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Which of following cannot be true if sum of k consecutive

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goodyear2013
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Which of following cannot be true if sum of k consecutive [#permalink] New post   14 Jan 2014, 05:46
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Which of the following cannot be true if the sum of k consecutive integers is 0?

I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative

A. I only
B. II only
C. III only
D. I and III
E. I, II and III

Explanation
Show Spoiler
(I) Because sum must be zero, series must include +ve & -ve numbers.
If series is -1, 0 and 1. Product will be zero, which is not +ve.
As any series of numbers we pick will have a product that is zero, product cannot be +ve
(Because integers must be consecutive, hence series must contain zero).
(I) cannot be true.

(II) Series could simply consist of integer 0.
(II) could be true.

(III) If largest integer is -1 → other integers must be -2, -3,….
Sum of these numbers could never be 0.
(III) cannot be true.


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D
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Bunuel
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Re: Which of following cannot be true if sum of k consecutive [#permalink] New post   14 Jan 2014, 06:56
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goodyear2013 wrote:
Which of the following cannot be true if the sum of k consecutive integers is 0?

I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative

A. I only
B. II only
C. III only
D. I and III
E. I, II and III

Explanation
Show Spoiler
(I) Because sum must be zero, series must include +ve & -ve numbers.
If series is -1, 0 and 1. Product will be zero, which is not +ve.
As any series of numbers we pick will have a product that is zero, product cannot be +ve
(Because integers must be consecutive, hence series must contain zero).
(I) cannot be true.

(II) Series could simply consist of integer 0.
(II) could be true.

(III) If largest integer is -1 → other integers must be -2, -3,….
Sum of these numbers could never be 0.
(III) cannot be true.


Which of the following cannot be true if the sum of k consecutive integers is 0?

I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative

A. I only
B. II only
C. III only
D. I and III
E. I, II and III

For the sum of k consecutive integers to be 0 we must have one of the following cases: {0}, {-1, 0, 1}, {-2, -1, 0, 1, 2}, ..., {..., -3, -2, -1, 0, 1, 2, 3, ...}.

I. The product of the k integers is positive. As you can see the product of the integers in either of these sets is always 0, thus I cannot be true.

II. The smallest of the k integers is zero. If the set is {0}, then it's possible.

III. The largest of the k integers is negative. As you can see the largest of the integers is always more than or equal to zero, thus III cannot be true.

Answer: D.

P.S. Overall the question is not good, because of the second option. I wouldn't expect GMAT to include a statement which is that ambiguous.
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Re: Which of following cannot be true if sum of k consecutive [#permalink] New post   19 Jun 2015, 14:18
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Bunuel wrote:

II. The smallest of the k integers is zero. If the set is {0}, then it's possible.

P.S. Overall the question is not good, because of the second option. I wouldn't expect GMAT to include a statement which is that ambiguous.


I completely agree with you - it really makes no logical sense to call the set "{0}" a set of "consecutive integers". For one thing, it's a set of only one integer, so it's not a set of "integers", but the bigger problem is that the word "consecutive" necessarily describes the relationship between two or more things. You can't say that a single number is a 'consecutive integer'; that's meaningless. Not a well-conceived question.
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Re: Which of following cannot be true if sum of k consecutive [#permalink] New post   21 Jun 2015, 04:14
Bunuel wrote:
goodyear2013 wrote:
Which of the following cannot be true if the sum of k consecutive integers is 0?

I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative

A. I only
B. II only
C. III only
D. I and III
E. I, II and III

Explanation
Show Spoiler
(I) Because sum must be zero, series must include +ve & -ve numbers.
If series is -1, 0 and 1. Product will be zero, which is not +ve.
As any series of numbers we pick will have a product that is zero, product cannot be +ve
(Because integers must be consecutive, hence series must contain zero).
(I) cannot be true.

(II) Series could simply consist of integer 0.
(II) could be true.

(III) If largest integer is -1 → other integers must be -2, -3,….
Sum of these numbers could never be 0.
(III) cannot be true.


Which of the following cannot be true if the sum of k consecutive integers is 0?

I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative

A. I only
B. II only
C. III only
D. I and III
E. I, II and III

For the sum of k consecutive integers to be 0 we must have one of the following cases: {0}, {-1, 0, 1}, {-2, -1, 0, 1, 2}, ..., {..., -3, -2, -1, 0, 1, 2, 3, ...}.

I. The product of the k integers is positive. As you can see the product of the integers in either of these sets is always 0, thus I cannot be true.

II. The smallest of the k integers is zero. If the set is {0}, then it's possible.

III. The largest of the k integers is negative. As you can see the largest of the integers is always more than or equal to zero, thus III cannot be true.

Answer: D.

P.S. Overall the question is not good, because of the second option. I wouldn't expect GMAT to include a statement which is that ambiguous.



Hi Bunuel,

Hope you're doing great. Somehow, I don't agree with you considering {0} as the smallest number when there is only one integer in set, as question clearly states k consecutive "integers". Though, I agree that question certainly is ambiguous. :? Hope not to see such Q in real GMAT.

Regards,
Gaurav
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Bunuel
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Re: Which of following cannot be true if sum of k consecutive [#permalink] New post   21 Jun 2015, 10:46
Expert Reply
GauravSolanky wrote:
Bunuel wrote:
goodyear2013 wrote:
Which of the following cannot be true if the sum of k consecutive integers is 0?

I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative

A. I only
B. II only
C. III only
D. I and III
E. I, II and III

Explanation
Show Spoiler
(I) Because sum must be zero, series must include +ve & -ve numbers.
If series is -1, 0 and 1. Product will be zero, which is not +ve.
As any series of numbers we pick will have a product that is zero, product cannot be +ve
(Because integers must be consecutive, hence series must contain zero).
(I) cannot be true.

(II) Series could simply consist of integer 0.
(II) could be true.

(III) If largest integer is -1 → other integers must be -2, -3,….
Sum of these numbers could never be 0.
(III) cannot be true.


Which of the following cannot be true if the sum of k consecutive integers is 0?

I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative

A. I only
B. II only
C. III only
D. I and III
E. I, II and III

For the sum of k consecutive integers to be 0 we must have one of the following cases: {0}, {-1, 0, 1}, {-2, -1, 0, 1, 2}, ..., {..., -3, -2, -1, 0, 1, 2, 3, ...}.

I. The product of the k integers is positive. As you can see the product of the integers in either of these sets is always 0, thus I cannot be true.

II. The smallest of the k integers is zero. If the set is {0}, then it's possible.

III. The largest of the k integers is negative. As you can see the largest of the integers is always more than or equal to zero, thus III cannot be true.

Answer: D.

P.S. Overall the question is not good, because of the second option. I wouldn't expect GMAT to include a statement which is that ambiguous.



Hi Bunuel,

Hope you're doing great. Somehow, I don't agree with you considering {0} as the smallest number when there is only one integer in set, as question clearly states k consecutive "integers". Though, I agree that question certainly is ambiguous. :? Hope not to see such Q in real GMAT.

Regards,
Gaurav


You are repeating the same thing I mention about this statement in my solution and this post.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: Which of following cannot be true if sum of k consecutive [#permalink]
21 Jun 2015, 10:46
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