Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Apr 2015, 04:31

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If (a – b)c < 0, which of the following cannot be true?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 19 Oct 2011
Posts: 134
Location: India
Followers: 2

Kudos [?]: 207 [1] , given: 33

If (a – b)c < 0, which of the following cannot be true? [#permalink] New post 23 Feb 2012, 19:27
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

81% (02:03) correct 19% (01:05) wrong based on 93 sessions
If (a – b)c < 0, which of the following cannot be true?

A. a < b
B. c < 0
C. |c| < 1
D. ac > bc
E. a^2 – b^2 > 0
[Reveal] Spoiler: OA

_________________

Encourage me by pressing the KUDOS if you find my post to be helpful.



Help me win "The One Thing You Wish You Knew - GMAT Club Contest"
the-one-thing-you-wish-you-knew-gmat-club-contest-140358.html#p1130989

Manager
Manager
User avatar
Status: Employed
Joined: 17 Nov 2011
Posts: 101
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 4

Kudos [?]: 81 [0], given: 10

Re: PS: Inequality [#permalink] New post 23 Feb 2012, 20:05
Question: If \((a-b)*c<0\) , which of the following cannot be true?

1. \(a<b\)
2. \(c<0\)
3. \(|c|<1\)
4. \(ac>bc\)
5. \(a^2-b^2>0\)

We know that if \((a-b)*c<0\) , either \(c<0\) or \((a-b)<0\) which means \(a<b\)

1. \(a<b\) true.
2. \(c<0\) true.
3. \(|c|<1\) Could be true since \(c\) could be \(-ve\) or \(+ve\).
4. \(ac>bc\) Now if \((a-b)\) is \(+ve\) then \(a>b\) but at the same time \(c\) is \(-ve\) so \(ac\) is less than \(bc\). On the other hand if \((a-b)\) is \(-ve\) than \(a<b\) and \(ac\) cannot be greater than \(bc\) since \(c\) is \(+ve\).
5. \(a^2-b^2>0\) Now from the original statement if \(c<0\) then \((a-b)>0\) so \(a>b\) and \(a^2\) and \(b^2\) are both \(+ve\) so this could be possible.

Hence Answer D
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27132
Followers: 4200

Kudos [?]: 40552 [1] , given: 5542

Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post 23 Feb 2012, 21:22
1
This post received
KUDOS
Expert's post
dvinoth86 wrote:
If (a – b)c < 0, which of the following cannot be true?

A. a < b
B. c < 0
C. |c| < 1
D. ac > bc
E. a^2 – b^2 > 0


Time saving approach:

Given: \((a-b)c<0\).

Now, since only option D has all three unknowns in it, I'd analyze this answer choice first:

D. \(ac > bc\) --> \(ac-bc>0\) --> \((a-b)c>0\). As you can see this option says directly opposite of what is given in the stem, hence it must be false.

There is no need even to check other options, as you cannot have two correct answers.

Answer: D.

P.S. Having all three unknowns does not mean that D is automatically a correct answer. An option could have two or even one unknown and still be a correct answer. For example if one of the options were \(c=0\) or \(a-b=0\) (a=b) then it would mean that it's false, since in this case \((a-b)c=0\), which means that this option would have been a correct answer.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4698
Followers: 291

Kudos [?]: 52 [0], given: 0

Premium Member
Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post 29 Jan 2014, 08:17
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4698
Followers: 291

Kudos [?]: 52 [0], given: 0

Premium Member
Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post 13 Feb 2015, 23:35
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 1818
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 73

Kudos [?]: 479 [0], given: 36

Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post 14 Feb 2015, 13:12
Expert's post
Hi All,

Since this question asks which of the following CANNOT be true, you will likely be able to disprove most (if not all) of the wrong answers with some simple examples. If we can prove that an answer IS possible (even just once), then we can eliminate it.

We're told that (A-B)(C) < 0

This means that one of the two parentheses MUST be POSITIVE while the other MUST be NEGATIVE. Recognizing THIS Number Property should speed you up - You can now either TEST VALUES or use this Number Property to eliminate answers.

Answer A: A < B

If A<B, then (A-B) is negative and C is positive. This IS possible. Eliminate A.

Answer B: C < 0

IF C<0, then (A-B) is positive. This IS possible. Eliminate B.

Answer C: |C| < 1

C can be positive or negative, so (A-B) would be the opposite. This IS possible. Eliminate C.

Between the remaining two answers, Answer E seems like the easier option to eliminate....

Answer E: A^2 - B^2 > 0

IF A>B and they're both positive, then (A-B) is positive and C is negative. This IS possible. Eliminate E.

There's only one answer left....

Final Answer:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

EMPOWERgmat GMAT Club Page, Study Plans, & Discounts
http://gmatclub.com/blog/courses/empowergmat-discount/?fl=menu

Image

Re: If (a – b)c < 0, which of the following cannot be true?   [#permalink] 14 Feb 2015, 13:12
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic If x < 0, which of the following must be true? Bunuel 6 03 Dec 2014, 07:19
7 Experts publish their posts in the topic If m<0, which of the following must be true? goodyear2013 11 13 Aug 2014, 09:25
1 Experts publish their posts in the topic If m<0, which of the following must be true? bagdbmba 8 10 Jun 2013, 19:50
2 Experts publish their posts in the topic If -1 < x < 0, which of the following must be true? rakesh20j 4 31 Jan 2013, 05:02
If (a b)c < 0, which of the following cannot be true? JCLEONES 1 02 Apr 2008, 14:12
Display posts from previous: Sort by

If (a – b)c < 0, which of the following cannot be true?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.