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CA Foundation · Quantitative Aptitude · Permutations and Combinations

If (n + 1)! = 30 × (n − 1)!, what is the value of n?

n equals 5. Expanding (n+1)! as (n+1)·n·(n−1)! gives n(n+1) = 30, so n² + n − 30 = 0, with positive root n = 5. Check: 6! = 720 equals 30 × 4! = 720. The option 6 mistakes n+1 for n.

  1. A4
  2. B5Correct
  3. C6
  4. D30

Explanation

(n+1)! = (n+1)(n)(n−1)!, so (n+1)n = 30. This gives n² + n − 30 = 0, so (n+6)(n−5) = 0 and n = 5 as n must be positive. Check: 6! = 720 and 30 × 4! = 720. The option 6 comes from taking n+1 = 6 instead of n.

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