2004 AMC 12B Problem 11

Attempt Problem 11 of the 2004 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12B solutions, or check the answer key.

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11.

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?

1010

1111

1212

1313

1414

Answer: D
Concepts:meanbounding to limit cases
Difficulty rating: 1440
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.

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