For a certain city's library, the average cost

jjjinapinch wrote:For a certain city's library, the average cost of purchasing each new book is $28. The library receives $15,000 from the city each year,the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000.Did the library receive the bonus last year ?

(1) The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.
(2) The lowest number of items checked out in one month was 459 .

We need to determine whether the library received a bonus of $2,000 last year. Keep in mind that the library will only receive the bonus if the total number of items checked out out last year exceeded 5,000.

Statement One Alone:

The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.

Since the library purchased 50 new books each month, it purchased 50 x 12 = 600 books last year. Since each new book cost $28, the total cost of the 600 books last year was 28 x 600 = $16,800. Since we are given that the library received enough money from the city to cover this cost, it must have received the $2,000 bonus in addition to the $15,000 from the city. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The lowest number of items checked out in one month was 459.

Since the lowest number of items checked out in one month was 459, the minimum number of items checked out last year was 459 x 12 = 5,508. Since 5,508 is more than 5,000, the library did receive the $2,000 bonus from the city. Statement two alone is sufficient to answer the question.

Answer: D

Hi All,

We're told that for a certain city's library, the average cost of purchasing each new book is $28, the library receives $15,000 from the city each year and the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000. We're asked if the library received the bonus last year. This is a YES/NO question and can be solved with some Arithmetic and 'rounding.'

1) The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.

With the information in Fact 1, we know that the library purchased (12)(50) = 600 books last year. If we 'round down' $28 to $25 (which would make the following calculation a bit easier to deal with), then the cost of those 600 books would be (600)($25) = $15,000 exactly. Since $28 is more than $25, we know that the actual cost of those books was GREATER than $15,000, so the library had to have spent MORE than the $15,000 it was initially given by the city. That extra money - whatever the actual total is - had to have come from the 'bonus', so the answer to the question can only be YES.
Fact 1 is SUFFICIENT

2) The lowest number of items checked out in one month was 459.

Here, if we 'round down' to 450 - and we assume that 450 books were checked out each month, then the total for the year would be (12)(450) = (6)(900) = 5400. Since 459 is GREATER than 450, then we know that the actual number of books checked out for the year would be GREATER than 5400. That number - whatever it actually is - would end up earning the library the bonus, so the answer to the question can only be YES.
Fact 2 is SUFFICIENT

Final Answer: D

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