It is currently 23 Feb 2018, 04:27

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If s is the sum of all integers from 1 to 30, inclusive, what is the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43893
If s is the sum of all integers from 1 to 30, inclusive, what is the [#permalink]

Show Tags

New post 28 Jun 2017, 00:28
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

62% (01:49) correct 38% (02:04) wrong based on 87 sessions

HideShow timer Statistics

Intern
Intern
User avatar
B
Joined: 25 Apr 2017
Posts: 48
GMAT 1: 700 Q49 V35
WE: General Management (Education)
Reviews Badge
Re: If s is the sum of all integers from 1 to 30, inclusive, what is the [#permalink]

Show Tags

New post 28 Jun 2017, 07:35
Sum of all the integers 1 through 30 inclusive = number of terms multiplied by (first term plus last term) divided by 2.
So, s = 30x31/2 = 465.
Factors of 465 = 1,3,5,15,31,93,155,465.
Sum = 768.
DS Forum Moderator
avatar
G
Joined: 21 Aug 2013
Posts: 799
Location: India
Premium Member CAT Tests
Re: If s is the sum of all integers from 1 to 30, inclusive, what is the [#permalink]

Show Tags

New post 28 Jun 2017, 08:30
2
This post was
BOOKMARKED
Sum of integers from 1 to 30 = 30*31/2 = 15*31 = 3*5*31

Now there is a formula for calculating sum of all factors of a number. First we write a number in its 'prime factorised' form as:

N = a^p * b^q * c^r.. where a,b,c.. are distinct prime numbers in the base and p,q,r.. are their powers.. Then the formula for calculating sum of factors of N is:

Sum of factors of N = (1 + a + a^2 + ...+ a^p)(1 + b + b^2 +...+ b^q)(1 + c + c^2 +...+ c^r)..

Applying the same here, our number = 3*5*31
Required sum = (1+3)(1+5)(1+31) = 4*6*32 = 768. Hence E answer
Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If s is the sum of all integers from 1 to 30, inclusive, what is the [#permalink]

Show Tags

New post 28 Jun 2017, 10:29
2
This post was
BOOKMARKED
Bunuel wrote:
If s is the sum of all integers from 1 to 30, inclusive, what is the sum of all the factors of s?

(A) 303
(B) 613
(C) 675
(D) 737
(E) 768


\(s = \frac{(30 + 1)30}{2}\)

Or, \(s = \frac{(30 + 1)15}{2}\)

Or, \(s = 465\)

Factors of \(465 = 3 * 5 * 31\)

So, sum of all the factors will be \((3+1)(5+1)(31+1) = 4*6*32 = 768\)

Thus, answer must be (E)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Intern
avatar
Joined: 18 Sep 2017
Posts: 4
Re: If s is the sum of all integers from 1 to 30, inclusive, what is the [#permalink]

Show Tags

New post 07 Feb 2018, 04:36
Hi Abhishek,

I don't understand why do you add one to each of the prime factors of 465 and then multiply them.

Besides that I find your methodology elegant and efficient!

Thanks
DS Forum Moderator
avatar
G
Joined: 21 Aug 2013
Posts: 799
Location: India
Premium Member CAT Tests
Re: If s is the sum of all integers from 1 to 30, inclusive, what is the [#permalink]

Show Tags

New post 07 Feb 2018, 04:42
louisd8 wrote:
Hi Abhishek,

I don't understand why do you add one to each of the prime factors of 465 and then multiply them.

Besides that I find your methodology elegant and efficient!

Thanks


Hi

Thats actually a formula to calculate the sum of factors of a number. I have explained that formula in this solution:

https://gmatclub.com/forum/if-s-is-the- ... l#p1878412
Re: If s is the sum of all integers from 1 to 30, inclusive, what is the   [#permalink] 07 Feb 2018, 04:42
Display posts from previous: Sort by

If s is the sum of all integers from 1 to 30, inclusive, what is the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.