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AMC 10 USA Math Olympiad

Average Problem – AMC 10B – 2019 – Problem No – 4

The simplest example of power mean inequality is the arithmetic mean – geometric mean inequality. Learn in this self-learning module for math olympiad

Average – AMC 10B – 2019 – Problem No – 4


Let’s try this problem based on average from AMC 10B, 2019.

Mr. Patrick teaches math to 15  students. He was grading tests and found that when he graded everyone’s test except Payton’s, the average grade for the class was 80 . After he graded Payton’s test, the test average became 81. What was Payton’s score on the test?

  • 81
  • 95
  • 85
  • 91

Key Concepts


Average

Mean

Arithmetic

Check the Answer


Answer: 95

AMC 10A – 2015 – Problem No – 5

Challenges and Thrills in Pre-College Mathematics

Try with Hints


If you are not getting correct answer you can start from here :

The average of a set of numbers is the value we get if we evenly distribute the total across all entries. So assume that the first  14 students each scored  80.

If Payton also scored an 80 the average would still be 80. In order to increase the overall average to 81 we need to add one more point to all of the scores, including Payton’s. This means we need to add a total of  15 more points, so Payton needs 80+15 = 95 .

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