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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, 06:44
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Question Stats:

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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
-------------------------------------
Please press KUDOS if you like my post.

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

Last edited by subhendu009 on 09 Apr 2013, 06:59, 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, 06:58
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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, 07:25
1
KUDOS
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, 04:18
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, 21:11
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Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink]

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20 Mar 2017, 04:38
Hello from the GMAT Club BumpBot!

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

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22 Mar 2017, 09:43
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Expert's post
Quote:

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

Since ab ≠ 0, neither a nor b is 0. So we can divide both sides of the equation by ab to obtain:

a^2 = b^2

This means |a| = |b|. That is, a = b or a = -b. Notice that we use the word “or”. Thus, while Roman numeral I could be true (because a could equal b), it is not necessarily true. Similarly, Roman numeral II could be true (because a could equal -b), but it is not necessarily true. Finally, Roman numeral III could be true (if a = 1 and b = -1), but, again, it is not necessarily true. Thus, none of them must be true.

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

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24 Apr 2017, 21:58
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
-------------------------------------
Please press KUDOS if you like my post.

[Reveal] Spoiler:
OA : A

None of these are true if you consider the example

(2)^3b=2b^3
8b=2b^3
4b=b^3
b=2
Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ?   [#permalink] 24 Apr 2017, 21:58
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