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# If abc = b^3 , which of the following must be true?

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If abc = b^3 , which of the following must be true? [#permalink]

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14 Aug 2011, 09:34
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If abc = b^3 , which of the following must be true?

I. ac = b^2
II. b = 0
III. ac = 1

A. None
B. I only
C. II only
D. I and III
E. II and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-abc-b-3-which-of-the-following-must-be-true-109723.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Jul 2013, 07:04, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: PS - 700 level - abc [#permalink]

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14 Aug 2011, 10:09
hmm, I think the answer is None.
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Re: PS - 700 level - abc [#permalink]

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14 Aug 2011, 10:21
b= 0 or ac= b^2

But we are looking for must be true conditions.

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Re: PS - 700 level - abc [#permalink]

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11 Sep 2011, 19:01
Guys i am not getting this "Must be a true condition", could you please explain ?
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Re: PS - 700 level - abc [#permalink]

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12 Sep 2011, 01:35
The question has a small trap by mentioning 'must be true'

If the question is 'can be true' =>

abc-b^3 = 0
=> b (ac - b^2) =0
So either b = 0 or ac = b^2 or both can be the possible solutions

Since our question is 'must be true', we should find a solution that ALWAYS holds true

but from the above solutions, we cannot confirm that b=0 and ac=b^2 together. So, the answer is NONE
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Re: If abc = b^3 , which of the following must be true? [#permalink]

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03 Aug 2014, 20:42
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Re: If abc = b^3 , which of the following must be true? [#permalink]

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03 Aug 2014, 21:26
There are two conditions in which the equation will be satisfied.

either ac=b^2, or
b = 0
it could be either, so neither is 'definitely true'.
Re: If abc = b^3 , which of the following must be true?   [#permalink] 03 Aug 2014, 21:26
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