2022 AMC 8

Complete problem set with solutions and individual problem pages

Problem 19 Hard

Mr. Ramos gave a test to his class of 20 students. The dot plot below shows the distribution of test scores.

Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students 5 extra points, which increased the median test score to 85. What is the minimum number of students who received extra points?

(Note that the median test score equals the average of the 2 scores in the middle if the 20 test scores are arranged in increasing order.)

  • A.

    2

  • B.

    3

  • C.

    4

  • D.

    5

  • E.

    6

Answer:C

We notice that 13 students have scores under 85 currently and only 5 have scores over 85. We find the median of these two numbers, getting:

13-5=8

\frac{8}{2}=4

13-4=9

Thus, we realize that 4 students must have their score increased by 5.

So, the correct answer is \boxed{\textbf{(C)}4}.

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