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

The digits of the three-digit integer ' $XYZ$ ' are all different. The sum of the digits of the three-digit integer ' $XXY$ ' is the two-digit integer ' $YZ$ '. The sum of the digits of the two-digit integer ' $YZ$ ' is the one-digit integer ' $Y$ '. What digit does ' $X$ ' represent?

(A) $4$ (B) $5$ (C) $6$ (D) $8$ (E) $9$

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