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# If x, y, and k are positive numbers such that

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Re: What is the value of k [#permalink]

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26 Oct 2009, 16:59
I got till the expression after simplifying

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

10x+20y=kx+ky

Now start putting the values from the options

put for an example x=2 then u will get y=8 which satisfies the condition given in the problem which is x<y .
So D is the correct answer.

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Re: What is the value of k [#permalink]

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26 Oct 2009, 18:09
Refer to Bunuel's post

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Re: What is the value of k [#permalink]

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26 Oct 2009, 21:37
the question tests weighted average.
x apple 10 kg each
y apple 20 kg each

weighted avg since y > x will be near 20. so ans is 18

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Re: What is the value of k [#permalink]

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26 Oct 2009, 22:45
rishi0609 wrote:
the question tests weighted average.
x apple 10 kg each
y apple 20 kg each

weighted avg since y > x will be near 20. so ans is 18

Actually, it will be within 15-20. If x=y, it would have been 15, if x>y, it would be within 10 to 15.

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Re: What is the value of k [#permalink]

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27 Oct 2009, 05:00
The above eqn can be re-framed as 10x+20y = k(x+y)

substituting values for k gives us with option 18 as the correct ans

I will go with option 18

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Re: What is the value of k [#permalink]

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20 Sep 2010, 07:17
I thought of solving this ques by forming an equation as
=>10x+20y=k(x+y)
=>x(10-k)=y(k-20)
=>x/y=k-20/10-k

now since x<y
=>k-20<10-k
=>2k<30
=>k<15

I know i am unable to reach a unique answer with this...but would like to know is there something else going wrong with this approach?

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Re: What is the value of k [#permalink]

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20 Sep 2010, 08:15
utin wrote:
I thought of solving this ques by forming an equation as
=>10x+20y=k(x+y)
=>x(10-k)=y(k-20)
=>x/y=k-20/10-k

now since x<y
=>k-20<10-k

=>2k<30
=>k<15

I know i am unable to reach a unique answer with this...but would like to know is there something else going wrong with this approach?

the step highlighted above is incorrect. This does not follow from x/y=(k-20)/(10-k)
Eg. If x/y=2/3=(k-20)/(10-k)
Now if k-20=2 then 20-k=3 so indeed your inequality holds
But if k-20=-2 then 20-k=-3 so the inequality you have concluded is wrong

In general when manipulating around with inequalities you have to be very careful and be-ware that you are not implicitly assuming the positive or negative nature of any of the terms o/w you can get such wrong results
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Re: What is the value of k [#permalink]

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20 Sep 2010, 19:22
tejal777 wrote:
I got that the expression reduces to:
k =10(1+ y/x+y)
Can somebody please elaborate after that?How are we getting values?

After this you need to think what values the expression y/(x+y) can take. Since x<y so x "limits to " y and expression can reach 0.5. So expression is greater than 0.5

x limits to 0 and expression can reach 1. So expression is smaller than 1. Hope this answers how we got the range.

Now 10 + 10 multiplied by range 0.5 to 1 will give you the limit. Pick answer choice fitting the range
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Re: What is the value of k [#permalink]

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21 Sep 2010, 17:26

The way I thought about it was that k is made up of (x/x+y) percent of 10 and (y/x+y) percent of 20. That is how interpolation is done. Then since y is greater than x, you will have the number close to 20 than to 10. It also has to be between 20 and 10, since it is made up of certain percentages of these two number.

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Re: What is the value of k [#permalink]

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22 Sep 2010, 07:24

given eqn can be written as:

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

now since x<y
=> k-20<10-k
=>k<15

but this doesn't solves the question...Please let me know where I am wrong...

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Re: What is the value of k [#permalink]

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22 Sep 2010, 07:29
utin wrote:

given eqn can be written as:

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

now since x<y
=> k-20<10-k
=>k<15

but this doesn't solves the question...Please let me know where I am wrong...

Look 3 posts up, I have told you where you are going wrong :

http://gmatclub.com/forum/what-is-the-value-of-k-85382-20.html#p785026
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Re: What is the value of k [#permalink]

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22 Sep 2010, 07:52
(10)x/(x+y) + (20)y/(x+y) = (10) (x/(x+y) + y/(x+y)) + (10)y/(x+y)

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

Now, x<y therefore, x+y < 2y => y/(x+y) > 1/2

If x and y are positive, x+y > y, therefore, y/(x+y) < 1

therefore,
10 + (10)y/(x+y) is between, 10 + 10(1/2) and 10 + 10(1), ie b/w 15 and 20.

Therefore, k is between 15 and 20 => 18

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Re: What is the value of k   [#permalink] 22 Sep 2010, 07:52

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