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A positive number x is multiplied by 2, and this product is
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20 Dec 2012, 05:04

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84% (01:20) correct 16% (01:48) wrong based on 932 sessions

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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 ?

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20 Dec 2012, 05:07

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

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16 Jul 2014, 23:25

1

1

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 ?

Re: A positive number x is multiplied by 2, and this product is
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23 Jun 2016, 08:37

2

1

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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Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: A positive number x is multiplied by 2, and this product is
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28 Aug 2017, 13:52

Top Contributor

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

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23 Sep 2018, 10:27

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