2014 AMC 10A Problem 10

Attempt Problem 10 of the 2014 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 2014 AMC 10A solutions, or check the answer key.

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10.

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

$a+3$

$a+4$

$a+5$

$a+6$

$a+7$

Note that the average of $5$ consecutive numbers starting with $x$ is $\dfrac{5x + 1 + 2 + 3 + 4}{5} = x + 2.$

This means that the average of $5$ consecutive integers starting with $a$ is $a + 2,$ which we know is $b.$

Furthermore, the average of $5$ consecutive numbers starting with $b$ is $b + 2 = a + 4.$

Thus, B is the correct answer.