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# which of the following could be k?

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Director
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which of the following could be k? [#permalink]

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06 Apr 2009, 23:15
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If x, y, k are positive numbers such that 10x/(x+y)+20y/((x+y)=k and x<y, which of the following could be the value of k?
A. 10
B. 12
C. 15
D. 18
E. 30
GMAT Tutor
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Re: which of the following could be k? [#permalink]

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07 Apr 2009, 04:21
I posted two different solutions to this question on another forum:

www.beatthegmat.com/two-questions-from- ... 34185.html
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Joined: 02 Mar 2009
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Re: which of the following could be k? [#permalink]

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07 Apr 2009, 07:16
I think Ian's common sense approach to everything is phenomenal! Unfortunately, I am not among those who can think in such a way during exam conditions. I went for the simple algebra:

Got: 10(x + 2y) = k (x+y)
Use the answer choices now and with x<y and both positive, you will see only 18 makes sense.

Director
Joined: 29 Aug 2005
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Kudos [?]: 362 [0], given: 7

Re: which of the following could be k? [#permalink]

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07 Apr 2009, 10:53
Thank you Ian - your solutions are eye opening!
OA D.
For others, I have copied Ian's reply below:

***************************************************
Say you were asked the following question: "There are x men and y women at a certain company. The average wage of the men is $10 per hour, and the average wage of the women is$20 per hour. If k is the average wage of all employees at the company, what is k?" Here, you have x+y employees in total, the men combined earn 10x in total, and the women combined earn 20y in total, so

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

That's the equation in the question -- it's just a weighted average. If the average of one group is 10, and the other is 20, the weighted average must be between 10 and 20, and if y > x (we have more women than men) then the average must be closer to 20 than to 10, so 18 is the only possible value of k among the answer choices.

Alternatively, you could do the question algebraically, as follows. Cross multiply to get:

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

We know y > x > 0, so the left side is bigger than 1. Notice that the right side is negative unless 10 <= k < 20, and that the numerator will only be larger than the denominator if k > 15. So 15 < k < 20.
Manager
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Re: which of the following could be k? [#permalink]

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07 Apr 2009, 17:56
Awesome problem.

Thanks a lot to Ian - great approaches one can learn from!
Re: which of the following could be k?   [#permalink] 07 Apr 2009, 17:56
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