2020 AMC 8

Complete problem set with solutions and individual problem pages

Problem 14 Medium

There are 20 cities in the County of Newton. Their populations are shown in the bar chart below. The average population of all the cities is indicated by the horizontal dashed line. Which of the following is closest to the total population of all 20 cities?

  • A.

    65{,}000

  • B.

    75{,}000

  • C.

    85{,}000

  • D.

    95{,}000

  • E.

    105{,}000

Answer:D

Solution 1

We can see that the dotted line is exactly halfway between 4{,}500 and 5{,}000, so it is at 4{,}750. As this is the average population of all 20 cities, the total population is simply 4{,}750 \cdot 20 = \boxed{\textbf{(D) }95{,}000}.

 

Solution 2

The dotted line is slightly below 5000. Since 5000\cdot20=100000, the answer is slightly below this, so \boxed{\textbf{(D) }95{,}000} would be the best choice to guess.

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