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If x, y and k are positive numbers such that

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

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New post 01 Nov 2009, 21:01
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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?

(A) 10
(B) 12
(C) 15
(D) 18
(E) 30

Open discussion of this question is here: if-x-y-and-k-are-positive-numbers-such-that-x-x-y-128231.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Apr 2012, 22:30, edited 1 time in total.
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Re: which could be the value of K? [#permalink]

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New post 01 Nov 2009, 21:11
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\(10*\frac{x+2y}{x+y}=k\)

\(10*(\frac{x+y}{x+y}+\frac{y}{x+y})=k\)

Finally we get: \(10*(1+\frac{y}{x+y})=k\)


We know that \(x<y\)

Hence \(\frac{y}{x+y}\) is more than \(0.5\) and less than \(1\)

\(0.5<\frac{y}{x+y}<1\)

So, \(15<10*(1+\frac{y}{x+y})<20\)


Only answer between \(15\) and \(20\) is \(18\).

Answer: D (18)

This question was discussed before, please refer to the other approaches at: what-is-the-value-of-k-85382.html#p640124
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Re: which could be the value of K? [#permalink]

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New post 01 Nov 2009, 21:29
Bunuel wrote:
\(10*\frac{x+2y}{x+y}=k\)

\(10*(\frac{x+y}{x+y}+\frac{y}{x+y})=k\)

Finally we get: \(10*(1+\frac{y}{x+y})=k\)


We know that \(x<y\)

Hence \(\frac{y}{x+y}\) is more than \(0.5\) and less than \(1\)

\(0.5<\frac{y}{x+y}<1\)

So, \(15<10*(1+\frac{y}{x+y})<20\)


Only answer between \(15\) and \(20\) is \(18\).

Answer: D (18)

This question was discussed before, please refer to the other approaches at: what-is-the-value-of-k-85382.html#p640124


Thanks for the solution and the pointer to the earlier thread.
I'd run a search but didn't hit that thread... maybe due to the mathematical formula.

hit a roadblock right in the first step of simplifying the equation... \(10(x+2y)/(x+y)\)
But now understood the approach :(

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Re: which could be the value of K? [#permalink]

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New post 09 May 2011, 05:13
Let us try x = 1, y = 4

=> 1/5 * 10 + 4/5 * 20 = k

=> 2 + 16 = k

=> k = 18


Answer - D
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Re: which could be the value of K? [#permalink]

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New post 27 Apr 2012, 19:46
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Hi Bunuel,

Is this approach ok?
since it is of the weighted averages form


10x + 20 y/x+y= k

and 20 pulls the averagge more twds itself we can eliminate other options and oly 18 wud be possible?

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Re: which could be the value of K? [#permalink]

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New post 27 Apr 2012, 22:28
shankar245 wrote:
Hi Bunuel,

Is this approach ok?
since it is of the weighted averages form


10x + 20 y/x+y= k

and 20 pulls the averagge more twds itself we can eliminate other options and oly 18 wud be possible?


Yes, you can use weighted average approach for this question:

We have: \(\frac{10x+20y}{x+y}=k\), if you look at this equation you'll notice that it's a weighted average.

There are \(x\) red boxes and \(y\) blue boxes. Red box weight is 10kg and blue box weight 20kg, what is the average weight of x red boxes and y blue boxes?

k represents the weighted average. As y>x, then the weighted average k, must be closer to 20 than to 10. 18 is the only choice satisfying this condition.

Answer: D.

In case of any question please post it here: if-x-y-and-k-are-positive-numbers-such-that-x-x-y-128231.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Kudos [?]: 128666 [0], given: 12181

Re: which could be the value of K?   [#permalink] 27 Apr 2012, 22:28
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