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Re M0103 [#permalink]
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16 Sep 2014, 00:14
Official Solution:If \(x\) is a positive number and \(\frac{1}{2}*\sqrt{x} = 2x\), what is the value of \(x\)?A. \(0\) B. \(\frac{1}{16}\) C. \(\frac{1}{4}\) D. \(\frac{1}{2}\) E. \(1\) Backsolve. Plug answer (C) into the equation for \(x\): \(\frac{1}{2}*\frac{1}{2} = 2*\frac{1}{4}\). Solve both sides of the equation: \(\frac{1}{4} \neq \frac{1}{2}\). Continue plugging in the answers. Plugging answer (B) into the equation for \(x\) gives: \(\frac{1}{2}*\frac{1}{4} = 2*\frac{1}{16}\)or \(\frac{1}{8} = \frac{1}{8}.\) Another option is to solve the equation for \(x\). \(\frac{1}{2}*\sqrt{x} = 2x\). Since \(x\) is a positive number, i.e., \(x \gt 0\), square both sides of equation to get: \(\frac{1}{4} * x = 4x^2\) Multiply both sides by 4: \(x = 16x^2\) \(16x^2  x = 0\) \(x(16x1) = 0\) The roots of this equation are \(x = 0\) and \(x = \frac{1}{16}\). Since \(x \gt 0\), the correct answer is \(x = \frac{1}{16}\). Answer: B
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Re: M0103 [#permalink]
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16 Oct 2016, 18:59
I understand why Choice B is a solution, but I don't understand why 0  Choice A  is not..  Need Kudos
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Re: M0103 [#permalink]
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16 Oct 2016, 22:40



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Re: M0103 [#permalink]
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17 Oct 2016, 07:47
Bunuel wrote: moulayabdesslam wrote: I understand why Choice B is a solution, but I don't understand why 0  Choice A  is not..
 Need Kudos The stem says that x is a positive number and 0 is neither positive nor negative. Thanks! That's funny how one can miss such obvious information.  Need Kudos
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Re: M0103 [#permalink]
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26 Jan 2017, 04:22
BunuelI think there is a little Typo: Backsolve. Plug answer (C) into the equation for \(x\): \(\frac{1}{2}*\frac{1}{2} = 2*\frac{1}{2}\). If you plugin answer (C) it should be "Backsolve. Plug answer (C) into the equation for \(x\): \(\frac{1}{2}*\frac{1}{2} = 2*\frac{1}{ 4}\)."



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Re: M0103 [#permalink]
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26 Jan 2017, 06:49



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Re: M0103 [#permalink]
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26 Aug 2017, 17:07
Instead of going from 1/4∗x=4x^2 and multiplying both sides by 4 and solving for roots, why not simply divide both sides by x, since you know x is positive?
You would then get 1/4 = 4x, then x = 1/16.



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Re: M0103 [#permalink]
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27 Aug 2017, 04:03



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Re: M0103 [#permalink]
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21 Sep 2017, 12:31
I am a little confused as to which one is the correct answer.
Is it now 1/4 or 1/16 ?
a) If you move 1/2 to RHS, square both sides and solve for x, then we would get 1/4. b) Instead, if we square both LHS and RHS as they are, then the answer would be 1/16.
Can you please clarify? Thanks.



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Re: M0103 [#permalink]
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21 Sep 2017, 12:35



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Re: M0103 [#permalink]
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21 Sep 2017, 13:04
Sorry, I made a rookie mistake. I missed squaring 4 when squaring both sides of the equation and ended up with 1/4. 1/16 is correct, like you mentioned



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Re: M0103 [#permalink]
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07 Jul 2018, 18:04
what about the negatives?



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Re: M0103 [#permalink]
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08 Jul 2018, 00:56










