Data Sufficiency

Hi all,
It seems to me this one is a relatively simple GMATPrep question, but I can't see why the OA is (C). Can anyone explain me why the product must to be positive? Even if you have an even number of integers, and the product of greatest and smallest is positive, you I could still have positive and negative integers that will make the final product negative!!!
Please, can anyone explain what I fail to see here...
Thanks,

From 1 list could be

a) even = 1,2 product greatest smallest + ve , final product + ve


b) odd = -3 -2 -1 product greatest smallest + ve , final product - ve


Hence insufficient knock off AD

From 2 list could be


1 ,2 final product + ve

1, -2 final product - ve


Hence insufficient knock of B left with CE


Combining

List is even and product greatest smallest + ve

List
1,2 product greatest smallest + ve , final product + ve

-4 -3 -2 -1 product greatest smallest + ve , final product + ve


Hence C

Hi sujaysolanki
Sorry, I cannot understand what ve means....Also, can you explained more detailed,
Thanks

Hi again sujaysolanki,
Ok, I kinda' see what you did in there, but I think you approach is limited to those specific numbers that you picked....How about when you have a list of 6 numbers for instance. When taken together (1) and (2), le's say you have a number of 6 integers and the product of the greatest and the smalest is positive. Now, you have 4 other numbers , which 3 of them could be positive and the 4th one negative, in this case you final product can be negative....See here I don't get it. I just need a stronger argument for this solution.
Thanks

I got it now.
Thanks

This is because
1) as per condition 1st the only 2 possibilities is either both numbers are +ve or -ve
2) as per 2nd cdt the whether the two are +ve or -ve the Product will be +ve as the no. Of integers is even

Hence c is the corect option