Multiple choice general knowledge math & puzzles

If n is a positive integer such that n! / (n - 2)! = 342, find n

  1. 16

  2. 17

  3. 18

  4. 19
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D Correct answer
Explanation

The expression $n! / (n - 2)!$ simplifies to $n(n - 1)$. We solve $n^2 - n - 342 = 0$. Factoring gives $(n - 19)(n + 18) = 0$. Since $n$ must be a positive integer, $n = 19$.

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