XAT 2015 Question 74
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XAT
None of the answers given are correct. The reasoning is as given below.
999000 is a multiple of 8 but not of 16. If N! is a multiple of 16, M! would also be a multiple of 16 and hence M!-N! would be a multiple of 16.
Hence, as M!-N! = 999000, it would imply that N! is a multiple of 8 and not of 16. Therefore, N is either 4 or 5. So, N! is either 24 or 120.
So, it would imply that M! is either 999024 or 999120. Both of which are not factorials for any natural number.
Hence, the given question is wrong.