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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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60% (02:08) correct
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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.

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

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!

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]

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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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Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

gmatclubot

Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ?
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22 Mar 2017, 09:43

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