A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result

[BTGmoderatorDC]

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


OA D

Source: Official Guide

[Brent@GMATPrepNow]

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


OA D

Source: Official Guide

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

[Scott@TargetTestPrep]

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


OA D

Source: Official Guide

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

2x/3

We are given that the positive square root of this result 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

Answer: D