GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Feb 2019, 00:54

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 in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If n is a positive integer, and n^2 has 25 factors, which of the follo

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Intern
Intern
avatar
B
Joined: 03 Sep 2016
Posts: 17
Location: India
GPA: 3.7
If n is a positive integer, and n^2 has 25 factors, which of the follo  [#permalink]

Show Tags

New post Updated on: 30 Nov 2016, 07:47
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (02:11) correct 67% (02:00) wrong based on 100 sessions

HideShow timer Statistics

If n is a positive integer, and n^2 has 25 factors, which of the following must be true.

1. n has 12 factors.
2. n > 50
3. \(\sqrt n\) is an integer.

A. 1 and 2
B. 2 only
C. 3 only
D. 2 and 3
E. none

Originally posted by Sorrow on 30 Nov 2016, 07:38.
Last edited by Bunuel on 30 Nov 2016, 07:47, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Community Reply
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1366
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: If n is a positive integer, and n^2 has 25 factors, which of the follo  [#permalink]

Show Tags

New post 30 Nov 2016, 08:58
2
3
Sorrow wrote:
If n is a positive integer, and n^2 has 25 factors, which of the following must be true.

1. n has 12 factors.
2. n > 50
3. \(\sqrt n\) is an integer.

A. 1 and 2
B. 2 only
C. 3 only
D. 2 and 3
E. none


\(25=1 \times 25 = 5 \times 5\)

So prime factorization of \(n^2\) could be \(p^{24}\) or \(p^4q^4\) with \(p,q\) are distinct prime numbers.
Hence, \(n\) could be \(p^{12}\) or \(p^2q^2\)

(1) If \(n=p^{12}\) then \(n\) has \(12+1=13\) different factors, so (1) is not true.

(2) If \(n=p^2q^2\), for example \(n=2^2 \times 3^2 =36 <50\), so (2) is not true.

(3)
If \(n=p^{12} \implies \sqrt{n}=p^6\) is an integer.
If \(n=p^2q^2 \implies \sqrt{n}=pq\) is an integer.
So (3) is true.

The answer is C
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

General Discussion
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9892
Premium Member
Re: If n is a positive integer, and n^2 has 25 factors, which of the follo  [#permalink]

Show Tags

New post 30 Mar 2018, 02:59
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

GMAT Club Bot
Re: If n is a positive integer, and n^2 has 25 factors, which of the follo   [#permalink] 30 Mar 2018, 02:59
Display posts from previous: Sort by

If n is a positive integer, and n^2 has 25 factors, which of the follo

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.