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If \(mn<0\) and \(\dfrac{k}{m}+\dfrac{l}{n} < mn,\) which of the following must be true?

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by VJesus12 » Sun Jun 14, 2020 8:12 am
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If \(mn<0\) and \(\dfrac{k}{m}+\dfrac{l}{n} < mn,\) 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) \(km > –ln\)

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT
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Re: If \(mn<0\) and \(\dfrac{k}{m}+\dfrac{l}{n} < mn,\) which of the following must be true?

by Jay@ManhattanReview » Mon Jun 15, 2020 9:12 pm
VJesus12 wrote: ↑
Sun Jun 14, 2020 8:12 am
 If \(mn<0\) and \(\dfrac{k}{m}+\dfrac{l}{n} < mn,\) 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) \(km > –ln\)

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT
So, we have \(mn<0\) and \(\dfrac{k}{m}+\dfrac{l}{n} < mn,\)

From \(\dfrac{k}{m}+\dfrac{l}{n} < mn,\)

\(\dfrac{kn + ml}{mn} < mn,\); taking LCM

Multiplying the inequality by \(mn\)

\(kn + ml > (mn)^2\); note the sign reversal of the inequality. Since \(mn\) is a negative quantity, its multiplication will reverse the sign.

Correct answer: C

Hope this helps!

-Jay
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