OG12-PS-148 qn

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kishokbabu: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed May 04, 2011 9:50 pmFollowed by: 2 members; Thanked: 2 times

by kishokbabu » Fri Jan 06, 2012 11:33 am

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

OG explanation for this qn is very big, is there any easy approach or is there any number plugging options for this qn?

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Source: Beat The GMAT — Problem Solving | Fri Jan 06, 2012 11:33 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Jan 06, 2012 11:39 am

kishokbabu 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

OG explanation for this qn is very big, is there any easy approach or is there any number plugging options for this qn?

Check my explanation here:

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Fri Jan 06, 2012 11:53 am

restated q.

10x/(x+y)+20y/(x+y) = K and x < y
find k?

(10x+20y)/(x+y) = K, (10(x+y)+10y)/(x+y), 10 + 10y/(x+y)
since x<y, we deduce y/(x+y) could be min. 1/2 and max 1
x<y, say x=0,.000001 or some other small value, x is +ve and less than y, y(x+y) gives close to 1 then OR say x=9.99999999 or some other value, x <y and y/(x+y) gives close to 1/2 then

Hence 10y/(x+y) is min. 5 and max. 10

answer choice d suits here only

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

OG explanation for this qn is very big, is there any easy approach or is there any number plugging options for this qn?[/quote]

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Sat Jan 07, 2012 3:46 am

below is my very strange approach

-

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

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

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

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

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

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

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

it means

x+y=10
y=k-10

now we see that our k cant be 10(then y=0) and 30 (then y=20 and x<0).so A and E are out

answ choice C is also out, since then x=y

answ choice B is also out, since then x>y

answ choice D k=18 .then y=18-10=8 x=10-8=2 bingo!

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