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

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Walkabout
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A positive number x is multiplied by 2, and this product is [#permalink] New post   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
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Re: A positive number x is multiplied by 2, and this product is [#permalink] New post   20 Dec 2012, 06:07
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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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BrentGMATPrepNow
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A positive number x is multiplied by 2, and this product is [#permalink] New post   Updated on: 04 Jul 2020, 06:46
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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


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

Answer: D

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Originally posted by BrentGMATPrepNow on 28 Aug 2017, 14:52.
Last edited by BrentGMATPrepNow on 04 Jul 2020, 06:46, edited 1 time in total.
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Re: A positive number x is multiplied by 2, and this product is [#permalink] New post   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] New post   17 Jul 2014, 00:25
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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



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] New post   23 Jun 2016, 09:37
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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


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] New post   21 Aug 2019, 01:58
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:
1. A positive number x is multiplied by 2, and this product is then divided by 3.
2. The the positive square root of the result of these two operations equals x

Asked: What is the value of x?

\(\sqrt{2x/3} = x\)
\(2x/3 = x^2\)
x = 2/3

IMO D
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Re: A positive number x is multiplied by 2, and this product is [#permalink] New post   02 Jan 2024, 08:18
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

Part by part -
Quote:
A positive number x is multiplied by 2, and this product is then divided by 3.

\(\frac{2x}{3}\)
Quote:
the positive square root of the result of these two operations equals x

\(\sqrt{\frac{2x}{3}}=x\)

Or, \(x^2 = \frac{2x}{3}\)

Or, \(x = \frac{2}{3}\), Answer must be (D)
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Re: A positive number x is multiplied by 2, and this product is [#permalink]
02 Jan 2024, 08:18
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