AbdurRakib 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
The question stem says the "average price" of a book purchased is $28. So for Statement 1, how can we assume that the price of the books purchases was $28? What if the library purchased just 15 books at $1,000 each? Surely then the library wouldn't have been able to meet the target for the bonus. Even if it did purchase more than 50 books, how do we know that the library was able to meet its target of checking out 50 books?