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In a class of 25 students, 3 students did not submit a book

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In a class of 25 students, 3 students did not submit a book  [#permalink]

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New post 06 Apr 2019, 10:17
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In a class of 25 students, 3 students did not submit a book report for extra credit. 8 students submitted 1 book report, 6 students each submitted 2 book reports and the rest of the students each submitted at least three book reports. If the average number of book reports submitted was 2, what is the maximum number of book reports that any individual student could have submitted?
A) 4
B) 5
C) 7
D) 9
E) 30

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Re: In a class of 25 students, 3 students did not submit a book  [#permalink]

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New post 06 Apr 2019, 22:55
Total number of Students = 25

# of students with no report = 3
# of students with 1 report = 8
# of students with 2 reports = 6
# of students with at least 3 reports = 25 - (3+8+6) = 8

\(Average number of book reports = \frac{Sum of (# of students * reports submitted)}{Total number of students}
= \frac{(3*0 + 8*1 + 6*2 + 8*3)}{25}
= \frac{44}{25}\)

For the average to be 2, the numerator in the above fraction should be 50. (6 greater than 44). So to get the maximum number of book reports, 7 of the 8 students with at least 3 reports should have submitted exactly 3 reports and the 8th student submitted 3 + 6 = 9 reports

Answer C
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Re: In a class of 25 students, 3 students did not submit a book  [#permalink]

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New post 07 Apr 2019, 00:28
students that submitted the book report= 22
total report submitted=8*1+6*2+8(3+x)
avg=2

equation become
20+8(3+x)=25*2
x=6

maximum report=3+6=9

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Re: In a class of 25 students, 3 students did not submit a book  [#permalink]

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New post 11 Apr 2019, 06:06
nm97 wrote:
In a class of 25 students, 3 students did not submit a book report for extra credit. 8 students submitted 1 book report, 6 students each submitted 2 book reports and the rest of the students each submitted at least three book reports. If the average number of book reports submitted was 2, what is the maximum number of book reports that any individual student could have submitted?
A) 4
B) 5
C) 7
D) 9
E) 30

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If 3 students didn't submit any BR= 0BR total
8 students submitted 1BR each = 8BR total
6 students submitted 2BR each = 12BR total
8 remaining students submitted atleast 3BR each = 8X BR total (let's assume)

Avg BR= Total #of BR/ Total #of students = 2
8BR+12BR+8X BR / 25 = 2BR
20 + 8X= 50

8X= 30 [ Out of these 8 students, if 7 students submitted atleast 3BR each, then total will be 21BR, remaining one students can submit 9BR highest]

7X+X= 30
7*3 + X= 30
X= 30-21= 9BR Ans.
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Re: In a class of 25 students, 3 students did not submit a book  [#permalink]

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New post 14 Apr 2019, 19:02
nm97 wrote:
In a class of 25 students, 3 students did not submit a book report for extra credit. 8 students submitted 1 book report, 6 students each submitted 2 book reports and the rest of the students each submitted at least three book reports. If the average number of book reports submitted was 2, what is the maximum number of book reports that any individual student could have submitted?
A) 4
B) 5
C) 7
D) 9
E) 30

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We let n = the sum of the book reports submitted by the 8 remaining students and create the equation:

(3 x 0 + 8 x 1 + 6 x 2 + n)/25 = 2

0 + 8 + 12 + n = 50

n = 30

In order to maximize the number of book reports by one of the 8 remaining students, we must minimize the number of books reports submitted by the other 7 students. The minimum number of reports for each of these 7 students is 3, for a total of 7 x 3 = 21 reports. Thus, the maximum number that the last person could have submitted was 30 - 21 = 9 reports.

Answer: D
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Re: In a class of 25 students, 3 students did not submit a book   [#permalink] 14 Apr 2019, 19:02
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