x is the sum of y consecutive integers

by **tim** Sat Jul 27, 2013 5:37 am

I would certainly not say that this concept MUST be memorized, although it is helpful to know and may save you some time on problems such as these.

As for Z, we cannot say anything about whether Z is odd or even simply from the fact that Y = 2Z.

by **divineacclivity** Sun Sep 15, 2013 11:26 pm

rfernandez Wrote:UPA's solution is akin to how I would solve it as well. I usually find it helpful to express consecutive sets using variables like a, a+1, a+2, etc. and seeing what insights I can draw from that analysis.

Rey

Thanks Rey.
Are consecutive integers equally spaced integers with a constant difference e.g. 2, 5, 8, 11, ... or with a difference of 1 always? Thanks.

by **RonPurewal** Mon Sep 16, 2013 9:21 am

"Consecutive integers", by definition, are spaced apart by intervals of 1 unit. Otherwise they wouldn't be consecutive.

by **divineacclivity** Thu Sep 19, 2013 9:00 pm

RonPurewal Wrote:"Consecutive integers", by definition, are spaced apart by intervals of 1 unit. Otherwise they wouldn't be consecutive.

Thank you.

by **RonPurewal** Fri Sep 20, 2013 12:01 am

You're welcome.

by **lsyang1212** Sun Apr 20, 2014 5:28 pm

Is there a way to solve this question by translating the given information into math formulas, and using these formulas to prove that answer choices A, B, D, and E COULD be true? I understand plugging in numbers is one way, and I understand why C could never be true, but I just want to understand the number theory a bit more.

Thank you!

by **RonPurewal** Mon Apr 21, 2014 5:52 pm

lsyang1212 Wrote:Is there a way to solve this question by translating the given information into math formulas, and using these formulas to prove that answer choices A, B, D, and E COULD be true?

I can't immediately think of anything.

Moreover, I think it's unlikely that any succinct formulas exist. The lack of such algebraic solutions is, in fact, the primary motivation for putting number-properties questions on the exam.

Did you have something in mind? If you do, I can certainly take a peek at it.

by **rustom.hakimiyan** Sun Nov 02, 2014 8:56 pm

For option B, can we rule out negative consecutive integers since the average is a positive 12.5? Meaning, averages do take signs into account, correct?

Thanks!

by **RonPurewal** Wed Nov 05, 2014 4:18 am

rustom.hakimiyan Wrote:For option B, can we rule out negative consecutive integers since the average is a positive 12.5? Meaning, averages do take signs into account, correct?

Thanks!

sorry, i'm not following this.
where are you getting this "average = +12.5"? does this come from the problem that's actually in this thread?

please clarify, thanks.

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