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

 It is currently 15 Jan 2019, 20:39

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### $450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # If x is a positive integer, is square_root x  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 11 Aug 2012 Posts: 116 Schools: HBS '16, Stanford '16 If x is a positive integer, is square_root x [#permalink] ### Show Tags Updated on: 26 May 2015, 05:24 1 00:00 Difficulty: 35% (medium) Question Stats: 67% (01:12) correct 33% (01:41) wrong based on 168 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! Originally posted by danzig on 29 Jul 2013, 15:18. Last edited by Bunuel on 26 May 2015, 05:24, edited 2 times in total. Edited the question. ##### Most Helpful Community Reply VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1061 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 1 bsahil wrote: can somebody please explain..i did not get this question... 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 I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] ##### General Discussion Manager Joined: 04 Apr 2013 Posts: 125 Re: If x is a positive integer, is square_root x [#permalink] ### Show Tags 02 Aug 2013, 18:12 1 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: 39 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 can somebody please explain..i did not get this question... Intern Joined: 05 Aug 2012 Posts: 18 WE: Project Management (Pharmaceuticals and Biotech) Re: If x is a positive integer, is square_root x [#permalink] ### Show Tags Updated on: 22 May 2015, 02:51 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. Originally posted by raeann105 on 21 May 2015, 15:50. Last edited by raeann105 on 22 May 2015, 02:51, edited 1 time in total. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13325 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x is a positive integer, is square_root x [#permalink] ### Show Tags 21 May 2015, 19:04 2 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 Co-Founder & 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: 24
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!

Intern
Joined: 24 Mar 2013
Posts: 24
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!

Never mind the analysis of [1]... I get it now. [1] is mainly to evaluate x as an integer or non-integer. Being the equivalent of a square of an integer x has to be positive.
Math Expert
Joined: 02 Sep 2009
Posts: 52108
Re: If x is a positive integer, is square_root x  [#permalink]

### Show Tags

26 May 2015, 05:25
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.
_________________
Director
Joined: 12 Nov 2016
Posts: 731
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
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 &nbs [#permalink] 24 May 2017, 18:19
Display posts from previous: Sort by

# If x is a positive integer, is square_root x

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.