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AMC 10 USA Math Olympiad

Arithmetic Mean Problem – AMC 10 (2020)

The simplest example of power mean inequality is the arithmetic mean – geometric mean inequality. Learn in this self-learning module for math olympiad

What is Arithmetic Mean?


The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.

Try the problem from AMC 10


The numbers 3,5,7,a and b have an average of 15. What is the average of a and b ?

Source
Competency
Difficulty
Suggested Book

American Mathematics Competition 10 (AMC 10), {2020}, {2}

Average

3 out of 10

A Study of Experts understanding of Arithmetic Mean

Knowledge Graph


Use some hints


First hint

Here is the first hint for this sum:

Try to find the arithmetic mean of the given numbers

i.e : \(\frac {3+5+7+a+b}{5}\)

=\(\frac {15+a+b}{5}\)

Second Hint

Now the arithmetic mean that we found in hint is actually equal to 15 given in the problem..

so \(\frac {15+a+b}{5} = 15\)

\(a+b = 60 \)

Final Step

So final step will be : if we divide the expression of hint 2 we can find the average of a and b

Answer : \(\frac {60}{2} = 30 \)

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