For a certain city's library, the average cost of purchasing each new

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
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Statement 1
Total cost of books purchased = 50 × 28 =16800
Total received = 15000
Because 15000 - 16800 = -1800
Statement state that library received enough $ to cover
Therefore, it must have received $2000. = Sufficient
Eliminate: B,C,E

Statement 2:
459 × 12 = 5508 > 5000 = Sufficient

Answer: D

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Stmt 1.
Number of books purchased = 50*12 = 600
Total cost = 600*28 = 16800
Money received from the city = $15000
Since the library received enough money from the city to cover this cost, they must have received the bonus to cover the extra cost (16800 - 15000 = 1800)
Stmt 2.
The lowest number of items checked out in one month was 459. Considering this is the number of items checked out every month, number of items = 459 * 12 = 5508 which is more than the target 5000. So receives bonus.

Either of them is sufficient.
Ans D.

(1) The total number of new books that the library purchased last year: 50 * 12 = 600 items < 5,000
=> The library didn't receive the bonus. Sufficient

(2) The total number of items checked out last year is equal to or greater than: 459 * 12 = 5,508 > 5,000
=> The library did receive the bonus. Sufficient.

The answer is D.
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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?

On the first question: We can assume each book is the average price since the total cost of the books purchased (regardless of the actual price of each book) is always equal to the average price times the number of books purchased. For example, statement 1 just said an average of 50 books were purchased each month, but the total number of books purchased for the year must be 50 x 12 = 600 even though we don’t know the actual number of books purchased in any particular month. Therefore, even though we don’t know the actual price of each book, we make the same argument: that the library must have spent a total of 600 x 28 = $16,800 on the books.

On the second question: We don’t know how many books are actually checked out. But the number of books (5000) required to be checked out to receive the bonus is like a red herring in the problem. Because in statement 1, it says “[the library] received enough money from the city to cover this cost.” Well, the total cost of the books is $16,800, and the routine receipt of $15,000 from the city would not be able to cover the total $16,800 spent unless the library also receive the $2000 bonus.
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What put me off in this question was St 1. St 2 can be solved using worst case scenario method.

The question explicitly says that the bonus is given if the total number of items checked out over the course of the year exceeds 5,000.

1) In St1, we do not know whether the library received the bonus. What if the fund of 15,000 dollars was increased this year to cover the cost?

2) Also, since in question statement, the condition of providing bonus is explicitly mentioned, how can we just assume that the bonus was provided in St 1 without even knowing the number of items checked out?

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Please help!

As per stmnt 1, the total money spent on buying the books during the year = 50*12 *28 = 16,800
We are given that the library received enough money from the city to cover this cost. So it received at least $16,800 from the city. But the city gives only $15,000 per year (given in the question). A bonus is given only if more than 5000 books are checked out. Since the city gave $16,800, the city must have given the bonus 2000. So more than 5000 books must have been checked out.
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1) For statement 1, we need to figure out how many books were purchased and how much they cost. Since 50 x 12 = 600 books were purchased and each book cost $28, the total cost was $16,800. There is no way the library can spend this much money unless they received the bonus. The fund of 15,000 is the same each year. It won’t increase; any extra money is from the bonus.

2) Because statement 1 states that “[the library] received enough money from the city to cover this cost,” which implies they did receive the bonus. Again, they spent $16,800 on books, but the regular amount they received is $15,000. So they must also received $2000 bonus in order to have $17,000 and spend $16,800 on books.
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Responding to a pm:



We are talking about a library. People check out books from it and then return them after a few days. The library's stock doesn't dwindle. Then the library may buy some new books which increases its stock. But it only rents out books.
The library gets a bonus if the total number of items checked out (and eventually returned) over the course of the year exceeds 5,000. The purchase of new books has nothing to do with this number. It just tells us the money the library spent in increasing its stock.
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What confuses me in this question is that statement 2 says - lowest no of items checked out in one month was 459

The statement does not mention that the lowest no of items necked out each month is 459 , so why are we multiplying it with 12 ?

Posted from my mobile device

What is meant by "the lowest number of items checked out in one month is 459"?

It means the lowest value of "no of items checked out in a month" is 459
Say No. of items checked out in Jan = 500
No of items checked out in Feb = 567
No of items checked out in March = 459
No of items checked out in April = 489
and so on...

The minimum value of no of items checked out in a month is 459. In all other months, the number of items checked out were either equal to 459 or more than 459.

So the minimum number of items checked out in the whole year = 459 * 12 = 5508

The question tells us: 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

Since more than 5000 items were checked out in the year, the library would have got the bonus.
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Answer: Option D

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This question ask us to call for some assumption. Whether bonus would be received last year or year before the last year is questionable. If statement 1 has to be true, we need to assume that at the start of last year, they would have received 15000$+ bonus to cover for the entire year expense for coming 12 months.

However if statement 2 has to be true, bonus could only be received this year (not last year), since we would come to know if checkout is more than 5000 Nos. ONLY after last month of Dec last year (and not in advance)

Thus either Statement 1 or statement 2 alone has to be true. If we are saying both are true, that means ,we are assuming last year, library received bonus twice.

Would request if you could shed light on this? Isn't this question ambiguous?

No, it is not necessary that books can be purchased only after the bonus is received. We are not given that.

(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.

We are given that the money received was enough to cover the cost of purchase. Was the purchase made using that money only, we don't know and we don't need to assume that it was. The library would have its own funds too and they could have easily purchased books using those. At the end of the year, they will find out whether the funds received that year were enough to cover their purchases or not. Also, things can easily be purchased on credit etc. Another possibility is that what if the 5000 number was reached in June itself and the bonus given at that time? There are lots of scenarios possible.

Also, whether the actual bonus payment happened in June last year or on 31st Dec last year or in Jan this year, doesn't matter. It will come as a receivable of last year.
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