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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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Math Expert
Joined: 02 Sep 2009
Posts: 51218
If a^3, b^3, and c^3 are all positive, does a^2 = b/c^3?  [#permalink]

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15 Jul 2018, 20:36
00:00

Difficulty:

15% (low)

Question Stats:

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

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

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

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