1.
This indicates that all the numbers in the list are either +ve or -ve, since the product of the greatest and smallest integers is +ve.
But we don't know how many integers are there in the list. So NS.

2. This indicates that there are even number of integers in the list, however we don't know the sign of the integers. There could be one -ve and 5 +ve integers or 6 +ve inetegers. So NS.

If we combine 1 and 2, we know both the signs and the no of integers in the list. Hence C is correct.

But no where in the question it says that numbers are in increasing order...

what if the numbers are

-1 2 -1

2 -2 2

Here stmt1 tells us that product of smallest "s" & largest "l" is +ve this can happen only if s & l have the same sign or either of them is "0", from here we cannot say about the sign of entire product as if s & l are -ve and list contains odd nos of -ve ints then product would be -ve hence NOT SUFF

stmt2 says that there are an even nos of terms , but this too is NOT SUFF as list might contain an odd nos of -ve nos but in totatily is even.

If we combine both we can say that
a) s & l have the same sign or either of them is 0

b) List contains even nos of ints

hence if both s & l are positive product of list is +ve
if both s & l are negative & list is even in size product is +ve
if either of then is "0" then nothing matters any way the product would be 0 (Whose sign I think should be taken as +ve in context of the GMAT & this problem)
SUFF

Hence answer should be "C"

Hi Hopefully,
Your interpretation is fair enough but as you mentioned
if we take a list like 2,-2,2

here smallest = -2 & largest =2 whose product is -4 negative ,this voilates the stmt 1, hence this cannot be interpreted as the list mentioned in the Q,

the idea is that if the list contains a -ve term then it must contain all negative terms in any Order or a 0 so that highest term is alos -ve thereby making their product +ve If the list contains even one +ve element this would become "l" & would voilate the stmt 1.

To sum up:
We cannot consider a list which has both -ve as well as positve terms
as s will be -ve & l would be + ve voilating the first statement.