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

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Is the product of all of the elements in Set S negative? [#permalink] New post 17 Jan 2012, 16:57
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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?
[Reveal] Spoiler: OA

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Re: Is the product of all of the elements in Set S negative? [#permalink] New post 17 Jan 2012, 17:29
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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.

Answer: C.

Hope it's clear.
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Re: Is the product of all of the elements in Set S negative? [#permalink] New post 17 Jan 2012, 17:45
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?
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Re: Is the product of all of the elements in Set S negative? [#permalink] New post 17 Jan 2012, 17:51
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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}.

Hope it's clear.
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Re: Is the product of all of the elements in Set S negative? [#permalink] New post 17 Jan 2012, 17:54
I understand now, thank you
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Re: Is the product of all of the elements in Set S negative? [#permalink] New post 22 May 2013, 02:40
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Re: Is the product of all of the elements in Set S negative? [#permalink] New post 12 Jul 2014, 18:56
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Re: Is the product of all of the elements in Set S negative?   [#permalink] 12 Jul 2014, 18:56
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