Data Sufficiency

Hi All,

I am posting a GMAT Prep DS problem. Requesting someone to explain the problem

The problem is asking us to find out whether the product of numbers in a set is positive or negative. now this can be answered if you know following things

1. the size of the set i.e set of 2 numbers or set of 3 and so on, and
2. How many numbers are positive and how many are negative in the set

Now as per statement a) you can not come to a conclusion bcoz you dont know the size of the set. hence Not Suff
With statement b) you know that set can be of 2 numbers or 4 or 6 and so on but you dont know that how many numbers are negative. hence, NOT Suff

Now when you combined two statement, a & b, you know that set is of even no of digits and 1st and last one can be negative or positive but you still dont know that rest of the numbers can be split up in negatives and positives. So there can be a chance if the set is of 6 (removing 1st and last) you are left wih 4 numbers and in this 3 can be negative or 2 can be negative. So i chose E

But OA say C is the right answer.