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A positive number x is multiplied by 2, and this product is
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20 Dec 2012, 06:04
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5% (low)
Question Stats:
84% (01:19) correct 16% (01:48) wrong based on 896 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, 06:07
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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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17 Jul 2014, 00:25
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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 ?
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23 Jun 2016, 09:37
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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, 14:52
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, 11:27
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