NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 14:16 It is currently 26 Apr 2024, 14:16
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
shikhar
Manager
Manager
Joined: 14 Feb 2012
Posts: 81
Own Kudos [?]: 1082 [18]
Given Kudos: 7
Send PM
Is the positive integer n equal to the square of an integer? [#permalink] New post   Updated on: 22 Apr 2012, 01:38
5
Kudos
13
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

59% (01:28) correct 41% (01:38) wrong based on 416 sessions
Hide Show 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
ShowHide Answer
Official Answer
B

Originally posted by shikhar on 22 Apr 2012, 01:16.
Last edited by Bunuel on 22 Apr 2012, 01:38, edited 1 time in total.
Edited the question
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619230 [6]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: Is the positive integer n equal to the square [#permalink] New post   22 Apr 2012, 01:36
3
Kudos
3
Bookmarks
Expert Reply
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.
General Discussion
avatar
ashiima86
Intern
Intern
Joined: 05 May 2013
Posts: 1
Own Kudos [?]: 5 [0]
Given Kudos: 0
Send PM
Re: Is the positive integer n equal to the square [#permalink] 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.
avatar
pritish2301
Intern
Intern
Joined: 24 Sep 2012
Posts: 23
Own Kudos [?]: 13 [0]
Given Kudos: 76
Send PM
Re: Is the positive integer n equal to the square of an integer? [#permalink] 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
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619230 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: Is the positive integer n equal to the square [#permalink] New post   05 May 2013, 04:11
Expert Reply
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.
User avatar
Bluelagoon
Manager
Manager
Joined: 21 Jan 2010
Posts: 193
Own Kudos [?]: 610 [0]
Given Kudos: 12
Send PM
Re: Is the positive integer n equal to the square of an integer? [#permalink] 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.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32689
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: Is the positive integer n equal to the square of an integer? [#permalink] New post   24 Sep 2023, 04:16
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 Club Bot
gmatclubot
Re: Is the positive integer n equal to the square of an integer? [#permalink]
24 Sep 2023, 04:16
Moderator:
Bunuel
Math Expert
92948 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions