Students......DS PROBLEM

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smclean23: Master | Next Rank: 500 Posts; Posts: 172; Joined: Mon Jun 23, 2008 12:00 pmFollowed by: 1 member; Thanked: 3 times

by smclean23 » Sun Jul 06, 2008 3:16 pm

The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If x of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
(A) Y/R
(B) Y/R-X
(C) XY/R-X
(D) XY/R(R-X)
(E) Y/R(R-X)

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Source: Beat The GMAT — Problem Solving | Sun Jul 06, 2008 3:16 pm

sibbineni: Master | Next Rank: 500 Posts; Posts: 222; Joined: Fri Jan 04, 2008 8:10 pm; Thanked: 15 times

by sibbineni » Sun Jul 06, 2008 3:29 pm

Total no of students =R

Teacher birthday present costs=y dollars

no of students failed=x

let y=100
R=10
and x=5

then for R students it costs 10 dollars per head

so forR-x students it costs 100/5==>20

so plugin the values to get 20

only B satisfies

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smclean23: Master | Next Rank: 500 Posts; Posts: 172; Joined: Mon Jun 23, 2008 12:00 pmFollowed by: 1 member; Thanked: 3 times

by smclean23 » Sun Jul 06, 2008 3:50 pm

thats what i thought but the answer is supposedly D.....CONFUSED...

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TRANGZON: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Mon Apr 14, 2008 3:36 pm; Location: California; Thanked: 1 times

by TRANGZON » Sun Jul 06, 2008 11:40 pm

Y/R is the money each student have to contribute as their first plan

Y/(R-x) is the money each remaining student contribute after x students fail

the additional money each student contribute: Y/R - Y/(R-x) = Yx/R(R-x)

D is the answer.

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Mon Jul 07, 2008 2:46 am

sibbineni wrote:Total no of students =R

Teacher birthday present costs=y dollars

no of students failed=x

let y=100
R=10
and x=5

then for R students it costs 10 dollars per head

so forR-x students it costs 100/5==>20

so plugin the values to get 20

only B satisfies

If we plug in the above values answer cannot be B, since the question is asking about additional dollars not the whole amount.

It is not a right choice of numbers to plug in because A and D both will give us the same answer.

Try using values R=4, Y=20, X=2. or R=25, Y=100, X=5. This will give only D as an answer.

But I must say the method used by you of plugging in numbers is the best for solving variable questions such as these. But make sure you test all the options before marking the answer!!!!

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