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by tonebeeze » Mon May 16, 2011 2:37 pm
If x is a positive number and 1/2 the square root of x is equal to 2x, then x =

a. 1/16
b. 1/4
c. 1/2
d. 2
e. 8

OA = A
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by MAAJ » Mon May 16, 2011 3:42 pm
Awww... took me a lot of time but got it at last... it's [spoiler](A)[/spoiler]

sqrt(x)/2 = 2x
sqrt(x) = 4x
x = 16x²
16x² - x + 0 = 0 -> z² = 16x² -> z = 4x -> x = z/4
z² - (1/4)z + 0 = 0
(z - 1/4)(z + 0) = 0
z = 1/4 OR z = 0

z² = (1/4)² = 16x²
1/16 = 16x²
1/16² = x²
1/16 = x
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by tonebeeze » Tue May 17, 2011 8:15 am
If progressed through the following deductions:
sqrt(x)/2 = 2x
sqrt(x) = 4x

then tested the answer choices, which saved me a lot of time. Does anyone else have any quick approaches to solving this problem?
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by Brent@GMATPrepNow » Tue May 17, 2011 11:56 am
tonebeeze wrote:If x is a positive number and 1/2 the square root of x is equal to 2x, then x =

a. 1/16
b. 1/4
c. 1/2
d. 2
e. 8

OA = A
One option is to plug in each answer choice.

Alternatively, we can use some equation-solving.

We're told that (1/2)(sqrt(x)) = 2x
So, sqrt(x) = 4x [multiply both sides by 2]
Then x = 16x^2 [square both sides]
Then 16x^2 - x = 0 [since we have a quadratic equation here, it usually helps to set it equal to zero]
Next, x(16x - 1) = 0 [factor the left-hand-side]

This means that x = 0 or 16x - 1 = 0

Since we're told that x is positive, we can rule out x=0

So, it must be the case that 16x - 1 = 0, and when we solve this, we get x=1/16 (A)
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