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GMATprep equality with x and y

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Senior Manager
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GMATprep equality with x and y [#permalink]

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New post 07 Oct 2008, 14:04
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

10
12
15
18
30

How r u supposed to solve this
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Re: GMATprep equality with x and y [#permalink]

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New post 07 Oct 2008, 16:30
The given equation can be simplified to:
10 + (10y/x+y)=k

Since K is a positive number, (10y/x+y) should be an integer or x+y a multiple of 10.
Given than y>x. (x,y) can be (1,4) or (2,3). With (1,4), we get k =18 and with (2,3) we get k=16.
Since 18 (D) is one of the answer choices, it is (D).

One more way of looking at the equation is- as a weighted average of x and y where the value of k is inclined towards 20 (as y>x). Here 18 is closest to 20 and is the answer.

If the answer choice had 17 and 18, I will go ahead and plug in the values to verify.
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Re: GMATprep equality with x and y [#permalink]

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New post 07 Oct 2008, 16:47
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 be the value of k?




K = 10(x/x+y + 2y/x+y) thus
k = 10 (x+2y/x+y) ,

A is ruled out , the numinator > doniminator question becomes can x+2y/x+y = (6/5 or 3/2 0r 9/5 0r 3)

D is my answer ( x= 1, y = 4)

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Re: GMATprep equality with x and y [#permalink]

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New post 08 Oct 2008, 01:35
Similar approach with a little difference.

10(1 + y/[x+y]) = k

k cannot be 10 as y is positive and it cannot be zero.
k cannot be >= 20 as then y/(x+y) will be >=1 and is not possible as y is smaller than x+y.

Hence, k has to be a value that is between 10 and 20 and the value will be such that y/(x+y) will be a decimal that is greater than 0.5 (because y > x).

Only value greater than 0.5 times 10 is 18 and hence D should be the answer.

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Re: GMATprep equality with x and y [#permalink]

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New post 08 Oct 2008, 06:12
My two cents:

Rewriting the equiation:

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

Because of x<y, thus (10-k)/(k-20)>1

solving this eq. k<15

Two possible solutions: A, B?

OA?

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Re: GMATprep equality with x and y   [#permalink] 08 Oct 2008, 06:12
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