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Summer Clouds moderators

27/08/2017 at 09:35
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In the addition shown on the figure the digits of the numbers are replaced by symbols. Different symbols represent different digits, and equal symbols represent equal digits. Find the digit replaced by the square.
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A) 9             B) 8                  C) 7              D) 6                      E) 5




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    Phan Thanh Tinh Coordinator 27/08/2017 at 10:40

    Denote : \(a+a+\overline{bb}=\overline{ccc}\) \(\left(a,b,c\in N;a,b,c< 10;b,c>0\right)\)

    \(a+a\le9+9=18;\overline{ccc}\ge111\)\(\Rightarrow\overline{bb}\ge93\Rightarrow b=9\)

    \(a+a+\overline{bb}< 9+9+99=117\Rightarrow c=1\)

    \(\Rightarrow a=\dfrac{111-99}{2}=6\)

    So, the answer is D

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