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by grandh01 » Sat Aug 11, 2012 4:39 pm
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
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by theCEO » Sat Aug 11, 2012 5:28 pm
[spoiler]ans = d[/spoiler]

sqrt (2x/3) = x
(2x/3) = x^2
2x/(x^2) = 3
2/x = 3
2 = 3x
x = 2/3
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by Brent@GMATPrepNow » Mon Oct 21, 2019 9:05 am
grandh01 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

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Wed Oct 23, 2019 5:55 pm
grandh01 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 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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