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# If x, y, and k are positive numbers such that 10 + 20 = k

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Manager
Joined: 04 Jan 2008
Posts: 114
If x, y, and k are positive numbers such that 10 + 20 = k  [#permalink]

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06 Sep 2008, 00:46
00:00

Difficulty:

(N/A)

Question Stats:

50% (00:59) correct 50% (01:17) wrong based on 5 sessions

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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

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Senior Manager
Joined: 28 Feb 2007
Posts: 293

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06 Sep 2008, 01:13
D.
Simplify the equation : 10 +10y/(x+y)=k. Since x, y,k are positive #s. and X<y.

Only D satisfies all constraints. Check it.
If k=18
then 10y/(x+y)=8
10y =8x +8y
2y=8x
y=4x, so y(or 4x) > x

Other choices doesn't satisfy X<Y condition.
VP
Joined: 05 Jul 2008
Posts: 1329

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06 Sep 2008, 10:37
dancinggeometry 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 be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30

Given eq can be rewritten as (10/x+y) [x+2y] =k x <y

For the equation to result in a+ve integer k (x+y) must divide 10 or x+2y without remainder.

Lets choose x=1, y=9 could result in x+2y being 19
x=2 y=8 results in K equal to 18

Hence D
Intern
Joined: 03 Sep 2008
Posts: 22

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06 Sep 2008, 11:01
3
This is a weighted average of 10 and 20. Since y > x, more weight is placed on the 20 so the answer must be 18, since this is the only answer between 10 and 20 that is closer to 20
Manager
Joined: 04 Jan 2008
Posts: 114

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06 Sep 2008, 23:54
OA is D. Bin 2 problem.

Good alternative explanation lsmv479!
SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York

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08 Sep 2008, 10:25
1
lsmv479 wrote:
This is a weighted average of 10 and 20. Since y > x, more weight is placed on the 20 so the answer must be 18, since this is the only answer between 10 and 20 that is closer to 20

Agree with this solution. this good approach.
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Manager
Status: Next engagement on Nov-19-2011
Joined: 12 Jan 2011
Posts: 70
Location: New Delhi, India
Schools: IIM, ISB, & XLRI
WE 1: B.Tech (Information Technology)

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19 Oct 2011, 04:42
dancinggeometry 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 be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30

Ans - D

This question is very well explained on MGMAT forum. Here is the explaination:

1. Solving the equation a little will yield following that represent a weighter Avg. equation
[10X + 20Y]/(X + Y)

2. Now, 10 < K < 20. This will eleminate option A & E
3. Since, Y > X and 20 > 10 therefore K should be quite close to 20. This eleminates B & C and D is the best guess
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Posts: 7747
Re: If x, y, and k are positive numbers such that 10 + 20 = k  [#permalink]

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23 Oct 2017, 07:50
Hello from the GMAT Club BumpBot!

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--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: If x, y, and k are positive numbers such that 10 + 20 = k &nbs [#permalink] 23 Oct 2017, 07:50
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