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If a^3, b^3, and c^3 are all positive, does a^2 = b/c^3?

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Posts: 51218
If a^3, b^3, and c^3 are all positive, does a^2 = b/c^3?  [#permalink]

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New post 15 Jul 2018, 20:36
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:03) correct 14% (00:47) wrong based on 36 sessions

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Re: If a^3, b^3, and c^3 are all positive, does a^2 = b/c^3?  [#permalink]

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New post 15 Jul 2018, 22:06
Bunuel wrote:
If a^3, b^3, and c^3 are all positive, does \(a^2 = \frac{b}{c^3}\)?


(1) \(c = \frac{b}{(ac)^2}\)

(2) \(c = \frac{\sqrt[3]{b}}{\sqrt[3]{a^2}}\)


Given, \(a^3, b^3, c^3\) are all positive
Implies \(a>0, b>0, {c>0}\)

St1:- \(c = \frac{b}{(ac)^2}\)
We can cross multiply;
\(a^2*c^2*c=b\)
Or, \(a^2*c^3=b\)
Or,\(a^2=\frac{b}{c^3}\)
Sufficient.

St2:- \(c = \frac{\sqrt[3]{b}}{\sqrt[3]{a^2}}\)
Taking cube both sides, we have
\(c^3=\frac{b}{a^2}\)
Or, \(a^2=\frac{b}{c^3}\)
Sufficient.

Ans. (D)
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Re: If a^3, b^3, and c^3 are all positive, does a^2 = b/c^3? &nbs [#permalink] 15 Jul 2018, 22:06
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