BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Divisors - PS

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Tue Dec 06, 2011 12:30 am
karthikpandian19 wrote:If pand q are prime numbers, how many divisors does the product p^3q^6 have?

(A) 9 (B) 12(C) 18(D) 28(E) 36[/list]
When we have to find the number of divisors of a number, then factorize the number into its prime factors, like, n = a^x * b^y, where a, b are distinct prime factors of n, and x, y are powers of prime factors a and b respectively.
Then number of divisors of n = (x + 1)(y + 1)

Here number of divisors of p^3 * q^6 = (3 + 1)(6 + 1) = 4 * 7 = 28

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1665
Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members
Thanked: 165 times

by karthikpandian19 » Tue Dec 06, 2011 12:57 am
Anurag,

Can this be taken as like this also?
n = a^x * b^y implies number of divisors of n = (x + 1)(y + 1)

Is it, n = a^x implies number of divisors of n = (x + 1)

How does it work for a number 36?

36 = 2^2 * 3^2
Which implies there should be (2+1) (2+1)
ie. 9 divisors

Divisors of 36 - 2,3,4,6,9,12,18,36 (we have only 8, is "1" also to be done included in each instances.?????
Anurag@Gurome wrote:
karthikpandian19 wrote:If pand q are prime numbers, how many divisors does the product p^3q^6 have?

(A) 9 (B) 12(C) 18(D) 28(E) 36[/list]
When we have to find the number of divisors of a number, then factorize the number into its prime factors, like, n = a^x * b^y, where a, b are distinct prime factors of n, and x, y are powers of prime factors a and b respectively.
Then number of divisors of n = (x + 1)(y + 1)

Here number of divisors of p^3 * q^6 = (3 + 1)(6 + 1) = 4 * 7 = 28

The correct answer is D.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Tue Dec 06, 2011 1:02 am
Anurag,

Can this be taken as like this also?
n = a^x * b^y implies number of divisors of n = (x + 1)(y + 1)

Is it, n = a^x implies number of divisors of n = (x + 1)

How does it work for a number 36?

36 = 2^2 * 3^2
Which implies there should be (2+1) (2+1)
ie. 9 divisors

Divisors of 36 - 2,3,4,6,9,12,18,36 (we have only 8, is "1" also to be done included in each instances.?????

Yes, that's correct, when we count we have to include 1 and the number itself.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 416
Joined: Thu Jul 28, 2011 12:48 amFollowed by: 6 members
Thanked: 28 times

by gunjan1208 » Tue Dec 06, 2011 1:22 am
Hi Anurag,

Can we take it as a rule everytime we see this kind of question?

Regards
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Tue Dec 06, 2011 1:23 am
gunjan1208 wrote:Hi Anurag,

Can we take it as a rule everytime we see this kind of question?

Regards
Yes, definitely.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Tue Dec 06, 2011 7:40 am
This question should state that p and q are DISTINCT prime numbers. I posted an explanation here:

https://www.beatthegmat.com/divisors-t85731.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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Sun Jul 31, 2011 9:39 pmFollowed by: 1 member
Thanked: 2 times

by Elena89 » Tue Dec 13, 2011 1:29 am
karthikpandian19 wrote:If pand q are prime numbers, how many divisors does the product p^3q^6 have?

(A) 9 (B) 12(C) 18(D) 28(E) 36[/list]
The question is asking to find the total factors of the product P^3*q^6

since p and q are prime numbers, lets take p=2 and q=3

=> 2^3*3^6

total factors = (total possibilities for 2 to be in a factor of the product)*(total possibilities for 3 to be in a factor of the product)

=> total factors = (none + 3)*(none + 6)
= (1 + 3)*(1 + 6)
= 4*7
= 28

Hence the correct option: D) 28
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1