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If mn < 0 and k/m + l/n < mn

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If mn < 0 and k/m + l/n < mn [#permalink] New post 12 Aug 2018, 09:59
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Question Stats:

60% (00:49) correct 40% (00:25) wrong based on 20 sessions
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) \(km > –ln\)
[Reveal] Spoiler: OA

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Re: If mn < 0 and k/m + l/n < mn [#permalink] New post 18 Nov 2018, 16:25
Explain please.
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Re: If mn < 0 and k/m + l/n < mn [#permalink] New post 19 Nov 2018, 07:32
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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) \(km > –ln\)


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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Brent
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Re: If mn < 0 and k/m + l/n < mn [#permalink] New post 20 Nov 2018, 00:55
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AE wrote:
Explain please.



k/m + l/n < mn

It becomes (kn + lm)/mn < mn

We multiplty by mn. Since it is is a negative number it will reverse the inequality sign.

Becoming kn + lm > (mn)^2

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Re: If mn < 0 and k/m + l/n < mn [#permalink] New post 27 Nov 2018, 21:38
thanks
Re: If mn < 0 and k/m + l/n < mn   [#permalink] 27 Nov 2018, 21:38
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