11$ . When $5879$ is divided by the same positive integer $N$ , the remainder is $14$ . What is the sum of the digits of $N$ ?

(A) $6$ (B) $7$ (C) $8$ (D) $9$ (E) $10$

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