Last visit was: 26 Jul 2024, 20:09 It is currently 26 Jul 2024, 20:09
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644171 [24]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink] If mn < 0 and k/m + l/n < mn, which of the following must be true ?   13 Aug 2018, 04:40
2
Kudos
22
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

65% (01:40) correct 35% (01:58) wrong based on 455 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
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) \(km > –ln\)
ShowHide Answer
Official Answer
C
User avatar
L
souvonik2k
Retired Moderator
Joined: 25 Nov 2015
Status:Preparing for GMAT
Posts: 959
Own Kudos [?]: 2023 [4]
Given Kudos: 751
Location: India
GPA: 3.64
Send PM
GMAT ToolKit User Reviews Badge
Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink] If mn < 0 and k/m + l/n < mn, which of the following must be true ?   13 Aug 2018, 07:22
2
Kudos
2
Bookmarks
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.
User avatar
D
KSBGC
VP
VP
Joined: 31 Oct 2013
Posts: 1259
Own Kudos [?]: 1197 [0]
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Send PM
Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink] If mn < 0 and k/m + l/n < mn, which of the following must be true ?   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.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30868 [2]
Given Kudos: 799
Location: Canada
Send PM
If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink] If mn < 0 and k/m + l/n < mn, which of the following must be true ?   Updated on: 17 May 2021, 07:17
2
Kudos
Expert Reply
Top Contributor
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

RELATED VIDEO

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.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19213
Own Kudos [?]: 22731 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink] If mn < 0 and k/m + l/n < mn, which of the following must be true ?   21 Jun 2020, 05:38
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
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5314
Own Kudos [?]: 4253 [0]
Given Kudos: 161
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge Forum Quiz Mode
If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink] If mn < 0 and k/m + l/n < mn, which of the following must be true ?   21 Jun 2020, 06:59
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
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 34111
Own Kudos [?]: 854 [0]
Given Kudos: 0
Send PM
Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink] If mn < 0 and k/m + l/n < mn, which of the following must be true ?   06 Mar 2024, 07:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If mn < 0 and k/m + l/n < mn, which of the following must be true ? [#permalink]
06 Mar 2024, 07:57
Moderator:
Bunuel
Math Expert
94619 posts