Question

The quiz scores of a class with $k > 12$ students have a mean of $8.$ The mean of a collection of $12$ of these quiz scores is $14.$ What is the mean of the remaining quiz scores in terms of $k?$

$\dfrac{14-8}{k-12}$

$\dfrac{8k-168}{k-12}$

$\dfrac{14}{12} - \dfrac{8}{k}$

$\dfrac{14(k-12)}{k^2}$

$\dfrac{14(k-12)}{8k}$

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Written solution:

The sum of the scores of everyone in the class is $8k.$ The sum of the scores in the collection of $12$ is $12 \cdot 14 = 168.$

This means that the sum of the scores of everyone not in the collection is $8k - 168.$ There are also $k - 12$ people not in the collection. Therefore, the average is $\dfrac{8k - 168}{k - 12}.$

Thus, B is the correct answer.

2021 AMC 10A Spring Problem 5

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Problem 5 in Other Years