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

Question

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

Posted from my mobile device

dru19 · Answer

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

TRINA6 · Answer

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

7X+X= 30
7*3 + X= 30 
 X= 30-21= 9BR  Ans.

ScottTargetTestPrep · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards