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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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New post 07 Dec 2018, 01:35
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A
B
C
D
E

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  35% (medium)

Question Stats:

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

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

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New post 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.

C is the answer

Posted from my mobile device
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x?  [#permalink]

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

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New post 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?

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

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

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

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New post 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.

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

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New post 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.

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

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New post 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.

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

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New post 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.

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
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of x? &nbs [#permalink] 16 Jan 2019, 14:31
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