GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Feb 2019, 23:52

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free GMAT Strategy Webinar

February 16, 2019

February 16, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# If a > 0, b > 0 and c > 0, is a(b - c) = 0?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Director
Joined: 25 Oct 2008
Posts: 504
Location: Kolkata,India
If a > 0, b > 0 and c > 0, is a(b - c) = 0?  [#permalink]

### Show Tags

Updated on: 30 Jun 2013, 07:03
8
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:12) correct 44% (01:10) wrong based on 463 sessions

### HideShow timer Statistics

If a > 0, b > 0 and c > 0, is a(b - c) = 0?

(1) b - c = c - b
(2) b/c = c/b

_________________

http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902

Originally posted by tejal777 on 21 Aug 2009, 18:24.
Last edited by Bunuel on 30 Jun 2013, 07:03, edited 2 times in total.
Edited the question and added the OA.
Manager
Joined: 14 Aug 2009
Posts: 119
Re: if a>0, b>0, c>0, is a(b-c)=0?  [#permalink]

### Show Tags

21 Aug 2009, 18:45
3
1

a>0, b>0, c>0
for 1), b-c=c-b ==>> 2b=2c ==>>b=c
therefore a(b-c)=0, suff

for 2), b/c=c/b ==>> b^2=c^2
because b>0, c>0, ==>>b=c
therefore a(b-c)=0, suff
_________________

Kudos me if my reply helps!

Retired Moderator
Joined: 05 Jul 2006
Posts: 1714
Re: if a>0, b>0, c>0, is a(b-c)=0?  [#permalink]

### Show Tags

25 Aug 2009, 09:32
[quote="tejal777"]if a>0, b>0, c>0, is a(b-c)=0?

I. b-c = c-b
II. b/c = c/b

A(B-C) = 0 and as a>0 thus it is POSSIBLE ONLY WHEN B = C

from 1

b-c-c+b = 0 thus 2b = 2c thus b=c...suff

from 2

b/c = c/b all +ve thus b^2 = c^2 thus b=c....suff

D
Director
Joined: 29 Nov 2012
Posts: 749
Re: if a>0, b>0, c>0, is a(b-c)=0? I. b-c = c-b II. b/c  [#permalink]

### Show Tags

30 Jun 2013, 06:33
2
For statement 2

we get $$b^2=c^2$$ then $$b^2 - C^2 = 0$$ >> $$(b-c) (b+c) = 0$$

Why is this manipulation incorrect?
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1057
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: if a>0, b>0, c>0, is a(b-c)=0? I. b-c = c-b II. b/c  [#permalink]

### Show Tags

30 Jun 2013, 06:37
1
fozzzy wrote:
For statement 2

we get $$b^2=c^2$$ then $$b^2 - C^2 = 0$$ >> $$(b-c) (b+c) = 0$$

Why is this manipulation incorrect?

That is not incorrect.

You get $$(b-c) (b+c) = 0$$ so one (or both) terms equal zero. However we know that both b and c are positive, so (b+c) is positive as well, so b-c=0
Hence $$a(b-c)=0$$ => sufficient
_________________

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]

Director
Joined: 29 Nov 2012
Posts: 749
Re: if a>0, b>0, c>0, is a(b-c)=0? I. b-c = c-b II. b/c  [#permalink]

### Show Tags

30 Jun 2013, 06:52
Zarrolou wrote:

That is not incorrect.

You get $$(b-c) (b+c) = 0$$ so one (or both) terms equal zero. However we know that both b and c are positive, so (b+c) is positive as well, so b-c=0
Hence $$a(b-c)=0$$ => sufficient

So basically B+C is just redundant information once we solve till that point? Hence that case is ignored and we focus on the second case?
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1057
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: if a>0, b>0, c>0, is a(b-c)=0? I. b-c = c-b II. b/c  [#permalink]

### Show Tags

30 Jun 2013, 06:56
1
fozzzy wrote:
Zarrolou wrote:

That is not incorrect.

You get $$(b-c) (b+c) = 0$$ so one (or both) terms equal zero. However we know that both b and c are positive, so (b+c) is positive as well, so b-c=0
Hence $$a(b-c)=0$$ => sufficient

So basically B+C is just redundant information once we solve till that point? Hence that case is ignored and we focus on the second case?

I do not know what you mean by "redundant information", but yes: we know that $$b+c$$ cannot be zero, so the other term ($$b-c$$) must be zero.

All we get from $$b^2-c^2=0$$ in this problem is that $$b-c=0$$
_________________

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]

Math Expert
Joined: 02 Sep 2009
Posts: 52902
Re: If a > 0, b > 0 and c > 0, is a(b - c) = 0?  [#permalink]

### Show Tags

30 Jun 2013, 07:09
1
3
If a > 0, b > 0 and c > 0, is a(b - c) = 0?

Is $$a(b - c) = 0$$? --> is $$a=0$$ or $$b-c=0$$? Since given that $$a > 0$$, then the questions basically asks whether $$b-c=0$$.

(1) b - c = c - b --> $$2b-2c=0$$ --> $$b-c=0$$. Sufficient.

(2) b/c = c/b --> $$b^2=c^2$$ --> $$(b-c)(b+c)=0$$ --> $$b+c=0$$ or $$b-c=0$$ but since $$b$$ and $$c$$ are positive, then $$b+c>0$$. Therefore $$b-c=0$$. Sufficient.

_________________
Manager
Joined: 22 Feb 2016
Posts: 90
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Re: If a > 0, b > 0 and c > 0, is a(b - c) = 0?  [#permalink]

### Show Tags

30 Nov 2016, 20:15
Whoo!!! another super tricky question which can take you off the hooks during exam.
The simplest way to look at this question is we have 3 conditions a>0, b>0 and c>0 so thy are positive numbers but can be integers or fraction. (always proceed with this thought process - even if irrelevant here, it helps in the long run).
Question asks if a(b-c)=0 now we know a>0 thus a not equal to 0 hence b-c=0 or B=C

Statement 1
B-c=0
B=c Sufficient

Statement 2
c^2=B^2
|C|=|B|
since they are both greater than 0 hence c=b
Suffcienet

+kudos I need to unlock the exams
Director
Joined: 26 Oct 2016
Posts: 636
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If a > 0, b > 0 and c > 0, is a(b - c) = 0?  [#permalink]

### Show Tags

06 Feb 2017, 06:26
Bunuel wrote:
If a > 0, b > 0 and c > 0, is a(b - c) = 0?

Is $$a(b - c) = 0$$? --> is $$a=0$$ or $$b-c=0$$? Since given that $$a > 0$$, then the questions basically asks whether $$b-c=0$$.

(1) b - c = c - b --> $$2b-2c=0$$ --> $$b-c=0$$. Sufficient.

(2) b/c = c/b --> $$b^2=c^2$$ --> $$(b-c)(b+c)=0$$ --> $$b+c=0$$ or $$b-c=0$$ but since $$b$$ and $$c$$ are positive, then $$b+c>0$$. Therefore $$b-c=0$$. Sufficient.

Nice Explanation Bunuel. Thanks for sharing your approach.
_________________

Thanks & Regards,
Anaira Mitch

Manager
Status: The journey is always more beautiful than the destination
Affiliations: Computer Science
Joined: 24 Apr 2017
Posts: 53
Location: India
Concentration: Statistics, Strategy
GMAT 1: 570 Q40 V28
GPA: 3.14
If a > 0, b > 0 and c > 0, is a(b - c) = 0?  [#permalink]

### Show Tags

26 Mar 2018, 01:08
tejal777 wrote:
If a > 0, b > 0 and c > 0, is a(b - c) = 0?

(1) b - c = c - b
(2) b/c = c/b

This is a yes/ no question.
After simplifying the equation we get,
if b=c then b-c = 0. so the question depends on two equation.
1. Whether a is 0.
or 2. b=c.

option 1 says b = c . sufficient.
option 2 says b^2=c^c. no as b>0 and c>0, b=c. sufficient.
_________________

Sky is the limit. 800 is the limit.

If a > 0, b > 0 and c > 0, is a(b - c) = 0?   [#permalink] 26 Mar 2018, 01:08
Display posts from previous: Sort by

# If a > 0, b > 0 and c > 0, is a(b - c) = 0?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.