2011 AMC 12B Problem 2

Attempt Problem 2 of the 2011 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 2011 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Josanna’s test scores to date are

90,

80,

70,

60,

and

85.

Her goal is to raise her test average at least

3

points with her next test. What is the minimum test score she would need to accomplish this goal?

80

82

85

90

95

Concepts:mean

Find the current average of the five scores

The six scores must total

6

times the target average

The five scores sum to

90+80+70+60+85=385,

giving an average of

77.

The goal is a new average of at least

80.

Six tests averaging

80

must total

6\cdot80=480,

so the sixth score must be at least

480-385=95.

Thus, the correct answer is E.

Problem 2 in other years