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TAGS: Founder  Joined: 18 Apr 2015
Posts: 6647
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Kudos [?]: 1275  , given: 6017

l/m+n=m/n+l [#permalink]
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Expert's post 00:00

Question Stats: 45% (00:55) correct 54% (01:45) wrong based on 55 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

_________________
Manager Joined: 23 Oct 2018
Posts: 57
Followers: 0

Kudos [?]: 0 , given: 0

Re: l/m+n=m/n+l [#permalink]
Can you provide with explanation to this problem? Intern Joined: 15 Sep 2018
Posts: 42
GRE 1: Q166 V158 Followers: 2

Kudos [?]: 7  , given: 5

Re: l/m+n=m/n+l [#permalink]
3
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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).
Manager  Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 43 , given: 22

Re: l/m+n=m/n+l [#permalink]
Expert's post
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!!! Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 111  , given: 4

Re: l/m+n=m/n+l [#permalink]
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 Joined: 04 Nov 2018
Posts: 44
Followers: 0

Kudos [?]: 6 , given: 8

Re: l/m+n=m/n+l [#permalink]
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 Joined: 21 Nov 2018
Posts: 21
Followers: 0

Kudos [?]: 2 , given: 1

Re: l/m+n=m/n+l [#permalink]
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: 370
Followers: 5

Kudos [?]: 111  , given: 4

Re: l/m+n=m/n+l [#permalink]
1
This post received
KUDOS
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
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