M06-35

Question

In a Commonwealth condominium complex, there are  k  apartments. Out of these,  n  apartments are currently rented, each at a rate of  s  dollars a month, yielding a total monthly revenue of  p  dollars. If the management plans to reduce the rent by  m % to achieve 100% occupancy, what will be the total monthly revenue?

A.  (k-n)\frac{p}{m}  
B.  k*\frac{s}{p}*\frac{m}{100}  
C.  k+\frac{s}{p} + km  
D.  \frac{sp}{100m}  
E.  ks(1 - \frac{m}{100})

saurabh9gupta · Accepted Answer

Nice question: Another method Assume - Total apt (k) 20 Total rented (n) = 10 Monthly rent (s) = 10 Total Rev (p) = 10 * 10 = 100 now M=50% so total revenue = 20 * 5 = 100 substitute and only E will stand. Give Kudos

Bunuel · Answer

Official Solution:

In a Commonwealth condominium complex, there are  k  apartments. Out of these,  n  apartments are currently rented, each at a rate of  s  dollars a month, yielding a total monthly revenue of  p  dollars. If the management plans to reduce the rent by  m % to achieve 100% occupancy, what will be the total monthly revenue?

A.  (k-n)\frac{p}{m}  
B.  k*\frac{s}{p}*\frac{m}{100}  
C.  k+\frac{s}{p} + km  
D.  \frac{sp}{100m}  
E.  ks(1 - \frac{m}{100})

Revenue is calculated as Occupancy multiplied by Rent. Given that the new occupancy is  k  (meaning all  k  apartments are rented at 100% occupancy) and the adjusted rent is  s(1-\frac{m}{100})  (reflecting a decrease of  m\%  from the original rent of  s  dollars), the Revenue can be expressed as  ks(1-\frac{m}{100}) .

Answer: E

Success2015 · Answer

when running out of time or if we get stuck, we can eliminate few options by analyzing them...
option A does not have s at all...s is needed to determine the new rent
option D does not have k, we need k as total occupancy needs to be considered.

we dont need p (old revenue) to determine new revenue as long as we have new rent and occupancy info.
we can eliminate B and C

hiranmay · Answer

A Commonwealth condominium complex has  k  apartments,  n  of which are rented at  s  dollars a month, providing a total monthly revenue of  p  dollars. If the management is planning to decrease the rent by  m %, to increase the occupancy to 100%, how much total revenue will it collect?

A.  (k-n)\frac{p}{m}  
B.  k*\frac{s}{p}*\frac{m}{100}  
C.  k+\frac{s}{p} + km  
D.  \frac{sp}{100m}  
E.  ks(1 - \frac{m}{100})  -->   correct 
 Solution :
`-----------------------------------------------------------|  before |  after  |
rent=>|decrease the rent per apartment by m % |  s ------|  s*(1-m/100) |
number of apartments rented =>--------------------| n ------| k  = 100% |
Total revenue =>---------------------------------------|p= ns --|= ks(1-m/100) |

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

ck77 · Answer

This is straight forward question which needs more clarity in question stem. As a reader, there is confusion if the rent for the rest of the apartments were increased or for all the K apartments. Not sure if it is just me, but I spent 7 minutes because of this confusion on solving.

Bunuel · Answer

The question clearly states that the  management plans to reduce the rent  to achieve 100% occupancy, meaning the new rent applies to  all k apartments . There is no mention of different rents for different groups of apartments. The confusion comes from overinterpreting the problem—reading it carefully makes it clear that the reduced rent applies to all units.

kouassidrissa047 · Answer

I like the solution - it’s helpful.

M06-35

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