Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.1 Junior Find the answer

If $(pq)(qr)(rp) = 16$ , what is a possible value for $pqr$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since $(pq)(qr)(rp) = 16$ , then $pqqrrp = 16$ or $p^2q^2r^2 = 16$ . Thus, $(pqr)^2 = 16$ and so $pqr = \pm 4$ . Using the given answers, $pqr$ is positive and so $pqr = 4$ .

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