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Could be the value of k?

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Could be the value of k?

by alex.gellatly » Thu Jul 12, 2012 5:47 am
If x, y, and k are positive numbers such that (x/x+y)(10) + (y/x+y)(20) = k and if x<y, which of the following could e the value of k?
10
12
15
18
30



My approach was to set extreme values for x and y (bc x<y) and approximate an answer. I somehow got the correct answer... but was very uncomfortable with my approach. Could someone share some insight?

Thanks
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by eagleeye » Thu Jul 12, 2012 6:43 am
alex.gellatly wrote:If x, y, and k are positive numbers such that (x/x+y)(10) + (y/x+y)(20) = k and if x<y, which of the following could e the value of k?
10
12
15
18
30



My approach was to set extreme values for x and y (bc x<y) and approximate an answer. I somehow got the correct answer... but was very uncomfortable with my approach. Could someone share some insight?

Thanks
Recognize that x(x+y)*10 + y/(x+y)*20 is the weighted average between 10 and 20.
Now y>x. If you need to visualize, draw a number line. Here k is the weighted average of 10 and 20 in the ratio of x : y.

10---------k----------20
x--------------------y
If y=x, the average will be 15.
Since y>x, the average must be between 15 and 20. Hence select the option that lies between 15 and 20.
18 is the correct answer.
Last edited by eagleeye on Fri Jul 13, 2012 3:49 am, edited 1 time in total.
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by GMATGuruNY » Thu Jul 12, 2012 7:13 am
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