Skip to main content

2004 AMC 12B Problem 11

Problem 11 of 25IntermediateAlgebra

All the students in an algebra class took a 100100-point test. Five students scored 100,100, each student scored at least 60,60, and the mean score was 76.76. What is the smallest possible number of students in the class?

Answer choices

Show solution

Solution

Each score of 100100 is 2424 above the mean, so the five contribute 120120 points above 76.76. These must be balanced by points below the mean, and each remaining student is at most 7660=1676 - 60 = 16 below. So at least 12016=7.5,\dfrac{120}{16} = 7.5, hence 88 more students are needed, for a total of 13.13. Five 100100s and eight 6161s achieve this. Thus, the correct answer is D.

More practice

Concepts: mean · bounding to limit cases

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.