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03 Sep 2021, 04:28
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (01:18) correct
22%
(01:26)
wrong
based on 407
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If the fraction \(\frac{m}{n}\) is negative, which of the following CANNOT be true?
A. \(\frac{n}{m}\)>\(\frac{m}{n}\)
B. mn < 0
C. n – m > 0
D. \(mn^3\) > 0
E. m – n > 0
A. \(\frac{n}{m}\)>\(\frac{m}{n}\)
B. mn < 0
C. n – m > 0
D. \(mn^3\) > 0
E. m – n > 0
03 Sep 2021, 07:00
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Bunuel
APPROACH #1: Number sense and inequality manipulation
If \(\frac{m}{n}\) is negative, then we know that one value (m or n) is positive, and the other value is negative.
When I scan the answer choices, answer choice D looks like a good contender.
If \(\frac{m}{n}\) is negative, we know that m ≠ 0 and n ≠ 0.
Next, if n ≠ 0, then we know that \(n^2\) is positive.
If \(n^2\) is positive, we can safely take the inequality \(mn^3\) > 0 and divide both sides by \(n^2\) to get: \(mn>0\)
If \(mn>0\), then we know that EITHER m and n are both positive OR m and n are both negative.
This, however, contradicts our earlier conclusion that one value (m or n) is positive, and the other value is negative.
Answer: D
APPROACH #2: Using counter-examples to eliminate 4 of the answer choices
The question asks, "which of the following CANNOT be true?"
So if we can find values for m and n that make a statement true, we can eliminate that answer choice.
A. \(\frac{n}{m}\)>\(\frac{m}{n}\)
If n = 1 and m = -2, then it's true that \(\frac{n}{m}\)>\(\frac{m}{n}\)
ELIMINATE A.
B. mn < 0
If n = 1 and m = -2, then it's true that mn < 0
ELIMINATE B
C. n – m > 0
If n = 1 and m = -2, then it's true that n – m > 0
ELIMINATE C
E. m – n > 0
If n = -1 and m = 2, then it's true that m – n > 0
ELIMINATE E
By the process of elimination, the correct answer is D
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General Discussion
03 Sep 2021, 07:14
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If m/n < 0, then multiplying by n^4 on both sides, we find mn^3 < 0, so answer D must be false.
Note that it's safe to multiply by n^4 on both sides, because n^4 must be positive here (it's an even power, and it can't be zero), so we don't need to worry about whether to reverse the inequality.
Note that it's safe to multiply by n^4 on both sides, because n^4 must be positive here (it's an even power, and it can't be zero), so we don't need to worry about whether to reverse the inequality.
