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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)

Answer: C

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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]
Expert Reply
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

Answer: C
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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

IMO C
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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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