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**topsquark** Neither is sufficient to answer the question by itself.

To refute #1 note that the list of integers may all be negative, in which case the product of the greatest and smallest will be positive. But we are not guarenteed that the product is positive: Consider the set of integers {-4, -2, -1}. The product of these is negative.

To refute #2 note that if we have the set {-2, 1, 3, 4}, the product is negative.

So, if BOTH 1 and 2 are correct, what do we have? We have a list of purely negative integers (from 1) and we have an even number of them (from 2). What is the sign of the product of an even number of negative integers? It is positive.

-Dan