Difference between revisions of "2021 AMC 10A Problems/Problem 5"
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==Problem== | ==Problem== | ||
The quiz scores of a class with <math>k > 12</math> students have a mean of <math>8</math>. The mean of a collection of <math>12</math> of these quiz scores is <math>14</math>. What is the mean of the remaining quiz scores of terms of <math>k</math>? | The quiz scores of a class with <math>k > 12</math> students have a mean of <math>8</math>. The mean of a collection of <math>12</math> of these quiz scores is <math>14</math>. What is the mean of the remaining quiz scores of terms of <math>k</math>? | ||
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~ pi_is_3.14 | ~ pi_is_3.14 | ||
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| + | ==Video Solution (Simple and Quick)== | ||
| + | https://youtu.be/STPoBU6A3yU | ||
| + | |||
| + | Education, the Study of Everything | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2021|ab=A|num-b=4|num-a=6}} | {{AMC10 box|year=2021|ab=A|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 15:35, 15 February 2021
Contents
Problem
The quiz scores of a class with 
students have a mean of 
. The mean of a collection of 
of these quiz scores is 
. What is the mean of the remaining quiz scores of terms of 
?
Solution
The total score in the class is 
The total score on the quizzes is 
Therefore, for the remaining quizzes (
of them), the total score is 
Their mean score is 
~MRENTHUSIASM
Solution 2 (Convenient Values and Observations)
Set 
The answer is the same as the last student's quiz score, which is 
From the answer choices, only 
yields a negative value for
~MRENTHUSIASM
Video Solution
https://www.youtube.com/watch?v=S4q1ji013JQ&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=5
~ North America Math Contest Go Go Go
Video Solution (Using average formula)
~ pi_is_3.14
Video Solution (Simple and Quick)
Education, the Study of Everything
See Also
| 2021 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
