If x, y, and k are positive numbers such that : (10) + : PS Archive
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# If x, y, and k are positive numbers such that : (10) +

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VP
Joined: 13 Jun 2004
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If x, y, and k are positive numbers such that : (10) + [#permalink]

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16 Oct 2004, 06:03
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If x, y, and k are positive numbers such that :
(10)[x/(x+y)] + (20)[y/(y+x)]=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
Manager
Joined: 13 Oct 2004
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Kudos [?]: 0 [0], given: 0

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16 Oct 2004, 06:21
let x/x+y = z , then y/x+y = 1-z

10 z + 20 (1-z) = k

or z = (20-k)/10

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

(x+y)/x = 10/(20-k)
y/x = 10/(20-k) -1 = (k-10)/(20-k)

y/x > 1

so, (k-10)/(20-k) >1

and K < 20

k-10 > 20-k or k > 15 and K < 20

Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Technology, Entrepreneurship
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GMAT 4: 700 Q48 V38
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16 Oct 2004, 09:35
(10)[x/(x+y)] + (20)[y/(y+x)]=k

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

Apply k from the answer choices.

lets say K = 30
we have
x+2y = 3x + 3y
or 2x=-y. => y<x

lets say K =18
we have
x+2y = 1.8x+1.8y
=>0.2y = 0.8x
or y=4x. =>X<Y. Hence D.
Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V0
GMAT 2: 700 Q V
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 7: Q42 V44
GMAT 8: Q42 V44
GMAT 9: 740 Q49 V42
GMAT 10: 740 Q V
GMAT 11: 500 Q47 V33
GMAT 12: 670 Q V
WE: Engineering (Manufacturing)
Followers: 0

Kudos [?]: 202 [0], given: 102338

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16 Oct 2004, 10:14
when K=18

y=4x. =>Y>X and not X>Y. Right ?
VP
Joined: 13 Jun 2004
Posts: 1118
Location: London, UK
Schools: Tuck'08
Followers: 7

Kudos [?]: 45 [0], given: 0

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16 Oct 2004, 23:01
sorry guys, I don't have the explanation for the answer. However, OA is D
16 Oct 2004, 23:01
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