It is currently 19 Jan 2018, 19:25

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is a positive integer and n2 is dividible by 72, then

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
avatar
Joined: 28 Jan 2005
Posts: 77

Kudos [?]: 177 [0], given: 0

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

Show Tags

New post 16 Feb 2005, 16:12
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:24) correct 0% (00:00) wrong based on 13 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

A : 6
B : 12
C : 24
D : 36
E : 48

OG PS #412
----------------------------

-----------------------------
* n2 : quadrat

The process I took :
n2 = 72 x k(for some positive integer) = (2 x 3)2 x 2 x k

1) if k = 2
n2 = (12)2 Then, 12 is the maximum number which can divide n.

2) if k = 8
n2 = (24)2 Then, 24 is the maximum number which can divide n.

3) if k = 18
n2 = (36)s Then, 36 is the maximum number which can divide n.

If my study above is correct, why is the correct answer B(n=12)? As the above, n can be 12, 24, 36 or more!

Can you someone advise me which I made a wrong understanding? Thank you.
_________________

Best regards,

Kudos [?]: 177 [0], given: 0

1 KUDOS received
VP
VP
User avatar
Joined: 25 Nov 2004
Posts: 1480

Kudos [?]: 134 [1], given: 0

Re: OG PS No. 412 [#permalink]

Show Tags

New post 16 Feb 2005, 18:49
1
This post received
KUDOS
1
This post was
BOOKMARKED
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.

explain later, if unclear.

Kudos [?]: 134 [1], given: 0

VP
VP
User avatar
Joined: 13 Jun 2004
Posts: 1110

Kudos [?]: 52 [0], given: 0

Location: London, UK
Schools: Tuck'08
 [#permalink]

Show Tags

New post 16 Feb 2005, 19:51
Is the question really good because in my mind there are other possible answers but those answers are not in the proposed choices a,b,c,d or e.

Because 144 could also be the answer, no ?
n=144, n^2 = 20736 it is divisble by 72

Is backsolving the only way or am I just missing something here ? :?

Kudos [?]: 52 [0], given: 0

1 KUDOS received
Manager
Manager
avatar
Joined: 28 Jan 2005
Posts: 77

Kudos [?]: 177 [1], given: 0

Re: OG PS No. 412 [#permalink]

Show Tags

New post 18 Feb 2005, 21:37
1
This post received
KUDOS
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.

explain later, if unclear.

_________________

Best regards,

Kudos [?]: 177 [1], given: 0

Senior Manager
Senior Manager
avatar
Joined: 02 Feb 2004
Posts: 343

Kudos [?]: 73 [0], given: 0

 [#permalink]

Show Tags

New post 19 Feb 2005, 11:58
quick solution:

72=2 x 6x6
n^2=nxn

therefore for n^2 to be divisable by 72, one of the n out of the two must be divisable by 12.

Kudos [?]: 73 [0], given: 0

Manager
Manager
avatar
Joined: 28 Jan 2005
Posts: 77

Kudos [?]: 177 [0], given: 0

 [#permalink]

Show Tags

New post 19 Feb 2005, 21:27
Dear mirhaque,
Thank you for your response, but what about below?

n^2 = 72 x k = 2x6x6xk

If k = 2, yes, as you explained, n^2 = 12^2 and then, n = 12

However,

If k = 8 = 2^3, n^2 = (2x2x2x3)^2 = 24^2 and then, n = 24

Can you please point out my mistake? Thank you.



mirhaque wrote:
quick solution:

72=2 x 6x6
n^2=nxn

therefore for n^2 to be divisable by 72, one of the n out of the two must be divisable by 12.

_________________

Best regards,

Kudos [?]: 177 [0], given: 0

VP
VP
User avatar
Joined: 25 Nov 2004
Posts: 1480

Kudos [?]: 134 [0], given: 0

Re: OG PS No. 412 [#permalink]

Show Tags

New post 19 Feb 2005, 22:14
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.

Kudos [?]: 134 [0], given: 0

Manager
Manager
avatar
Joined: 28 Jan 2005
Posts: 77

Kudos [?]: 177 [0], given: 0

Re: OG PS No. 412 [#permalink]

Show Tags

New post 23 Feb 2005, 03:32
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.

_________________

Best regards,

Kudos [?]: 177 [0], given: 0

SVP
SVP
User avatar
Joined: 03 Jan 2005
Posts: 2226

Kudos [?]: 400 [0], given: 0

Re: OG PS No. 412 [#permalink]

Show Tags

New post 23 Feb 2005, 07:14
Taku wrote:
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.

Kudos [?]: 400 [0], given: 0

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14229

Kudos [?]: 291 [0], given: 0

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

Show Tags

New post 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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 291 [0], given: 0

Re: If n is a positive integer and n2 is dividible by 72, then   [#permalink] 31 Oct 2017, 17:59
Display posts from previous: Sort by

If n is a positive integer and n2 is dividible by 72, then

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.