Let's assume that the list of the integers are: -3,-2,-1.
Although the product of the greatest and smallest of the integers in the list is positive (-3)*(-1)=3, the product of all the integers in the list is negative.
Let's assume another list of the integers: -4,-3,-2,-1.
the product of the greatest and smallest of the integers in the list is positive (-4)*(-1)=4, the product of all the integers in the list is positive.
Thus (1) is insufficient.
Obviously (2) alone is insufficient.
Combine (1) and (2), we know that there are even number of integers in the list, thus as long as the product of the greatest and smallest of the integers are positive, the product of all the integers in the list must be positive. (negative*negative=positive and each number will be paired with another number. ) Thus (1) and (2) together is sufficient.
Answer is (C)
Yiliang
