shreeman wrote:x,y and k are positive and x < y. what is the value of k

(10x/x+y) + (20y/x+y) = k

1. 10
2. 12
3. 15
4. 18
5. 30

OA is 18.

I got the solution but what is wrong in this approach which i tried initially.

10x + 20y = kx + ky
10x - kx = ky - 20y
x(10-x) = y(k-20)

As x < y Here for above equation it implies 10-x > k - 20
=> 2k < 30 or k < 15

Also, From given equation k = 10 + 10y/x+y
so K > 10

Hence ans 12.

GMATGuruNY wrote:

shreeman wrote:x,y and k are positive and x < y. what is the value of k

(10x/x+y) + (20y/x+y) = k

1. 10
2. 12
3. 15
4. 18
5. 30

OA is 18.

I got the solution but what is wrong in this approach which i tried initially.

10x + 20y = kx + ky
10x - kx = ky - 20y
x(10-x) = y(k-20)

As x < y Here for above equation it implies 10-x > k - 20
=> 2k < 30 or k < 15

Also, From given equation k = 10 + 10y/x+y
so K > 10

Hence ans 12.

The problem is that 10-k and k-20 are negative values, so the direction of the inequality has to change. If k=18 (the correct answer), then 10-k = 10-18 = -8 and k-20 = 18-20 = -2, and -8<-2. So you should have concluded:

10-k < k-20 (because each side of the inequality is negative)
30 < 2k
15 < k

Your approach illustrates why plugging in with real numbers is much safer than using algebra. I solved this problem safely and efficiently by plugging in the answer choices for k. Please check the following thread:

https://www.beatthegmat.com/tough-algebr ... tml#292229

Hope this helps!