i'm not sure if I got your question right but let me give it a try. The question is asking whether the product of a set S is negative. There are three possibilities you have to consider in this question. Set S could be 0, negative or positive. You MUST consider 0 as a possibility.
You will encounter expressions in the GMAT like a<0
That means a is negative.a>0
That means a is positive.a=0
That means it is zero.
There ARE always three states in a number or value. So, 0 is ALWAYS an option.ii) There are 5 negative numbers in Set S
The test taker put this odd numbers of negative to make us think that the product is negative. But that is a trap. Unless, it is stated that there is NO zero element OR there are no other elements. Then we are certain, it's negative. Hence Insufficient.
Please help me understand the concept. In Chapter 2 pg 40 of the guide 1 there is a Q
Is product of all the elements in Set S negative?
i) All of the elements in S are negative
ii) There are 5 negative numbers in Set S
Book explains :
i) Odd number of negatives so ans will be negative - INSUFFICIENT (understood).
ii) " Based on what we have learned so far it seems that the statement (ii) tells us that the product must be negative. However if any of the elements in Set S equals zero, then the product of the element in Set S will be zero which is NOT negative. Therefore Statement (ii) is INSUFFICIENT"
I am unable to understand why is zero an option here. Zero is neither +ve not -ve. So how can we consider 0 as an option here?
Thanks in advance.