A certain library charges a flat fee of $\$5$ for any overdue book for the first $x$ days the book is overdue, and - The Beat The GMAT Forum

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BTGmoderatorLU wrote: ↑
Sat Jul 22, 2023 7:49 am
Source: Manhattan Prep

A certain library charges a flat fee of $\$5$ for any overdue book for the first $x$ days the book is overdue, and an additional fee of $m$ dollars per day for every day after $x$ that the book is overdue. What is the fee for a book that is $12$ days overdue?

1) The fee for a book that is $9$ days overdue is $\$2$ more than the fee for a book that is $8$ days overdue

2) The fee for a book that is $8$ days overdue is the same as the fee for a book that is $7$ days overdue

The OA is C

We have a library that charges money for late books. And there are different fees based on how late the book is. We need to find out how much is charged for a book that is n days late.

Statement 1: They say, "The fee for a book that is m days overdue is p more than the fee for a book that is k days overdue." So we know that the difference in cost between a book that is m days late and one that is k days late is p. But we do not know exact number of days and we do not know starting flat fee and daily fee. This is not enough to answer question.

Statement 2: "The fee for a book that is n days overdue is the same as the fee for a book that is j days overdue." So two different days, n and j, have same fee. But again, we do not know the specific fee structure, flat fee and daily fee. This is also not enough to answer question.

But when we take both Statement 1 and Statement 2 together, they might provide enough information. We can set up a system of equations using these statements and solve for the unknowns. This would give us enough information to find out what the fee for a book that is n days overdue. So, answer is C - both statements together are sufficient.