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# If mn < 0 and k/m + l/n < mn, which of the following must be true ?

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If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink]
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Bunuel 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) $$km > –ln$$

Take: $$\frac{k}{m} + \frac{l}{n} < mn$$

Rewrite fractions with common denominator: $$\frac{kn}{mn} + \frac{lm}{mn} < mn$$

Combined fractions: $$\frac{kn+lm}{mn} < mn$$

Multiply both sides of the inequality by $$mn$$ to get: $$kn+lm > m^2n^2$$ (Aside: since we're told $$mn < 0$$, we must REVERSE the direction of the inequality symbol when we multiply both sides by a NEGATIVE value)

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Originally posted by BrentGMATPrepNow on 18 Jun 2020, 11:48.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:17, edited 1 time in total.
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Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink]
Bunuel 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) $$km > –ln$$

Solution:

First, let’s get a common denominator on the left side of the equation:

k/m + l/n < mn

kn/mn + lm/mn < mn

(kn + lm)/mn < mn

Now we multiply both sides by mn. However, since mn < 0, we need to switch the inequality sign and obtain:

kn + lm > (mn)^2

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If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink]
Bunuel 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) $$km > –ln$$

Asked: If $$mn < 0$$ and $$\frac{k}{m} + \frac{l}{n} < mn$$, which of the following must be true ?

$$\frac{k}{m} + \frac{l}{n} < mn$$
$$\frac{kn + lm}{mn} < mn$$
$$kn + lm > (mn)^2$$ since mn<0

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Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink]
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Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink]
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