if x is a positive number and 1/2 the sqaure root of x is eq

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by Brent@GMATPrepNow » Wed Jul 28, 2010 8:44 am
szy wrote:Is there an easier way to go about this instead of plugging in all the answer choices?

if x is a positive number and 1/2 the sqaure root of x is equal to 2x, then x =

A) 1/16
B) 1/4
C) 1/2
D) 2
E) 8

Answer: [spoiler]1/16[/spoiler]
We can write the equation: (1/2)(rootx) = 2x
If we square both sides we get:(1/4)x = 4x^2
Rewrite as 4x^2 - (1/4)x = 0
Multiply both sides by 4 to get: 16x^2 - x = 0
Factor to get: x(16x-1)=0
So x=0 or (16x-1)=0

Case 1: x=0 is no good since we are told that x is positive
Case 2: 16x-1=0 --> solve to get x=1/16

Cheers,
Brent
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by szy » Wed Jul 28, 2010 9:44 am
ah im beating myself over as to how simple this was -- thanks for the explanation!