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A certain library charges a flat fee of $5 for any overdue book for the first x days the book is overdue, and an

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by BTGmoderatorDC » Sun Jan 17, 2021 8:18 pm

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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.



OA C

Source: Manhattan Prep
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Source: — Data Sufficiency |
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Re: A certain library charges a flat fee of $5 for any overdue book for the first x days the book is overdue, and an

by swerve » Mon Jan 18, 2021 4:37 pm
BTGmoderatorDC wrote: ↑
Sun Jan 17, 2021 8:18 pm
 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.



OA C

Source: Manhattan Prep
For \(12\) days amount should be \(5 +( 12-x)m\)

1) \(5 + (9-x)m - [ 5 + (8-x)m]= 2\) solving this we get \(m=2\) Not Sufficient. Ss we do not know the value of \(x\). \(\Large{\color{red}\chi}\)

2) This tells us that flat rate of \(\$5\) is applicable to both \(7\) and \(8\) days, so minimum days or \(x\) could be \(8, 9, 10,\) etc, etc. Not Sufficient. \(\Large{\color{red}\chi}\)

Combining \(1+2\)
We know Flat rate is applicable to \(7\) days and \(8\) days but NOT \(9\) days , hence X must be \(8\) and from \((1)\) we already know that \(m=2\)
Hence \(5 +(12-x)m \Longrightarrow 5+(12-8)2 \Longrightarrow 5+8 = 13 \quad\Large{\color{green}\checkmark}\)
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