The Q members of the senior class agree to split the cleanup costs equ

Question

The Q members of the senior class agree to split the cleanup costs equally for their graduation dance, which will be P dollars. If R students fail to graduate and do not pay their share, but the cleanup costs remain the same, how many additional dollars will each of the remaining students have to contribute to pay the cleanup costs?

A. P/(Q - R)

B. (P/Q)(R - Q)

C. PQ/(Q - R)

D. PR/(Q(Q - R))

E. PQR/(Q(Q - R) )

A. P/(Q - R)

B. (P/Q)(R - Q)

C. PQ/(Q - R)

D. PR/(Q(Q - R))

E. PQR/(Q(Q - R) )

GMATinsight · Answer

Totral Cost = P
Cost per person with Q members  = \frac{P}{Q}

R students opt out

Remaining students = Q-R

Cost per student  = \frac{P}{(Q-R)}

Additional Amount Per person  = \frac{P}{Q-R} - \frac{P}{Q}

Additional Amount Per person  = \frac{PQ-PQ+PR}{Q*(Q-R)} = \frac{PR}{Q*(Q-R)}

Answer: Option D

GMATWhizTeam · Answer

Solution 
 • Let us make the following table:

https://www.dropbox.com/s/rehjpt2qvtycs9m/18_07_20.jpg?dl=1

• So, the additional dollars that each of the remaining Q-R students will pay  = \frac{P}{Q-R} - \frac{P}{Q} = P*( \frac{1}{Q-R} - \frac{1}{Q}) = \frac{P*R}{Q(Q-R)}  
Thus, the correct answer is  Option D.

chetan2u · Answer

I.  Quickest - logical  
We are looking for ' additional dollars per remaining student', so we should have dollars, here P, in numerator, and number of students in denominator in simplified form. Remember each of Q, R, or Q-R will give number of students.
Only A and D are possible.... A clearly gives us the total amount that each would pay, but we are looking for additional dollars.. 
D is the answer

II.  Take numbers 
Let P = 20, Q=10 and R=8..
So Initial they were to pay =  \frac{20}{10}=2 , but now  \frac{20}{(10-8)} =10...addl dollars = 10-2=8
A.  \frac{P}{(Q - R)}=\frac{20}{2}=10

B.  (\frac{P}{Q})(R - Q) ..R-Q<0, so discard

C.  \frac{PQ}{(Q - R)}=\frac{10*20}{8}=25 ...NO

D.  \frac{PR}{(Q(Q - R))}=\frac{20*8}{10*(10-8)}=8 ...YES

E.  \frac{PQR}{(Q(Q - R) )}=\frac{10*20*8}{10*2}=80 ...NO

III.  Proper method 
Initial each of Q were paying =  \frac{P}{Q} ...(i)
After R left, each of Q-R were to pay =  \frac{P}{Q-R} ...(ii)
Additional paid per person = ii-i 
 \frac{P}{Q-R}-\frac{P}{Q}=\frac{P(Q-(Q-R))}{Q(Q-R)}=\frac{PR}{Q(Q-R)} .

D

The Q members of the senior class agree to split the cleanup costs equ

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The Q members of the senior class agree to split the cleanup costs equ

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