Stmt I

list : -3 -2 -1

NO

list : 1 2 3

YES

INSUFF

Stmt II

list : 1 2 3 4
YES

list: -3 -2 -1 0

product is 0 which is non positive

INSUFF

Stmt I and II together

SUFF

C)
The product has to be positive since 0 cant be in the list (0 cant be the greatest number If the other numbers are negative or as the smallest number if the other numbers are positive since stmt I would be false as the product would be 0)

thanks, didn't think of 0

From 1 :

Highest and lowest product is +ve => 2 cases

1: Highest and lowest are -ve - can't say anything about the product of all integers inbetween and including them without knowing whether the number of integers is even or odd
2: Highest and lowest are +ve : Pretty straightforward , the product of all integers has to be positive.

So 1 is Suff

2 is clearly Insuff

Combining : If the number of integers are even - their product has to be positive - Suff, Hence C