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# 10x/x+y) + (20y/x+y) = k, where x, y and k are integers. If

Author Message
Senior Manager
Joined: 08 Aug 2005
Posts: 251
10x/x+y) + (20y/x+y) = k, where x, y and k are integers. If  [#permalink]

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26 Apr 2006, 02:40
(10x/x+y) + (20y/x+y) = k, where x, y and k are integers. If x<y. k=?

10
12
15
18
20

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Intern
Joined: 02 Mar 2006
Posts: 21

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26 Apr 2006, 03:02
(10x/x+y) + (20y/x+y) = k

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

=> 10(x + 2y/x+y) = k

as it is given x, y & k are integers we should select x & y such that it divides 10,
factors of 10 are 2 and 5

so we can take x=1 & y=1 or x=1 or y=4

as it is given x<y

x=1 and y=4

by substituting these values we get k=18
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4836
Location: Singapore

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26 Apr 2006, 03:07
1
(10x+20y)/(x+y) = k
10(x+2y)/(x+y) = k

Since K is an integer, x+y must be a 10 to cancel out the 10 in the numerator.

x+y = 10 and we have x<y, so possible sets:

x,y
1,9 --> K = 19
2,8 --> K = 18
3,7 --> K = 17
4,6 --> K = 16

Only 18 is in the list of answers given.
VP
Joined: 06 Jun 2004
Posts: 1008
Location: CA

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28 Apr 2006, 23:22
Concur with ywilfred's working, should be 18!
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Manager
Joined: 31 Mar 2006
Posts: 160

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29 Apr 2006, 06:29
We want x+y =10, so why cannot we have x=0 and y=10?
Intern
Joined: 14 Jan 2006
Posts: 21

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29 Apr 2006, 12:22
amansingla4 wrote:
We want x+y =10, so why cannot we have x=0 and y=10?

bump..

any answer to Aman's Q ?

Or if i use x=0, y=1 then k = 20

i think the question is ambiguous. anyone ?
Senior Manager
Joined: 05 Jan 2006
Posts: 373

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29 Apr 2006, 14:09
easy to take y=0 so for any x even negative integer K will be 10.. what is OA/OE

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Non-Human User
Joined: 09 Sep 2013
Posts: 9128
Re: 10x/x+y) + (20y/x+y) = k, where x, y and k are integers. If  [#permalink]

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09 Aug 2018, 19:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: 10x/x+y) + (20y/x+y) = k, where x, y and k are integers. If &nbs [#permalink] 09 Aug 2018, 19:19
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