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SMO 2015 Junior Round 1 Question 20

SMO · SMO 2015 Junior Round 1

Question 20

Find the value of $p+q$, where $p$ and $q$ are two positive integers such that $p$ and $q$ have no common factor larger than 1 and $$\frac1{20}+\frac1{30}+\frac1{42}+\frac1{56}+\frac1{72}+\frac1{90}=\frac pq.$$