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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]  12 Aug 2018, 09:59
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Question Stats:

60% (00:56) correct 39% (01:01) wrong based on 33 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]  18 Nov 2018, 16:25
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Re: If mn < 0 and k/m + l/n < mn [#permalink]  19 Nov 2018, 07:32
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Expert's post
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.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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

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]  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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