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Factorial Difference Properties

XAT 2015 · Quantitative Ability & Data Interpretation · Hard · Quantitative Ability

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If the last 6 digits of [(M)!−(N)!][(M)! - (N)!] are 999000999000, which of the following option is not possible for (M)×(M−N)(M) \times (M - N)? Both (M)(M) and (N)(N) are positive integers and M>NM > N. ((M)!(M)! is factorial MM.)

  1. A.

    150

  2. B.

    180

  3. C.

    200

  4. D.

    225

  5. E.

    234

Answer

B

Explanation

Analyzing power of 2 in 999000 shows 999000 is divisible by 8 but not 16. No natural number factorial satisfies M!−N!=999000M! - N! = 999000. Hence option B is identified.

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