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If mn < 0 and k/m + l/n < mn, which of the following must be true?
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12 Aug 2018, 09:59
12 Aug 2018, 09:59
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If \(mn < 0\) and \(\frac{k}{m} + \frac{l}{n} < mn\), which of the following must be true ?
(A) \(km + ln < (mn)^2\)
(B) \(kn + lm < 1\)
(C) \(kn + lm > (mn)^2\)
(D) \(k + l > mn\)
(E) \(km > –ln\)
(A) \(km + ln < (mn)^2\)
(B) \(kn + lm < 1\)
(C) \(kn + lm > (mn)^2\)
(D) \(k + l > mn\)
(E) \(km > –ln\)
Re: If mn < 0 and k/m + l/n < mn, which of the following must be true?
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18 Nov 2018, 16:25
18 Nov 2018, 16:25
Explain please.
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Joined: 10 Apr 2015
Posts: 6218
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Re: If mn < 0 and k/m + l/n < mn, which of the following must be true?
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19 Nov 2018, 07:32
19 Nov 2018, 07:32
3
Carcass wrote:
If \(mn < 0\) and \(\frac{k}{m} + \frac{l}{n} < mn\), which of the following must be true ?
(A) \(km + ln < (mn)^2\)
(B) \(kn + lm < 1\)
(C) \(kn + lm > (mn)^2\)
(D) \(k + l > mn\)
(E) \(km > –ln\)
(A) \(km + ln < (mn)^2\)
(B) \(kn + lm < 1\)
(C) \(kn + lm > (mn)^2\)
(D) \(k + l > mn\)
(E) \(km > –ln\)
GIVEN: \(\frac{k}{m} + \frac{l}{n} < mn\)
Rewrite fractions with common denominator: \(\frac{kn}{mn} + \frac{lm}{mn} < mn\)
Combine fractions: \(\frac{kn+lm}{mn} < mn\)
Multiply both sides of inequality by \(mn\) to get: \(kn+lm > (mn)^2\)
ASIDE: Since we're told that \(mn < 0\), we REVERSED the direction of the inequality symbol, because in the last step, we multiplied both sides by a NEGATIVE value.
Answer: C
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