Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 May 2012
Posts: 14
Concentration: General Management, Finance
GRE 1: 330 Q168 V162
GPA: 3.82
WE: Research (Health Care)

Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? [#permalink]
Show Tags
21 Jul 2015, 10:00
1
This post received KUDOS
15
This post was BOOKMARKED
Question Stats:
48% (01:02) correct 52% (00:52) wrong based on 241 sessions
HideShow timer Statistics
Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? (a) 2^1/2 (b) 3^1/3 (c) 4^1/4 (d) 6^1/6 (e) 12^1/12 Kudos if you like Source: GMAT prep notes (Shiksha GMAT, Ahmadabad)
Official Answer and Stats are available only to registered users. Register/ Login.



Current Student
Joined: 25 Jun 2014
Posts: 42
WE: Operations (Computer Software)

Re: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? [#permalink]
Show Tags
21 Jul 2015, 20:52
7
This post received KUDOS
5
This post was BOOKMARKED
2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 Multiply each number raised to the power of 12 So, 2^1/2 = 2^6 = 64 3^1/3 = 3^4 = 81 4^1/4 = 4^3 = 64 6^1/6 = 6^2 = 36 12^1/12 = 12^1 = 12 So, the greatest is 3^1/3
_________________
Did I Help You..If Yes.. Then Kudos Please..



SVP
Joined: 08 Jul 2010
Posts: 1959
Location: India
GMAT: INSIGHT
WE: Education (Education)

Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? [#permalink]
Show Tags
21 Jul 2015, 21:14
3
This post received KUDOS
Expert's post
5
This post was BOOKMARKED
GMATnavigator wrote: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? (a) 2^1/2 (b) 3^1/3 (c) 4^1/4 (d) 6^1/6 (e) 12^1/12 Kudos if you like Source: GMAT prep notes (Shiksha GMAT, Ahmadabad) CONCEPT: The comparison of Difficult Surds and Indices can be done when either their bases are equal or their powers are equal.Here the bases of numbers can't be made same so making their powers equal \(2^{1/2}\), \(3^{1/3}\), \(4^{1/4}\) , \(6^{1/6}\) and \(12^{1/12}\) \(2^{1/2}\) = \((2^6)^{1/12}\) = \(64^{1/12}\) \(3^{1/3}\) = \((3^4)^{1/12}\) = \(81^{1/12}\) LARGEST \(4^{1/4}\) = \((4^3)^{1/12}\) = \(64^{1/12}\) \(6^{1/6}\) = \((6^2)^{1/12}\) = \(36^{1/12}\) \(12^{1/12}\) = \(12^{1/12}\) = \(12^{1/12}\) Answer: option B
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Senior Manager
Joined: 28 Jun 2015
Posts: 298
Concentration: Finance
GPA: 3.5

Re: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? [#permalink]
Show Tags
21 Jul 2015, 22:53
2^(1/2), 3^(1/3), 4^(1/4), 6^(1/6), 12^(1/12). LCM(2,3,4,6,12) = 24. Now, let's compare 2^(24/2), 3^(24/3), 4^(24/4), 6^(24/6), 12^(24/12). => 2^(12), 3^(8), 4^(6), 6^(4), 12^(2). => 2^(12), 3^(8), 2^(12), (3^4 * 2^4), (144). We only need to compare 3^(8) and (3^4 * 2^4). (3^8) = (3^4 * 3*4), which is clearly greater than (3^4 * 2^4). Therefore, 3^8 (=3^[1/3]) is the largest. Ans (B).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.



NonHuman User
Joined: 09 Sep 2013
Posts: 13760

Re: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? [#permalink]
Show Tags
17 Sep 2016, 16:38
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



eGMAT Representative
Joined: 04 Jan 2015
Posts: 806

Which among 2^{1/2}, 3^{1/3}....... [#permalink]
Show Tags
26 Apr 2017, 22:51
Which among \(2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 4^{\frac{1}{4}}, 6^{\frac{1}{6}}, 12^{\frac{1}{12}}\) is the largest? A. \(2^{\frac{1}{2}}\) B. \(3^{\frac{1}{3}}\) C. \(4^{\frac{1}{4}}\) D. \(6^{\frac{1}{6}}\) E. \(12^{\frac{1}{12}}\) Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
_________________
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



eGMAT Representative
Joined: 04 Jan 2015
Posts: 806

Re: Which among 2^{1/2}, 3^{1/3}....... [#permalink]
Show Tags
26 Apr 2017, 22:52
Reserving this space to post the official solution.
_________________
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Senior Manager
Joined: 02 Mar 2017
Posts: 271
Location: India
Concentration: Finance, Marketing

Re: Which among 2^{1/2}, 3^{1/3}....... [#permalink]
Show Tags
26 Apr 2017, 23:33
1
This post received KUDOS
2^(1/2) 3^(1/3 ) 4^(1/4) 6^(1/6) 12^(1/12) Are the given numbers Raising each term to the power of 12 (2)^6 (3)^4 (4)^3 (6)^2 (12)^1 Clearly (3)^4 is largest among the numbers >3^(1/3 ) largest B
_________________
Kudos> If my post was Helpful



Senior Manager
Joined: 24 Apr 2016
Posts: 333

Re: Which among 2^{1/2}, 3^{1/3}....... [#permalink]
Show Tags
26 Apr 2017, 23:46
1
This post received KUDOS
1
This post was BOOKMARKED
As the bases are different, we can try to make their powers equal.
2^(1/2) can be written as (2^6) ^ (1/12) = 64 ^ (1/12) 3^(1/3) can be written as (3^4) ^ (1/12) = 81 ^ (1/12) 4^(1/4) can be written as (4^3) ^ (1/12) = 64 ^ (1/12) 6^(1/6) can be written as (6^2) ^ (1/12) = 36 ^ (1/12) 12^(1/12) can be written as (12^1) ^ (1/12) = 12 ^ (1/12)
Clearly we can see that 3^(1/3) is the largest of all.
Answer is B



Intern
Joined: 25 Jul 2011
Posts: 48
Location: India
Concentration: Strategy, Operations
GPA: 3.5
WE: Engineering (Energy and Utilities)

Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? [#permalink]
Show Tags
17 Aug 2017, 08:08
GMATnavigator wrote: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ?
(a) 2^1/2 (b) 3^1/3 (c) 4^1/4 (d) 6^1/6 (e) 12^1/12
Kudos if you like :)
Source: GMAT prep notes (Shiksha GMAT, Ahmadabad) Although method elaborated earlier is the easiest and the quickest, I will put forward "Log method" for such questions too... take Log of all numbers given.. log 2^1/2 becomes 1/2 log 2 log 3^1/3 becomes 1/3 log 3 log 4^1/4 becomes 1/4 log 4 which becomes 1/4 log 2^2 which becomes 1/2 log 2 (A and C equal hence eliminated) log 6^1/6 becomes 1/6 log 6 which becomes 1/6 log (2*3) which becomes 1/6 (log 2+log 3) which is less than 1/3 (log3) as 1/3 log3 = 1/6 (log 3+log3) (D eliminated) log 12^1/12 becomes 1/12 log 12 which becomes 1/12 log (2^2*3) which becomes 1/12 {2log2+log3} which is less than 1/3 log 3 as 1/3 log 3 =1/12 {2log3+2log3} (E eliminated) Answer= B
_________________
Please hit kudos button below if you found my post helpful..TIA



SVP
Joined: 08 Jul 2010
Posts: 1959
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? [#permalink]
Show Tags
17 Aug 2017, 08:40
devarshi9283 wrote: GMATnavigator wrote: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ?
(a) 2^1/2 (b) 3^1/3 (c) 4^1/4 (d) 6^1/6 (e) 12^1/12
Kudos if you like :)
Source: GMAT prep notes (Shiksha GMAT, Ahmadabad) Although method elaborated earlier is the easiest and the quickest, I will put forward "Log method" for such questions too... take Log of all numbers given.. log 2^1/2 becomes 1/2 log 2 log 3^1/3 becomes 1/3 log 3 log 4^1/4 becomes 1/4 log 4 which becomes 1/4 log 2^2 which becomes 1/2 log 2 (A and C equal hence eliminated) log 6^1/6 becomes 1/6 log 6 which becomes 1/6 log (2*3) which becomes 1/6 (log 2+log 3) which is less than 1/3 (log3) as 1/3 log3 = 1/6 (log 3+log3) (D eliminated) log 12^1/12 becomes 1/12 log 12 which becomes 1/12 log (2^2*3) which becomes 1/12 {2log2+log3} which is less than 1/3 log 3 as 1/3 log 3 =1/12 {2log3+2log3} (E eliminated) Answer= B Logarithms is not part of GMAT hence GMAT specific readers may avoid any solution concerning Logarithms (log function) Posted from my mobile device
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Director
Joined: 29 Jun 2017
Posts: 512
GPA: 4
WE: Engineering (Transportation)

Re: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ? [#permalink]
Show Tags
17 Aug 2017, 09:32
Answer is B clearly make multiply all by 12th power new numbers will become 2^6, 3^4, 4^3, 6^2 , 12 64,81,64,36,12 clearly 81 is biggest number. hence B
_________________
Give Kudos for correct answer and/or if you like the solution.




Re: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ?
[#permalink]
17 Aug 2017, 09:32






