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Is S negative .........

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Is S negative .........

by akashkumar1987 » Tue Oct 16, 2012 7:00 am
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.

Answer says the statement 2 is insufficient but why ??

The Correct Answer s 'C'
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Oct 16, 2012 7:33 am
akashkumar1987 wrote:Answer says the statement 2 is insufficient but why ??
It would seem that if there are 5 negative numbers, then the product should be negative. However, if one of the other numbers is 0, then the product is not negative.

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by Brent@GMATPrepNow » Tue Oct 16, 2012 7:40 am
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

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by anuprajan5 » Tue Oct 16, 2012 9:42 am
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

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Brent,

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

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by Brent@GMATPrepNow » Tue Oct 16, 2012 9:52 am
anuprajan5 wrote: Brent,

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

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You're right. Zero is non-negative integer.
However, statement 2 does not say that all of the numbers are negative. In fact, it doesn't say that there are exactly 5 numbers in set S.
All it tells us is that, within set S, you will find 5 negative numbers (and possibly some other non-negative numbers).

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by anuprajan5 » Tue Oct 16, 2012 9:55 am
brilliant! Missed that.

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by gaurvipul » Wed Oct 17, 2012 5:54 am
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.
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by akashkumar1987 » Sat Oct 27, 2012 7:11 am
@ All -- Thanks Guys
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