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 of the students each borrowed at least 3 books.If the arithmetic mean number of books borrowed per student was 2,what is the maximum number of books that any single student could have borrowed?
1.3
2.5
3.8
4.13
5.15
Arithmetic Mean
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Total number of books borrowed = (average)*(number of students) = 2*30 = 60.In a class of 30 students, 2 did not borrow any books, 12 borrowed 1 book, 10 borrowed 2 books and the rest borrowed at least 3 books. The average (arithmetic mean) number of book borrowed per student was 2. What is the maximum number of books that any single student could have borrowed?
1. 3
2. 5
3. 8
4. 13
5. 15
Since 2 students do not borrow any books, the number of students borrowing = 30-2 = 28.
From here we can plug in the answer choices, which represent the maximum number of books that any single student could have borrowed.
Answer choice E: 15
60-15 = 45 books left.
10 students borrowed 2 books each = 10*2 = 20 books.
45-20 = 25 books left.
12 students borrowed 1 book each = 12*1 = 12 books.
25-12 = 13 books left.
Number of students left = 28-1-10-12 = 5.
These remaining students must borrow at least 3 books each:
5*3 = 15 books.
Doesn't work, since only 13 books remain.
Since 2 MORE BOOKS are required for the 5 remaining students, the maximum number of books that a student can borrow must DECREASE BY 2.
The correct answer is D.
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Another approach:VIGNESHWARR wrote: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 of the students each borrowed at least 3 books.If the arithmetic mean number of books borrowed per student was 2,what is the maximum number of books that any single student could have borrowed?
1.3
2.5
3.8
4.13
5.15
The average (arithmetic mean) number of book borrowed per student was 2.
Since there are 30 students altogether, the total number of borrowed books = (2)(30) = 60
2 students borrowed 0 books: total of 0 books
12 students borrowed 1 book each: total of 12 books
10 students borrowed 2 books each: total of 20 books
6 students borrowed 3 or more books each: total of 28 books (since the total borrowed books must equal 60)
Now we'll focus on the 6 students who borrowed a total of 28 books.
In order to MAXIMIZE the number of books that one students borrowed, we need to MINIMIZE the number of books that the other 5 students borrowed.
Each student must borrow at least 3 books, so let's say that those 5 students borrowed 3 books each.
This accounts for 15 books, which means the last remaining student borrowed 13 books.
Cheers,
Brent
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Not sure what you mean.VIGNESHWARR wrote:but in the GMAT prep it is 13.pLEASE HELP
Mitch and I are both saying that the answer is 13.
Cheers,
Brent