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Sub 505 Level|   Algebra|                        
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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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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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Walkabout
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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Walkabout
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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Walkabout
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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