It is currently 17 Nov 2017, 16:19

### 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: 141

Kudos [?]: 109 [1], given: 18

Location: Montreal
Schools: Harvard, Yale, HEC
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:

68% (00:50) correct 32% (01:17) wrong based on 252 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.

Kudos [?]: 109 [1], given: 18

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132513 [1], given: 12324

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.

_________________

Kudos [?]: 132513 [1], given: 12324

Retired Moderator
Joined: 02 Sep 2010
Posts: 793

Kudos [?]: 1208 [0], given: 25

Location: London
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 ?
_________________

Kudos [?]: 1208 [0], given: 25

Non-Human User
Joined: 09 Sep 2013
Posts: 15702

Kudos [?]: 281 [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.
_________________

Kudos [?]: 281 [0], given: 0

Manager
Joined: 06 Jun 2013
Posts: 177

Kudos [?]: 17 [0], given: 314

Location: India
Concentration: Finance, Economics
Schools: Tuck
GMAT 1: 640 Q49 V30
GPA: 3.6
WE: Engineering (Computer Software)
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.

Kudos [?]: 17 [0], given: 314

Re: If x is a positive integer, is x an integer?   [#permalink] 27 Sep 2015, 08:36
Display posts from previous: Sort by