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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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20 Dec 2012, 06:04
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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
[Reveal] Spoiler: OA
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Posts: 44319
Re: A positive number x is multiplied by 2, and this product is [#permalink]

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20 Dec 2012, 06:07
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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

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 $$x=\frac{2}{3}$$.

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

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22 May 2014, 13:50
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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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17 Jul 2014, 00:25
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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

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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23 Jun 2016, 09:37
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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

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]

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28 Aug 2017, 14:52
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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

A positive number x is multiplied by 2...
We get: 2x

...and this product is then divided by 3
We get: 2x/3

If the positive square root of the result of these two operations equals x...
We get: √(2x/3) = x

From here, we can EITHER solve this equation for x, OR we can plug in the answer choices until we find a value that satisfies the equation.

Let's SOLVE the equation: √(2x/3) = x
Square both sides to get: 2x/3 = x²
Multiply both sides by 3 to get: 2x = 3x²
Subtract 2x from both sides to get: 0 = 3x² - 2x
Factor the right side: 0 = x(3x - 2)

So, EITHER x = 0 OR (3x - 2) = 0
Since we're told that x is a positive number, we can rule out the possibility that x = 0
So, it must be the case that (3x - 2) = 0
Add 2 to both sides to get: 3x = 2
Solve: x = 2/3

[Reveal] Spoiler:
D

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Re: A positive number x is multiplied by 2, and this product is   [#permalink] 28 Aug 2017, 14:52
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