If (n+5)!/(n+1)! = 11880, what is the value of n?

Correct answer: 7

Answer: 7, so option B is correct. Expand (n+5)! down to (n+1)!: (n+5)!=(n+5)(n+4)(n+3)(n+2)(n+1)!. Cancelling the denominator gives (n+5)(n+4)(n+3)(n+2)=11880. Test the choices or match consecutive factors. For n=7, the factors are 12, 11, 10 and 9, and 12×11×10×9=132×90=11880. Thus n=7. Option A gives 11×10×9×8=7920, option C gives 13×12×11×10=17160, and option D gives 14×13×12×11, which is still larger. Since the product of positive consecutive factors increases as n increases, the matching choice is unique. Memory cue: cancel the smaller factorial first, then inspect the remaining consecutive factors.