Could be the value of k?

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 amFollowed by: 16 members; Thanked: 48 times

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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eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jul 12, 2012 7:13 am

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