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Manhattan Question Set # 9

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by richachampion » Sun Oct 09, 2016 6:01 pm
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. a² - b² > 0

OA: D
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by [email protected] » Sun Oct 09, 2016 8:27 pm
Hi richachamption,

While this question looks 'thin', it might take longer to solve than you first think - since the question asks which of the 5 answers CANNOT be true, you might want to prove that 4 of the answers COULD be true (meaning that whichever answer is left would be the correct one) - and that will take a bit of work.

We're told that (A - B)(C) < 0. This means that...
(A - B) = negative and C = positive

OR

(A - B) = positive and C = negative

Answer A: A < B. IF (A - B) is negative, then we could have A=1 and B=2. Eliminate Answer A

Answer B: C < 0. C could be negative (as discussed above). Eliminate Answer B

Answer C: |C| < 1. C could be a positive fraction or a negative fraction (see above). Eliminate Answer C

Between the remaining two answers, Answer E focuses on just 2 of the variables, so I'll deal with that answer first...

Answer E: A^2 - B^2 > 0. IF (A - B) is positive, then we could have A=2 and B=1. Eliminate Answer E

Final Answer: D

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by GMATGuruNY » Mon Oct 10, 2016 5:57 am
richachampion 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. a² - b² > 0
(a-b)c < 0
ab - bc < 0
ab < bc.

Thus, D cannot be true.

The correct answer is D.
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by Matt@VeritasPrep » Fri Oct 14, 2016 2:26 am
Factored out, the prompt gives us

ac - bc < 0

But D says that

ac > bc, or

ac - bc > 0

which is the opposite!
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