Data Sufficiency

From 1, the product of the largest and smallest is positive. This means the largest and smallest have the same sign: both are positive *or* both are negative. Well, if the largest and smallest are both positive, so is everything in-between. Similarly, if the largest and smallest are both negative, so is everything in-between. So from 1, we know everything in the list is positive, *or* everything in the list is negative. If everything's positive, the product is of course positive. But if everything is negative, you'll only get a positive product if you're multiplying an even number of terms. That's why you also need statement 2.