Last visit was: 19 Jul 2025, 19:29 It is currently 19 Jul 2025, 19:29
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,802
 [35]
3
Kudos
Add Kudos
32
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
DavidTutorexamPAL
User avatar
examPAL Representative
Joined: 07 Dec 2017
Last visit: 09 Sep 2020
Posts: 1,035
Own Kudos:
1,953
 [10]
Given Kudos: 26
Posts: 1,035
Kudos: 1,953
 [10]
4
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
User avatar
exc4libur
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,702
Own Kudos:
1,431
 [7]
Given Kudos: 607
Location: United States
Posts: 1,702
Kudos: 1,431
 [7]
6
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
General Discussion
User avatar
varundixitmro2512
Joined: 04 Apr 2015
Last visit: 14 Jul 2025
Posts: 76
Own Kudos:
303
 [1]
Given Kudos: 3,991
Posts: 76
Kudos: 303
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DavidTutorexamPAL
Bunuel
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
User avatar
DavidTutorexamPAL
User avatar
examPAL Representative
Joined: 07 Dec 2017
Last visit: 09 Sep 2020
Posts: 1,035
Own Kudos:
Given Kudos: 26
Posts: 1,035
Kudos: 1,953
Kudos
Add Kudos
Bookmarks
Bookmark this Post
varundixitmro2512
DavidTutorexamPAL
Bunuel
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.
avatar
Coggi
Joined: 21 Mar 2019
Last visit: 08 Oct 2019
Posts: 20
Own Kudos:
Given Kudos: 17
Posts: 20
Kudos: 17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I don't understand something, maybe you can help me clarify some point.
When it's written :
(1) n is the square root of an integer; it means n = (int)^2 or n =(int)^1/2 ? For me it means n = (int)^1/2
Same question for (2) √(9n) is square of an integer, does it mean √(9n) = (int)^2 ? For me yes
But I think I am misunderstanding something (I am not a native speaker).

When you write :

" √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. " I don't understand why √n = k/3 and not k^2/3 ...

What am I getting wrong DavidTutorexamPAL, Bunuel ?
avatar
aviejay
Joined: 19 Feb 2017
Last visit: 19 Nov 2019
Posts: 34
Own Kudos:
Given Kudos: 5
Posts: 34
Kudos: 14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Is n the square of an integer?

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


Hi Bunuel,

Could you please provide the detailed solution for this question?
avatar
deelakmi
Joined: 20 Jan 2019
Last visit: 09 Jul 2020
Posts: 4
Own Kudos:
Given Kudos: 17
Posts: 4
Kudos: 2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I don't understand how statement 2 is valid for n= 4/9.
for n=4/9, LHS is 2, as per the question 2 should be a square of some integer- which is not possible.
Can someone help me understand this?
User avatar
TheNightKing
Joined: 18 Dec 2017
Last visit: 20 Mar 2024
Posts: 1,139
Own Kudos:
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
GMAT 1: 600 Q46 V27
Posts: 1,139
Kudos: 1,226
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DavidTutorexamPAL
Bunuel
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.

Hello, Can you help me understand "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" Why it has to be of the form k/3?
avatar
sthahvi
Joined: 30 Nov 2018
Last visit: 24 Jan 2022
Posts: 62
Own Kudos:
Given Kudos: 194
Posts: 62
Kudos: 9
Kudos
Add Kudos
Bookmarks
Bookmark this Post
can someone provide a detailed solution for this Bunuel ?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,452
Own Kudos:
Posts: 37,452
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102627 posts
455 posts