2022 AMC 8 Problem 19
Attempt Problem 19 of the 2022 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2022 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Mr. Ramos gave a test to his class of 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 extra points, which increased the median test score to What is the minimum number of students who received extra points?
(Note that the median test score equals the average of the scores in the middle if the test scores are arranged in increasing order.)
Answer: C
Small hint:
The median is controlled by the th and th scores
Big hint:
Count how many scores are at least before and after regrading
Solution:
All scores are multiples of and adding preserves that fact. If the th and th scores average but are not both then the th score must be at least That would require at least scores of or more.
However, even after regrading, only the original scores of or more can reach The plot has only such scores, so the two middle scores must both be
The plot initially has scores of at least To make the th and th scores both there must be at least scores of at least Raising four of the ’s to is both necessary and sufficient.
Thus, the correct answer is C.
Problem 19 in other years
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