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# There are 26 students who have read a total of 56 books amon

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There are 26 students who have read a total of 56 books amon  [#permalink]

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28 Sep 2008, 02:27
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Tere are 26 students who have read a total of 56 books among them. The only books they have read, though, are Aye, Bee, Cod, and Dee. If 10 students have only
read Aye, and 8 students have read only Cod and Dee, what is the smallest number of books any of the remaining students could have read?
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Re: Overlapping sets  [#permalink]

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16 Dec 2011, 14:51
6
1
One note, we should be careful about wording. I found the original question and it differs slightly from the question posted.

The question posted states "only 10 students have read A"
This implies that no one else read A except for those 10 students. And it also implies that those 10 students may have read other books.

The question source actually states "10 students have only read A", which means that 10 students read book A and nothing else, and others may have also read A.
@shinbhu has worked through the problem well. I'll outline a similar approach walking through how I think about the question:

1. We start with 56 books and 26 students. Each student can read up to 4 books: A, B, C, and D.
2.. 10 students only read A. That's 10 students and 10 books. Now we have 46 books and 16 students
3. 8 students read only C and D. That's 8 more students and 16 more books. Now we have 30 books and 8 student remaining.
4. Each of the remaining students can read at most 4 books. But all 8 cannot read 4 books, because that would be 32 books and we only have 30 left. So 7 could read 4 books, and that's 28 books. We still have 1 student and 2 books left. So the minimum number of books a student could read is 2.

I hope that helps!
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Re: PS: Smallest Number of Books  [#permalink]

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28 Sep 2008, 03:00
2
Is it 2?

Since, 18 students have already read a total of 26 books. Thus, remaining 8 students would read the remaining 30 books.

Now, a student can read a maximum of four books. Thus, if seven students read four books each then the eighth student will need to read two books.
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Re: PS: Smallest Number of Books  [#permalink]

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29 Sep 2008, 07:44
How it comes total 26 books ?

Have you people consider 8 for C and 8 for D , and 10 for A (10 +8 +8= 26?)

what does "8 students have read only Cod and Dee" mean?

I think we need to take 8 as combine value for Cod and Dee, why we need to take 8 for c and 8 for D

Thanks
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Re: PS: Smallest Number of Books  [#permalink]

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29 Sep 2008, 09:36
vr4indian wrote:
How it comes total 26 books ?

Have you people consider 8 for C and 8 for D , and 10 for A (10 +8 +8= 26?)

what does "8 students have read only Cod and Dee" mean?

I think we need to take 8 as combine value for Cod and Dee, why we need to take 8 for c and 8 for D

Thanks

what does "8 students have read only Cod and Dee" mean?

This means 8 students have read 16 books.

10 students have read only Aye

This means 10 students read 10 books

18 students read 26 books together

8 students are left with 30 books.
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There are 26 students who have read a total of 56 books..  [#permalink]

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14 Feb 2010, 07:41
There are 26 students who have read a total of 56 books among them. The only books they have read, though, are Aye, Bee, Cod, and Dee. If 10 students have only read Aye,
and 8 students have read only Cod and Dee, what is the smallest number of books any of the remaining students could have read?

Ans: 2
Explanation:
According to the problem, 10 students have read only 1 book: Aye, and 8 students have read 2 books: Cod and Dee. This accounts for 18 students, who have read a total of 26 books among them. Therefore, there are 8 students left to whom we can assign books, and there are 30 books left to assign. We can assume that one of these 8 students will have read the smallest possible number if the other 7 have read the maximum number: all 4 books. If 7 students have read 4 books each, this accounts for
another 28 books, leaving only 2 for the eighth student to have read. Note that it is impossible for the eighth student to have read only one book. If we assign one of the students to have read only I book, this leaves 29 books for 7 students. This is slightly more than 4 books per students. However, we know that there are only four books available; it is therefore impossible for one student to have read more than four books.

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Re: There are 26 students who have read a total of 56 books..  [#permalink]

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16 Feb 2010, 09:57
1
1. initially: 26 students - 56 books
2. 10 students read only one book. Other students: 16 students - 46 books
3. 8 students read 2 books. Other students: 8 students - 30 books.
4. If reminding 8 students read 4 books each, it would be 32 books in total. So, we need to take 2 books from one of students and 2 remains.
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Re: There are 26 students who have read a total of 56 books..  [#permalink]

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17 Feb 2010, 19:04
2 books

Students | Books
----------------------------------
10 | 10
8 | 16
==================================
18 | 26

Remaining 8 Students, 30 books
Smallest by 1 person = 7x4 + 1x2
So, 2 books
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Re: There are 26 students who have read a total of 56 books..  [#permalink]

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14 Feb 2011, 12:26
I am not too convinced with the explanation; why can't 1 person read 23 of the 30 remaining books and let the rest 7 read 7 different books, 1 each. In that case; the smallest number of books that any of the remaining students reads is going to be 1. And that 1 is just not read by one person; but 7. There are no mandates that a student must read different books. Am I misinterpreting something?
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Re: 700 level question  [#permalink]

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08 Sep 2011, 23:42
If 10 students have read only Aye, and 8 have read only Cod and Dee, the 8 remaining students must:
(1) Have read at least Bee
(2) Read 30 books among themselves (because of the 56 books, the other 18 students have already read 26)

Of the 8 students, 7 can read a maximum of 28 books (i.e. each of the 7 students reads all of Aye, Bee, Cod, and Dee)
Therefore the last student may read a minimum of 2 books.

The answer is (A)
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Re: There are 26 students who have read a total of 56 books..  [#permalink]

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09 Sep 2011, 12:22
i got 2 after rereading the question. I only 8 once for c and d and not 16. not a bad question just a little tricky on the wording
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Re: There are 26 students who have read a total of 56 books..  [#permalink]

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14 Nov 2011, 17:02
fluke wrote:
I am not too convinced with the explanation; why can't 1 person read 23 of the 30 remaining books and let the rest 7 read 7 different books, 1 each. In that case; the smallest number of books that any of the remaining students reads is going to be 1. And that 1 is just not read by one person; but 7. There are no mandates that a student must read different books. Am I misinterpreting something?

Kind of a confusing question this one, i see your point but I believe that the only books available are Aye, Bee, Cod and Dee. Therefore in order to execute your idea a student would have to repeat the same book several times,... at least this I what I understand from this question... veeery ambiguous I must say.
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There are 26 students who have read a total of 56 books amon  [#permalink]

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15 Dec 2011, 08:41
There are 26 students who have read a total of 56 books among them. The only books they have read are A,B,C,D.If only 10 students have read A and 8 students have read only C and D ,what is the smallest number of books any of the remaining students could have read ?

A. 2
B. 4
C. 12
D. 10
E. 5
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Re: Overlapping sets  [#permalink]

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15 Dec 2011, 16:21
2
1
Let break this down step-by-step, Let B = books, S = students

Begin: B = 56, S = 26
10 students read only A, B = 46, S = 16
8 students read C+D, B = 46 - (8x2) = 30, S = 16 - 8 = 8

30 books, 8 students. Lets have the least read person be 8th
What is the closest multiple to 30 for the remaining 7 students - 7 x 4 = 28. That is 7 students read 4 books each on average.
So, 8th read 30-28 = 2, which is the least.
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Re: Overlapping sets  [#permalink]

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19 Dec 2011, 05:25
bhavinp wrote:
One note, we should be careful about wording. I found the original question and it differs slightly from the question posted.

The question posted states "only 10 students have read A"
This implies that no one else read A except for those 10 students. And it also implies that those 10 students may have read other books.

The question source actually states "10 students have only read A", which means that 10 students read book A and nothing else, and others may have also read A.
@shinbhu has worked through the problem well. I'll outline a similar approach walking through how I think about the question:

1. We start with 56 books and 26 students. Each student can read up to 4 books: A, B, C, and D.
2.. 10 students only read A. That's 10 students and 10 books. Now we have 46 books and 16 students
3. 8 students read only C and D. That's 8 more students and 16 more books. Now we have 30 books and 8 student remaining.
4. Each of the remaining students can read at most 4 books. But all 8 cannot read 4 books, because that would be 32 books and we only have 30 left. So 7 could read 4 books, and that's 28 books. We still have 1 student and 2 books left. So the minimum number of books a student could read is 2.

I hope that helps!

I must have misread the question and posted with the same understanding.
Thanks for the explanation.
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Re: Overlapping sets  [#permalink]

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19 Dec 2011, 12:32
No problem! Glad I could help.
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Re: There are 26 students who have read a total of 56 books amon  [#permalink]

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20 Feb 2019, 00:43
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Re: There are 26 students who have read a total of 56 books amon   [#permalink] 20 Feb 2019, 00:43
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