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

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

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07 Dec 2018, 02:35
00:00

Difficulty:

35% (medium)

Question Stats:

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

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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

_________________
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]

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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.

Posted from my mobile device
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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]

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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.
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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]

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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
_________________
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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]

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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..
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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]

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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
Joined: 12 Sep 2017
Posts: 267
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

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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.

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]

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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.

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.
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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]

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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.

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/
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Karishma
Veritas Prep GMAT Instructor

Senior Manager
Joined: 12 Sep 2017
Posts: 267
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

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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.

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
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