Problem Solving

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

The product of the k integers is positive
The smallest of the k integers is zero
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

E?

assuming k = 2 and higher

I don't have much confidence when it comes to the GMAT, but let's see if I can tackle this. Hopefully, it'll give me some confidence needed to motivate me.

I) If some of the consecutive numbers are negatives, and if the number of integers in the set could be either even or odd, the product of the consecutive numbers could be either positive or negative. So (I) could be true, but not necessarily so.

(II) If the smallest of the k integers is zero, then each other integers in the set is a positive value greater than zero. Adding all these positives together will give you a larger positive value and not the zero indicated in the question stem. So (II) cannot be true.

(III) If the largest of the integers is negative, then each other integer in the set is a negative. Adding together negatives will only give you a larger negative value and not zero. So (III) cannot be true.

I think the answer is III only.

k does not have to be greater than 1 (no where given) - This is the catch to this problem in my opinion

k could be 1 consecutive integer i.e 0 The smallest /largest of the k integers are both zero


The product of the k integers is positive -2 -1 1 2



The largest of the k integers is negative - This cannot be true since there has to be some positives to make the sum 0 or just 0 which is non negative

Emawk wrote:I don't have much confidence when it comes to the GMAT, but let's see if I can tackle this. Hopefully, it'll give me some confidence needed to motivate me.

I) If some of the consecutive numbers are negatives, and if the number of integers in the set could be either even or odd, the product of the consecutive numbers could be either positive or negative. So (I) could be true, but not necessarily so.

(II) If the smallest of the k integers is zero, then each other integers in the set is a positive value greater than zero. Adding all these positives together will give you a larger positive value and not the zero indicated in the question stem. So (II) cannot be true.

(III) If the largest of the integers is negative, then each other integer in the set is a negative. Adding together negatives will only give you a larger negative value and not zero. So (III) cannot be true.

I didn't think this through carefully enough.

No worries.I made a mistake also.

-2 -1 1 2 are not consecutive integers.

So the answer is D) (0 is non positive non negative so the product cannot be positive)

I give up if thats not it I think the key in GMAT is to check/recheck as quickly as possible if indeed u have confirmed to the question stem in picking numbers. Fro eg: They would have asked x+2 and we would be answering x and both will be answer choices in the problem

cramya wrote:No worries.I made a mistake also.

-2 -1 1 2 are not consecutive integers.

So the answer is D) (0 is non positive non negative so the product cannot be positive)

I give up if thats not it I think the key in GMAT is to check/recheck as quickly as possible if indeed u have confirmed to the question stem in picking numbers. Fro eg: They would have asked x+2 and we would be answering x and both will be answer choices in the problem

How did you come to the conclusion that (I) cannot be true?

How did you come to the conclusion that (I) cannot be true?

The product will always be 0(since 0 will occur in the list if its just 1 consectuive intger or more), correct which is non positive so I cannot be true.

cramya wrote:

How did you come to the conclusion that (I) cannot be true?

The product will always be 0(since 0 will occur in the list if its just 1 consectuive intger or more), correct which is non positive so I cannot be true.

cramya is correct, D is the OA.

I wanted to make sure everyone sees the tricky part of (II). I got this wrong because I automatically assumed that "consecutive" number has to be greater than 1.. but since it's not stated that k>0, it's a possibility that these consecutive number was actually a single digit, 0.

The smallest of the k integers is zero

If this statement is CORRECT...and the trick is oh the set is 0...I dont call this a trick or a trap..it is just stupid!

I am mad

cramya wrote:

How did you come to the conclusion that (I) cannot be true?

The product will always be 0(since 0 will occur in the list if its just 1 consectuive intger or more), correct which is non positive so I cannot be true.

Damn, I should have seen that.

lunarpower wrote:as many posters have already noted, the correct answer to this problem is (d).

you guys can rest easy re: the trick thing. i simply can't imagine that the gmat would actually include a cheap shot such as statement (ii), which is only true when k = 0.

there are two grammatical hurdles there: first of all, it distinctly says "integers" (plural), and, second of all, it distinctly says "smallest" (-est implies 3 or more numbers).

Thanks Lunarpower. This is exactly why I thought that this question could not be a good representative of GMAT.

But I guess - I should have been more careful and thought all the possible solutions.

lol

good stuff