If ab ≠ 0 and a^3b = ab^3, then which option must be true ? : GMAT Problem Solving (PS)
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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]

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09 Apr 2013, 05:44
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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
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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]

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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]

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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]

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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]

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01 Nov 2014, 20:11
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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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