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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # If (a – b)c < 0, which of the following cannot be true?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 19 Oct 2011 Posts: 104 Location: India If (a – b)c < 0, which of the following cannot be true? [#permalink] ### Show Tags 23 Feb 2012, 19:27 2 1 00:00 Difficulty: 15% (low) Question Stats: 79% (01:27) correct 21% (01:40) wrong based on 191 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 Manager Status: Employed Joined: 17 Nov 2011 Posts: 80 Location: Pakistan Concentration: International Business, Marketing GMAT 1: 720 Q49 V40 GPA: 3.2 WE: Business Development (Internet and New Media) Re: PS: Inequality [#permalink] ### Show Tags 23 Feb 2012, 20:05 1 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 Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: If (a – b)c < 0, which of the following cannot be true? [#permalink] ### Show Tags 23 Feb 2012, 21:22 3 1 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. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13087 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 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. 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: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Manager
Joined: 25 Mar 2013
Posts: 240
Location: United States
Concentration: Entrepreneurship, Marketing
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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
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Re: If (a – b)c < 0, which of the following cannot be true?  [#permalink]

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07 Mar 2018, 00:33
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?
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Re: If (a – b)c < 0, which of the following cannot be true?  [#permalink]

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07 Mar 2018, 00:41
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?
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Re: If (a – b)c < 0, which of the following cannot be true? &nbs [#permalink] 07 Mar 2018, 00:41
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