Data Sufficiency

If M is a finite set of negative integers, is the total numbers of integers in M an odd number?

1) The product of all integers in M is odd

2) The product of all integers in M is negative


OA is B

I thought Answer is E , because we do not know how many negative numbers are in a set M. If they are 3 numbers in a set , it would be B because there is no indication in the question, how many total numbers are in the set M.

Can someone please point out to me why I am wrong?

1) The product of all integers in M is odd
We agree "odd x odd = odd" so we cannot state anything. Insufficient.

2) The product of all integers in M is negative
You do not need to know how many negative numbers are in the set.
You know the total numbers of integers in M is an odd number:
- if the number of negative integers which are multiplied is odd so the result is negative.
- if the number of negative integers which are multiplied is even so the result is positive.

For example,
-3 * -2 * -1 = -6
-4 * -3 * -2 * -1= 24

Hope it's ok.

Thanks! I over analyzed the problem. But your explanation cleared my confusion.