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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
Vote for Target Test Prep, Newsweek Readers’ Choice Awards 2026
NEWSWEEK READERS’ CHOICE 2026

BIG NEWS! Target Test Prep has been nominated, and they’d love your vote!

TTP has worked incredibly hard to build the best test prep experience possible, and winning Newsweek’s 2026 Readers’ Choice Award for Best Test Prep would mean a lot to them. If TTP has helped you, they’d be incredibly grateful for your vote. You can vote once each day through September 9.

Vote for TTP
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

positive integers....2

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 198
Joined: Fri Mar 09, 2007 8:40 pm
Thanked: 7 times

by kris610 » Sat Oct 25, 2008 9:15 am
Given n is a positive integer.

The largest positive integer that would divide n is n itself.

Find n*n such that it is a multiple of 72 and is also a perfect square.

Of the given choices, 24 fits the bill.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2467
Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members
Thanked: 331 times

by cramya » Sat Oct 25, 2008 9:16 am
https://www.beatthegmat.com/og-quant-rev ... 11652.html
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 2134
Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members
Thanked: 237 times
GMAT Score:730

by logitech » Sat Oct 25, 2008 10:13 am
Kris,

if n^2 is divided by 72, which is 2^3 x 3^2

The closest way to make this a perfect square is to multiply by 2

So N^2 = 144 and N: 12

so is the answer!
kris610 wrote:Given n is a positive integer.

The largest positive integer that would divide n is n itself.

Find n*n such that it is a multiple of 72 and is also a perfect square.

Of the given choices, 24 fits the bill.
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 198
Joined: Fri Mar 09, 2007 8:40 pm
Thanked: 7 times

by kris610 » Sat Oct 25, 2008 11:48 am
Well..the question asks for the *greatest* possible number n such n^2 is a perfect square and is a multiple of 72.

Let's take n=24. 24^2 is divisible by 72 and is a perfect square.

Why is that not the answer?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 2134
Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members
Thanked: 237 times
GMAT Score:730

by logitech » Sat Oct 25, 2008 12:15 pm
kris610 wrote:Well..the question asks for the *greatest* possible number n such n^2 is a perfect square and is a multiple of 72.

Let's take n=24. 24^2 is divisible by 72 and is a perfect square.

Why is that not the answer?
well how about 48 ? :lol:

maybe there is a typo here ? Maybe the question is not asking the GREATEST because it does not make any sense. THE GREATEST NUMBER IS INFINITE! ;-)
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 65
Joined: Sun Oct 19, 2008 2:18 pm
Thanked: 1 times

Re: positive integers....2

by yezz » Sat Oct 25, 2008 12:44 pm
acorra wrote:If n is a positive integer and n^2 is divisible by 72, then the largest positive intefer that must divide n is:

A) 6

B) 12

C) 24

D) 36

E) 48
72 = 2^3*3^2

N^2 at least = 2^4*3^2

N is least = 2^2*3.....12
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 198
Joined: Fri Mar 09, 2007 8:40 pm
Thanked: 7 times

by kris610 » Sat Oct 25, 2008 1:47 pm
logitech wrote:
kris610 wrote:Well..the question asks for the *greatest* possible number n such n^2 is a perfect square and is a multiple of 72.

Let's take n=24. 24^2 is divisible by 72 and is a perfect square.

Why is that not the answer?
well how about 48 ? :lol:

maybe there is a typo here ? Maybe the question is not asking the GREATEST because it does not make any sense. THE GREATEST NUMBER IS INFINITE! ;-)
Logitech, the square of 48 is not a multiple of 72.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

by Ian Stewart » Sat Oct 25, 2008 5:10 pm
logitech wrote:
kris610 wrote:Well..the question asks for the *greatest* possible number n such n^2 is a perfect square and is a multiple of 72.

Let's take n=24. 24^2 is divisible by 72 and is a perfect square.

Why is that not the answer?
well how about 48 ? :lol:

maybe there is a typo here ? Maybe the question is not asking the GREATEST because it does not make any sense. THE GREATEST NUMBER IS INFINITE! ;-)
There's no typo. The question asks what the greatest integer is that *must* divide n, not what the greatest integer is that *could* divide n. Since n could be equal to 12, the answer certainly can't be 24 or 48, since 24 and 48 are not divisors of 12. I posted a solution in an earlier thread, which cramya linked to above. It's identical to yezz's solution above, but with a bit more detail.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Tue Mar 15, 2011 12:08 am

by TrueLie » Fri Apr 01, 2011 7:52 am
acorra wrote:If n is a positive integer and n^2 is divisible by 72, then the largest positive intefer that must divide n is:

A) 6

B) 12

C) 24

D) 36

E) 48
I have a problem with this kind of question. What does "the largest positive integer that must divide n" mean? Suppose that this "largest positive integer" is X. Hence, does the question mean "X is divisible by n" or "n is divisible by x"? If the second case is correct, that mean we can re-write the question as "If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that n must divide is:". Is this true?

I am not a native English speaker, that's why I have this problem.

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