It is currently 22 Mar 2018, 16:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The sum of the odd positive integers from 1 to k equals to

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Senior Manager
Joined: 19 Mar 2008
Posts: 350
The sum of the odd positive integers from 1 to k equals to [#permalink]

### Show Tags

15 Aug 2008, 09:21
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions

### HideShow timer Statistics

The sum of the odd positive integers from 1 to k equals to 441. What is the value of k?

47
41
37
33
29

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Director
Joined: 12 Jul 2008
Posts: 513
Schools: Wharton
Re: PS: Sum to 441 [#permalink]

### Show Tags

15 Aug 2008, 12:23
judokan wrote:
The sum of the odd positive integers from 1 to k equals to 441. What is the value of k?

47
41
37
33
29

Fastest way, I think, is just to do the addition. There is a trick for adding evenly spaced numbers. Just do the lowest number first. Then you can do quick addition to get the other ones.

If you want to do it mathematically:

Number of odd digits between 1 and k = (k+1)/2

If (k+1)/2 is odd, then

Sum of digits = ((k-1)/4)*(k+1) + (k+1)/2

If (k+1)/2 is even, then

Sum of digits = ((k+1)/4)*(k+1)

A: 576
B: 441
C: 380
D: 289
E: 225
SVP
Joined: 30 Apr 2008
Posts: 1850
Location: Oklahoma City
Schools: Hard Knocks
Re: PS: Sum to 441 [#permalink]

### Show Tags

15 Aug 2008, 13:02
You can also know that

Sum of odd positive integers from 1 to $$k = (\frac{k+1}{2})^2$$

so here, we have 47+1= 48 / 2 = 24 * 24 > 441

41+1=42/2 = 21 * 21 = 441 - bingo

for EVEN NUMBERS

Sum of even positive integers from 2 to k where k is even $$= (\frac{k}{2})*(\frac{k}{2}+1)$$
Example:

The sum of 2 to k = 30

$$(\frac{k}{2})*(\frac{k}{2}+1)=30$$

$$(\frac{k^2}{4}+\frac{k}{2})=30$$

$$(\frac{k^2}{4}+\frac{2k}{4})=30$$

$$\frac{k^2 + 2k}{4}=30$$

$$k^2 + 2k=120$$

$$k^2 + 2k - 120 = 0$$

$$(k + 12)(k - 10) = 0$$

k = -12 or k = 10

k must be positive, so k = 10

judokan wrote:
The sum of the odd positive integers from 1 to k equals to 441. What is the value of k?

47
41
37
33
29

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a.

GMAT Club Premium Membership - big benefits and savings

Re: PS: Sum to 441   [#permalink] 15 Aug 2008, 13:02
Display posts from previous: Sort by

# The sum of the odd positive integers from 1 to k equals to

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.