NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 23:09 It is currently 27 Apr 2024, 23:09
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
dvinoth86
Manager
Manager
Joined: 19 Oct 2011
Posts: 87
Own Kudos [?]: 1236 [9]
Given Kudos: 33
Location: India
Send PM
If (a – b)c < 0, which of the following cannot be true? [#permalink] New post   23 Feb 2012, 20:27
2
Kudos
7
Bookmarks
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

76% (01:22) correct 24% (01:39) wrong based on 322 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92959
Own Kudos [?]: 619530 [8]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post   23 Feb 2012, 22:22
6
Kudos
2
Bookmarks
Expert Reply
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.
User avatar
omerrauf
Manager
Manager
Joined: 17 Nov 2011
Status:Employed
Posts: 67
Own Kudos [?]: 433 [5]
Given Kudos: 10
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE:Business Development (Internet and New Media)
Send PM
Re: PS: Inequality [#permalink] New post   23 Feb 2012, 21:05
4
Kudos
1
Bookmarks
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
General Discussion
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11669 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post   14 Feb 2015, 14:12
Expert Reply
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:
Show Spoiler
D


GMAT assassins aren't born, they're made,
Rich
User avatar
S
kanusha
Manager
Manager
Joined: 25 Mar 2013
Posts: 166
Own Kudos [?]: 130 [0]
Given Kudos: 101
Location: United States
Concentration: Entrepreneurship, Marketing
Schools: Yale '17 HBS '17 Stanford '17
GPA: 3.5
Send PM
GMAT ToolKit User Reviews Badge
Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post   14 Jan 2017, 18:56
(a-b)c < 0 = Negative
c < 0
a - b < 0
a < b
ac - bc < 0
ac < bc
D
avatar
sowmyamenon
Intern
Intern
Joined: 29 Jan 2018
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 9
Send PM
Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post   07 Mar 2018, 01:33
Hi guys, can someone explain to me why we accepted Option C to be plausible? How can modulus of C be negative? Modulus of a negative number is always positive, right?
User avatar
L
abhimahna
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3600
Own Kudos [?]: 5429 [0]
Given Kudos: 346
Send PM
Reviews Badge
Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] New post   07 Mar 2018, 01:41
Expert Reply
sowmyamenon wrote:
Hi guys, can someone explain to me why we accepted Option C to be plausible? How can modulus of C be negative? Modulus of a negative number is always positive, right?


Hey sowmyamenon ,

You are absolutely correct.

But please not that option C is saying |c| < 1, which could also mean |c| = 0.3, right?

|c| < 1 basically means |c| is > or equal to zero but less than 1.

Does that make sense?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32714
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If (a b)c < 0, which of the following cannot be true? [#permalink] New post   24 Mar 2022, 01:36
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 Club Bot
gmatclubot
Re: If (a b)c < 0, which of the following cannot be true? [#permalink]
24 Mar 2022, 01:36
Moderators:
Bunuel
Math Expert
92959 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions