Data Sufficiency

Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000

Edit: At the first look, I got confused by the word - non-zero numbers. Now I understand. Will post the OA, If needed. Thanks

OA is B.

1) n is even . Not sufficient.
there can be 3 negative and 5 positive numbers.
There can be 4 negative and positive numbers.

2) Product is positive.
suggests that it contains an even number of negative numbers. ( 0 or 2 or 4 etc)

OA: B

pingu wrote:Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000.

Edit: At the first look, I got confused by the word - non-zero numbers. Now I understand. Will post the OA, If needed. Thanks

Non-zero means not zero. In other words, positive or negative.

Statement 1: n is even.
Let Q = {-2, 50,000}.
Does set Q contain an even number of negative numbers? No.
Let Q = (-2, -50,000}.
Does set Q contain an even number of negative numbers? Yes.
Since in the first case the answer is No and in the second case the answer is Yes, insufficient.

Statement 2: The product of all the numbers in Q is 100,000.
If there are an odd number of negative numbers in Q, then the product will be negative.
Thus, the number of negative numbers in Q must be even.
Sufficient.

The correct answer is B.

I'm a bit skeptical of the trap in this question.
Nothing in the problem requires that set Q contain any negative values.
For statement 2 to be sufficient, we have to consider no negative values an even number of negative values.
Such logic typically isn't used in the real world (or on the GMAT). If my candy car contained no lollipops -- perish the thought! -- I wouldn't claim that the jar contained an even number of lollipops.
To avoid confusion, the question could be rephrased:

Does set Q contain an odd number of negative numbers?

The answer would remain the same.

Thanks a Ton. My understanding of non-zero number was wrong. I thought only numbers with out zeros are non-zero numbers. e.g. I did not consider 10, 100, 10,000

My Example Set answers the question:

Let Q = {1, 10,000}.

Does set Q contain an even number of negative numbers?

First the set Q contains NO negative numbers => Zero number of negative Numbers => Even number of negative numbers=> YES


Let Q = (-1, -10,000}.
Does set Q contain an even number of negative numbers? Yes.

I THINK THE ANSWER IS E. THERE MAY OR MAY NOT BE NEGATIVE NUMBERS.

GMATGuruNY wrote:

pingu wrote:Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000.

Edit: At the first look, I got confused by the word - non-zero numbers. Now I understand. Will post the OA, If needed. Thanks

Non-zero means not zero. In other words, positive or negative.

Statement 1: n is even.
Let Q = {-2, 50,000}.
Does set Q contain an even number of negative numbers? No.
Let Q = (-2, -50,000}.
Does set Q contain an even number of negative numbers? Yes.
Since in the first case the answer is No and in the second case the answer is Yes, insufficient.

Statement 2: The product of all the numbers in Q is 100,000.
If there are an odd number of negative numbers in Q, then the product will be negative.
Thus, the number of negative numbers in Q must be even.
Sufficient.

The correct answer is B.

I'm a bit skeptical of the trap in this question.
Nothing in the problem requires that set Q contain any negative values.
For statement 2 to be sufficient, we have to consider no negative values an even number of negative values.
Such logic typically isn't used in the real world (or on the GMAT). If my candy car contained no lollipops -- perish the thought! -- I wouldn't claim that the jar contained an even number of lollipops.
To avoid confusion, the question could be rephrased:

Does set Q contain an odd number of negative numbers?

The answer would remain the same.

According to me the answer should be E. As there can be no negative numbers and only positive numbers and still the product will be a positive number. The question says that set q contains all non-zero numbers and hence it can be positive or negative. please reply....

THE ANSWER SHOULD BE EEEEEEEEEEEEEEEEEEEEE.
FROM 1: IT CAN BE -1,-2,-3,-4 OR IT CAN BE 1,2,3,4. HENCE NOT SUFFICIENT.
FROM 2: THE NO. CAN BE BOTH NEGATIVE AND POSITIVE. ALTHOUGH FROM THIS STATEMENT WE KNOW THAT IF THERE ARE NEGATIVE NO.-- THEIR NUMBERS ARE EVEN. BUT WE DON'T KNOW THAT THE NUMBERS ARE POSITIVE OR NEGATIVE.
FROM STATEMENT 1 AND 2 NOTHING HELP.
HENCE ANSWER IS EEEEEEEEEE

GMATGuruNY wrote:

pingu wrote:Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000.

Edit: At the first look, I got confused by the word - non-zero numbers. Now I understand. Will post the OA, If needed. Thanks

Non-zero means not zero. In other words, positive or negative.

Statement 1: n is even.
Let Q = {-2, 50,000}.
Does set Q contain an even number of negative numbers? No.
Let Q = (-2, -50,000}.
Does set Q contain an even number of negative numbers? Yes.
Since in the first case the answer is No and in the second case the answer is Yes, insufficient.

Statement 2: The product of all the numbers in Q is 100,000.
If there are an odd number of negative numbers in Q, then the product will be negative.
Thus, the number of negative numbers in Q must be even.
Sufficient.

The correct answer is B.

I'm a bit skeptical of the trap in this question.
Nothing in the problem requires that set Q contain any negative values.
For statement 2 to be sufficient, we have to consider no negative values an even number of negative values.
Such logic typically isn't used in the real world (or on the GMAT). If my candy car contained no lollipops -- perish the thought! -- I wouldn't claim that the jar contained an even number of lollipops.
To avoid confusion, the question could be rephrased:

Does set Q contain an odd number of negative numbers?

The answer would remain the same.

Hi Mitch,

I have another view for statement 2. Can we say that the set Q consists of positive numbers?? Hence, we have ZERO negative numbers and zero is even number and therefore it is sufficient.

Thanks

Mo2men wrote:Hi Mitch,

I have another view for statement 2. Can we say that the set Q consists of positive numbers?? Hence, we have ZERO negative numbers and zero is even number and therefore it is sufficient.

Thanks

This line of reasoning is incorrect.
As {-2, -50,000} illustrates, Set Q can be composed of negative numbers and still satisfy the constraint in Statement 2 that the product of the numbers in Q = 100,000.

GMATGuruNY wrote:

Mo2men wrote:Hi Mitch,

I have another view for statement 2. Can we say that the set Q consists of positive numbers?? Hence, we have ZERO negative numbers and zero is even number and therefore it is sufficient.

Thanks

This line of reasoning is incorrect.
As {-2, -50,000} illustrates, Set Q can be composed of negative numbers and still satisfy the constraint in Statement 2 that the product of the numbers in Q = 100,000.

In all cases there is Even number:

if set Q has {-2, -50,000} so we have 2 negative numbers. Even number.

If set Q has {2, 50,000}, we have zero negative number. zero is even.

In all cases, we have EVEN number.

is the line of reasoning valid?