A Commonwealth Condominium Complex has k Apartments, n of Which are Rented at s Dollars a Month, Providing Total Monthly Revenue of p Dollars.

Question: A Commonwealth condominium complex has k apartments, n of which are rented at s dollars a month, providing 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?

1. \((k-n)\frac{p}{m}\)
2. \(k*\frac{s}{p}*\frac{m}{100 }\)
3. \(k+\frac{s}{p}+km\)
4. \(\frac{sp}{100m}\)
5. \(ks(1-\frac{m}{100})\)

“A Commonwealth condominium complex has k apartments, n of which are rented at s dollars a month, providing 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? ” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer

Approach 1

As we know that
Revenue = Occupancy * Rent
As given: New occupancy = k
New Rent will be old rent decreased by m%

So, New Rent = \(s(1-\frac{m}{100})\)

Then using formula, we will get the value of Revenue as:

Revenue = k * \(s(1-\frac{m}{100})\)

So, Revenue = \(ks(1-\frac{m}{100})\)

Correct option: E

Approach 2:

Let us assume that:
Total apt = k = 20
Total rented = n = 10
Monthly rent = s = 10
So, Total Revenue = Total rented * Monthly rented
Total Revenue = 10 * 10 = 100
Now,
M = 50%
So, Total Revenue = 20 * 5 = 100
So, from this we can see that only option E satisfies our answer.

Correct option: E

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