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

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2005 AMC 10A Problem 6

Attempt Problem 6 of the 2005 AMC 10A 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 2005 AMC 10A solutions, or check the answer key.

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

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?

$23$

$24$

$25$

$26$

$27$

Answer: B

Concepts:mean ratio and proportion

Difficulty rating: 1020

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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