2014 AMC 12A Problem 9 — Solution | LIVE by Po-Shen Loh

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2014 AMC 12A Problem 9

Attempt Problem 9 of the 2014 AMC 12A 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 2014 AMC 12A solutions, or check the answer key.

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

9.

Five positive consecutive integers starting with $a$ have average $b.$ What is the average of $5$ consecutive integers that start with $b?$

$a+3$

$a+4$

$a+5$

$a+6$

$a+7$

Answer: B

Concepts:mean arithmetic sequence

Difficulty rating: 1270

Solution:

The integers $a,a+1,a+2,a+3,a+4$ have average $a+2,$ so $b=a+2.$

The integers starting at $b$ have average $b+2=(a+2)+2=a+4.$

Thus, the correct answer is B.

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