If x is a positive integr is x^(1/2) (Sq root of x) is an : DS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 16:52

### 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 integr is x^(1/2) (Sq root of x) is an

Author Message
Director
Joined: 08 Jul 2004
Posts: 598
Followers: 2

Kudos [?]: 214 [0], given: 0

If x is a positive integr is x^(1/2) (Sq root of x) is an [#permalink]

### Show Tags

22 Aug 2005, 11:27
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If x is a positive integr is x^(1/2) (Sq root of x) is an integer?
1. (4x)^(1/2) is an intger
2. (3x)^(1/2) is not integer.

from 1
let (4x)^(1/2) =k where k is an integer

x^(1/2)=k/2 . so does value of root x depends on odd/even. What wrong am I doing.
What is the way to approach this sort of problem.
S

Source og 222
_________________

Regards, S

Last edited by saurya_s on 22 Aug 2005, 11:43, edited 3 times in total.
Manager
Joined: 06 Aug 2005
Posts: 197
Followers: 3

Kudos [?]: 12 [0], given: 0

### Show Tags

22 Aug 2005, 11:34
Could you use more brackets or describe the question more precisely please
Senior Manager
Joined: 04 May 2005
Posts: 282
Location: CA, USA
Followers: 1

Kudos [?]: 51 [0], given: 0

### Show Tags

22 Aug 2005, 15:54
A ?

1. (4x)^(1/2) is an intger
=> x^(1/2) has to be integer

2. (3x)^(1/2) is not integer.
=> since 3^(1/2) is not integer already, we cannot decide the property of
x
Senior Manager
Joined: 29 Nov 2004
Posts: 484
Location: Chicago
Followers: 1

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

### Show Tags

22 Aug 2005, 16:36
I choose A too..Inline with qpoo..
_________________

Fear Mediocrity, Respect Ignorance

SVP
Joined: 05 Apr 2005
Posts: 1731
Followers: 5

Kudos [?]: 74 [0], given: 0

Re: DS IS Root x an integer [#permalink]

### Show Tags

22 Aug 2005, 17:28
saurya_s wrote:
If x is a positive integr is x^(1/2) (Sq root of x) is an integer?
1. (4x)^(1/2) is an intger
2. (3x)^(1/2) is not integer.

from i, (4x)^(1/2) = (4)^(1/2) (x)^(1/2) = +or- 2 (x)^(1/2) is an integer. so sqrt (x) is an integer.

from ii, (3x)^(1/2) is not integer means sqrt(x) could or couldnot be an integer because sqrt(3) doesnot give any integer.

so only A is correct.
Director
Joined: 08 Jul 2004
Posts: 598
Followers: 2

Kudos [?]: 214 [0], given: 0

### Show Tags

23 Aug 2005, 01:00
Himalaya, can you know what is conceptual error in my method?
Thanks mate
_________________

Regards, S

Current Student
Joined: 28 Dec 2004
Posts: 3384
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 281 [0], given: 2

### Show Tags

23 Aug 2005, 06:35
hmm what if X=1/4

then Sqrt (4X)=Sqrt(1)=1,

or Sqrt(4X)=2Sqrt(x), if this is an integer then Sqrt(x) is either an integer or is equal to 1/2 or Y/2....in that case its not an integer... again I am assuming irrational numbers can be viewed as fractions....there is no precise defintion that they are not...

I would go with E on this...
VP
Joined: 18 Nov 2004
Posts: 1440
Followers: 2

Kudos [?]: 37 [0], given: 0

### Show Tags

23 Aug 2005, 17:17
fresinha12 wrote:
hmm what if X=1/4

then Sqrt (4X)=Sqrt(1)=1,

or Sqrt(4X)=2Sqrt(x), if this is an integer then Sqrt(x) is either an integer or is equal to 1/2 or Y/2....in that case its not an integer... again I am assuming irrational numbers can be viewed as fractions....there is no precise defintion that they are not...

I would go with E on this...

Shud be "A"...X is +ve integer can't be 1/4.

Saurya, u r correct in ur approach except that ur variable K has to be an even integer as the LHS has a factor of 2.
Director
Joined: 08 Jul 2004
Posts: 598
Followers: 2

Kudos [?]: 214 [0], given: 0

### Show Tags

24 Aug 2005, 00:55
banerjeea_98 wrote:
fresinha12 wrote:
hmm what if X=1/4

then Sqrt (4X)=Sqrt(1)=1,

or Sqrt(4X)=2Sqrt(x), if this is an integer then Sqrt(x) is either an integer or is equal to 1/2 or Y/2....in that case its not an integer... again I am assuming irrational numbers can be viewed as fractions....there is no precise defintion that they are not...

I would go with E on this...

Shud be "A"...X is +ve integer can't be 1/4.

Saurya, u r correct in ur approach except that ur variable K has to be an even integer as the LHS has a factor of 2.

So baner, what is wrong with my approach. So, answer should be E with my way as we can't say if k is odd or even?
Can you plz explain this.
S
_________________

Regards, S

SVP
Joined: 05 Apr 2005
Posts: 1731
Followers: 5

Kudos [?]: 74 [0], given: 0

### Show Tags

24 Aug 2005, 06:04
saurya_s wrote:
Himalaya, can you know what is conceptual error in my method? Thanks mate
saurya_s wrote:
If x is a positive integr is x^(1/2) (Sq root of x) is an integer?
1. (4x)^(1/2) is an intger
2. (3x)^(1/2) is not integer.
from 1, let (4x)^(1/2) =k where k is an integer. x^(1/2)=k/2. so does value of root x depends on odd/even. What wrong am I doing. What is the way to approach this sort of problem.

surya, it doesnot matter. if (4x)^(1/2) is an intger, x^(1/2) must be an intger because sqrt(4) is an integer (+or-2).

you did x^(1/2)=k/2, which still must give you an integer. if you are supposing x as fraction (e.g1/4 or 0.25), which is not possible in this case because x is a positive integer as per the statement. so sqrt(x) must have an integer.

hope that helps.
24 Aug 2005, 06:04
Display posts from previous: Sort by