It is currently 21 Oct 2017, 12:53

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

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

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

Hide Tags

4 KUDOS received
Manager
Manager
avatar
Joined: 14 Feb 2012
Posts: 226

Kudos [?]: 291 [4], given: 7

Is the positive integer n equal to the square of an integer? [#permalink]

Show Tags

New post 22 Apr 2012, 01:16
4
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (00:58) correct 44% (01:07) wrong based on 192 sessions

HideShow timer Statistics

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, 01:38, edited 1 time in total.
Edited the question

Kudos [?]: 291 [4], given: 7

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129148 [1], given: 12194

Re: Is the positive integer n equal to the square [#permalink]

Show Tags

New post 22 Apr 2012, 01:36
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129148 [1], given: 12194

Intern
Intern
avatar
Joined: 05 May 2013
Posts: 1

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

Re: Is the positive integer n equal to the square [#permalink]

Show Tags

New post 05 May 2013, 00:40
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.

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

Intern
Intern
avatar
Joined: 24 Sep 2012
Posts: 38

Kudos [?]: 6 [0], given: 76

Re: Is the positive integer n equal to the square of an integer? [#permalink]

Show Tags

New post 05 May 2013, 01:34
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

Kudos [?]: 6 [0], given: 76

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129148 [0], given: 12194

Re: Is the positive integer n equal to the square [#permalink]

Show Tags

New post 05 May 2013, 04:11
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129148 [0], given: 12194

Senior Manager
Senior Manager
avatar
Joined: 21 Jan 2010
Posts: 329

Kudos [?]: 226 [0], given: 12

Re: Is the positive integer n equal to the square of an integer? [#permalink]

Show Tags

New post 06 May 2013, 13:00
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.

Kudos [?]: 226 [0], given: 12

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16585

Kudos [?]: 273 [0], given: 0

Premium Member
Re: Is the positive integer n equal to the square of an integer? [#permalink]

Show Tags

New post 10 Nov 2016, 08:34
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 [?]: 273 [0], given: 0

Re: Is the positive integer n equal to the square of an integer?   [#permalink] 10 Nov 2016, 08:34
Display posts from previous: Sort by

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

  new topic 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®.