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by shreeman » Tue Sep 21, 2010 3:32 am
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.
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by GMATGuruNY » Tue Sep 21, 2010 3:55 am
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!
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by xxpatzz » Tue Sep 21, 2010 9:29 am
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!
Thanks for sharing the K>15 part, that's very good!
The way I solve for K<30 part is because we know that x/(x+y) and y/(x+y) are both lest than 1, hence, 10*x/(x+y) + 20*y/(x+y) <30 which is equal to K, thus K<30
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by HPengineer » Tue Sep 21, 2010 4:17 pm
Is it safe to use the weighted average approach on this problem?

Really you have the equation (10(x) + 20(Y))/(x + y) x and y are individual weights and x + y is the total weight.

THe problem tells you that X < Y so you know that this equation should give you a number closer to Y then X..

But not larger then the value of 20... So 18 is the only choice?? is this a dangerous approach? If it is i wont use it but i solved this problem in less then 10 seconds using this logic.
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