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

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

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23 Feb 2012, 20:27
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79% (01:27) correct 21% (01:42) wrong based on 200 sessions

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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
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23 Feb 2012, 21:05
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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.

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

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23 Feb 2012, 22:22
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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.
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Re: If (a – b)c < 0, which of the following cannot be true?  [#permalink]

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14 Feb 2015, 14:12
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.

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

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14 Jan 2017, 18:56
(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, 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?
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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, 01:41
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?   [#permalink] 07 Mar 2018, 01:41
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