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20 Dec 2012, 06:04
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D
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Difficulty:
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86% (01:15) correct
14%
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wrong
based on 2322
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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
(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2
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20 Dec 2012, 06:07
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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 \(x=\frac{2}{3}\).
Answer: D.
Updated on: 04 Jul 2020, 06:46
Originally posted by BrentGMATPrepNow on 28 Aug 2017, 14:52.
Last edited by BrentGMATPrepNow on 04 Jul 2020, 06:46, edited 1 time in total.
Last edited by BrentGMATPrepNow on 04 Jul 2020, 06:46, edited 1 time in total.
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Walkabout
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
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