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Is the product of all of the elements in Set S negative? [#permalink]

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17 Jan 2012, 17:57

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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.

--- I understand the official answer, but I am having trouble with an explanation by the MGMAT book given for Statement 2.

The book says that statement 2 is insufficient: "However, if any of the elements in Set S equals zero, then the product of the elements in Set S will be zero, which is NOT negative."

What? I thought that statement two is telling us that there are basically five negative elements in Set S, and if 0 is not positive or negative, then why are we even considering 0 as an element in Set S?

Re: Is the product of all of the elements in Set S negative? [#permalink]

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17 Jan 2012, 18:29

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rdevorse 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.

--- I understand the official answer, but I am having trouble with an explanation by the MGMAT book given for Statement 2.

The book says that statement 2 is insufficient: "However, if any of the elements in Set S equals zero, then the product of the elements in Set S will be zero, which is NOT negative."

What? I thought that statement two is telling us that there are basically five negative elements in Set S, and if 0 is not positive or negative, then why are we even considering 0 as an element in Set S?

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

First of all, in order the product of all of the elements in Set S to be negative: A. there should be odd number of negative terms in set S AND B. zero shouldn't be in set S. Note that we are not concerned about positive terms at all. Also note that if even one of the condition fails, the product of all of the elements will not be negative: it'll be either zero (in case zero is in the set) or positive (if there is no zero in the set but number of negative terms is even: 0, 2, 4, ...)

(1) All of the elements in Set S are negative --> the second condition is met: there is no zero in the set. Though we don't know whether the first condition is met: if number of all these negative terms is even, then the product will be positive but if number of all these negative terms is odd, then the product will be negative. Not sufficient.

(2) There are 5 negative numbers in Set S --> the first condition is met: there is odd number of negative terms in the set. But again we don't know whether the second condition is met: if zero is in the set, then the product will be zero but if it is not, then the product will negative. Not sufficient.

(1)+(2) From (1) the second condition is met and from (2) the first condition is met, hence the product is odd (there are only 5 terms in the set and all are negative --> product=negative). Sufficient.

Re: Is the product of all of the elements in Set S negative? [#permalink]

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17 Jan 2012, 18:45

I'm still stuck on Statement 2. It says that "There are 5 negative numbers in the set."

If we know for sure that there are 5 negative numbers in the set, although zero is an integer, it is neither positive or negative. Then why are considering zero to possibly be in the set of 5 numbers if it is not negative? _________________

"Continuos effort - not strength or intelligence - is the key to unlocking our potential." - Winston Churchill

Re: Is the product of all of the elements in Set S negative? [#permalink]

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17 Jan 2012, 18:51

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Expert's post

rdevorse wrote:

I'm still stuck on Statement 2. It says that "There are 5 negative numbers in the set."

If we know for sure that there are 5 negative numbers in the set, although zero is an integer, it is neither positive or negative. Then why are considering zero to possibly be in the set of 5 numbers if it is not 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}.

Re: Is the product of all of the elements in Set S negative? [#permalink]

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12 Jul 2014, 19:56

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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

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.

Re: Is the product of all of the elements in Set S negative? [#permalink]

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13 Mar 2015, 23:39

rdevorse 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.

--- I understand the official answer, but I am having trouble with an explanation by the MGMAT book given for Statement 2.

The book says that statement 2 is insufficient: "However, if any of the elements in Set S equals zero, then the product of the elements in Set S will be zero, which is NOT negative."

What? I thought that statement two is telling us that there are basically five negative elements in Set S, and if 0 is not positive or negative, then why are we even considering 0 as an element in Set S?

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

Re: Is the product of all of the elements in Set S negative? [#permalink]

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19 Mar 2016, 19:47

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: Is the product of all of the elements in Set S negative? [#permalink]

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20 Apr 2016, 15:29

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.

Re: Is the product of all of the elements in Set S negative? [#permalink]

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21 Apr 2016, 00:23

Expert's post

amritar wrote:

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. _________________

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