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A positive number x is multiplied by 2, and this product is

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A positive number x is multiplied by 2, and this product is [#permalink]

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A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2
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Re: A positive number x is multiplied by 2, and this product is [#permalink]

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Walkabout wrote:
A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2


Given that: \(\sqrt{\frac{2x}{3}}=x\) --> \(\frac{2x}{3}=x^2\) --> \(x(3x-2)=0\) --> \(x=0\) (dscard since we are told that x is a positive number) or \(x=\frac{2}{3}\).

Answer: D.
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Re: A positive number x is multiplied by 2, and this product is [#permalink]

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Given Sqrt(2x/3)=x => 2x/3 = x^2
Since, x#0 we can divide both sides by x, so x=2/3
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Re: A positive number x is multiplied by 2, and this product is [#permalink]

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New post 17 Jul 2014, 00:25
Walkabout wrote:
A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2



2 in the numerator; 3 in the denominator

Answer \(= \frac{2}{3}\) = D
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Re: A positive number x is multiplied by 2, and this product is [#permalink]

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Re: A positive number x is multiplied by 2, and this product is [#permalink]

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New post 23 Jun 2016, 09:37
Walkabout wrote:
A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2


We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:

2x/3

Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us

√(2x/3) = x

2x/3 = x^2

2x = 3x^2

3x^2 – 2x = 0

x(3x – 2) = 0

x = 0 or

3x – 2 = 0

3x = 2

x = 2/3

Because x is positive, x = 2/3. The answer is D.
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Re: A positive number x is multiplied by 2, and this product is   [#permalink] 23 Jun 2016, 09:37
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A positive number x is multiplied by 2, and this product is

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