2005 AMC 12A Problem 5

Below is the professionally curated solution for Problem 5 of the 2005 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12A solutions, or check the answer key.

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Concepts:mean

Difficulty rating: 1020

5.

The average (mean) of 2020 numbers is 30,30, and the average of 3030 other numbers is 20.20. What is the average of all 5050 numbers?

2323

2424

2525

2626

2727

Solution:

The total of all 5050 numbers is 2030+3020=600+600=1200.20 \cdot 30 + 30 \cdot 20 = 600 + 600 = 1200.

The average is 1200÷50=24.1200 \div 50 = 24.

Thus, the correct answer is B.

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