Bunuel wrote:
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.
If i, t, and c are the monthly charges, then c = 0.75(i + t).
total revenue internet = (0.6)(n)(i), where n is the total number of customers.
total revenue TV = (0.2)(n)(t)
total revenue internet & TV = (0.2)(n)(0.75)(i + t) = (0.15)(n)(i + t)
We need to answer the question:
Which total revenue is the greatest? => MAX{60i, 20t, 15(i + t)} = ?
[n is a common factor, so we can leave it. Also, multiplying each term by 100 won’t change the order.]
Statement One Alone:=> The monthly charge for Internet only is $25 per customer.
i = $25, but without information about t, we can’t answer the question.
Statement one is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:=> The monthly charge for TV only is 20% greater than the monthly charge for Internet only.
t = 1.2i
MAX{60i, 20(1.2i), 15(2.2i)} = 60i => Internet only packages generated the greatest monthly revenue.
Statement two is sufficient.
Answer: B