Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 20:48

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x is a positive integer, is x an integer?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Oct 2009
Posts: 145
Location: Montreal
Schools: Harvard, Yale, HEC
Followers: 1

Kudos [?]: 90 [1] , given: 18

If x is a positive integer, is x an integer? [#permalink]

### Show Tags

29 Sep 2010, 07:09
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

67% (01:50) correct 33% (01:17) wrong based on 243 sessions

### HideShow timer Statistics

If x is a positive integer, is $$\sqrt{x}$$ an integer?

(1) $$\sqrt{4x}$$ is an integer.

(2) $$\sqrt{3x}$$ is not an integer.
[Reveal] Spoiler: OA

Last edited by ezinis on 29 Sep 2010, 09:39, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106258 [1] , given: 11618

Re: If x is a positive integer, is x an integer? [#permalink]

### Show Tags

29 Sep 2010, 07:29
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
ezinis wrote:
If x is a positive integer, is \sqrt{x} an integer?
(1) $$\sqrt{4x}$$ is an integer4.
(2) $$\sqrt{3x}$$ is an integer.

I am not satisfied with the official explanation. Please give yours, thanks.

I think (2) should be $$\sqrt{3x}$$ is NOT an integer.

If $$x=integer$$, is $$\sqrt{x}=integer$$?

(1) $$\sqrt{4x}$$ is an integer --> $$2\sqrt{x}=integer$$ --> $$2\sqrt{x}$$ to be an integer $$\sqrt{x}$$ must be an integer or integer/2, but as $$x$$ is an integer, then $$\sqrt{x}$$ can not be integer/2, hence $$\sqrt{x}$$ is an integer. Sufficient.

(2)$$\sqrt{3x}$$ is not an integer --> if $$x=9$$, condition $$\sqrt{3x}=\sqrt{27}$$ is not an integer satisfied and $$\sqrt{x}=3$$ IS an integer, BUT if $$x=2$$, condition $$\sqrt{3x}=\sqrt{6}$$ is not an integer satisfied and $$\sqrt{x}=\sqrt{2}$$ IS NOT an integer. Two different answers. Not sufficient.

_________________
Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London
Followers: 111

Kudos [?]: 1020 [0], given: 25

Re: If x is a positive integer, is x an integer? [#permalink]

### Show Tags

29 Sep 2010, 08:10
ezinis wrote:
If x is a positive integer, is \sqrt{x} an integer?
(1) \sqrt{4x} is an integer4.
(2) \sqrt{3x} is an integer.

I am not satisfied with the official explanation. Please give yours, thanks.

(1) $$\sqrt{4x} = 2 * \sqrt{x}$$
If this is an integer, then $$\sqrt{x}$$ has to be an integer

(2) $$\sqrt{3x} = \sqrt{3} * \sqrt{x}$$
For this to be an integer, $$\sqrt{x}$$ must be of the form $$\sqrt{3} * Integer$$
So $$\sqrt{x}$$ is not an integer

I am not sure if the question is correct as (1) and (2) are contradicting. Is it supposed to say $$\sqrt{3x}$$ is not an integer ?
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15472
Followers: 649

Kudos [?]: 209 [0], given: 0

Re: If x is a positive integer, is x an integer? [#permalink]

### Show Tags

09 Feb 2014, 09:55
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.
_________________
Manager
Joined: 06 Jun 2013
Posts: 126
Location: India
Concentration: Finance, Economics
Schools: Tuck
GMAT 1: 640 Q49 V30
GPA: 3.6
WE: Engineering (Computer Software)
Followers: 0

Kudos [?]: 11 [0], given: 297

Re: If x is a positive integer, is x an integer? [#permalink]

### Show Tags

27 Sep 2015, 08:36
Bunuel wrote:
ezinis wrote:
If x is a positive integer, is \sqrt{x} an integer?
(1) $$\sqrt{4x}$$ is an integer4.
(2) $$\sqrt{3x}$$ is an integer.

I am not satisfied with the official explanation. Please give yours, thanks.

I think (2) should be $$\sqrt{3x}$$ is NOT an integer.

If $$x=integer$$, is $$\sqrt{x}=integer$$?

(1) $$\sqrt{4x}$$ is an integer --> $$2\sqrt{x}=integer$$ --> $$2\sqrt{x}$$ to be an integer $$\sqrt{x}$$ must be an integer or integer/2, but as $$x$$ is an integer, then $$\sqrt{x}$$ can not be integer/2, hence $$\sqrt{x}$$ is an integer. Sufficient.

(2)$$\sqrt{3x}$$ is not an integer --> if $$x=9$$, condition $$\sqrt{3x}=\sqrt{27}$$ is not an integer satisfied and $$\sqrt{x}=3$$ IS an integer, BUT if $$x=2$$, condition $$\sqrt{3x}=\sqrt{6}$$ is not an integer satisfied and $$\sqrt{x}=\sqrt{2}$$ IS NOT an integer. Two different answers. Not sufficient.

i think it does not matter whether statement 2 is integer or not, as in both the cases we are getting different solution. and answer will be one in both the cases.
Re: If x is a positive integer, is x an integer?   [#permalink] 27 Sep 2015, 08:36
Similar topics Replies Last post
Similar
Topics:
Is a positive integer x square of an integer? 1 23 Nov 2016, 00:21
If x is a positive integer then find x? 1 17 Oct 2016, 05:19
2 If X is a positive integer, is X even? 1 24 Jun 2016, 05:28
2 If x is a positive integer, is x odd? 4 16 Apr 2016, 02:42
20 If x is a positive integer, is x prime? 9 17 Mar 2016, 06:26
Display posts from previous: Sort by