treehouse

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ace_gre: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Nov 23, 2009 2:30 pmFollowed by: 1 member; Thanked: 26 times

by ace_gre » Mon Jan 25, 2010 9:15 pm

One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two fairies in order to complete the same job in the same amount of time. If one elf and one fairy worked together, it would take them four hours to build the treehouse. Assuming that work rates for smurfs, elves, and fairies remain constant, how many hours would it take one smurf, one elf, and one fairy, working together, to build the treehouse?

(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7

I do not have the OA. Please help solve this. thanks

Source: Beat The GMAT — Problem Solving | Mon Jan 25, 2010 9:15 pm

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Mon Jan 25, 2010 11:26 pm

imo D
soln attached

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Tue Jan 26, 2010 12:49 am

ace_gre wrote:One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two fairies in order to complete the same job in the same amount of time. If one elf and one fairy worked together, it would take them four hours to build the treehouse. Assuming that work rates for smurfs, elves, and fairies remain constant, how many hours would it take one smurf, one elf, and one fairy, working together, to build the treehouse?

(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7

I do not have the OA. Please help solve this. thanks

One Elf's rate + One Smurf's rate = 2 Fairies' rate + One Smurf's rate

One Elf's rate , E = 2 Fairies' rate, F

E = 2F

(E+F)*4 = T (T= work required to finish tree house) ------- (1)
(E+S)*2 = T --------- (2)
(2F+S)*2 = T ------ (3)

Solving we get E=T/6, S=T/3 and F =T/12 now we have to find T/(E+S+F) = T/T (1/(1/3+1/6+1/12) = 1/(7/12) = 12/7

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