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

It is currently 21 Sep 2018, 18:36

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

Is n the square of an integer? (1) n is the square root of an integer

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Is n the square of an integer? (1) n is the square root of an integer  [#permalink]

Show Tags

New post 01 Jul 2018, 21:47
1
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

20% (01:56) correct 80% (01:28) wrong based on 93 sessions

HideShow timer Statistics

examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 597
Is n the square of an integer? (1) n is the square root of an integer  [#permalink]

Show Tags

New post Updated on: 02 Jul 2018, 00:13
1
1
Bunuel wrote:
Is n the square of an integer?

(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer


Questions dealing with number properties can often be solved with very little calculations, using logic only.
We'll look for such a solution, a logical approach.

(1) Every positive integer is the square root of another integer (i.e x is the sqrt of x^2). But this doesn't mean that it also has to be the square of an integer!
Insufficient

(2) So \(\sqrt{9n}=3\sqrt{n}\) is the square of an integer meaning that \(\sqrt{n}\) can be written as k/3 for some integer k. That means that n = k^2/9 for some integer k. This is an integer only if k is divisible by 3, which it does not have to be.
Insufficient.

Combined:
So from (1) we know that n^2 must be an integer, and from (2) we know that n = k^2/9 for some integer k.
Combining, if n=k^2/9 then n^2 = k^4/81. Since this must be an integer then k^4 is divisible by 81 so k^2 is divisible by 9 and k is divisible by 3. Therefore n must be an integer.

(C) is our answer.
_________________

Image
Image
Sign up for 7-day free trial

Watch free GMAT tutorials in Math, Verbal, IR, and AWA.

GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.

You can watch all the action from the interview here.


Originally posted by DavidTutorexamPAL on 01 Jul 2018, 22:38.
Last edited by DavidTutorexamPAL on 02 Jul 2018, 00:13, edited 1 time in total.
Manager
Manager
avatar
G
Joined: 04 Apr 2015
Posts: 109
Re: Is n the square of an integer? (1) n is the square root of an integer  [#permalink]

Show Tags

New post 01 Jul 2018, 22:58
1
DavidTutorexamPAL wrote:
Bunuel wrote:
Is n the square of an integer?

(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer


Questions dealing with number properties can often be solved with very little calculations, using logic only.
We'll look for such a solution, a logical approach.

(1) Every positive integer is the square root of another integer (i.e x is the sqrt of x^2). But this doesn't mean that it also has to be the square of an integer!
Insufficient

(2) So \(\sqrt{9n}=3\sqrt{n}\) is the square of an integer meaning it is also an integer. Then \(\sqrt{n}\) must be an integer meaning that n must be a square of an integer.
Sufficient.

(B) is our answer.





Answer should be C

if n =4/9 statement 2 still holds.

Waiting for the OA
examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 597
Re: Is n the square of an integer? (1) n is the square root of an integer  [#permalink]

Show Tags

New post 02 Jul 2018, 00:13
varundixitmro2512 wrote:
DavidTutorexamPAL wrote:
Bunuel wrote:
Is n the square of an integer?

(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer


Questions dealing with number properties can often be solved with very little calculations, using logic only.
We'll look for such a solution, a logical approach.

(1) Every positive integer is the square root of another integer (i.e x is the sqrt of x^2). But this doesn't mean that it also has to be the square of an integer!
Insufficient

(2) So \(\sqrt{9n}=3\sqrt{n}\) is the square of an integer meaning it is also an integer. Then \(\sqrt{n}\) must be an integer meaning that n must be a square of an integer.
Sufficient.

(B) is our answer.





Answer should be C

if n =4/9 statement 2 still holds.

Waiting for the OA


You're right! My bad, fixed.
_________________

Image
Image
Sign up for 7-day free trial

Watch free GMAT tutorials in Math, Verbal, IR, and AWA.

GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.

You can watch all the action from the interview here.

Re: Is n the square of an integer? (1) n is the square root of an integer &nbs [#permalink] 02 Jul 2018, 00:13
Display posts from previous: Sort by

Is n the square of an integer? (1) n is the square root of an integer

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

Events & Promotions

PREV
NEXT


cron

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®.