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# Each of a, b, and c is positive. Does b = root(ac)

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Intern
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Joined: 13 May 2013
Posts: 11
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Kudos [?]: 7 [1] , given: 7

Each of a, b, and c is positive. Does b = root(ac) [#permalink]

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29 Aug 2013, 13:51
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Difficulty:

25% (medium)

Question Stats:

73% (01:41) correct 27% (00:46) wrong based on 47 sessions

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Each of a, b, and c is positive. Does $$b = \sqrt{ac}$$?

(1) $$\frac{a}{b} = \frac{b}{c}$$
(2) $$\frac{1}{b^3} = \frac{1}{abc}$$
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Aug 2013, 13:55, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 32558
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Kudos [?]: 68465 [0], given: 9805

Re: Each of a, b, and c is positive. Does b = root(ac) [#permalink]

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29 Aug 2013, 13:58
Expert's post
Each of a, b, and c is positive. Does $$b = \sqrt{ac}$$?

(1) $$\frac{a}{b} = \frac{b}{c}$$. Cross-multiply: $$b^2=ac$$ --> $$b = \sqrt{ac}$$. Sufficient.

(2) $$\frac{1}{b^3} = \frac{1}{abc}$$. Cross-multiply: $$b^3=abc$$ --> reduce by b: $$b^2=ac$$. Sufficient.

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Re: Each of a, b, and c is positive. Does b = root(ac)   [#permalink] 29 Aug 2013, 13:58
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