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# Three musical tones have frequencies x, y, and z, respectively. If x,

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Math Expert
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Three musical tones have frequencies x, y, and z, respectively. If x, [#permalink]

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09 Nov 2015, 00:22
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Three musical tones have frequencies x, y, and z, respectively. If x, y, and z are positive, x/y = y/z, and 2x = z, what is y in terms of x ?

(A) 2

(B) $$\sqrt{2}x$$

(C) $$\frac{x}{\sqrt{2}}$$

(D) x/2

(E) $$\frac{\sqrt{2}}{3}x$$
[Reveal] Spoiler: OA

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Re: Three musical tones have frequencies x, y, and z, respectively. If x, [#permalink]

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09 Nov 2015, 00:58
Bunuel wrote:
Three musical tones have frequencies x, y, and z, respectively. If x, y, and z are positive, x/y = y/z, and 2x = z, what is y in terms of x ?

(A) 2

(B) $$\sqrt{2}x$$

(C) $$\frac{x}{\sqrt{2}}$$

(D) x/2

(E) $$\frac{\sqrt{2}}{3}x$$

Y^2= XZ, so substitute 2X instead of Z so it becomes 2X^2 therefore Y^2=2X^2, Y= Root of 2 and X, There fore my choice goes for B.

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Re: Three musical tones have frequencies x, y, and z, respectively. If x, [#permalink]

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09 Nov 2015, 01:43
x/y = y/z ---1
=>y^2 = xz

Now substituting 2x=z , we have
y^2=x*2x= 2*x^2
=>y = x* 2^(1/2)
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Re: Three musical tones have frequencies x, y, and z, respectively. If x, [#permalink]

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21 Oct 2017, 09:26
$$\frac{x}{y}$$=$$\frac{y}{z}$$ => $$y^2=xz$$ -------------(1)
2x=z
Putting the value of z in equation (1)
$$y^2=2x^2$$
y=$$\sqrt{2}x$$ or $$-\sqrt{2}x$$
Since x,y,z are positive,
y=$$\sqrt{2}x$$

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Re: Three musical tones have frequencies x, y, and z, respectively. If x,   [#permalink] 21 Oct 2017, 09:26
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