vcbabu wrote:

40! =40! +1-1= (40! +1)+40-41

when 40! / 41 remainder is 40 since except 40 other terms are divisble by 41 and hence the remainder is 40/41 i.e. 40 .

Hmmmm. Please demonstrate to me some proof or method to determine that (40! + 1) is divisible by 41. This is the same as saying 40! mod 41 = 40. Essentially, you are using the answer to the problem to find the answer -- circular logic.

If you are claiming that (n! + 1) is always divisible by n + 1, THAT IS WRONG; here is a simple counter example: (3! + 1) = 7 which is certainly NOT divisible by 4.

The ONLY time (n! + 1) is divisible by n + 1 is when n + 1 is PRIME, which is the essense of Wilson's formula and which no GMAT student should be expected to know.

Nuff said.

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Former Senior Instructor, Manhattan GMAT and VeritasPrep

Vice President, Midtown NYC Investment Bank, Structured Finance IT

MFE, Haas School of Business, UC Berkeley, Class of 2005

MBA, Anderson School of Management, UCLA, Class of 1993