If \(\frac{(n+1)!}{(n-2)!}=60\), what is the value of (n)?

Correct answer: \(4\)

On cancelling \((n-2)!\) from \((n+1)!\), we get \(\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1)\). Hence, \((n+1)n(n-1)=60\). For \(n=4\), \(5\times4\times3=60\), so the correct value is \(\boxed{4}\). The nearby option \(n=3\) gives \(4\times3\times2=24\), not 60. Exam tip: In factorial fractions, expand the numerator factorial up to the denominator factorial and cancel common factors.