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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
"The average number of books per student was 2" means that total of 2*30=60 books were borrowed; 2+12+10=24 students borrowed total of 2*0+12*1+10*2=32 books; So 60-32=28 books are left to distribute among 30-24=6 students, these 6 are "the rest who borrowed at least 3 books";
To maximize the number of books one student from above 6 could have borrowed we should minimize the number of books other 5 students from 6 could have borrowed. Minimum these 5 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 5*3=15 books. So the 6th student could have borrowed is 28-15=13 books.
In a class of 30 students, 2 students did not borrow any book from the library, 12 students each borrowed 1 book,10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?
Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...