I think it is C - both together.

From (1) we know that the integers are either all positive or all negative since the greatest and least among them are either both negative or both positive. Still, we don't know if the product of them is positive or negative. Consider the set

S = {-5,-3,-1}

This satisfies (1), but the product of all the members is -15. However,

S = {-5,-4,-3,-1}

also satisfies (1) and the product is 60.

(2) alone clearly does not tell us anything about the numbers in the list.

However, combining (1) and (2), we know that the list is either all positive or all negative AND the number of items in the list is even. If they are all positive, clearly the product of them all is positive. If they are all negative and we know that there is an even number of elements, then the product will be positive as well, since the product of an even number of negative integers will always be positive.

I think you're right. all negative + odd number will fail...so we need 2) as well. so, it must be C) Thank you!