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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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New post 13 Aug 2018, 04:40
1
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:42) correct 35% (01:44) wrong based on 109 sessions

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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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New post 13 Aug 2018, 07:22
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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) \(km > –ln\)


\(\frac{k}{m} + \frac{l}{n} < mn\)
Taking LCM and cross multiplying;
\(\frac{(kn+lm)}{mn}< mn\)
Transferring mn in denominator to RHS, since mn<0, < sign will be reversed to >
\(kn+lm>(mn)^2\)
Answer 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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New post 27 Nov 2018, 18:51
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) \(km > –ln\)



\(mn < 0\)

either m or n is negative.

\(\frac{k}{m} + \frac{l}{n} < mn\)

mn^2 must be there in the answer but inequality sign must flip as one of them between m and n is negative.

C is our answer.
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Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ?   [#permalink] 27 Nov 2018, 18:51
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