It is currently 27 Jun 2017, 00:40

### 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

# PS - Factor (m04q31)

Author Message
Director
Joined: 20 Sep 2006
Posts: 653

### Show Tags

17 Sep 2008, 14:34
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A perfect number is defined as one for which the sum of all the unique factors less the number itself equals to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$ . Which of the following is also a perfect number?

(A) 12
(B) 20
(C) 28
(D) 48
(E) 60

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions
SVP
Joined: 30 Apr 2008
Posts: 1874
Location: Oklahoma City
Schools: Hard Knocks

### Show Tags

17 Sep 2008, 21:40
2
KUDOS
There is not really a better way to do this other than realizing that the authors know you're going to have to figure out each answer and sum the numbers to determine if the factors (aside from the number itself) total the number. Because of this quasi-trial & error, it seems that often the test makers will put the correct answer towards the end. I would start with C, D E, A B. That's the order I would work them in. Maybe here A first because 12 is a small number and there certainly are less numbers to total. 1, 2, 3, 4, & 6. That's clearly over 12. Then move to C or D.

In the end, the safest bet is to just work all answers through and be diligent in making sure you rememebr ever factor.

Even if you only save 15 seconds by getting done in 1 min 45 seconds on this question, when you do that on 8 questions, you're an entire question "ahead".
_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings SVP Joined: 30 Apr 2008 Posts: 1874 Location: Oklahoma City Schools: Hard Knocks Re: PS - Factor [#permalink] ### Show Tags 19 Sep 2008, 06:30 2 This post received KUDOS Or, you can just remember that the only perfect numbers less than a million are: 6 28 496 8128 Your choice. This is unlikely to be a GMAT type problem. _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

Joined: 19 Feb 2010
Posts: 394
Re: PS - Factor (m04q31) [#permalink]

### Show Tags

19 Oct 2010, 09:02
1
KUDOS
Wow, I'm surprised that many of you say it's a difficult question. I'm not as good as many of you but could anyways answer it correctly in a short time. I didn't see it difficult because the stem tells you what the perfect number is. Otherwise I would have had to guess...
Intern
Joined: 17 Sep 2008
Posts: 6
Schools: Chicago Booth, Wharton, MIT, Haas

### Show Tags

17 Sep 2008, 14:46
I just brute-forced it :

A- 12: 1,2,3,4,6 ; sum = 16
B- 20: 1,2,4,5,10 ; sum = 22
C- 28: 1,2,4,7,14 ; sum = 28 Yes

Would be interested to know if there's a better way to do this.
Director
Joined: 20 Sep 2006
Posts: 653

### Show Tags

17 Sep 2008, 19:09
Thanks guys .. under the presure of time .. I forgot to take into consideration 4 for 12.
SVP
Joined: 29 Aug 2007
Posts: 2473

### Show Tags

17 Sep 2008, 21:52
rao_1857 wrote:
A perfect number is defined as one for which the sum of all the unique factors less the number itself equals to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$ . Which of the following is also a perfect number?

a) 12
b) 20
c) 28
d) 48
e) 60

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Intern
Joined: 28 Jun 2008
Posts: 8

### Show Tags

18 Sep 2008, 21:30
GMAT TIGER wrote:
rao_1857 wrote:
A perfect number is defined as one for which the sum of all the unique factors less the number itself equals to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$ . Which of the following is also a perfect number?

a) 12
b) 20
c) 28
d) 48
e) 60

Lets take the "luck" factor away from all this, I would start with B or D, if used B and need a higher number, then use D, if after that you need a lower one C is the answer, in case a higher is needed E is the one ( if D is used first same logic aplies). Like in the case a present choosing C as the first one will be the same if you need a higer number you have to use D or E, in case of a lower use A or B. Now assuming you did not get to the answer here you find that a maximum of two plug-ins must be done before getting there.

The difference comes if you use B and need a lower you know the answer is A and if you start with D and need a higher the answer is E.
_________________

Let us to't pell-mell...

VP
Joined: 30 Jun 2008
Posts: 1034

### Show Tags

19 Sep 2008, 00:40
MRGiacalone wrote:

Lets take the "luck" factor away from all this, I would start with B or D, if used B and need a higher number, then use D, if after that you need a lower one C is the answer, in case a higher is needed E is the one ( if D is used first same logic aplies). Like in the case a present choosing C as the first one will be the same if you need a higer number you have to use D or E, in case of a lower use A or B. Now assuming you did not get to the answer here you find that a maximum of two plug-ins must be done before getting there.

The difference comes if you use B and need a lower you know the answer is A and if you start with D and need a higher the answer is E.

Good technique !! But how is this applicable in this case because we just have to find the number which is perfect from the presented choices? Please elaborate

Thanks
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

SVP
Joined: 29 Aug 2007
Posts: 2473

### Show Tags

19 Sep 2008, 06:52
MRGiacalone wrote:
GMAT TIGER wrote:
rao_1857 wrote:
A perfect number is defined as one for which the sum of all the unique factors less the number itself equals to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$ . Which of the following is also a perfect number?

a) 12
b) 20
c) 28
d) 48
e) 60

Lets take the "luck" factor away from all this, I would start with B or D, if used B and need a higher number, then use D, if after that you need a lower one C is the answer, in case a higher is needed E is the one ( if D is used first same logic aplies). Like in the case a present choosing C as the first one will be the same if you need a higer number you have to use D or E, in case of a lower use A or B. Now assuming you did not get to the answer here you find that a maximum of two plug-ins must be done before getting there.

The difference comes if you use B and need a lower you know the answer is A and if you start with D and need a higher the answer is E.

its all chance. either approach needs a max. of 3 attempts but if you start from C, you do not need to do back and forth: first hammer C then D and then finally E. if you start from B and go to D and then C, one may get confused.

anybody has shorter approach?
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Intern
Joined: 28 Jun 2008
Posts: 8

### Show Tags

19 Sep 2008, 09:22
I don't think both approaches need a max of 3 attemps, they need a max of 2, remember that on the GMAT time is everything, after pluging-in two answers you don't need to plug-in a third one just answer it and go to next. In this case is a bit more difficult but try the example below

PS: Remainder Theory
Posted: Mon Sep 15, 2008 5:33 pm
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n ?
A) 7
B) 9
C) 10
D) 11
E) 13
(original choices have been modified)

Get to the right ecuation and try pluging-in numbers for n.

I'll start with B. 10 = 14, too high, I'll need a lower number, only 7 is left so answer is A and go to next. If I needed a higher number I would choose D, as my second attempt, after that if I need an even higher number E is your answer and, if a lower one is needed, C will be your answer. A max. of two attempts, and, without choosing the right answer as my first plug-in by luck, I still have a chance of doing only one attempt.
_________________

Let us to't pell-mell...

SVP
Joined: 30 Apr 2008
Posts: 1874
Location: Oklahoma City
Schools: Hard Knocks

### Show Tags

18 Oct 2010, 06:57
I'm very familiar with the B or D, then adjust depending on whether you need a higher or lower number type approach. This will not work with the perfect number question this threat started with. If you try B) 20, and it doesn't work, then you still don't know if you need a higher or lower number. This question is not the same as an equation question where we will be able to analyze the result of plugging in one number and seeing if it was close or far away from the value given for the equation in the question.

The B or D then higher/lower works well for plugging in numbers but this isn't a typical plugging the numbers question. It's a brute-force question where you just have to figure out which of the 5 possibilities is correct.

MRGiacalone wrote:
I don't think both approaches need a max of 3 attemps, they need a max of 2, remember that on the GMAT time is everything, after pluging-in two answers you don't need to plug-in a third one just answer it and go to next. In this case is a bit more difficult but try the example below

PS: Remainder Theory
Posted: Mon Sep 15, 2008 5:33 pm
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n ?
A) 7
B) 9
C) 10
D) 11
E) 13
(original choices have been modified)

Get to the right ecuation and try pluging-in numbers for n.

I'll start with B. 10 = 14, too high, I'll need a lower number, only 7 is left so answer is A and go to next. If I needed a higher number I would choose D, as my second attempt, after that if I need an even higher number E is your answer and, if a lower one is needed, C will be your answer. A max. of two attempts, and, without choosing the right answer as my first plug-in by luck, I still have a chance of doing only one attempt.

_________________

------------------------------------
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

Intern
Joined: 18 Oct 2010
Posts: 5
Re: PS - Factor (m04q31) [#permalink]

### Show Tags

18 Oct 2010, 15:07
Worked this out quickly by knowing bases. Base 60 and base 10 are the two common bases we use, base 10 for counting, base 60 for time. Both of these are useful because they have a lot of factors. Base 60 is divisible by 1,2,3,4,6. Base 10 divisible by 1,2,5.

12 => base 60
20 => base 10
28 => base 7 (most likely this, check it first)
48 => base 60
60 => base 60
Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London
Re: PS - Factor (m04q31) [#permalink]

### Show Tags

18 Oct 2010, 16:12
This is a really tough question, and I would guess beyond GMAT level as well. There is no easy way to check for perfect numbers very quickly except knowing that the first four are 6,28,496,8128 ... which no sane person should know by heart anyway (for the record, I took it off wikipedia and don't remember them by heart either !!)
_________________
Manager
Joined: 07 Jan 2010
Posts: 143
Location: So. CA
WE 1: 2 IT
WE 2: 4 Software Analyst
Re: PS - Factor (m04q31) [#permalink]

### Show Tags

19 Oct 2010, 08:16
From the GMAT Club math book --

Finding the Sum of the Factors of an Integer

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The sum of factors of n will be expressed by the formula: $$\frac{(a^{p+1}-1)*(b^{q+1}-1)*(c^{r+1}-1)}{(a-1)*(b-1)*(c-1)}$$

Example: Finding the sum of all factors of 450: 450=2^1*3^2*5^2

The sum of all factors of 450 is $$\frac{(2^{1+1}-1)*(3^{2+1}-1)*(5^{2+1}-1)}{(2-1)*(3-1)*(5-1)}=\frac{3*26*124}{1*2*4}$$=1209

Is this technique worth memorizing for the GMAT?
Manager
Joined: 10 Jan 2011
Posts: 237
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)

### Show Tags

21 Oct 2011, 01:47
mmond4 wrote:
I just brute-forced it :

A- 12: 1,2,3,4,6 ; sum = 16
B- 20: 1,2,4,5,10 ; sum = 22
C- 28: 1,2,4,7,14 ; sum = 28 Yes

Would be interested to know if there's a better way to do this.

Such questions requries to factor all the answers. My stratergy for such question is alsways to start with middle number that is C
_________________

-------Analyze why option A in SC wrong-------

Senior Manager
Joined: 15 Sep 2009
Posts: 265
Re: PS - Factor (m04q31) [#permalink]

### Show Tags

22 Oct 2012, 05:24
Prepared test takers are always quick in deciding how to approach a question. Typically, one should decide his/her approach not more than 10 seconds after reading the questions. Next step would be stick to your approach with reasonable conviction; however, one should bear in mind that the key to excelling on quant is flexibility, so there is no need not to try another approach if the first does not work.

DO's
Pick a method and start solving
Be flexible--try another if the first is not working
Start writing stuff down as soon as you understand what is being asked

DONT's
Don't stare at a question for too long

Cheers,
Der alte Fritz
_________________

+1 Kudos me - I'm half Irish, half Prussian.

Re: PS - Factor (m04q31)   [#permalink] 22 Oct 2012, 05:24
Similar topics Replies Last post
Similar
Topics:
2 PS 4 14 Feb 2013, 06:41
3 ps 2 28 Mar 2011, 00:18
factors 3 12 Nov 2010, 19:05
divisors and factors 9 06 Jan 2011, 01:55
PS: Divisors 6 26 Feb 2009, 07:36
Display posts from previous: Sort by

# PS - Factor (m04q31)

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO 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®.