It is currently 19 Nov 2017, 07:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Jan 2010
Posts: 24

Kudos [?]: 37 [1], given: 3

Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink]

### Show Tags

09 Apr 2013, 06:44
1
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:10) correct 42% (01:23) wrong based on 224 sessions

### HideShow timer Statistics

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.

Kudos [?]: 37 [1], given: 3

 Kaplan GMAT Prep Discount Codes Economist GMAT Tutor Discount Codes Optimus Prep Discount Codes
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2370 [0], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink]

### Show Tags

09 Apr 2013, 06:58
1
This post was
BOOKMARKED
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
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2370 [0], given: 219

Current Student
Joined: 02 Jan 2013
Posts: 57

Kudos [?]: 63 [1], given: 2

GMAT 1: 750 Q51 V40
GPA: 3.2
WE: Consulting (Consulting)
Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink]

### Show Tags

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

KUDOS +1 IF THIS HELPED YOU (PLEASE!).

Kudos [?]: 63 [1], given: 2

Current Student
Joined: 04 Mar 2013
Posts: 68

Kudos [?]: 58 [0], given: 27

Location: India
Concentration: Strategy, Operations
Schools: Booth '17 (M)
GMAT 1: 770 Q50 V44
GPA: 3.66
WE: Operations (Manufacturing)
Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ? [#permalink]

### Show Tags

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
_________________

When you feel like giving up, remember why you held on for so long in the first place.

Kudos [?]: 58 [0], given: 27

Non-Human User
Joined: 09 Sep 2013
Posts: 15690

Kudos [?]: 282 [0], given: 0

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

### Show Tags

01 Nov 2014, 21:11
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 282 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15690

Kudos [?]: 282 [0], given: 0

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

### Show Tags

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 282 [0], given: 0

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 902 [1], given: 5

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

### Show Tags

22 Mar 2017, 09:43
1
KUDOS
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 902 [1], given: 5

Director
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

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

### Show Tags

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

Kudos [?]: 36 [0], given: 165

Re: If ab ≠ 0 and a^3b = ab^3, then which option must be true ?   [#permalink] 24 Apr 2017, 21:58
Display posts from previous: Sort by