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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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Senior Manager
Joined: 02 Jan 2017
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If a^3, b^3, and c^3 are all positive, does a^2=b/c^3?  [#permalink]

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23 Feb 2017, 20:19
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:09) correct 24% (01:13) wrong based on 62 sessions

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

1. c= b/(ac)^2
2. c=b^1/3/a^2/3
Manager
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Location: India
Schools: ISB '19, Fox"19
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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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23 Feb 2017, 20:25
D I guess coz
Using either statement alone I can arrive at an equation which shows c is not equal to b/c^3

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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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23 Feb 2017, 21:00
Give : a^3,b^3,c^3 >0 hence a,b,c>0

F1 ) c = b / (ac)^2 since a,b,c>0 C^3*a^2 = B Suff

F2 ) C = B^1/3 / A^2/3
cubing on both sides

c^3 = B/a^2 since a,b,c >0 Suff

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

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23 Feb 2017, 21:47
vikasp99 wrote:
If a^3, b^3, and c^3 are all positive, does a^2=b/c^3?

1. c= b/(ac)^2
2. c=b^1/3/a^2/3

Is $$a^2=b/c^3$$ ?

St I
$$c= b/(ac)^2 => c = b/(a^2*c^2) => a^2 = b / c^3$$ ------------Sufficient

St II
$$c=b^{1/3}/a^{2/3}$$
cubing both sides, we have
$$c^3=b/a^2 => a^2 = b/c^3$$ ---------------Sufficient

Hence option D is correct
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If a^3, b^3, and c^3 are all positive, does a^2=b/c^3? &nbs [#permalink] 23 Feb 2017, 21:47
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