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 →

If n is a positive integer and n^2 is divisible by 72, then

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 124
Joined: Wed May 19, 2010 10:20 pm
Thanked: 3 times
GMAT Score:1100
by mitzwillrockgmat » Sat Jun 26, 2010 5:29 am
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is

a. 6
b. 12
c. 24
d. 36
e. 48

Hello! Can someone help me out with this question? It's been posted a few times but none of the answers really make sense to me. Can someone give a simple, straight forward answer? Much appreciated!!!!!!!!!!

This is all I get so far:

72 = 2^3 * 3^2

so n^2/2^3 * 3^2

HELP!!!!!!!!!

answer is B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1460
Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members
Thanked: 135 times

by selango » Sat Jun 26, 2010 6:02 am
n^2 is divisible by 72

72=2*2*3*3*2

To make it the perfect square,put 2 above

72=2*2*2*2*3*3

Take common factor from each square,

2*2*3=12

Hence B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 124
Joined: Wed May 19, 2010 10:20 pm
Thanked: 3 times
GMAT Score:1100

by mitzwillrockgmat » Sat Jun 26, 2010 6:09 am
selango wrote:n^2 is divisible by 72

72=2*2*3*3*2

To make it the perfect square,put 2 above

72=2*2*2*2*3*3

Take common factor from each square,

2*2*3=12

Hence B
Thanks but a bit confused here is the below what you are saying to do...?

72 ^2 = [2^3 * 3^2 ]^2

becomes 72^2 = 2^6 * 3^4

pls elaborate, thaaaaaanks :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1460
Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members
Thanked: 135 times

by selango » Sat Jun 26, 2010 6:22 am
mitzwillrockgmat,

Method1
---------------------

Split 72 according to prime factorization,

72=2*2*2*3*3

Since n is a perfect square,make the factors as the perfect square.

How can we make them as perfect square?

By multiplying 2 with the factors.[remember n is multiple of 72]

72=2*2*2*2*3*3

So n^2 is divisible 2*2*2*2*3*3

Take each common factor.2*2*3

Hence 12.

Method 2
-----------------------------------------------------


n^2 is divisible by 72

n^2=72q+r[q is quotient r=0]

n^2=72q

n^2=2^3*3^2*q

n^2=2^4*3^2*q[multiply by 2]

n^2=12*12*q

So 12 is the highest positive integer that divides n^2

Hope this clarifies.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 124
Joined: Wed May 19, 2010 10:20 pm
Thanked: 3 times
GMAT Score:1100

by mitzwillrockgmat » Sat Jun 26, 2010 6:31 am
selango wrote:mitzwillrockgmat,

Method1
---------------------

Split 72 according to prime factorization,

72=2*2*2*3*3

Since n is a perfect square,make the factors as the perfect square.

How can we make them as perfect square?

By multiplying 2 with the factors.[remember n is multiple of 72]

72=2*2*2*2*3*3

So n^2 is divisible 2*2*2*2*3*3

Take each common factor.2*2*3

Hence 12.

Method 2
-----------------------------------------------------


n^2 is divisible by 72

n^2=72q+r[q is quotient r=0]

n^2=72q

n^2=2^3*3^2*q

n^2=2^4*3^2*q[multiply by 2]

n^2=12*12*q

So 12 is the highest positive integer that divides n^2

Hope this clarifies.

Thanks!!! That helps but just to confirm you are saying...

since n^2 is a perfect square then its divisor must be a perfect square too.

so i need to find the factors of 72 & to square all of its factors , so we multiply the entire set of no.s by 2.

correct?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1460
Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members
Thanked: 135 times

by selango » Sat Jun 26, 2010 7:32 am
tats correct..
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Mon Nov 18, 2013 2:03 pmFollowed by: 1 member

by ozlemmetje » Mon May 05, 2014 12:16 pm
Hello,

there is something I don't understand:

I agree that 12 is an integer that must divide n is 12 as 72= (2^4)(3^2)is a perfect square. However (2^6)(3^2) is also a perfect square so n could also be 24 and so it is divisible by 24.

Thanks
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1