Set \(S\) consists of more than two integers. Are all the numbers in set \(S\) negative?

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Set \(S\) consists of more than two integers. Are all the numbers in set \(S\) negative?

(1) The product of any three integers in the list is negative.
(2) The product of the smallest and largest integers in the list is a prime number.

Answer: C

Source: GMAT Club Tests