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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

if n^2 (nxn) is divided by 72 (i.e 6X6X2), n^2 is also divided by 144(72X2) because n^2 is a square and its dividors must be squars. therefore, the factors of n^2 must be at least 2X2X2X2X3X3 (12). the sqrt of n^2 is n, which must be divided by 12, sqrt of 144.

Dear MA,
Thank you for your kind support. I have just one question to your responses below. I see your point that the factors of n^2 must be at least 2X2X2X2X3X3 (12).

However, what do you think of " the factors of n^2 are for instance 2X2X2X2X2X2X3X3 (24)? Because the question is asking the "largest" positive number that must divide n, I'm wondering why 12 is the "largest" number. As shown, 24 can also devide n and 576(24^2) can be divided by 72(576 / 72 = 8).

Can you clarify my question, please? Thank you.

MA wrote:

if n^2 (nxn) is divided by 72 (i.e 6X6X2), n^2 is also divided by 144(72X2) because n^2 is a square and its dividors must be squars. therefore, the factors of n^2 must be at least 2X2X2X2X3X3 (12). the sqrt of n^2 is n, which must be divided by 12, sqrt of 144.

what do you think of " the factors of n^2 are for instance 2X2X2X2X2X2X3X3 (24)? Because the question is asking the "largest" positive number that must divide n, I'm wondering why 12 is the "largest" number. As shown, 24 can also devide n and 576(24^2) can be divided by 72(576 / 72 = 8). Can you clarify my question, please? Thank you.

taku,
n^2 is divisible by 72 means one n is divisible by 12 (6x2=2x2x3) and another n is divisible by 6 (2x3) and another number, lets say.

n^2/72=nxn/2x2x2x3x3=n/(2x2x3) x n/(2x3xk). k must be 2 because n/(2x2x3)=n/(2x3xk)

your question why k can not be 8? k can not be 8 because n^2 is divisible by 72 means it is also be divisible by 144 because factor of n^2 must have square factors, which 144 fullfils. if k =8, then 288, instead of 72, would be the divisor. but if n=12 and n^2 = 144, does n^2 (144) divided by 288. no it is not possible. therefore, it is only 12 the largest positive integer that divides n under the given circumstances.

Dear MA,
First of all, thank you very much for your support in this regards. Really appreciate your kind attention. Sorry but can I ask just one question about your responses.

You are stating that if k =8, then 288, instead of 72, would be the divisor. Can you tell me why "288"? Of course, I see n^2=(24)^2=576 which can be divided by 288(576 / 2 = 288). Is this why you are mentioning "288"? Sorry I don't see the reason or background of "288". Can you explain it? Thank you very much.

MA wrote:

Taku wrote:

what do you think of " the factors of n^2 are for instance 2X2X2X2X2X2X3X3 (24)? Because the question is asking the "largest" positive number that must divide n, I'm wondering why 12 is the "largest" number. As shown, 24 can also devide n and 576(24^2) can be divided by 72(576 / 72 = 8). Can you clarify my question, please? Thank you.

taku, n^2 is divisible by 72 means one n is divisible by 12 (6x2=2x2x3) and another n is divisible by 6 (2x3) and another number, lets say.

n^2/72=nxn/2x2x2x3x3=n/(2x2x3) x n/(2x3xk). k must be 2 because n/(2x2x3)=n/(2x3xk)

your question why k can not be 8? k can not be 8 because n^2 is divisible by 72 means it is also be divisible by 144 because factor of n^2 must have square factors, which 144 fullfils. if k =8, then 288, instead of 72, would be the divisor. but if n=12 and n^2 = 144, does n^2 (144) divided by 288. no it is not possible. therefore, it is only 12 the largest positive integer that divides n under the given circumstances.

If n is a positive integer and n2 is dividible by 72, then largest positive integer that must divide n is

The key word is "must". This means for each and every possible n, this integer must divide it.

We know that 2 must divide n, as well as 6, as well as 12. However, for some ns, eg. n=12, n[sup]2[/sup]=144 is divisible by 72, 18 cannot be a divisor. Therefore we have to choose the largest among 2, 3, 6 and 12. And the answer is 12.

Re: If n is a positive integer and n2 is dividible by 72, then [#permalink]

Show Tags

31 Oct 2017, 17:59

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________