Brent@GMATPrepNow wrote:

akashkumar1987 wrote: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.

Target question: Is the product of all of the elements in Set S negative?

Statement 1: All of the elements in Set S are negative.
There are several scenarios that satisfy this condition. Here are two:
case a: Set S = {-2, -3}, in which case the product is not negative
case b: Set S = {-2, -3, -4}, in which case the product is negative
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: There are 5 negative numbers in Set S.
There are several scenarios that satisfy this condition. Here are two:
case a: Set S = {-1, -1, -1, -1, -1, 0}, in which case the product is not negative
case b: Set S = {-1, -1, -1, -1, -1, 1}, in which case the product is negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
The combined statements tell us that set S consists of 5 negative numbers only, in which case the product is definitely negative
SUFFICIENT

Answer = C

Cheers,
Brent

PS: When posting questions, please use the spoiler function to hide the correct answer. This gives others a chance to try the question

Brent,

Isn't zero a non negative integer? I assume then that you cannot use 0 in the case for statement 2.

REgards
Anup

brilliant! Missed that.

Cheers,
Anup

I would mostly be reiterating what the esteemed members have jotted down above, but here are my 2 cents.

Considering first statement:
(1) All of the elements in Set S are negative.

- If we focus on negating this condition, let us consider 2 sets:
- 1 of 2 elements all -ve. {-1,-1} & another of 3 elements all -ve. {-1,-1,-1}

- In first case product will be +ve and in another case product will be -ve.

So first statement is Insufficient

Considering second statement
(2) There are 5 negative numbers in Set S.

Again, if there is one more negative element in this set, product will be +ve, so 2nd statement alone is insufficient

Combining 1 & 2, it can be rephrased as, All of the 5 elements in Set S are negative.
So, product will be surely -ve, hence Sufficient

I think this is from official guide.

@ All -- Thanks Guys