Data Sufficiency

Q. Is the product of all the elements in Set S negative?
I. All of the elements in Set S are negative.
II. There are 5 negative numbers in Set S.

Here's how I have thought this problem:

From ST1: We don't know how many elements are there in the set S. If there are odd number of elements then the product is negative otherwise obviously positive. Hence ST1 is insufficient.

From ST2: It is mentioned that set S has 5 elements and all of them are -ve. So clearly their product is negative. So, according to me ST2 is SUFFICIENT.

But the given answer is choice C. Can anyone please help me with this?
Also, from ST2: 'There are 5 negative numbers in set S' --> Does this mean there are ONLY 5 elements in set S and can't be more? If this is the case then clearly the answer should be B.

Thanks,
Kaushik K

Statement 2 says that there are 5 negative nos.
But, that does not infer that there are only 5 elements in Set S. There could be more.
With both the statements, we can come to the conclusion that the products would be negative.
Hope it helps.

kaushikkumar1987 wrote:Q. Is the product of all the elements in Set S negative?
I. All of the elements in Set S are negative.
II. There are 5 negative numbers in Set S.

From ST2: It is mentioned that set S has 5 elements and all of them are -ve. So clearly their product is negative. So, according to me ST2 is SUFFICIENT.

But the given answer is choice C. Can anyone please help me with this?
Also, from ST2: 'There are 5 negative numbers in set S' --> Does this mean there are ONLY 5 elements in set S and can't be more? If this is the case then clearly the answer should be B.

Hi,
Where is it mentioned that there are only 5 elements in S and all are negative?
From(2): I don't know if we can say that there are more than 5 negative numbers or not but there can be any number of non-negative numbers. Assuming there are only 5 negative numbers, what if there is zero in the set? The product will then become zero. So, we can't surely say that the product will be negative.
Example: Set S = {-5,-4,-3,-2,-1,0,1,2,..}
there are five negative numbers in S. But the product is not negative.

Using (1)&(2) clearly helps us arrive at the answer.

Frankenstein wrote:

kaushikkumar1987 wrote:Q. Is the product of all the elements in Set S negative?
I. All of the elements in Set S are negative.
II. There are 5 negative numbers in Set S.

From ST2: It is mentioned that set S has 5 elements and all of them are -ve. So clearly their product is negative. So, according to me ST2 is SUFFICIENT.

But the given answer is choice C. Can anyone please help me with this?
Also, from ST2: 'There are 5 negative numbers in set S' --> Does this mean there are ONLY 5 elements in set S and can't be more? If this is the case then clearly the answer should be B.

Hi,
Where is it mentioned that there are only 5 elements in S and all are negative?
From(2): I don't know if we can say that there are more than 5 negative numbers or not but there can be any number of non-negative numbers. Assuming there are only 5 negative numbers, what if there is zero in the set? The product will then become zero. So, we can't surely say that the product will be negative.
Example: Set S = {-5,-4,-3,-2,-1,0,1,2,..}
there are five negative numbers in S. But the product is not negative.

Using (1)&(2) clearly helps us arrive at the answer.

Hi,

Thanks for writing in. The reason I am not including zero is because zero is neither positive nor negative. And those 5 elements are negative so there can't be zero AND positive numbers!

Thanks,
Kaushik

kaushikkumar1987 wrote:Q. Is the product of all the elements in Set S negative?
I. All of the elements in Set S are negative.
II. There are 5 negative numbers in Set S.

If we have a even numbered set of numbers that are negative, then the product will be positive. Ex: -2^2= 4. If we have a odd numbered set of numbers that are negative, then the product will be negative. Ex -2^3 = -8

I: We know that all of the integers are negative, but we don't know if our set has an even or odd number of integers. (insufficient)

II: We are told there are five negative numbers in the set, but we don't know if that is all of the numbers in the set. (insufficient)

I/II: We have an set of an odd amount of negative integers, so the product must be negative.


Answer: C

kaushikkumar1987 wrote: Hi,

Thanks for writing in. The reason I am not including zero is because zero is neither positive nor negative. And those 5 elements are negative so there can't be zero AND positive numbers!

Thanks,
Kaushik

Hi,
There are 5 negative numbers in Set S doesn't mean there are only 5 numbers in set S. We know that there are only 5 negative numbers in it and we have no information about other numbers in the set.
I didn't say there is zero in those 5 negative numbers. We know that there are 5 negative numbers but other numbers in the set can be positive or zero. If all others are positive, you can say that the product of all numbers is negative. But if there is a zero, the product cannot be negative. So, using statement 2 alone, you cannot conclude whether the product is negative or not.

a the numbers in the set can be even or odd. not sufficient.

b there can be a zero as an element in the set. not sufficient.

a+b 5 elements (-1,-2,-3,-4,-10) or so. all elements are negative. sufficient.

C it is.