statement 1 says that product of smallest and the greatest no is positive, so this tells us that there are either all positive nos or all negative nos in the list coz if any no is negative in a list of positive nos then the product will not be positive and vice versa. Now here if we all the nos are negative then we have to confirm whether there re odd no of numbers or even coz negative odd times is negative, but negative even times is positive. but here from statement 1 alone we don't know how many nos in total are there in the list.
hence insufficient.

take 2 alone: there are even number of integers in the list. here we don't know that how many nos are negative or positive . so we don't know whether
the product will be positive or negative. so insuff.

take both the statements : we know there are even nos from 2 and either all the nos are positive or negative from 1. so this confirms that whatever may be the case, the product of all the nos should be positive.
hence suff.
thus C is the correct answer.