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UKMT Senior Mathematical Challenge, 2015

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

The positive integer $n$ is between 1 and 20. Milly adds up all the integers from 1 to $n$ inclusive. Billy adds up all the integers from $n+1$ to 20 inclusive. Their totals are the same. What is the value of $n$ ?

(A) $11$ (B) $12$ (C) $13$ (D) $14$ (E) $15$

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