How many factors does 36^2 have?
A. 2
B. 8
C. 24
D. 25
E. 26
OA: [spoiler]D[/spoiler]
Can someone please explain the OA? Thanks.
700-800 Level PS Question
This topic has expert replies
-
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Wed Nov 07, 2012 8:23 am
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
For any real number N, if the prime factorization of N is (p^a)*(q^b)*(r^c)*..., then the number of factors of N is given by (a + 1)(b + 1)(c + 1)...davidlee05 wrote:How many factors does 36^2 have?
Here, 36^2 = 2^4 * 3^4
So, number of factors of 36^2 = (4 + 1)(4 + 1) = 25
The correct answer is D.
Last edited by Anju@Gurome on Sat Mar 16, 2013 10:05 pm, edited 1 time in total.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
-
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Wed Nov 07, 2012 8:23 am
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
Please check my previous post.davidlee05 wrote:Can you please expand on your method?
I've edited the reply with the explanation.
To explain more, let us assume for some real number N the prime factorization of N is (p^a)*(q^b)*(r^c)*...
Now number of factors of N = (Number of ways to select the prime factor p)*(Number of ways to select the prime factor q)*(Number of ways to select the prime factor r)*... = (a + 1)(b + 1)(c + 1)...
Now, for each prime factor we may or may not select that factor. When none of the prime factors are selected we get the factor 1. Hence, for the prime factor p, number of ways to select p to include it in a factor of N is exponent of p in the prime factorization of N, i.e. a and number of ways to not select p is 1. That's why we are adding 1 to each of the exponents of the prime factors of N.
Hope that helps.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
You might find my posts here helpful:
https://www.beatthegmat.com/factor-question-t123158.html
https://www.beatthegmat.com/all-factors- ... 15019.html
https://www.beatthegmat.com/factor-question-t123158.html
https://www.beatthegmat.com/all-factors- ... 15019.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3