If \( \frac{(n+2)!}{(n-2)!}=1680 \), what is the value of (n)?

Correct answer: 6

Cancelling the common factorial terms gives \(\frac{(n+2)!}{(n-2)!}=(n+2)(n+1)n(n-1)\). Thus, the product of four consecutive integers must be 1680. Since \(8\times7\times6\times5=1680\), we get \(n-1=5\), so \(n=6\). For the closest distractor, \(n=7\) gives \(9\times8\times7\times6\), not 1680. Exam tip: In factorial ratios, expand the larger factorial first and cancel the common factorial part.