This is a tough question.

Does the statement (1) provide sufficient information?

Statement (1) tells us that the min and max numbers have the same sign i.e. both are positive or both are negative. This means that all the numbers are positive or all the numbers are negative.

This on its own is insufficient.

Does the statement (2) provide sufficient information?

Knowing there are an even number of integers on the list tell us nothing unless we know the signs of these numbers so on its own is insufficient.

Do both statements together provide sufficient information?

If all the numbers are the same sign and there are an even number of them then the product will be positive.

So statements 1 and 2 together are sufficient and the answer is C.

Does that make sense to you?

certain list consists of several different integers. Is th eproduct of all integers positive?
a. The product of the greatest and smallest integer on the list is positive
b. There is an even number of integers in the list

If there are odd number of negative integers on the list the product would be negative. On the other hand if there are even nuumber of odd integers on the list then the product would be positive.

Statement I: It means the greatest and smallest integer both are either positive or negative. However look at the two following lists
{-5,-3,-2,-1} and {-14,-11,-10,-3,-1}. In both cases the product of first and last term is positive, but the product of all integers is not necessarily positive

Statement II just says there are even number of integers on the list.The list could look like {-2,-3,-6,9,5,7} or {-1,-2,-3,-4,-5,5}. Thus II alone is insufficient

After combining the two we know for sure that the product of all integers would be positive

Hence C

Thanks for explaining