Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2015, 06:04
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is the positive integer n equal to the square of an integer?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Manager
Manager
avatar
Joined: 14 Feb 2012
Posts: 228
Followers: 2

Kudos [?]: 104 [3] , given: 7

Is the positive integer n equal to the square of an integer? [#permalink] New post 22 Apr 2012, 00:16
3
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (02:02) correct 46% (01:00) wrong based on 136 sessions
Is the positive integer n equal to the square of an integer?

(1) For every prime number p, if p is a divisor of n, then so is p^2
(2) \(\sqrt{n}\) is an integer
[Reveal] Spoiler: OA

_________________

The Best Way to Keep me ON is to give Me KUDOS !!!
If you Like My posts please Consider giving Kudos

Shikhar


Last edited by Bunuel on 22 Apr 2012, 00:38, edited 1 time in total.
Edited the question
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28781
Followers: 4592

Kudos [?]: 47381 [1] , given: 7123

Re: Is the positive integer n equal to the square [#permalink] New post 22 Apr 2012, 00:36
1
This post received
KUDOS
Expert's post
shikhar wrote:
Is the positive integer n equal to the square of an integer?
(1) For every prime number p, if p is a divisor of n, then so is p2.
(2) is an integer.


Is the positive integer n equal to the square of an integer?

Question: is \(n=integer^2\)? So, basically we are asked whether \(n\) is a perfect square (a perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.).

(1) For every prime number p, if p is a divisor of n, then so is p^2 --> if \(n=2^2\) then the answer is YES but if \(n=2^3\) then the answer is NO (notice that in both case prime number 2 as well as 2^2 are divisors of n, so our condition is satisfied). Not sufficient.

(2) \(\sqrt{n}\) is an integer --> \(\sqrt{n}=integer\) --> \(n=integer^2\). Sufficient.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 04 May 2013
Posts: 1
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: Is the positive integer n equal to the square [#permalink] New post 04 May 2013, 23:40
Bunuel wrote:
shikhar wrote:
Is the positive integer n equal to the square of an integer?
(1) For every prime number p, if p is a divisor of n, then so is p2.
(2) is an integer.


Is the positive integer n equal to the square of an integer?

Question: is \(n=integer^2\)? So, basically we are asked whether \(n\) is a perfect square (a perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.).

(1) For every prime number p, if p is a divisor of n, then so is p^2 --> if \(n=2^2\) then the answer is YES but if \(n=2^3\) then the answer is NO (notice that in both case prime number 2 as well as 2^2 are divisors of n, so our condition is satisfied). Not sufficient.

(2) \(\sqrt{n}\) is an integer --> \(\sqrt{n}=integer\) --> \(n=integer^2\). Sufficient.

Answer: B.



ST 1-isnt this telling you all the prime factors of n are raised to even powers which makes n a square number-i got wrong can you please re-explain.
Intern
Intern
avatar
Joined: 24 Sep 2012
Posts: 40
Followers: 0

Kudos [?]: 3 [0], given: 76

Re: Is the positive integer n equal to the square of an integer? [#permalink] New post 05 May 2013, 00:34
Hi Ashima,

This is how I verified statement 1.

Take n = 36, p = 2
If p is a divisor of n, then so is p2. Check for p^2 => 2^2 => 4, 36 is divisible by 4. - OK

Take n = 15, p = 3
If p is a divisor of n, then so is p2. Check for p^2 => 3^2 => 9, 15 is not divisible by 9 - Not OK

Hence statement 1 is insufficient. Hope this is OK.

Maybe Bunuel can help us better.

Regards,
Pritish
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28781
Followers: 4592

Kudos [?]: 47381 [0], given: 7123

Re: Is the positive integer n equal to the square [#permalink] New post 05 May 2013, 03:11
Expert's post
ashiima86 wrote:
Bunuel wrote:
shikhar wrote:
Is the positive integer n equal to the square of an integer?
(1) For every prime number p, if p is a divisor of n, then so is p2.
(2) is an integer.


Is the positive integer n equal to the square of an integer?

Question: is \(n=integer^2\)? So, basically we are asked whether \(n\) is a perfect square (a perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.).

(1) For every prime number p, if p is a divisor of n, then so is p^2 --> if \(n=2^2\) then the answer is YES but if \(n=2^3\) then the answer is NO (notice that in both case prime number 2 as well as 2^2 are divisors of n, so our condition is satisfied). Not sufficient.

(2) \(\sqrt{n}\) is an integer --> \(\sqrt{n}=integer\) --> \(n=integer^2\). Sufficient.

Answer: B.



ST 1-isnt this telling you all the prime factors of n are raised to even powers which makes n a square number-i got wrong can you please re-explain.


No, the first statement says that if a prime number p is a factor of n, then so is p^2, which means that the power of p is more than or equal to 2: it could be 2, 3, ... So, n is not necessarily a prefect square. For example, if \(n=2^2\) then the answer is YES but if \(n=2^3\) then the answer is NO (notice that in both case prime number 2 as well as 2^2 are divisors of n, so our condition is satisfied).

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
avatar
Joined: 21 Jan 2010
Posts: 347
Followers: 1

Kudos [?]: 107 [0], given: 12

Re: Is the positive integer n equal to the square of an integer? [#permalink] New post 06 May 2013, 12:00
Is the positive integer n equal to the square of an integer?

(1) For every prime number p, if p is a divisor of n, then so is p^2
(2) root n is an integer

From 1 ) If p=4, than 16 is also a factor. Which can qualify n to be a perfect square.But if p=2 than 4 is also a factor. However we can't say if n is square of an integer or not. Hence Insufficient.

2) If root n is an integer -> N has to be the square of an integer. Sufficient.

Answer B.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5699
Followers: 322

Kudos [?]: 62 [0], given: 0

Premium Member
Re: Is the positive integer n equal to the square of an integer? [#permalink] New post 12 Dec 2014, 06:04
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

Re: Is the positive integer n equal to the square of an integer?   [#permalink] 12 Dec 2014, 06:04
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Is the positive integer n equal to the square of an integer? tracyyahoo 5 16 Jul 2011, 01:51
18 Experts publish their posts in the topic Is the positive integer N a perfect square? PTK 14 23 May 2010, 11:02
8 Experts publish their posts in the topic If N is a positive Integer, is the units digit of N equal to meaglesp345 6 20 Mar 2010, 13:57
11 Experts publish their posts in the topic Is the positive integer N a perfect square? netcaesar 17 13 Aug 2009, 05:49
47 Experts publish their posts in the topic Is the positive integer N a perfect square? (1) The number mbaMission 29 02 Jun 2009, 04:18
Display posts from previous: Sort by

Is the positive integer n equal to the square of an integer?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.