Last visit was: 31 Dec 2024, 06:37 It is currently 31 Dec 2024, 06:37
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

l/m+n=m/n+l

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30559
Own Kudos [?]: 36907 [31]
Given Kudos: 26113
Send PM
l/m+n=m/n+l [#permalink] New post   17 Sep 2018, 20:27
4
2
Expert Reply
25
Bookmarks
00:00

Question Stats:

56% (01:36) correct 43% (01:56) wrong based on 274 sessions

Hide Show timer Statistics



\(\frac{l}{m+n}=\frac{m}{n+l}=\frac{n}{l+m}=k\) , where k is a real number

Quantity A
Quantity B
k
\(\frac{1}{3}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
ShowHide Answer
Official Answer
A
Most Helpful Expert Reply
avatar
chetan2u
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Own Kudos [?]: 471 [5]
Given Kudos: 0
Send PM
l/m+n=m/n+l [#permalink] New post   04 Nov 2018, 02:20
5
Expert Reply
Carcass wrote:
\(\frac{l}{m+n}=\frac{m}{n+l}=\frac{n}{l+m}=k\) , where k is a real number

Quantity A
Quantity B
k
\(\frac{1}{3}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


\(\frac{l}{m+n}=\frac{m}{n+l}=\frac{n}{l+m}=k\)....
three equations can be formed :-
    \(\frac{l}{m+n}=k........l=(m+n)k\)
    \(\frac{m}{l+n}=k........m=(l+n)k\)
    \(\frac{n}{m+l}=k........n=(m+l)k\)

add the three equations...
\(l+m+n=(m+n)k+(l+n)k+(m+l)k...........l+m+n=(m+n+l+n+m+l)k..........
l+m+n=2(m+n+l)k.........2k=1.....k=\frac{1}{2}=A\) and \(B=\frac{1}{3}\) thus \(A>B\)

A
Most Helpful Community Reply
avatar
jarabhuiyan
Intern
Intern
Joined: 15 Sep 2018
Posts: 41
Own Kudos [?]: 31 [15]
Given Kudos: 0
GRE 1: Q166 V158
Send PM
Re: l/m+n=m/n+l [#permalink] New post   23 Oct 2018, 14:35
14
1
Bookmarks
16. The given equation is l
m+ n
= m
n + l
= n
l + m
= k . Forming the three equations yields l = (m + n)k, m =
(n + l)k, n = (l + m)k. Summing these three equations yields
l + m + n = (m + n)k + (n + l)k + (l + m)k
= k[(m + n) + (n + l) + (l + m)]
= k(m + n + n + l + l + m)
= k(2m + 2n + 2l)
= 2k(m + n + l)
1 = 2k by canceling m + n + l from each side
1/2 = k
Hence, Column A equals 1/2. Since 1/2 is greater than 1/3, Column A is greater than Column B, and the
answer is (A).
General Discussion
avatar
Hovsep
Manager
Manager
Joined: 23 Oct 2018
Posts: 57
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: l/m+n=m/n+l [#permalink] New post   23 Oct 2018, 09:46
Can you provide with explanation to this problem?
User avatar
HappyMathtutor
Manager
Manager
Joined: 01 Nov 2018
Posts: 87
Own Kudos [?]: 146 [2]
Given Kudos: 0
Send PM
Re: l/m+n=m/n+l [#permalink] New post   02 Nov 2018, 10:36
2
Expert Reply
jarabhuiyan wrote:
16. The given equation is l
m+ n
= m
n + l
= n
l + m
= k . Forming the three equations yields l = (m + n)k, m =
(n + l)k, n = (l + m)k. Summing these three equations yields
l + m + n = (m + n)k + (n + l)k + (l + m)k
= k[(m + n) + (n + l) + (l + m)]
= k(m + n + n + l + l + m)
= k(2m + 2n + 2l)
= 2k(m + n + l)
1 = 2k by canceling m + n + l from each side
1/2 = k
Hence, Column A equals 1/2. Since 1/2 is greater than 1/3, Column A is greater than Column B, and the
answer is (A).


You, are incredible!! Thanks!! This opened up my eyes to a whole new way of problem solving!!!
avatar
Mercychee
Intern
Intern
Joined: 04 Nov 2018
Posts: 44
Own Kudos [?]: 22 [0]
Given Kudos: 0
Send PM
Re: l/m+n=m/n+l [#permalink] New post   09 Nov 2018, 15:48
jarabhuiyan wrote:
16. The given equation is l
m+ n
= m
n + l
= n
l + m
= k . Forming the three equations yields l = (m + n)k, m =
(n + l)k, n = (l + m)k. Summing these three equations yields
l + m + n = (m + n)k + (n + l)k + (l + m)k
= k[(m + n) + (n + l) + (l + m)]
= k(m + n + n + l + l + m)
= k(2m + 2n + 2l)
= 2k(m + n + l)
1 = 2k by canceling m + n + l from each side
1/2 = k
Hence, Column A equals 1/2. Since 1/2 is greater than 1/3, Column A is greater than Column B, and the
answer is (A).


Thank you so much for this.
avatar
kunalkmr62
Intern
Intern
Joined: 21 Nov 2018
Posts: 21
Own Kudos [?]: 11 [0]
Given Kudos: 0
Send PM
Re: l/m+n=m/n+l [#permalink] New post   27 Nov 2018, 10:57
I tried the following approach and got k = -1 , can someone explain where I went wrong.
l(n+l)=m(m+n) { cross multiplying the first 2 terms}
ln+lpow2 = mpow2 +mn
n(l-m)= (m+l)*(m-l)
n= -(m+l)

Substituting this value in the last equation, yields k=-1 , and hence B>A
@chetan2u
avatar
chetan2u
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Own Kudos [?]: 471 [2]
Given Kudos: 0
Send PM
Re: l/m+n=m/n+l [#permalink] New post   27 Nov 2018, 18:08
2
Expert Reply
kunalkmr62 wrote:
I tried the following approach and got k = -1 , can someone explain where I went wrong.
l(n+l)=m(m+n) { cross multiplying the first 2 terms}
ln+lpow2 = mpow2 +mn
n(l-m)= (m+l)*(m-l)
n= -(m+l)

Substituting this value in the last equation, yields k=-1 , and hence B>A
@chetan2u



You cannot cancel out l-m from both sides..
n(l-m)= (m+l)*(m-l).....
n(l-m)-(m+l)(m-l)=0
n(l-m)+(m+l)(l-m)=0
(l-m)(n+m+l)=0
So either l=m or n=-(m+l)
Now you do not know which one is correct.
If l=m, then also (l-m)(n+m+l)=0 and then n+m+l is not necessarily equal to 0
avatar
B
santosh93
Intern
Intern
Joined: 15 Jul 2021
Posts: 11
Own Kudos [?]: 20 [1]
Given Kudos: 17
Location: India
Concentration: Statistics, Technology
GPA: 3.78
WE:Design (Manufacturing)
Send PM
Re: l/m+n=m/n+l [#permalink] New post   19 Jul 2021, 10:00
1
As nothing is mentioned about l,m,n , they can be fraction or integer or any real number which satisfies the equation
\(\frac{l}{m+n}=\frac{m}{n+l}=\frac{n}{l+m}\)

The above equation is satisfied only when l=m=n

Hence the least value either \(\frac{l}{m+n}\) or \(\frac{m}{n+l}\) or \(\frac{n}{l+m}\) can take is \(\frac{1}{2}\)

So Quantity A = \(\frac{1}{2}\) and Quantity B is \(\frac{1}{3}\)

Therefore the answer is Quantity A is greater
avatar
ChandanPednekar
Intern
Intern
Joined: 06 Jan 2022
Posts: 6
Own Kudos [?]: 4 [0]
Given Kudos: 0
Send PM
Re: l/m+n=m/n+l [#permalink] New post   20 May 2022, 06:15
What about l = -4 and m = n = 2?

l / (m + n) = -4 / 4 = -1
m / (n + l) = 2 / (2 - 4) = -1
n / (m + l) = 2 / (2 - 4) = -1

what about this case?
avatar
ChandanPednekar
Intern
Intern
Joined: 06 Jan 2022
Posts: 6
Own Kudos [?]: 4 [0]
Given Kudos: 0
Send PM
Re: l/m+n=m/n+l [#permalink] New post   20 May 2022, 06:16
santosh93 wrote:
As nothing is mentioned about l,m,n , they can be fraction or integer or any real number which satisfies the equation
\(\frac{l}{m+n}=\frac{m}{n+l}=\frac{n}{l+m}\)

The above equation is satisfied only when l=m=n

Therefore the answer is Quantity A is greater


What when l = -4 and m = n = 2?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30559
Own Kudos [?]: 36907 [1]
Given Kudos: 26113
Send PM
Re: l/m+n=m/n+l [#permalink] New post   20 May 2022, 07:18
1
Expert Reply
here the substitution method does not work best because could lead to a conflict answers

The best is to boil down the equality and see if k is > or < 1/3

regards
avatar
B
BoomBoom
Manager
Manager
Joined: 09 May 2022
Posts: 50
Own Kudos [?]: 21 [0]
Given Kudos: 12
Send PM
l/m+n=m/n+l [#permalink] New post   20 May 2022, 17:22
Very simple.

Just use Componendo, Dividendo property, and you'll come up with l=m=n.
Hence K which is = l/(m+n) gets equal to 1/2.

Hence A is greater.
avatar
B
nharakakos420
Intern
Intern
Joined: 25 Jun 2024
Posts: 1
Own Kudos [?]: 4 [4]
Given Kudos: 0
Send PM
Re: l/m+n=m/n+l [#permalink] New post   28 Jun 2024, 13:38
4
All previous answers are wrong.

2 cases can be distinguished for the equation l + m + n = 2 * k * (l + m + n)

1) If l + m + n is not zero, then k = 1 /2 as indicated by previous answers.

2) If it is zero, k = -1, as shown by the values l = 2, m = -1, n = -1

Therefore, the correct answer is D.
avatar
mskethan
Intern
Intern
Joined: 29 Jul 2024
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 3
GRE 1: Q170 V150
Send PM
Re: l/m+n=m/n+l [#permalink] New post   30 Jul 2024, 03:01
nharakakos420 wrote:
All previous answers are wrong.

2 cases can be distinguished for the equation l + m + n = 2 * k * (l + m + n)

1) If l + m + n is not zero, then k = 1 /2 as indicated by previous answers.

2) If it is zero, k = -1, as shown by the values l = 2, m = -1, n = -1

Therefore, the correct answer is D.


Exactly, all the above answers are wrong. Please think more than blindly substituting one possible solution
Prep Club for GRE Bot
gmatclubot
Re: l/m+n=m/n+l [#permalink]
30 Jul 2024, 03:01
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1126 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact