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

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

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07 Dec 2018, 01:35
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35% (medium)

Question Stats:

76% (01:12) correct 24% (02:04) wrong based on 104 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

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Director
Joined: 18 Jul 2018
Posts: 570
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, 01:44
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
_________________

If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

VP
Joined: 18 Aug 2017
Posts: 1212
Location: India
Concentration: Sustainability, Marketing
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, 01:51
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: 570
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, 02:03
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
_________________

If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

VP
Joined: 18 Aug 2017
Posts: 1212
Location: India
Concentration: Sustainability, Marketing
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, 02:08
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

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: 17
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, 02:42
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
Intern
Joined: 12 Sep 2017
Posts: 49
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

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12 Jan 2019, 16:19
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: 570
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, 21:28
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.
_________________

If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8790
Location: Pune, India
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

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16 Jan 2019, 02:40
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/
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 12 Sep 2017
Posts: 49
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

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16 Jan 2019, 14:31
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? &nbs [#permalink] 16 Jan 2019, 14:31
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