Library Books-GMATPREPII

medea66 · Posted: Fri Aug 29, 2008 9:19 pm Post subject: Library Books-GMATPREPII

Please help me w/ this......

anju · Posted: Fri Aug 29, 2008 11:03 pm Post subject:

50 books issued as per data (12*1 + 10*2 + 6*3)
average is 2 per student and total students are 30 so total books issued 30*2 = 60

60 - 50 = 10 books extra
max a student has issued is 3 books so in all 3+10 = 13 books is the mac that a student could have issued

vishubn · Posted: Sat Aug 30, 2008 5:55 am Post subject:

Number of students =30
2 - No books borrowed
12 people borrowed one book each---12 books
10-people borrowed 2 each - 20 books

6 peopel atleast 3 ---C

average =2
sum/30=2
number of books =60

so 60 books to be distributed amongst 28 people

Now 12 people take 12 books
10 people take 20 books

So remaining ius 60-10-20

which is 28 books remaining

no 6 people take min 3 so 6th person can take the max

so 5 taking minimum 3books -5*3=15 books

so 6th person can take the max - 13 books

pepeprepa · Posted: Sat Aug 30, 2008 6:12 am Post subject:

Write the average which will be 2 with the information they give you:
(2*0+12*1+10*2+6*x)/30=2
It gives:
32+6x=60
6x=28

You want the maximum number of book one of 6 guys can borrow, so let's write the equation like this to be clearer:
5x+y=28

y=28-5x

You want to Maximize y, so you need to Minimize x. However, you cannot give x 0 because the question told you they borrowed 3 books or more. So let's chose 3 for the 5 guys.
y=28-5*3
y=13

lunarpower · Posted: Sat Aug 30, 2008 10:53 pm Post subject:

here's the deal:
if you want to maximize the number of books taken by one person, then you need to minimize the number of books taken by the other people.

incidentally, this is a really common theme in 'optimization' problems:
to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.
this is supremely obvious in some circumstances - for instance, if a baseball team with a salary cap wants to pay superstar X as much as possible, it can only do so by paying all the other players as little as possible.

--

another common theme:
if you're given a statement about an average, then you should transform it into a statement about a sum.

--

if we follow both of the above points of advice, we arrive at the following solution:
first, realize that the 'average of 2 books' statement is really just a roundabout way of telling you that the 30 students took out a total of 60 books.
the mentioned quantities add up to 32 books, so you have to account for the other 28 books, among 6 students.
if you minimize the book count for five of the six students, that's 3 books per student = 15 books.
28 - 15 = 13 books for the lucky sixth student.