2005 AMC 10A Problem 6 — Solution | LIVE by Po-Shen Loh

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2005 AMC 10A Problem 6

Below is the professionally curated solution for Problem 6 of the 2005 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 10A solutions, or check the answer key.

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Concepts:mean ratio and proportion

Difficulty rating: 1020

6.

The average (mean) of $20$ numbers is $30,$ and the average of $30$ other numbers is $20.$ What is the average of all $50$ numbers?

$23$

$24$

$25$

$26$

$27$

Solution:

The combined sum is $20 \cdot 30 + 30 \cdot 20 = 600 + 600 = 1200.$ The average of all $50$ numbers is $\dfrac{1200}{50} = 24.$

Thus, the correct answer is B.

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Problem 6 in Other Years

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