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# M01-03

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Math Expert
Joined: 02 Sep 2009
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M01-03  [#permalink]

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16 Sep 2014, 00:14
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Difficulty:

5% (low)

Question Stats:

83% (00:57) correct 17% (00:53) wrong based on 188 sessions

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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. $$1$$

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Re M01-03  [#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:
$$x = 16x^2$$
$$16x^2 - x = 0$$
$$x(16x-1) = 0$$

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: M01-03  [#permalink]

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16 Oct 2016, 18:59
1
I understand why Choice B is a solution, but I don't understand why 0 - Choice A - is not..

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Re: M01-03  [#permalink]

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16 Oct 2016, 22:40
moulayabdesslam wrote:
I understand why Choice B is a solution, but I don't understand why 0 - Choice A - is not..

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The stem says that x is a positive number and 0 is neither positive nor negative.
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Re: M01-03  [#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..

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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.

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Re: M01-03  [#permalink]

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26 Jan 2017, 04:22
1
Bunuel

I 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 plug-in 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: M01-03  [#permalink]

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26 Jan 2017, 06:49
BoomHH wrote:
Bunuel

I 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 plug-in answer (C) it should be "Backsolve. Plug answer (C) into the equation for $$x$$: $$\frac{1}{2}*\frac{1}{2} = 2*\frac{1}{4}$$."

Thank you. Edited.
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Re: M01-03  [#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: M01-03  [#permalink]

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27 Aug 2017, 04:03
alainca wrote:
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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Yes, you can do this way too.
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Re: M01-03  [#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: M01-03  [#permalink]

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21 Sep 2017, 12:35
1
theHermes5 wrote:
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.

The correct answer is B: 1/16. You can see it under the spoiler in the first post as well as in the solution. How are you getting 1/4?
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Re: M01-03  [#permalink]

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21 Sep 2017, 13:04
1
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: M01-03  [#permalink]

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07 Jul 2018, 18:04
what about the negatives?
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Posts: 55170
Re: M01-03  [#permalink]

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08 Jul 2018, 00:56
1
hephzi_bah wrote:
what about the negatives?

If $$x$$ is a positive number and $$\frac{1}{2}*\sqrt{x} = 2x$$, what is the value of $$x$$?
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Re: M01-03  [#permalink]

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19 Feb 2019, 04:40
simplify the equation and then go by options
Re: M01-03   [#permalink] 19 Feb 2019, 04:40
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# M01-03

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