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

[VJesus12]

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

[Jay@ManhattanReview]

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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