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

 It is currently 15 Oct 2018, 04:47

### 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

# If x is a positive integer, is x^(1/2) an integer ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49965
If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

15 Jan 2015, 07:09
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:25) correct 38% (02:07) wrong based on 145 sessions

### HideShow timer Statistics

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

(1) $$\sqrt{36x}$$ is an integer

(2) $$\sqrt{3x + 4}$$ is an integer

_________________
Manager
Joined: 27 Jun 2014
Posts: 69
Location: New Zealand
Concentration: Strategy, General Management
GMAT 1: 710 Q43 V45
GRE 1: Q161 V163

GRE 2: Q159 V166
GPA: 3.6
WE: Editorial and Writing (Computer Software)
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

15 Jan 2015, 18:09
4
Bunuel wrote:
If x is a positive integer, is $$\sqrt{x}$$ an integer?

(1) $$\sqrt{36x}$$ is an integer

(2) $$\sqrt{3x + 4}$$ is an integer

Kudos for a correct solution.

Have started following you Bunuel and this is my first crack at any of your questions.

1. Sufficient: Can be written as $$\sqrt{36}$$ * $$\sqrt{x}$$. $$\sqrt{36}$$ is an integer and therefore $$\sqrt{x}$$ must be an integer given that x is a positive integer.
2. Insufficient: Let's take x to be 7 in which case $$\sqrt{3x + 4}$$ = $$\sqrt{25}$$, which is an integer, but root of 7 is not an integer. On the other hand, if you take x=4, then the statement holds true and root of x is also an integer.

Answer is A. Will I get my first Kudo from you? :D If the solution is incorrect, your feedback will be more valuable than a Kudo
_________________

"Hardwork is the easiest way to success." - Aviram

One more shot at the GMAT...aiming for a more balanced score.

Senior Manager
Joined: 02 Dec 2014
Posts: 387
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

17 Jan 2015, 09:43
1
If x is a positive integer, is \sqrt{x} an integer?

(1) \sqrt{36x} is an integer

(2) \sqrt{3x + 4} is an integer
Statement 1. \sqrt{36x}=6(x^(1/2)). Hence 6 is an integer then (x^1/2) should be integer too. Sufficient
Statement 2. X can be 4 and then (x^1/2) is an integer. Or x=7 then (x^1/2) is not an integer. Insufficient.
_________________

"Are you gangsters?" - "No we are Russians!"

Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 422
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

07 Feb 2015, 10:36
Well, I am not sure if I am off here, but this is what I though:

x>0, is \sqrt{x} an integer?

For SQRT of x to be an integer, then x=1, or x>=4 and a perfect square (otherwise the SQRT would not be an integer). Just some initial thoughts.

[1] says that SQRT of 36x is an integer.
Based on my thinking above, 36x must be a perfect square, apparently greater than 36. For this to be true, x must be a perfect square. Any perfect square multiplied by 36 would have a SQRT that is an integer. So, if x is a perfect sqaure its SQRT will be an integer. So, [1] is sufficient.

[2] says that SQRT of 3x+4 is an integer.
For x=4, we have 3*4+4=16, and SQRT 16 is 4, which is an integer.
For x=5, we have 3*5+4=19, and SQRT 19 is not a integer. So, [2] is not sufficient. ANS A.

Am I right...?
Intern
Joined: 03 Aug 2014
Posts: 16
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

10 Feb 2015, 18:14
Hi Bunuel - I'm a little confused about the OA. If X = 1, then (1)^(1/2) is an integer but if X = 2, then 2^(1/2) is not an integer. Why is A correct?
Senior Manager
Joined: 02 Dec 2014
Posts: 387
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

11 Feb 2015, 02:29
Hi cg0588!
We are told that $$\sqrt{36x}$$ is an integer. Hence if you square out 6 then root of x should be integer (in order to \sqrt{36x} to be integer). Hence you can't say that x=2 since square root of 2 is not an integer. Hope it is clear
_________________

"Are you gangsters?" - "No we are Russians!"

Board of Directors
Joined: 17 Jul 2014
Posts: 2654
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

03 May 2016, 19:45
Bunuel wrote:
If x is a positive integer, is $$\sqrt{x}$$ an integer?

(1) $$\sqrt{36x}$$ is an integer

(2) $$\sqrt{3x + 4}$$ is an integer

Kudos for a correct solution.

1. sqrt(36x) = 6*sqrt(x) if this is an integer, then sqrt(x) is an integer. sufficient

2. if x=4, then yes. if x=7 then no. 2 alone not sufficient.

Senior Manager
Status: To infinity and beyond
Joined: 26 Sep 2017
Posts: 259
Location: India
Concentration: Finance, Technology
GMAT 1: 660 Q50 V30
GPA: 3.31
WE: Engineering (Computer Software)
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

05 Oct 2017, 20:21
(1) 36x−−−√36x is an integer since x is a positive integer root[x] needs to be an integer

(2) 3x+4−−−−−√3x+4 is an integer : if x is 7 then answer will be 5 hence not sufficient

A it is
_________________

Please give kudos if you like my post.Thanks

Intern
Joined: 07 Jun 2018
Posts: 34
Location: India
Schools: ISB '19
GMAT 1: 720 Q50 V35
GPA: 3.88
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

16 Jul 2018, 00:31
From statement 1 :

\sqrt{36x}= 6\sqrt{x}
Thus for \sqrt{36x} to be an integer, \sqrt{x} has to be an integer.

Statement 1 : Sufficient.

Statement 2 :

\sqrt{3x+4} :

putting x =1 ,
\sqrt{7} -- > not an integer
putting x =4
\sqrt{16} =4 -- > integer

_________________

Taking GMAT on 16th August 2018. Aiming for ISB YLP and MiM programs in Europe. Please give kudos if you like something I do.

Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1207
Location: India
WE: Engineering (Other)
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

16 Jul 2018, 00:44
sidsst

Quote:
Statement 2 :

\sqrt{3x+4} :

putting x =1 ,
\sqrt{7} -- > not an integer

I am unsure if above approach is correct. We are given that $$\sqrt{3x+4}$$ is an integer
so if we take x=1 we are not satisfying this condition. Note that each statement by itself is suff

I took x as 1,2,3 ..and so on, and found statement 2 satisfying for values of 4 and 7

niks18 pushpitkc Bunuel chetan2u pikolo2510
Any better approach?
_________________

It's the journey that brings us happiness not the destination.

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1218
Location: India
GPA: 3.82
Re: If x is a positive integer, is x^(1/2) an integer ?  [#permalink]

### Show Tags

16 Jul 2018, 02:33
sidsst

Quote:
Statement 2 :

\sqrt{3x+4} :

putting x =1 ,
\sqrt{7} -- > not an integer

I am unsure if above approach is correct. We are given that $$\sqrt{3x+4}$$ is an integer
so if we take x=1 we are not satisfying this condition. Note that each statement by itself is suff

I took x as 1,2,3 ..and so on, and found statement 2 satisfying for values of 4 and 7

niks18 pushpitkc Bunuel chetan2u pikolo2510
Any better approach?

yes you are correct in your assessment. we need to find whether $$\sqrt{x}$$ is an integer and not the validity of statement 2. if $$x=1$$, then $$\sqrt{x}$$ is an integer

Statement 2: Given $$\sqrt{3x+4}=Integer$$, square both sides to get

$$3x+4=I^2=>x=\frac{I^2-4}{3}$$. Now take square root of both sides

$$\sqrt{x}=\sqrt{\frac{I^2-4}{3}}$$, now this expression may or may not be an Integer. For eg, if I=2, then it will be an integer and if I=3, then it will be not an integer.

This is just one way to analyze statement 2
Re: If x is a positive integer, is x^(1/2) an integer ? &nbs [#permalink] 16 Jul 2018, 02:33
Display posts from previous: Sort by