How many factors does 36^2 have? 2 8 24 25 26 : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 18:00

### 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

# How many factors does 36^2 have? 2 8 24 25 26

Author Message
Senior Manager
Joined: 16 Jul 2008
Posts: 289
Followers: 3

Kudos [?]: 16 [0], given: 4

How many factors does 36^2 have? 2 8 24 25 26 [#permalink]

### Show Tags

02 Sep 2008, 12:14
1
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many factors does 36^2 have?

2
8
24
25
26
_________________

http://applicant.wordpress.com/

SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 34

Kudos [?]: 867 [0], given: 5

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 12:18
Nerdboy wrote:
How many factors does 36^2 have?

2
8
24
25
26

2^4*3^4

No of factors = (4+1)*(4+1)=25
_________________

Smiling wins more friends than frowning

Intern
Joined: 08 Jun 2008
Posts: 14
Location: United States (AL)
Concentration: Strategy, Finance
Schools: McCombs '14
GMAT 1: 710 Q46 V42
GPA: 3.81
WE: Information Technology (Accounting)
Followers: 0

Kudos [?]: 16 [0], given: 2

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 13:50
@x2suresh: Can you explain this a little further? I'm not sure I understand how how you did this.

Also, thanks for all your posts on this site. They are very helpful!
VP
Joined: 05 Jul 2008
Posts: 1430
Followers: 39

Kudos [?]: 360 [0], given: 1

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 14:12
Manager
Joined: 11 Apr 2008
Posts: 202
Followers: 2

Kudos [?]: 17 [0], given: 1

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 14:15
36^2=36*36
=4*9*4*9
=16*81
=2^4*3^4
=(4+1)(4+1)
=25 ( For 16 you can see there are 5 factors and similarly for 81 there are 5 factors) So the ans is the total number of combinations.
Is it right suresh?
_________________

Nobody dies a virgin, life screws us all.

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 422

Kudos [?]: 1510 [0], given: 4

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 17:31
The answer choices make this easy: every positive perfect square has an odd number of divisors (because in a perfect square's prime factorization, all of the exponents must be even; when you add one to each and multiply, you will be multiplying only odd numbers, and the product will therefore be odd). So without doing any work, the answer must be 25.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Current Student
Joined: 11 May 2008
Posts: 556
Followers: 8

Kudos [?]: 174 [0], given: 0

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 17:57
yes IAN... it is def an out of the box thinking...
SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 34

Kudos [?]: 867 [0], given: 5

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 19:02
samiam7 wrote:
@x2suresh: Can you explain this a little further? I'm not sure I understand how how you did this.

Also, thanks for all your posts on this site. They are very helpful!

In general here is the formula for finding factors

2^n * 3^m

factors for 2^n
2^0, 2^1, 2^2 ... 2^n ---> (n+1) factors for 2^n
factors for 3^m
3^0, 3^1, 3^2,....3^m ---->(m+1) factors for 3^m

So No.of factors for 2^n * 3^m = combination of factors for 2^n *3^m
= (n+1)(m+1)

Is it clear.
_________________

Smiling wins more friends than frowning

Last edited by x2suresh on 02 Sep 2008, 19:07, edited 1 time in total.
SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 34

Kudos [?]: 867 [0], given: 5

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 19:02
subarao wrote:
36^2=36*36
=4*9*4*9
=16*81
=2^4*3^4
=(4+1)(4+1)
=25 ( For 16 you can see there are 5 factors and similarly for 81 there are 5 factors) So the ans is the total number of combinations.
Is it right suresh?

you are right! buddy.
_________________

Smiling wins more friends than frowning

VP
Joined: 05 Jul 2008
Posts: 1430
Followers: 39

Kudos [?]: 360 [0], given: 1

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 19:33
x2suresh wrote:
samiam7 wrote:
@x2suresh: Can you explain this a little further? I'm not sure I understand how how you did this.

Also, thanks for all your posts on this site. They are very helpful!

In general here is the formula for finding factors

2^n * 3^m

factors for 2^n
2^0, 2^1, 2^2 ... 2^n ---> (n+1) factors for 2^n
factors for 3^m
3^0, 3^1, 3^2,....3^m ---->(m+1) factors for 3^m

So No.of factors for 2^n * 3^m = combination of factors for 2^n *3^m
= (n+1)(m+1)

Is it clear.

Just want to add that it does not need to be in the form of 2^n 3^m It just needs to be expressed in the form of its prime factors raised to some power.
SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 34

Kudos [?]: 867 [0], given: 5

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 20:17
icandy wrote:
x2suresh wrote:
samiam7 wrote:
@x2suresh: Can you explain this a little further? I'm not sure I understand how how you did this.

Also, thanks for all your posts on this site. They are very helpful!

In general here is the formula for finding factors

2^n * 3^m

factors for 2^n
2^0, 2^1, 2^2 ... 2^n ---> (n+1) factors for 2^n
factors for 3^m
3^0, 3^1, 3^2,....3^m ---->(m+1) factors for 3^m

So No.of factors for 2^n * 3^m = combination of factors for 2^n *3^m
= (n+1)(m+1)

Is it clear.

Just want to add that it does not need to be in the form of 2^n 3^m It just needs to be expressed in the form of its prime factors raised to some power.

thats correct!! It is just an example.
_________________

Smiling wins more friends than frowning

Senior Manager
Joined: 16 Jul 2008
Posts: 289
Followers: 3

Kudos [?]: 16 [0], given: 4

Re: MGMAT - good one [#permalink]

### Show Tags

02 Sep 2008, 23:38
25 is the answer, if anyone doubts it.

I just love these types of questions - high difficulty level, but with a 'shortcut' to solve it in less than a minute. I got this question in the CAT this weekend, couldn't figure out how to solve it and guessed wrong. Saw the explanation after the test and it struck me as beautiful
_________________

http://applicant.wordpress.com/

Intern
Joined: 08 Jun 2008
Posts: 14
Location: United States (AL)
Concentration: Strategy, Finance
Schools: McCombs '14
GMAT 1: 710 Q46 V42
GPA: 3.81
WE: Information Technology (Accounting)
Followers: 0

Kudos [?]: 16 [0], given: 2

Re: MGMAT - good one [#permalink]

### Show Tags

03 Sep 2008, 03:46
That makes sense now. Thanks guys!
Intern
Joined: 02 Sep 2008
Posts: 45
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: MGMAT - good one [#permalink]

### Show Tags

03 Sep 2008, 10:31
Hi,

I have thought on it to learn the concept in depth.

we have only just two prime number (2 and 3)

for example, how many factors does 900?

900 = 2^2 * 3^2 * 5^2

so it is 2^n * 3^m * 5^k

= (n+1) (m+1) (k+1)

= 3 * 3 * 3

= 27.

so, no of factors for 900 is 27.

Is answer correct? or there is a different theory for more than 2 prime numbers.

Thanks
Re: MGMAT - good one   [#permalink] 03 Sep 2008, 10:31
Display posts from previous: Sort by

# How many factors does 36^2 have? 2 8 24 25 26

 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®.