Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 11 Aug 2012
Posts: 123

If x is a positive integer, is square_root x [#permalink]
Show Tags
29 Jul 2013, 15:18
1
This post was BOOKMARKED
Question Stats:
68% (00:54) correct 32% (01:34) wrong based on 161 sessions
HideShow timer Statistics
If x is a positive integer, is \((x^{0.5})^{0.5}\) an integer? (1) x is the square of an integer. (2) \(\sqrt{x}\) is the square of an integer. I agree with the OA. However, I have a doubt with (2):
\(\sqrt{x} = i^2\) , being \(i\) an integer.
Should we unsquare or use an additional square root on \(i\)? Is there a difference? I know that the square root only provide the positive root of the number.
Thanks!
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 26 May 2015, 05:24, edited 2 times in total.
Edited the question.



Manager
Joined: 04 Apr 2013
Posts: 149

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
02 Aug 2013, 18:12
1
This post was BOOKMARKED
danzig wrote: If x is a positive integer, is [(x)^(1/2)]^(1/2) ? (1) x is the square of an integer. (2) \(\sqrt{x}\) is the square of an integer.
I agree with the OA. However, I have a doubt with (2):
\(\sqrt{x} = i^2\) , being \(i\) an integer.
Should we unsquare or use an additional square root on \(i\)? Is there a difference? I know that the square root only provide the positive root of the number.
Thanks! danzig, my understanding since x is + ve, sq_rt(x) is +ve also i^2 is always +ve. since both are +ve, it doesnt matter if you unsquare of use additional sq rt. Hope I clarified your doubt.
_________________
Maadhu
MGMAT1  540 ( Trying to improve )



Intern
Status: Waiting for Decisions
Joined: 23 Dec 2012
Posts: 41
Location: India
Sahil: Bansal
GMAT 1: 570 Q49 V20 GMAT 2: 690 Q49 V34
GPA: 3
WE: Information Technology (Computer Software)

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
03 Aug 2013, 07:39



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1121
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
03 Aug 2013, 07:46
5
This post received KUDOS
1
This post was BOOKMARKED
bsahil wrote: The question asks if \(x^{\frac{1}{4}}\) is a positive integer (1) x is the square of an integer.So x can be \(4\), and \(4^{\frac{1}{4}}\) is NOT a positive integer. But x can be \(16\), and \(16^{\frac{1}{4}}\) is a positive integer. Not sufficient (2) \(\sqrt{x}\) is the square of an integer.So \(\sqrt{x}=n^2\), \(x^{\frac{1}{4}}=n^{2*\frac{1}{2}}=n\) where n is an integer. Sufficient Hope it's clear
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



NonHuman User
Joined: 09 Sep 2013
Posts: 13759

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
21 May 2015, 11:53
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 05 Aug 2012
Posts: 19
WE: Project Management (Pharmaceuticals and Biotech)

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
21 May 2015, 15:50
Zarrolou wrote: (1) x is the square of an integer. So x can be \(4\), and \(4^{\frac{1}{4}}\) is NOT a positive integer.
How is \(4^{\frac{1}{4}}\) not a positive integer?? Edit: You can ignore this post...I get it.
Last edited by raeann105 on 22 May 2015, 02:51, edited 1 time in total.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11074
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
21 May 2015, 19:04
Hi Bunuel, It looks like the prompt is incomplete. From the other posts, it appears that the question is supposed to ask "Is.......an integer?", but the original prompt is missing that language. The original poster also appears to be long gone, so could you edit the original post accordingly? Thanks. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 24 Mar 2013
Posts: 28

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
25 May 2015, 13:02
Experts, please critique if my approach...esp. in analyzing [1] is accurate.....Thanks in advance! I found that if I use the techniques taught by the Quant experts on GC, i arrive at the right solution. Solving [1] with my personal logic ... that X being the square of another integer (+ve or ve)....will make x a +ve integer (always), I arrived at the conclusion that [1] is also sufficient Your help is much appreciated! The way I understood this question is: We need to answer if √(√x) is a positive integer?
Given: [1] x is the square of an integer. So x = y^2 taking Sqrt on LHS and RHS √x = √(y^2) According to GMATCLUB math guide √(y^2) = y Therefore, √(√x) = √(y) Solving for y as (+y & y) we can't say if √(√x) is +ve or ve.....Not sufficient!
(2) √x is the square of an integer. So √x=y^2 taking Sqrt on LHS and RHS √(√x) = √(y^2) √(√x) = y...........hence sufficient!
Answer is B



Intern
Joined: 24 Mar 2013
Posts: 28

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
25 May 2015, 17:02
rohitd80 wrote: Experts, please critique if my approach...esp. in analyzing [1] is accurate.....Thanks in advance! I found that if I use the techniques taught by the Quant experts on GC, i arrive at the right solution. Solving [1] with my personal logic ... that X being the square of another integer (+ve or ve)....will make x a +ve integer (always), I arrived at the conclusion that [1] is also sufficient Your help is much appreciated! The way I understood this question is: We need to answer if √(√x) is a positive integer?
Given: [1] x is the square of an integer. So x = y^2 taking Sqrt on LHS and RHS √x = √(y^2) According to GMATCLUB math guide √(y^2) = y Therefore, √(√x) = √(y) Solving for y as (+y & y) we can't say if √(√x) is +ve or ve.....Not sufficient!
(2) √x is the square of an integer. So √x=y^2 taking Sqrt on LHS and RHS √(√x) = √(y^2) √(√x) = y...........hence sufficient!
Answer is B
Never mind the analysis of [1]... I get it now. [1] is mainly to evaluate x as an integer or noninteger. Being the equivalent of a square of an integer x has to be positive.



Math Expert
Joined: 02 Sep 2009
Posts: 43898

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
26 May 2015, 05:25



Director
Joined: 12 Nov 2016
Posts: 790

Re: If x is a positive integer, is square_root x [#permalink]
Show Tags
24 May 2017, 18:19
Bunuel wrote: EMPOWERgmatRichC wrote: Hi Bunuel,
It looks like the prompt is incomplete. From the other posts, it appears that the question is supposed to ask "Is.......an integer?", but the original prompt is missing that language. The original poster also appears to be long gone, so could you edit the original post accordingly? Thanks.
GMAT assassins aren't born, they're made, Rich Done. Thank you for noticing this. With this question it easier to convert the exponents into fractions (x^.5)^.5 = (x^1/2)^1/2 x^1/4  translates to the 4th root of x (x^1/3 would be the cube root of x and x^2/3 would be the cube root of x^2  that's the pattern/rule) Statement 1 is insufficient because 2 is the square of 4 but the 4th root of 2 is not an integer Statement 2 is sufficient because it we take say 16, the square root of 16 is 4 and 4 is a perfect square, it is 2 squared so 16 =2^4




Re: If x is a positive integer, is square_root x
[#permalink]
24 May 2017, 18:19






