Is the product of all of the elements in Set S negative?

"There are 5 negative numbers in the set" means that number of negative terms in the set is 5, but it doesn't necessarily mean that there is ONLY 5 terms in the set. There can be more than 5 terms in the set: 6, 7, 100, ... (out of which 5 are negative) and one of these other terms can be zero, for example: {-1, -2, -3, -4, -5, 0}.

Hope it's clear.

I understand now, thank you

From Stmt 1 : We can get to know if all numbers are negative then if there were an even set of negative numbers their product would be positive ,
else if there were an odd set of negative numbers their product would be negative.
Statement 1 lacks this information on the number of negative numbers ( ' All of the elements in Set S are negative' is too broad ) .
Hence insufficient.

From Stmt 2 : It only tells us there are 5 negative numbers in the set , but what about other numbers in the set , there could be a 0 also in the set .
Then the product of all elements in the set would be 0 and not negative . Hence Stmt 2 is also insufficient .

When we combine Stmt 1 and Stmt 2 , we now are aware of both the number of elements ( 5 elements ) and all elements are negative . Hence we will be able to get a definitive answer. Answer is C


Refer to : https://gmatclub.com/forum/is-the-product-of-all-of-the-elements-in-set-s-negative-126212.html similar question

Hi webhishek,

Some Test Takers will read this question and naturally "see" all of the possibilities. That can be a dangerous way of dealing with this Test though, since if you "miss" any of the possibilities or don't properly note a given detail, then you'll get the question wrong and not even know it. As such, proper note-taking is a MUST; you should get in the habit of finding a way to PROVE that you're correct. Here, we can TEST VALUES.

The prompt asks us if the PRODUCT of all the numbers in Set S is NEGATIVE. This is a YES/NO question. We are NOT told how many numbers are in the set, nor if they're positive, negative or 0.

Fact 1: All of the elements in Set S are NEGATIVE.

IF the set is...
{-1, -2]
Then the product is positive and the answer to the question is NO.

IF the set is....
{-1, -2, -3}
Then the product is negative and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: There are 5 negative numbers in Set S.

This does NOT tell us the total number of items in Set S (nor what those additional numbers might be)

IF the set is...
{-1, -2, -3, -4, -5}
Then the product is negative and the answer to the question is YES.

IF the set is...
{-1, -2, -3, -4, -5, 0}
Then the product is 0 and the answer to the question is NO.
Fact 2 is INSUFFICIENT.

Combined, we know:
ALL of the elements in Set S are NEGATIVE
There are 5 NEGATIVE numbers.
This mean that there are only 5 numbers AND that they're all negative, so the product MUST be negative and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

The approach is
1. if all of the elements is set are negative, we don't know whether there are even or odd number of elements .
Product might be or might not be -ve ,Not sufficient
2. If there are 5 elements in set S,Answer is sufficient but if there are 6 elements in set and 6th element is 0, product is 0.
Hence Not sufficient.

I+II

Tells there are 5 elements in Set S ,All are negative
OA=C

I dont understand why after both statements, Its Data sufficient.
The first statement gives us there are all negative elements in the set and second statement combined gives us that 5 of them are negative.
So the S={-1,-2,-3,-4,-5,-x,-y,... } How does this make the both statements sufficient together?

Apologise but then i feel they are not sufficient together.

When combined we have that there are 5 negative integers in the set. Therefore their product is negative. Please read the solutions provided above for better understanding.

We don't know whether or not 0 is in the set

B

Brilliant question by manhattan. It really does not require any pen and paper to solve but need logic .
Statement 1 says only that All elements are negative. However we do not know whether no. of elements are odd or even. So Not sufficient

Statement 2 says that There are 5 negative numbers in the set but we do not know if there are only five negative numbers in the set and nothing else. May be there are some 0s as well. SoNot sufficient

But when you combined both, you have all numbers are negative and there are five negative numbers in the set . So basically there are only five negative numbers in the set and nothing else.
HenceSufficient

Answer should be C

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