In a class of 30 students, 2 students did not borrow-TOUGH

[Guest]

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

I reached a point and get stuck on how to deal with the overlapping tests. Please help.
OA is D.

[VIKSNME]

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

I reached a point and get stuck on how to deal with the overlapping tests. Please help.
OA is D.

If you read the question carefully, you will realise that there are no overlapping sets here. If 12 students each borrowed 1 book then if the sets were overlapping, there would be more than 12 students who each borrowed 2 books. But since there are only 10 students who each borrowed 2 books that indicates that each group i.e. group that borrowed 1 book, group that borrowed 2 books etc are treated as distinct groups for this problem.

This determined, let's find out how many students borrowed at least 3 books. students in the 3rd group who borrowed at least 3 books = 30-(12+10+2) = 6

Now, let''s find out how many books are left for the group that borrowed at least 3 books:
12 students each 1 book = 12*1 = 12
10 students each 2 books = 10*2 = 20

Since, on an average 2 books were borrowed, that means a total of 60 books were borrowed.

Hence, 60-12-20 = 38 books were borrowed by the 3rd group.

To find out the maximum number of books a student of this group could have borrowed, we must allow 5 of the 6 students to borrow exactly 3 books allowing the 6th student to borrow the maximum number. 5*3 = 15 books

Hence, the 6th student must have borrowed, 38-15=13 books, which is the correct answer.

[RonPurewal]

http://www.manhattangmat.com/forums/post11366.html

yeah, like the last poster said, this isn't an overlapping sets problem. if you're confusing it with overlapping sets problems, the best thing for you to do is go back and look at many, many overlapping sets problems at once, until you've absorbed their general appearance into your heart, soul, and bones.

i guarantee you that you will not mistake this problem for an overlapping-sets problem after looking at ten or twenty overlapping-sets problems in a row.
try it.

[emma]

VIKSNME: The calculation seems a little off. Its amazing how you still arrived at the right answer:

For the 3rd group:

60-12-20 = 28 books borrowed by the 3rd group.

Since each group member in this group has at least 3 borrowed books, that takes out 3*6 books from the pool = 18 books.

That leaves 28-18 = 10 books still available for borrowing. So a person can borrow all 10 of these along with the 3 they already have to arrive at 13 books.

13 is the answer

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

I reached a point and get stuck on how to deal with the overlapping tests. Please help.
OA is D.

If you read the question carefully, you will realise that there are no overlapping sets here. If 12 students each borrowed 1 book then if the sets were overlapping, there would be more than 12 students who each borrowed 2 books. But since there are only 10 students who each borrowed 2 books that indicates that each group i.e. group that borrowed 1 book, group that borrowed 2 books etc are treated as distinct groups for this problem.

This determined, let's find out how many students borrowed at least 3 books. students in the 3rd group who borrowed at least 3 books = 30-(12+10+2) = 6

Now, let''s find out how many books are left for the group that borrowed at least 3 books:
12 students each 1 book = 12*1 = 12
10 students each 2 books = 10*2 = 20

Since, on an average 2 books were borrowed, that means a total of 60 books were borrowed.

Hence, 60-12-20 = 38 books were borrowed by the 3rd group.

To find out the maximum number of books a student of this group could have borrowed, we must allow 5 of the 6 students to borrow exactly 3 books allowing the 6th student to borrow the maximum number. 5*3 = 15 books

Hence, the 6th student must have borrowed, 38-15=13 books, which is the correct answer.

[shyam83]

I have a small doubt in this question .. its given that average number of books borrowed per student is 2 also given that 2 students didnt borrow any books,if thats the case then total number of books should be 28*2=56 right nstead of 30*2=60???
if u take it as 56 and proceed further u will get the final answer as 9 which fortunately is not among the choices !!Can someone clear my confusion ???

[suneelv001]

I have a small doubt in this question .. its given that average number of books borrowed per student is 2 also given that 2 students didnt borrow any books,if thats the case then total number of books should be 28*2=56 right nstead of 30*2=60???
if u take it as 56 and proceed further u will get the final answer as 9 which fortunately is not among the choices !!Can someone clear my confusion ???

If two student did not borrow any books doesn't mean we should not include those two student. Problem clearly state that,

total no.of students = 30

Avg no.of books = 2.

hence, total no.of books = 30*2 = 60

[RonPurewal]

If two student did not borrow any books doesn't mean we should not include those two student. Problem clearly state that,

total no.of students = 30

Avg no.of books = 2.

hence, total no.of books = 30*2 = 60

yep.

basically, 0 is a number, and therefore needs to be included in statistical analysis, just as much as any other number.

for instance, if you are calculating the average number of children per family in a certain city, you absolutely need to include those families that have 0 children when you compute the average.
this is the same thing.

[JbhB682]

http://www.manhattangmat.com/forums/post11366.html

yeah, like the last poster said, this isn't an overlapping sets problem. if you're confusing it with overlapping sets problems, the best thing for you to do is go back and look at many, many overlapping sets problems at once, until you've absorbed their general appearance into your heart, soul, and bones.

i guarantee you that you will not mistake this problem for an overlapping-sets problem after looking at ten or twenty overlapping-sets problems in a row.
try it.

Hi Sage - I unfortunately fell for the trap, thinking this was a Venn Diagram overlap set problem (wasting an entire minute thinking overlap sets was the strategy to solve this problem)

How do you recognize that this is NOT an overlap set problem ? Is this the way ?

-- if i assume circle 1 represents students who borrow one book only
-- if i assume circle 2 represents students who borrow two books only
-- if i assume circle 3 represents students who borrow 3 or more books only

The concept of an overlap between circle 1 and circle 2 in this scenario does not really make sense.

The overlap between circle 1 and circle 2 would be students who borrow one book only and students who borrow two books which really does not make sense

Is this how you recognize, this is NOT an overlap set problem ?

Thank you !

[Sage Pearce-Higgins]

Yes, I agree: as soon as you notice that there's no possibility of overlap, then thinking of sets isn't useful. For set problems, I look out for word such as 'both' or 'neither': these indicate that there's overlap between the sets.