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

It is currently 20 Oct 2018, 02:07

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

For integers a, b, and c, if ab = bc, then which of the foll

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

Hide Tags

Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 118
For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post Updated on: 11 Feb 2013, 15:22
6
29
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (01:01) correct 46% (01:03) wrong based on 664 sessions

HideShow timer Statistics

For integers a, b, and c, if ab = bc, then which of the following must also be true?

A. a = c
B. a^2*b=b*c^2
C. a/c = 1
D. abc > bc
E. a + b + c = 0

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.


Originally posted by emmak on 11 Feb 2013, 10:54.
Last edited by Bunuel on 11 Feb 2013, 15:22, edited 1 time in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50003
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 11 Feb 2013, 15:22
9
10
emmak wrote:
For integers a, b, and c, if ab = bc, then which of the following must also be true?

A. a = c
B. a^2*b=b*c^2
C. a/c = 1
D. abc > bc
E. a + b + c = 0


\(ab = bc\) --> \(ab-bc=0\) --> \(b(a-c)=0\)--> \(b=0\) or \(a=c\).


A. a = c. If \(b=0\), then this option is not necessarily true.

B. a^2*b=b*c^2 --> \(b(a^2-c^2)=0\) --> \(b(a-c)(a+c)=0\). Now, since \(b=0\) or \(a=c\), then \(b(a-c)(a+c)\) does equal to zero. So, we have that this options must be true.

C. a/c = 1. If \(b=0\), then this option is not necessarily true.

D. abc > bc. If \(b=0\), then this option is not true.

E. a + b + c = 0. If \(b=0\), then this option is not necessarily true (if b=0 then a+c can take any value this option is not necessarily true.).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
avatar
Joined: 17 Oct 2012
Posts: 16
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 12 Mar 2013, 05:08
1
b(a-c)=0 => b=0 or a=c

You can see B in an easier way:
Inequalities hold when we raise them to power on both sides. so a^2= c^2. => b.a^2= b.c^2. Thus B follows right away.

I agree with other explainations by Bunuel.
Intern
Intern
avatar
Joined: 05 Mar 2013
Posts: 13
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 11 Jun 2013, 20:47
Bunuel wrote:
emmak wrote:
For integers a, b, and c, if ab = bc, then which of the following must also be true?

A. a = c
B. a^2*b=b*c^2
C. a/c = 1
D. abc > bc
E. a + b + c = 0


\(ab = bc\) --> \(ab-bc=0\) --> \(b(a-c)=0\)--> \(b=0\) or \(a=c\).


B. a^2*b=b*c^2 --> \(b(a^2-c^2)=0\) --> \(b(a-c)(a+c)=0\). Now, since \(b=0\) or \(a=c\), then \(b(a-c)(a+c)\) does equal to zero. So, we have that this options must be true.

Answer: B.



for answer choice B, could you also say that if a = -c it also equals zero?

Also, why do all of the possible answers equaling zero in choice B mean that B must be true?
Manager
Manager
avatar
Status: Training
Joined: 03 Jun 2013
Posts: 90
Location: Canada
GPA: 3.7
GMAT ToolKit User Reviews Badge
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 11 Jun 2013, 21:21
1
dhlee922 wrote:
Bunuel wrote:

\(ab = bc\) --> \(ab-bc=0\) --> \(b(a-c)=0\)--> \(b=0\) or \(a=c\).

B. a^2*b=b*c^2 --> \(b(a^2-c^2)=0\) --> \(b(a-c)(a+c)=0\). Now, since \(b=0\) or \(a=c\), then \(b(a-c)(a+c)\) does equal to zero. So, we have that this options must be true.

Answer: B.


for answer choice B, could you also say that if a = -c it also equals zero?


The point here is that analyzing the initial equation ab = bc, we know that either b = 0 or a = c.
Plugging in either of these values results in b(a-c)(a+c) being equal to zero.
I think you're confusion comes from extracting "a = -c" from "b(a-c)(a+c) = 0" as opposed to extracting information from the original equation ab = bc (which is what we need to do).

dhlee922 wrote:
Also, why do all of the possible answers equaling zero in choice B mean that B must be true?


Continuing from above:
So recall that from the first equation, b = 0 or a = c.
The expanded term b(a-c)(a+c) is an alternate expression for the second option; i.e, the fact that both of the possible necessary truths (b = 0; a = c) lead to b(a-c)(a+c) = 0 means that the equivalent expression, a^2 * b = b * c^2 must also be true.

I hope that's clear!
_________________

KUDOS please if my post was useful!

Intern
Intern
avatar
Joined: 05 Mar 2013
Posts: 13
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 12 Jun 2013, 15:29
i'm still a little confused by the answer choices.

is it because the question stem equates to B=0 OR A=C

so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0

but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true?
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1076
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 12 Jun 2013, 15:34
dhlee922 wrote:
i'm still a little confused by the answer choices.

is it because the question stem equates to B=0 OR A=C

so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0

but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true?



Yes, exactly. We know that or b=0 or a-c=0 ( or both) .

We can rewrite B as \(b(a-c)(a+c)\), and since at least one of the terms is 0, the whole expression is 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
User avatar
V
Joined: 02 Sep 2009
Posts: 50003
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 12 Jun 2013, 15:38
dhlee922 wrote:
i'm still a little confused by the answer choices.

is it because the question stem equates to B=0 OR A=C

so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0

but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true?


Yes, for A, if b=0, then a may or may not equal to c.

As for B, since b=0 or a=c (a-c=0), then b(a-c)(a+c)=0 must be true, since either the first or the second multiple (or both) is 0.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 05 Mar 2013
Posts: 13
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 12 Jun 2013, 15:49
yes, thank you everyone for your replies! geez, i find this one to be pretty tricky, but it's only 600-700 level, ugh
Intern
Intern
avatar
B
Joined: 26 Jan 2018
Posts: 1
Re: For integers a, b, and c, if ab = bc, then which of the foll  [#permalink]

Show Tags

New post 11 Oct 2018, 12:11
Hi everyone,

This question is messing with everything I know (which is good). Isn't it legal to divide both parts of the equation by the same value? In this case, by b:

ab = bc --> (ab)/b = (bc)/b --> a = c

What am I doing wrong here?

Thanks!
GMAT Club Bot
Re: For integers a, b, and c, if ab = bc, then which of the foll &nbs [#permalink] 11 Oct 2018, 12:11
Display posts from previous: Sort by

For integers a, b, and c, if ab = bc, then which of the foll

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.