Data Sufficiency

Following is Example from Manhattan Number system series. Is this correct?


Is the product of all of the elements in Set S negative?
(1) All of the elements in Set S are negative.
(2) There are 5 negative numbers in Set S.


This is a tricky problem. Based on what we have learned so far, it would seem that Statement
(2) tells us that the product must be negative. (5 is an odd number, and when the GMAT
says "there are 5" of something, you CAN conclude there are EXACfLY 5 of that thing.)
However, if any of the elements in Set 5equals zero, then the product of the elements in
Set 5will be zero, which is NOT negative. Therefore Statement (2) is INSUFFICIENT.
Statement (1) tells us that all of the numbers in the set are negative. If there are an even number
of negatives in Set 5, the product of its elements will be positive; if there are an odd number
of negatives, the product will be negative. This also is INSUFFICIENT.
Combined, we know that Set 5contains 5 negative numbers and nothing else. SUFFICIENT.
The product of the elements in Set 5must be negative. The correct answer is (C).