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

It is possible to choose, in two different ways, six different integers from 1 to 9 inclusive such that their product is a square. Let the two squares so obtained be $p^2$ and $q^2$ , where $p$ and $q$ are both positive. What is the value of $p+q$ ?

(A) $72$ (B) $84$ (C) $96$ (D) $108$ (E) $120$

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