data sufficiency question

you have to select if the 1st piece of information will answer the question alone, if the second will answer the question alone. or if you need both pieces to answer the question. here is the problem:

a cetain list contains several different integers. is the product of all the integers positive?

1. the product of the greatest integer and the smallest is positive

2. the list contains an even number of integers.

the answer is both of the pieces of information are needed to answer the question. i thought that each piece of information by itself would be sufficient. does anyone know why you would need both pieces to answer the question? thanks