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

Question

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

Bunuel · Accepted Answer

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.

BrentGMATPrepNow · Answer

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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NoHalfMeasures · Answer

Given Sqrt(2x/3)=x => 2x/3 = x^2 
Since, x#0 we can divide both sides by x, so x=2/3

PareshGmat · Answer

2 in the numerator; 3 in the denominator

Answer  = \frac{2}{3}  = D

JeffTargetTestPrep · Answer

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.

Kinshook · Answer

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

Abhishek009 · Answer

Part by part -
 
 \frac{2x}{3} 
 
 \sqrt{\frac{2x}{3}}=x

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

Or,  x = \frac{2}{3} , Answer must be (D)

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