CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
If (n+2)! = 90 × n!, what is the value of n?
The value of n is 8. Expanding (n+2)! as (n+2)(n+1) times n! and cancelling n! gives (n+2)(n+1) = 90. Since 10 times 9 equals 90, n+2 equals 10, so n is 8. Testing n = 9 gives 110, which fails.
- A7
- B8Correct
- C9
- D10
Explanation
(n+2)! = (n+2)(n+1) n!, so (n+2)(n+1) = 90. Since 10 × 9 = 90, n+2 = 10, giving n = 8. Option 9 comes from setting n+1 = 10 wrongly, which would give 11 × 10 = 110.
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