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40! mod 41 = 40 (any prime number - 1) mod prime number = prime number - 1 39! mod 41 = 1 (any prime number - 2) mod Prime number = 1

Think about it.

Proof to follow....
_________________

Best,

AkamaiBrah 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

40! mod 41 = 40 (any prime number - 1) mod prime number = prime number - 1 39! mod 41 = 1 (any prime number - 2) mod Prime number = 1

Think about it.

Proof to follow....

Actually, I don't think this is a fair GMAT question. The problem is an application of "Wilson's Theorem" which is far beyond the knowledge needed for the GMAT. I would be happy to see an answer that has a solution which falls under GMAT-required knowledge.
_________________

Best,

AkamaiBrah 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

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.
_________________

Best,

AkamaiBrah 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