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If ab ≠ 0 and a^3b = ab^3, then which option must be true ?

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If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post 09 Apr 2013, 05:44
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Question Stats:

61% (02:10) correct 39% (01:21) wrong based on 119 sessions
I got this question from Kaplan Daily GMAT question and wanted to share with all members of gmatclub for practice.

If ab ≠ 0 and \(a^3\)b = a\(b^3\), then which of the following must be true?

I. a = b
II. a = –b
III. ab = 1

Options :
A. None
B. I only
C. III only
D. I and III only
E. I, II, and III
-------------------------------------
Please press KUDOS if you like my post.

[Reveal] Spoiler:
OA : A
[Reveal] Spoiler: OA

Last edited by subhendu009 on 09 Apr 2013, 05:59, edited 1 time in total.
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Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post 09 Apr 2013, 05:58
subhendu009 wrote:
I got this question from Kaplan Daily GMAT question and wanted to share with all members of gmatclub for practice.

If ab ≠ 0 and \(a^3\)b = a\(b^3\), then which of the following must be true?

I. a = b
II. a = –b
III. ab = 1

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

[Reveal] Spoiler:
OA : A


\(a^3b=ab^3\), since ab does not equal 0 we we divide by ab
\(a^2=b^2\) so \(|a|=|b|\)

I. a could be -b, it must not be true.
II. a could be +b, same as I
III. simply too much...
A
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Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post 09 Apr 2013, 06:25
Think of it this way:

(a^3).b = a.(b^3) => a.b.(a^2-b^2) = 0 => a.b.(a+b).(a-b) = 0

For this product to be zero, since ab≠ we can have: a=-b OR a= b

Let's look at the options:
1. DOES NOT HAVE TO BE TRUE. Take a = 1, b = -1, for instance
2. DOES NOT HAVE TO BE TRUE. Take a = 1, b = 1, for instance
3. DOES NOT HAVE TO BE TRUE. Take a = 2, b = 2, for instance

OPTION A

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Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post 12 Apr 2013, 03:18
The correct option does seem to be " A "

indeed
a = b is not always true
a = -b also not required
ab can aquire any value
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Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post 01 Nov 2014, 20:11
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ?   [#permalink] 01 Nov 2014, 20:11
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If ab ≠ 0 and a^3b = ab^3, then which option must be true ?

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