Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, prefe

VJesus12 wrote: ↑

Fri Feb 19, 2021 6:30 am

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid \(\$3.99\) for each additional compact disc purchased. If a preferred customer purchased a total of \(6\) compact discs and paid \(\$15.95\) for the first compact disc, then the dollar amount that the customer paid for the \(6\) compact discs is equivalent to which of the following?

(A) \(5(4.00) + 15.90\)
(B) \(5(4.00) + 15.95\)
(C) \(5(4.00) + 16.00\)
(D) \(5(4.00 - 0.01) + 15.90\)
(E) \(5(4.00 - 0.05) + 15.95\)

Answer: A

Source: Official Guide

Solution:

The preferred customer paid 15.95 + 5(3.99) dollars for the 6 CDs. However, we don’t see this expression in the answer choices. We can see that had the 15.90 in choice D been 15.95, then D would be the correct answer. Or had the 0.05 in choice E been 0.01, then E would be the correct answer. However, since they aren’t, neither one is the correct answer.

Now let’s analyze the remaining three answer choices. A, B and C. Notice that each one has 4.00, which is 0.01 more than 3.99 and the difference between 5(4.00) and 5(3.99) is 5(0.01) = 0.05. Thus we see that, since 5(4.00) overvalued the cost by 0.05, we must undervalue 15.95 by 0.05 to 15.90 to have an equivalent cost. Thus, equivalently, the customer paid 5(4.00) + 15.90 dollars.

Answer: A