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

It is currently 18 Jun 2019, 20:05

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If √√√(3x) = 4√(2x), what is the greatest possible value of x?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55670
If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 07 Dec 2018, 02:35
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:48) correct 35% (01:59) wrong based on 148 sessions

HideShow timer Statistics

Director
Director
User avatar
D
Joined: 18 Jul 2018
Posts: 938
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 07 Dec 2018, 02:44
3
1
(3x)^(1/8) = (2x)^(1/4)

Taking 8th power on both sides.

3x = 4x^2
4x^2-3x = 0.
x(4x-3) = 0.
x = 0 or 3/4.

C is the answer

Posted from my mobile device
_________________
Press +1 Kudo If my post helps!
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3889
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 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
Director
User avatar
D
Joined: 18 Jul 2018
Posts: 938
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 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
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3889
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 07 Dec 2018, 03:08
1
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


Afc0892
I 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
Intern
avatar
B
Joined: 08 Jan 2018
Posts: 20
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
CAT Tests
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 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^2-3x=0
x(4x-3)=0
x=0 or x=3/4
Ans.C
Senior Manager
Senior Manager
User avatar
S
Joined: 12 Sep 2017
Posts: 267
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 12 Jan 2019, 17:19
Afc0892 wrote:
(3x)^(1/8) = (2x)^(1/4)

Taking 8th power on both sides.

3x = 4x^2
4x^2-3x = 0.
x(4x-3) = 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
Director
User avatar
D
Joined: 18 Jul 2018
Posts: 938
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 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^2-3x = 0.
x(4x-3) = 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
User avatar
D
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

New post 16 Jan 2019, 03:40
1
jfranciscocuencag wrote:
Afc0892 wrote:
(3x)^(1/8) = (2x)^(1/4)

Taking 8th power on both sides.

3x = 4x^2
4x^2-3x = 0.
x(4x-3) = 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 ... -the-gmat/
_________________
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
Senior Manager
User avatar
S
Joined: 12 Sep 2017
Posts: 267
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

Show Tags

New post 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^2-3x = 0.
x(4x-3) = 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
GMAT Club Bot
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?   [#permalink] 16 Jan 2019, 15:31
Display posts from previous: Sort by

If √√√(3x) = 4√(2x), what is the greatest possible value of x?

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


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne