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

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by fskilnik@GMATH » Sun Nov 18, 2018 6:09 am
BTGmoderatorDC 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
Source: Official Guide
$$? = x\,\,\,\,\left( {x > 0} \right)$$
$$\sqrt {{{2x} \over 3}} = x\,\,\,\,\mathop \Rightarrow \limits^{{\rm{squaring}}} \,\,\,\,{{2x} \over 3} = {x^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,x\left( {3x - 2} \right) = 0\,\,\,\,\,\mathop \Rightarrow \limits^{x\,\, > \,\,0} \,\,\,\,3x - 2 = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,? = {2 \over 3}$$

This solution follows the notations and rationale taught in the GMATH method.

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by deloitte247 » Sun Nov 18, 2018 11:43 am
$$x\cdot2=2x$$
$$2x\ divided\ by\ 3=\frac{2x}{3}$$
$$positive\ square\ root\ of\ \frac{2x}{3}=\sqrt{\frac{2x}{3}}$$
$$positive\ square\ root\ of\ \frac{2x}{3}=\sqrt{\frac{2x}{3}}$$
$$\sqrt{\frac{2x}{3}}=x$$
$$sqauring\ both\ sides$$
$$\left(\sqrt{\frac{2x}{3}}\right)^2=x^2$$
$$\frac{2x}{3x}=\frac{3x^2}{3x}$$
$$x=\frac{2}{3}$$
$$answer\ is\ option\ D$$
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by Scott@TargetTestPrep » Tue Apr 02, 2019 6:09 pm
BTGmoderatorDC 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

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

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