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M06-35

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Bunuel
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M06-35 [#permalink] New post   16 Sep 2014, 00:33
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Question Stats:

85% (02:02) correct 15% (02:31) wrong based on 642 sessions
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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. \(ks(1 - \frac{m}{100})\)
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E
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Bunuel
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Re M06-35 [#permalink] New post   16 Sep 2014, 00:33
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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
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saurabh9gupta
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Re: M06-35 [#permalink] New post   15 Aug 2019, 01:19
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Bunuel wrote:
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. \(ks(1 - \frac{m}{100})\)



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.

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Success2015
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Re: M06-35 [#permalink] New post   14 Aug 2015, 23:03
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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
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hiranmay
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Re: M06-35 [#permalink] New post   20 Jul 2020, 09:14
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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)|
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Bunuel
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Re: M06-35 [#permalink] New post   05 Oct 2023, 01:48
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M06-35 [#permalink]
05 Oct 2023, 01:48
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Bunuel
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