Consecutive numbers

[sri_r]

If the sum of n consecutive integers is 2, which of the following
must be true?
I. n is an even number
II. n is an odd number
III. The median of the n integers is equal to the average
(arithmetic mean).
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III

For case (I) to be true, the only possible set of values is {-1,0,1,2}. But suppose if n is 2, then there won't be any solution. The question asks for "must be" true and not "could be".

So I think the answer for this question is C.

Is it right?

[Brent@GMATPrepNow]

If the sum of n consecutive integers is 2, which of the following
must be true?
I. n is an even number
II. n is an odd number
III. The median of the n integers is equal to the average
(arithmetic mean).
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III

For case (I) to be true, the only possible set of values is {-1,0,1,2}. But suppose if n is 2, then there won't be any solution. The question asks for "must be" true and not "could be".

So I think the answer for this question is C.

Is it right?

You're correct - the answer is C

First off, there's a nice rule that says, "If the numbers in a set are equally spaced, then the mean and median of that set are equal"
Since the numbers in this question are consecutive (which are equally spaced), we know that the mean = median.
This means that statement III must be true, so we can eliminate answer choices A and B.

Regarding the even/odd thing, consider two possible cases.
Case a: The numbers are {-1, 0, 1, 2} in which case the sum is 2 and there are 4 integers, which means n is even
Case b: The number is {2} in which case the sum is 2 and there is 1 integer, which means n is odd
Since n need not be even or odd, statements I and II need not be true.

Answer = C

Aside: I have a feeling that you're asking this question because you're curious whether one number (as in case b) can be consider "consecutive integers." I've never seen a GMAT question hinge on this concept. So, if a question were to exclude the possibility of having 1 consecutive integer, there would be some wording around that. Since there's no such wording here, I believe the answer is C.

Cheers,
Brent

[Rudy414]

If the sum of n consecutive integersis 2, which of the following
must be true?

Case b: The number is {2} in which case the sum is 2 and there is 1 integer, which means n is odd

Doesn't the word 'integers' imply that n > 1, and since it represents a set of integers,it can't just be the number 2? As far as I can tell, the only possible solution for n consecutive integers that equal 2 is {-1, 0, 1, 2}, and that means n is even. So isn't I. true also?

[Brent@GMATPrepNow]

Doesn't the word 'integers' imply that n > 1, and since it represents a set of integers,it can't just be the number 2? As far as I can tell, the only possible solution for n consecutive integers that equal 2 is {-1, 0, 1, 2}, and that means n is even. So isn't I. true also?

No, the word "integers" does not imply that n > 1.
Similarly, if a question says that "Joe has x children" we cannot assume that Joe has more than 1 child because "children" is plural.

Take this official guide question: If q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

Here, the words "consecutive integers" do not rule out the possibility that the set = {120}. In fact, the fastest approach to the question is to consider this possibility.

See https://www.beatthegmat.com/og13-q91-wor ... 18035.html for the complete question (and 2 different solutions).

Cheers,
Brent

[Rudy414]

Thanks. I find that wording of the question to be confusing, but that example does make a lot of sense.