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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richachampion
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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(a-b)c < 0richachampion 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
ab - bc < 0
ab < bc.
Thus, D cannot be true.
The correct answer is D.
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Factored out, the prompt gives us
ac - bc < 0
But D says that
ac > bc, or
ac - bc > 0
which is the opposite!
ac - bc < 0
But D says that
ac > bc, or
ac - bc > 0
which is the opposite!
