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

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subhendu009
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If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post  Updated on: 09 Apr 2013, 06:59
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00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

62% (01:34) correct 38% (01:44) wrong based on 308 sessions
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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.

Show Spoiler
OA : A
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Official Answer and Stats are available only to registered users. Register/Login.

Originally posted by subhendu009 on 09 Apr 2013, 06:44.
Last edited by subhendu009 on 09 Apr 2013, 06:59, edited 1 time in total.
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Zarrolou
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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, 06:58
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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

Show 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, 07:25
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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

KUDOS +1 IF THIS HELPED YOU (PLEASE!).
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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, 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] New post  22 Mar 2017, 09:43
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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.

Answer: A
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Nunuboy1994
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Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post  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.

Show 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
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NitishJain
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Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post  24 May 2020, 08:29
A.

a^3b - ab^3=0
ab(a^2-b^2)=0
ab(a+b)(a-b) =0
==> ab= 0 Not possible
OR a=b
OR a=-b

Not a unique answer as question states MUST be TRUE.

Hence A.
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Re: If ab 0 and a^3b = ab^3, then which option must be true ? [#permalink] New post  17 Jan 2023, 23:42
Asked: If ab ≠ 0 and \(a^3\)b = a\(b^3\), then which of the following must be true?

aˆ3b - abˆ3 = 0
ab(aˆ2-bˆ2) = ab(a+b)(a-b) = 0
(a+b)(a-b)=0
a = -b or
a = b

I. a = b
If a = -b , then may NOT be true

II. a = –b
If a = b , then may NOT be true

III. ab = 1
MAY or MAY NOT be true

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

IMO A
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gmatclubot
Re: If ab 0 and a^3b = ab^3, then which option must be true ? [#permalink]
17 Jan 2023, 23:42
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