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2011 AMC 12B Problem 2

Problem 2 of 25EasierAlgebra

Josanna’s test scores to date are 90,90, 80,80, 70,70, 60,60, and 85.85. Her goal is to raise her test average at least 33 points with her next test. What is the minimum test score she would need to accomplish this goal?

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Solution

The five scores sum to 90+80+70+60+85=385,90+80+70+60+85=385, giving an average of 77.77. The goal is a new average of at least 80.80. Six tests averaging 8080 must total 6⋅80=480,6\cdot80=480, so the sixth score must be at least 480−385=95.480-385=95. Thus, the correct answer is E.

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Concepts: mean

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