gmattokyo wrote:

If the sum of \(N\) consecutive odd integers is \(N^2\) , what is the sum of all odd integers between 13 and 39 inclusive?

* 351

* 364

* 410

* 424

* 450

I calculated this as (the stem says N consecutive odd integers):

\((39-13)/2 + 1=14\)

\(14^2=196\), which is not in answer list.

OE says calculate the range 1-39 and subtract the range 1-11. \(20^2 - 6^2\)

I think this applies if the question stem says "sum of 1st N consecutive odd integers?"

Else please comment on which part is causing the misunderstanding...

Yes. It has to be N consecutive odd integers starting from 1.

In fact, this is a property and not just specific for this particular question.

The property is that for n consecutive odd integers starting from 1 (or -1 when all values are negative),

(a) sum = \(n^2\) for all positive values.

(b) sum = \(-n^2\) for all negative values.

Another interesting property is that for n consecutive even integers starting from 0 (0 included) ,

(a) sum = \(n^2 - n\) for all positive values.

(b) sum = \(-(n^2 - n)\) for all negative values.

Note: In either case, the property is not valid when the set contains both positive and negative values.

Ps. We can even combine both of them to find the sum of N consecutive integers starting from 0.

_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders!

http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!

1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html

2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html

3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html