2005 AMC 12B Problem 4

Below is the professionally curated solution for Problem 4 of the 2005 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12B solutions, or check the answer key.

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Concepts:percentage

Difficulty rating: 1050

4.

At the beginning of the school year, Lisa's goal was to earn an A on at least 80%80\% of her 5050 quizzes for the year. She earned an A on 2222 of the first 3030 quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lower than an A?

11

22

33

44

55

Solution:

Lisa needs an A on at least 0.850=400.8 \cdot 50 = 40 quizzes.

She has 2222 already, so she needs 4022=1840 - 22 = 18 more of the remaining 2020 quizzes.

She can earn a lower grade on at most 2018=220 - 18 = 2 of them.

Thus, the correct answer is B.

Problem 4 in Other Years