If (a – b)c < 0, which of the following cannot be true? : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 08:08

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 19 Oct 2011
Posts: 132
Location: India
Followers: 3

Kudos [?]: 374 [1] , given: 33

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

### Show Tags

23 Feb 2012, 19:27
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

78% (02:05) correct 22% (01:02) wrong based on 148 sessions

### HideShow 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
[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"
http://gmatclub.com/forum/the-one-thing-you-wish-you-knew-gmat-club-contest-140358.html#p1130989

Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 100
Location: Pakistan
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 7

Kudos [?]: 135 [1] , given: 10

### Show Tags

23 Feb 2012, 20:05
1
KUDOS
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.

_________________

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

Math Expert
Joined: 02 Sep 2009
Posts: 36609
Followers: 7099

Kudos [?]: 93530 [2] , given: 10578

Re: If (a – b)c < 0, which of the following cannot be true? [#permalink]

### Show Tags

23 Feb 2012, 21:22
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13516
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If (a – b)c < 0, which of the following cannot be true? [#permalink]

### Show Tags

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 Club Legend
Joined: 09 Sep 2013
Posts: 13516
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If (a – b)c < 0, which of the following cannot be true? [#permalink]

### Show Tags

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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8328
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 382

Kudos [?]: 2472 [0], given: 163

Re: If (a – b)c < 0, which of the following cannot be true? [#permalink]

### Show Tags

14 Feb 2015, 13:12
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.

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

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

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.

[Reveal] Spoiler:
D

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

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13516
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If (a – b)c < 0, which of the following cannot be true? [#permalink]

### Show Tags

12 Nov 2016, 07:05
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.
_________________
Manager
Joined: 25 Mar 2013
Posts: 219
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Followers: 2

Kudos [?]: 21 [0], given: 90

Re: If (a – b)c < 0, which of the following cannot be true? [#permalink]

### Show Tags

14 Jan 2017, 17:56
(a-b)c < 0 = Negative
c < 0
a - b < 0
a < b
ac - bc < 0
ac < bc
D
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Re: If (a – b)c < 0, which of the following cannot be true?   [#permalink] 14 Jan 2017, 17:56
Similar topics Replies Last post
Similar
Topics:
If rs>0, which of the following cannot be true? 2 20 Jan 2017, 05:27
If b<c<d and c>0, which of the following cannot be true if b,c and d 3 19 Jan 2017, 19:35
4 If y<x<0, which of the following CANNOT be true? 2 18 Nov 2016, 01:41
1 If 0<b, and 0>ab, which of the following CANNOT be true? 4 15 Nov 2016, 08:49
7 If d>a and L<a, which of the following cannot be true? 10 23 Jun 2015, 22:48
Display posts from previous: Sort by