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This problem trains for: SAT-I, AMC-8.

P is the product of 5 consecutive integers and S is their sum. If P = 0 there are m possible values for S and, if S = 0 there are k possible values for P. What is m + k?

The product of 5 consecutive integers is:

and their sum is:

The product is zero only if one of the factors is zero. There are 5 possible values for n:

giving 5 possible values for the sum S:

The sum is zero only if:

Therefore: