If mn

Question

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

souvonik2k · Accepted Answer

\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.

KSBGC · Answer

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.

BrentGMATPrepNow · Answer

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

RELATED VIDEO
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ScottTargetTestPrep · Answer

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

Kinshook · Answer

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

marwaharuchika · Answer

Why do we need to reverse the signs when the square of a negative product is happening? it will any which way give a positive number know?

Krunaal · Answer

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign. Since, mn < 0 => a negative value And we multiply, LHS and RHS of \frac{kn + lm }{ mn} < mn by mn (a negative value) , we get kn + lm > (mn)^2 with the sign flipped .

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

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