GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 23:54

### 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

# Find the sum of divisors of 544 excluding 1 and 544

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

### Hide Tags

Current Student
Joined: 28 May 2014
Posts: 515
GMAT 1: 730 Q49 V41
Find the sum of divisors of 544 excluding 1 and 544  [#permalink]

### Show Tags

23 Jan 2017, 20:48
2
00:00

Difficulty:

45% (medium)

Question Stats:

66% (02:36) correct 34% (02:14) wrong based on 29 sessions

### HideShow timer Statistics

Find the sum of divisors of 544 excluding 1 and 544.
(A) 1089
(B) 545
(C) 589
(D) 1134
(E)1589

_________________
Manager
Joined: 25 Jun 2016
Posts: 61
GMAT 1: 780 Q51 V46
Re: Find the sum of divisors of 544 excluding 1 and 544  [#permalink]

### Show Tags

23 Jan 2017, 21:30
We can prime factor 544 to 2*2*2*2*2*17. And we can find all the factors of 544 by considering every way the prime factors can be combined. So:

2=2
2*2=4
2*2*2=8
2*2*2*2=16
2*2*2*2*2=32
17=17
17*2=34
17*2*2=68
17*2*2*2=136
17*2*2*2*2=272
17*2*2*2*2*2=544 (Disregard, since the question stem tells us to)
(We can also think of the factor of 1 as the case in which we don't choose any of the PFs, but we disregard that here since the question stem tells us to)

So we have:

2+4+8+16+32+17+34+68+136+272 = 589

(There are lots of ways to do the addition. Looking for shortcuts, I first saw that the sum would be odd since there was only one odd number in our list. Sadly, this only eliminated one answer. Then I just added up the units digits to find that our sum would end in 9. Sadly, this just eliminated one more answer. Then I added them up out of order, something like this:

(2+8) + (16+4) + (32+68) + (34+136) + 272 + 17=
10 + 20 + 100 + 170 + 272 + 17 =
300 + 272 + 17 = 589

For this question, I think it might have been faster just to add them up the conventional way, but the odd/even trick and the last digit trick often pay off on such questions. Perhaps a combination of estimation and the last digit trick would have been fastest here.)

For more on the logic behind finding all the factors of a number see this video: https://www.youtube.com/watch?v=njePP0ZK2bY
Manager
Joined: 27 Nov 2016
Posts: 53
Location: India
Concentration: General Management, International Business
GPA: 2.71
WE: Consulting (Consulting)
Re: Find the sum of divisors of 544 excluding 1 and 544  [#permalink]

### Show Tags

23 Jan 2017, 22:20
4
saswata4s wrote:
Find the sum of divisors of 544 excluding 1 and 544.
(A) 1089
(B) 545
(C) 589
(D) 1134
(E)1589

544 = ( 2^5 * 17 )

The sum of divisors of 544 =

(2^0 + 2^1 + 2^2 + 2^3 + 2^4 + + 2^5 ) (17^0 + 17 ^1 ) = (1 + 2 + 4 + 8 + 16 + 32 ) (1 + 17)
= 63 * 18 = 1134

Since we have to exclude 1 & 544 , subtract 545 from 1134 = 589 (Answer )

Similarly , for number of divisor. Considering this expression (2^0 + 2^1 + 2^2 + 2^3 + 2^4 + + 2^5 ) (17^0 + 17 ^1 )

6 * 2 = 12

Then subtract 2 from this as we don't have to consider 1 & 544.
Non-Human User
Joined: 09 Sep 2013
Posts: 13384
Re: Find the sum of divisors of 544 excluding 1 and 544  [#permalink]

### Show Tags

04 Feb 2019, 19:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Find the sum of divisors of 544 excluding 1 and 544   [#permalink] 04 Feb 2019, 19:20
Display posts from previous: Sort by

# Find the sum of divisors of 544 excluding 1 and 544

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne