Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jun 23 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55670

If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
07 Dec 2018, 02:35
Question Stats:
65% (01:48) correct 35% (01:59) wrong based on 148 sessions
HideShow timer Statistics
If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x? A. 1/4 B. 1/2 C. 3/4 D. 4/3 E. 8/3
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Director
Joined: 18 Jul 2018
Posts: 938
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
07 Dec 2018, 02:44
(3x)^(1/8) = (2x)^(1/4) Taking 8th power on both sides. 3x = 4x^2 4x^23x = 0. x(4x3) = 0. x = 0 or 3/4. C is the answer Posted from my mobile device
_________________
Press +1 Kudo If my post helps!



CEO
Joined: 18 Aug 2017
Posts: 3889
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
07 Dec 2018, 02:51
Bunuel wrote: If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?
A. 1/4 B. 1/2 C. 3/4 D. 4/3 E. 8/3 we can solve by plugin values as well: upon doing plugin at x=3/4 we would get value (3/2)^1/4 = (3/2)^1/4 IMO C , x=3/4 is correct.
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Director
Joined: 18 Jul 2018
Posts: 938
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
07 Dec 2018, 03:03
Archit3110 wrote: Bunuel wrote: If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?
A. 1/4 B. 1/2 C. 3/4 D. 4/3 E. 8/3 we can solve by plugin values as well: upon doing plugin at x=3/4 we would get value (3/2)^1/4 = (3/2)^1/4 IMO C , x=3/4 is correct. Archit3110, how did you choose 3/4 to plugin? Posted from my mobile device
_________________
Press +1 Kudo If my post helps!



CEO
Joined: 18 Aug 2017
Posts: 3889
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
07 Dec 2018, 03:08
Afc0892 wrote: Archit3110 wrote: Bunuel wrote: If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?
A. 1/4 B. 1/2 C. 3/4 D. 4/3 E. 8/3 we can solve by plugin values as well: upon doing plugin at x=3/4 we would get value (3/2)^1/4 = (3/2)^1/4 IMO C , x=3/4 is correct. Archit3110, how did you choose 3/4 to plugin? Posted from my mobile device Afc0892I plugged in from the given value of x into the question Given LHS (3*x)^1/8 so upon plugin it becomes (9/4)^1/8 or we can say ( 3/2)^1/4 and RHS given (2x)^1/4 upon plug in x=3/4 we would get , ( 3/2)^1/4 hence LHS = RHS so sufficient..
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Intern
Joined: 08 Jan 2018
Posts: 20
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)

Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
07 Dec 2018, 03:42
Bunuel wrote: If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?
A. 1/4 B. 1/2 C. 3/4 D. 4/3 E. 8/3 Ans. √√√(3x) = (3x)^(1/2*1/2*1/2)=(3x)^1/8 (3x)^1/8=(2x)^1/4 3x=(2x)^2 4x^23x=0 x(4x3)=0 x=0 or x=3/4 Ans.C



Senior Manager
Joined: 12 Sep 2017
Posts: 267

Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
12 Jan 2019, 17:19
Afc0892 wrote: (3x)^(1/8) = (2x)^(1/4)
Taking 8th power on both sides.
3x = 4x^2 4x^23x = 0. x(4x3) = 0. x = 0 or 3/4.
C is the answer
Posted from my mobile device Hello Afc0892 ! Could you please give a detailed explanation on how to get rid of the square roots? Kind regards!



Director
Joined: 18 Jul 2018
Posts: 938
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
15 Jan 2019, 22:28
jfranciscocuencag wrote: Afc0892 wrote: (3x)^(1/8) = (2x)^(1/4)
Taking 8th power on both sides.
3x = 4x^2 4x^23x = 0. x(4x3) = 0. x = 0 or 3/4.
C is the answer
Posted from my mobile device Hello Afc0892 ! Could you please give a detailed explanation on how to get rid of the square roots? Kind regards! Hey jfranciscocuencag, Sure. \(\sqrt{}\) can be written as any number power \(\frac{1}{2}\) As the question contains 3 squareroots. 3x will have a power of \(\frac{1}{8} (\frac{1}{2}*\frac{1}{2}*\frac{1}{2})\) And 2x has fourth power root. hence \((2x)^\frac{1}{4}\) In order to cancel the root power, we'll take 8th power on both sides (as LCM of 4 and 8 is 8). Then the equation can be written as 3x = \((2x)^2\) Reducing this further will yield x as 0 or 3/4. Hope it's clear.
_________________
Press +1 Kudo If my post helps!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9330
Location: Pune, India

Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
16 Jan 2019, 03:40
jfranciscocuencag wrote: Afc0892 wrote: (3x)^(1/8) = (2x)^(1/4)
Taking 8th power on both sides.
3x = 4x^2 4x^23x = 0. x(4x3) = 0. x = 0 or 3/4.
C is the answer
Posted from my mobile device Hello Afc0892 ! Could you please give a detailed explanation on how to get rid of the square roots? Kind regards! Check out our post on roots here: https://www.veritasprep.com/blog/2011/0 ... thegmat/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 12 Sep 2017
Posts: 267

Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
Show Tags
16 Jan 2019, 15:31
Afc0892 wrote: jfranciscocuencag wrote: Afc0892 wrote: (3x)^(1/8) = (2x)^(1/4)
Taking 8th power on both sides.
3x = 4x^2 4x^23x = 0. x(4x3) = 0. x = 0 or 3/4.
C is the answer
Posted from my mobile device Hello Afc0892 ! Could you please give a detailed explanation on how to get rid of the square roots? Kind regards! Hey jfranciscocuencag, Sure. \(\sqrt{}\) can be written as any number power \(\frac{1}{2}\) As the question contains 3 squareroots. 3x will have a power of \(\frac{1}{8} (\frac{1}{2}*\frac{1}{2}*\frac{1}{2})\) And 2x has fourth power root. hence \((2x)^\frac{1}{4}\) In order to cancel the root power, we'll take 8th power on both sides (as LCM of 4 and 8 is 8). Then the equation can be written as 3x = \((2x)^2\) Reducing this further will yield x as 0 or 3/4. Hope it's clear. Thank you Afc0892 ! +KU




Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?
[#permalink]
16 Jan 2019, 15:31






