2004 AMC 12A Problem 2

Below is the professionally curated solution for Problem 2 of the 2004 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12A solutions, or check the answer key.

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Concepts:inequalityfloor and ceiling functions

Difficulty rating: 1020

2.

On the AMC 12, each correct answer is worth 66 points, each incorrect answer is worth 00 points, and each problem left unanswered is worth 2.52.5 points. If Charlyn leaves 88 of the 2525 problems unanswered, how many of the remaining problems must she answer correctly in order to score at least 100?100?

1111

1313

1414

1616

1717

Solution:

The 88 unanswered problems are worth 2.5×8=202.5 \times 8 = 20 points, so Charlyn needs at least 10020=80100 - 20 = 80 more points from correct answers.

Each correct answer is worth 66 points, and the smallest multiple of 66 that is at least 8080 is 84=6×14.84 = 6 \times 14. So she needs at least 1414 correct answers.

Thus, the correct answer is C.

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