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06 Aug 2023, 05:00
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Difficulty:
45%
(medium)
Question Stats:
74% (02:45) correct
26%
(02:49)
wrong
based on 920
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A cable company sells exactly 3 service packages: Internet only, TV only, and an Internet-TV combination. The monthly charge for the Internet-TV combination is 25% less than the sum of the monthly charges for Internet only and TV only. If 60% of the company's customers purchased Internet only and the remaining customers were divided equally between the 2 other service packages, which of the service packages would generate the greatest monthly revenue for the company?
(1) The monthly charge for Internet only is $25 per customer.
(2) The monthly charge for TV only is 20% greater than the monthly charge for Internet only.
(1) The monthly charge for Internet only is $25 per customer.
(2) The monthly charge for TV only is 20% greater than the monthly charge for Internet only.
06 Aug 2023, 06:04
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Bunuel
Number of customers = n
Plans offered by the company
- Internet Only : Cost = $\(i\)
- TV Only : $\(t\)
- Internet + TV: $\(\frac{3}{4}(i+t)\)
Monthly Revenue
- Internet Only : $\( \frac{60}{100} * n * i\) = \(\frac{3}{5} * n * i\)
- TV Only : $\(\frac{20}{100} * n * t\) = \(\frac{1}{5} * n * t\)
- Internet + TV: $\(\frac{20}{100} * n *\frac{3}{4}(i+t)\) = \(\frac{3}{20} * n * (i+t)\)
Statement 1
(1) The monthly charge for Internet only is $25 per customer.
We don't have information on the price of the telephone-only service. Hence, this statement is not sufficient to evaluate that of the three services which service would generate the most revenue.
We can eliminate A and D.
Statement 2
(2) The monthly charge for TV only is 20% greater than the monthly charge for Internet only.
\(t = 1.20i\)
As we have a multiplicative relationship between '\(t\)' and '\(i\)' we can express the revenues using only one variable.
- Internet Only : \(\frac{3}{5} * n * i\)
- TV Only : \(\frac{1}{5} * n * 1.20i\)
- Internet + TV: \(\frac{3}{20} * n * (i+1.20i)\)
\(n*i\) is common to all three revenues, hence the coefficients can help us determine the service package that would generate the greatest monthly revenue for the company.
We don't need to solve the equations to the reduced form. We can conclude from the presented information that if needed we can do so. Hence, the information is sufficient.
Option B
09 Dec 2024, 00:35
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Bunuel
Answer: Option B
Please check the video solution here.
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