It is currently 12 Dec 2018, 11:49
My Tests

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.

l/m+n=m/n+l

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 5151
Followers: 77

Kudos [?]: 1031 [1] , given: 4643

CAT Tests
l/m+n=m/n+l [#permalink] New post 17 Sep 2018, 20:27
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

39% (00:28) correct 60% (01:52) wrong based on 38 sessions
\(\frac{l}{m+n}=\frac{m}{n+l}=\frac{n}{l+m}=k\) , 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.
[Reveal] Spoiler: OA

_________________

Get the 2 FREE GREPrepclub Tests

Manager
Manager
Joined: 23 Oct 2018
Posts: 58
Followers: 0

Kudos [?]: 0 [0], given: 0

CAT Tests
Re: l/m+n=m/n+l [#permalink] New post 23 Oct 2018, 09:46
Can you provide with explanation to this problem?
3 KUDOS received
Intern
Intern
Joined: 15 Sep 2018
Posts: 42
GRE 1: Q166 V158
Followers: 1

Kudos [?]: 7 [3] , given: 5

Re: l/m+n=m/n+l [#permalink] New post 23 Oct 2018, 14:35
3
This post received
KUDOS
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).
Intern
Intern
Joined: 01 Nov 2018
Posts: 5
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: l/m+n=m/n+l [#permalink] New post 02 Nov 2018, 10:36
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!!!
1 KUDOS received
Supreme Moderator
Joined: 01 Nov 2017
Posts: 201
Followers: 3

Kudos [?]: 63 [1] , given: 1

CAT Tests
Re: l/m+n=m/n+l [#permalink] New post 04 Nov 2018, 02:20
1
This post received
KUDOS
Expert's post
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
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Intern
Intern
Joined: 04 Nov 2018
Posts: 44
Followers: 0

Kudos [?]: 6 [0], given: 8

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.
Intern
Intern
Joined: 21 Nov 2018
Posts: 12
Followers: 0

Kudos [?]: 1 [0], given: 0

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
Supreme Moderator
Joined: 01 Nov 2017
Posts: 201
Followers: 3

Kudos [?]: 63 [0], given: 1

CAT Tests
Re: l/m+n=m/n+l [#permalink] New post 27 Nov 2018, 18:08
Expert's post
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
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: l/m+n=m/n+l   [#permalink] 27 Nov 2018, 18:08
Display posts from previous: Sort by

l/m+n=m/n+l

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.