CA Foundation · Quantitative Aptitude · Permutations and Combinations
If (n+2)! = 56 × n!, what is the value of n?
n equals 6. Writing (n+2)! as (n+2)(n+1)·n! reduces the equation to (n+2)(n+1) = 56. Since 8 × 7 = 56, n+1 = 7, so n = 6. Taking n = 7 would wrongly give 72.
- A5
- B6Correct
- C7
- D8
Explanation
(n+2)! = (n+2)(n+1)·n!, so (n+2)(n+1) = 56. Since 8×7 = 56, n+1 = 7 and n = 6. Option 5 would give 7×6 = 42, and option 7 would give 9×8 = 72, so both fail.
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