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A
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Difficulty:
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Question Stats:
43% (02:39) correct
57%
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wrong
based on 128
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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. 5
D. 10
E. 12
A. 2
B. 4
C. 5
D. 10
E. 12
16 Dec 2011, 14:51
Kudos
Bookmarks
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!
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!
General Discussion
28 Sep 2008, 03:00
Kudos
Bookmarks
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.
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.
